AARES AUSTRALASIAN AGRICULTURAL & RESOURCE ECONOMICS SOCIETY
The Law of One Food Price
Ken Clements, Long Vo, and Jiawei Si
The University of Western Australia, Australia
Contributed paper prepared for presentation at the 64th AARES Annual Conference, Perth, Western Australia 12-14 February 2020.
Copyright 2020 by the Authors. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. THE LAW OF ONE FOOD PRICE*
by
Kenneth W. Clements†, Jiawei Si‡ and Long H. Vo
Economics Department, Business School The University of Western Australia
Abstract Are food prices more or less equalised across countries? In view of obvious barriers to trade (both naturally occurring and of a man-made nature) and currency gyrations, the answer would seem to be an unambiguous “No”, but we show this question is worthy of further investigation. In order for the law of one price (LOP) to hold, domestic prices must respond one- for-one to changes in world prices and exchange rates, but this is usually prevented by variations in mark-ups and/or trade barriers. We use data on consumer prices from the International Comparison Program and producer prices from the Food and Agriculture Organization to test for the LOP for food. While not completely conclusive, these tests show the various market wedges appear to be insufficiently important to prevent food prices to equalise over the longer term.
Keywords: Food and agricultural prices, law of one price, exchange rates, market integration, panel unit root tests JEL Classifications: F30, F31, Q17
* For providing us with unpublished data, we thank the World Bank. We also appreciate excellent research assistance provided by Aiden Depiazzi and Haiyan Liu, as well as the comments from our discussant, Peter Phelps, and other participants at the Australasian Commodity Markets Conference, Macquarie University, 2017. We thank Timothy Neal for valuable advice regarding the use of his Stata code (Neal, 2014). This research was financed in part by the ARC and BHP. Long Vo gratefully acknowledges financial support from an Australian Government Research Training Program Scholarship at the University of Western Australia. All errors are ours. † Corresponding author. Address: Economics Department, UWA Business School, 35 Stirling Highway, Crawley, Perth, Australia. Phone: 08-6488-2898. ‡ Deceased.
1. Introduction
How does the cost of food vary across countries? Panel A of Figure 1.1 shows the relative price of food is cheaper in more affluent countries. While there is considerable dispersion around the regression line, it still has a highly significant negative slope. This can possibly be interpreted in terms of the productivity bias hypothesis (Balassa, 1964, Samuelson, 1964), whereby due to lagging productivity in the nontraded or service sector, these goods are more expensive in richer countries, causing their overall price level (which includes both traded and nontraded goods) to be higher. Thus, when food prices are deflated by the higher price levels in rich countries, the result is a declining relative price, as in this panel.1
Panel B tells an apparently contradictory story of food prices rising with country income.
In the two plots in this panel prices are not deflated and are expressed in US dollars. Panel B1 refers to an index of food prices, while B2 uses the price of a specific item of food, a Big Mac hamburger. The elasticity of prices with respect to income is not dissimilar in the two cases -- 0.2 for the food index and 0.3 for Big Macs. Rising food prices here can also reflect the possible influence of the productivity bias in two related ways: (i) On account of transport costs, packaging, wholesale and retail margins and other service components, consumer prices contain important components of nontraded goods. The higher price of nontraded goods in rich countries thus makes for higher consumer prices of food in those countries. (ii) As the currencies of rich
1 Two other possible explanations for the lower food prices should be mentioned. First, because of their superior endowment of agricultural land and favourable climate, rich countries may simply have a comparative advantage in producing food at lower prices. A second explanation is Engel’s law. Higher income is likely to lead to growth in the consumption of most goods, but because of the Engel effect, food consumption grows slower than average. If on the supply side all sectors (food and non-food) expand at approximately the same rate, at constant relative prices there will be an excess supply of food. The end result of both effects is lower relative food prices in rich countries.
2 countries tend to be overvalued, their food prices, converted into a common currency using market exchange rates, tend to be higher than those in poor countries.
Suppose the nontraded parts of food prices were eliminated. With just the traded component remaining, would prices then tend to be equalized via the arbitrage mechanism of the law of one price? Or would the barriers to trade – import tariffs and the like, health standards, transport costs, etc. -- be sufficient to prevent this? Panel C of Figure 1.1 illustrates a case in which the “law of one food price” tends to hold. It can be seen that the price of a particular brand of beer (more or less a tradable item) seems approximately unrelated to country income.2 But as some countries are a considerable distance from the regression line, this can only be taken as
3 suggestive of price equalization.
By how much do food-related commodities exhibit a tendency to reflect this law of one food price is the topic of this paper. Our results point to a surprising degree of food price equalization across countries. Nevertheless, it should be acknowledged that this finding needs to be qualified as it refers to a long-run tendency – as there are substantial deviations from this law for many commodities and countries in the short term and even in the long run, rather than being universal, the law of one food price is a tendency that seems to hold over the longer term. This is in agreement with the broad consensus reached by previous studies that the law of one price and its macroeconomic counterpart, purchasing power parity, also tend to hold over the longer term, not the short term (see, e. g., Lothian and Taylor, 2008; Lothian, 2016; Mark and Choi, 1997; and
Marsh et al., 2012).
2 The data source, the International Comparison Program (World Bank, 2013, unpublished), does not reveal the actual brand name of the beer.
3 The Economist’s approach of adjusting Big Mac prices for differences in country income can also be interpreted as a type of adjustment for differing nontraded components (The Economist, ongoing). This leads to a tendency for price equalization by construction, and therefore cannot be taken as support for the LOP.
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As indicated above, the contribution of the paper is to establish that the law of one food price holds (with qualification). This entails the use of prices of actual food items to test the LOP.
Our panel unit-root and panel co-integration tests show that about three-quarters of products obey the law and deviations tend to be eliminated relatively quickly. The average half-life is of the order of one year, substantially faster than the 4- to 5-year “glacial adjustment speed” highlighted by Rogoff (1996). This is probably due to our use of transaction prices of individual commodities, rather than price indexes that average over components, which blur the dynamics of adjustment and lead to implausibly long lags. Relatedly, we also use a novel approach to analyse the short-term dynamic relationship between wheat prices in Australia and the US and the exchange rate. This reveals that prices tend to respond more than the exchange rate in adjusting to deviations from the LOP.
The next section of the paper discusses prior studies dealing with the relationship between exchange rates and prices, including price transmission from one market to another and pass- through. This is followed in Section 3 by a descriptive analysis of the deviations from the LOP using two data sets. The first refers to prices paid by consumers, from the International
Comparisons Program (World Bank, 2013), while the second is for prices of unprocessed agricultural products received by producers, from the Food and Agriculture Organisation (FAO,
2018). The FAO data have a time dimension in addition to product and country dimensions, allowing us to use a number of recently developed panel unit-root and panel co-integration tests to investigate stationarity. Sections 4 and 5 contain the tests of the LOP with the two data sets. In order to examine the dynamics of adjustment in finer detail, in Section 6 we use wheat prices in
Australia and the US, and find that prices tend to shoulder most of the burden of adjustment.
Section 7 presents concluding comments.
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2. Related Literature
In its simplest form, the law of one price (hereafter, the LOP) states that an identical good will sell for the same price, expressed in terms of a common currency, in different locations.
When prices are not equalised, prima facie there is a deadweight efficiency loss that could be eliminated by transferring the product from the low-cost location to where it is more highly valued. Of course, this “strong” form of the LOP only holds under the stringent conditions of the product being identical in all aspects other than the currency in which it is denominated, and with no barriers to trade. If it is costly to transport the good, however, the law can be restated in a
“weaker” version, which is also referred to as the “spatial arbitrage condition”: Prices will differ by (at most) the cost of moving the good from where the price is low to where it is high (Fackler and Goodwin, 2001). The “no barriers to trade” condition rules out a large class of goods that do not enter into international/interregional trade because of prohibitively high transport costs. Many services are in this class – haircuts are the classic example of a nontraded good.
Closely related to the LOP is purchasing power parity (hereafter, PPP), according to which the value of the country’s currency equals the ratio of some macroeconomic index of prices at home to that abroad. On the basis of a substantial literature, Marsh et al. (2012) conclude that though the evidence is not unanimous, there is now increasing acceptance that the
LOP and PPP hold as long-run tendencies. In their words: “While it is fair to say that a universal consensus may not exist yet, the emerging consensus at the present time is converging toward the view that deviations from the LOP are transitory and therefore the LOP holds in the long run among a broad range of tradable goods and currencies” (p. 213). They also state: “Overall, our reading of the literature suggests that PPP is a good first approximation to the long-run behaviour of exchange rates” (p. 203). For earlier reviews of PPP theory, see, e. g., Dornbusch (1980,
5
1988), Frenkel (1978), Froot and Rogoff (1995), Manzur (2008), O’Connell (1998), Officer
(1982), Rogoff (1996) and Taylor and Taylor (2004).
It is difficult to find a commodity that conforms to the LOP in its “strong”, stark, unalloyed form, but gold, with its high value-to-weight ratio and lack of barriers to trade, might come close. Agriculture products, in contrast, are characterized by extensive spatial areas of production and large transportation costs relative to their value. Because of the complex web of marketing in agriculture, there is considerable interest in modelling agricultural price determination and market performance, as shown in the extensive survey by Fackler and
Goodwin (2001). According to these authors, the concepts of spatial arbitrage and the LOP are often not distinguished in the literature, and are much less ambiguous than various interpretations of the concepts of “agricultural market integration” and “market efficiency”. The former can generally be thought of as a measure of the degree to which price shocks arising in one region are transmitted to another, while the latter refers to conditions in which prices accurately reflect all available information about demand, supply and transaction costs. Direct evidence of market integration from LOP deviations is crucial to establish whether market-oriented reforms create or remove distortions (Iregui and Otero, 2017; Li et al., 2018). Typically, perfect market integration implies the strong form of the LOP, which in turn implies its weak form (see, e.g., Crucini and
Shitani, 2008; Engel and Rogers, 1996; and Parsley and Wei, 2001).
A popular approach to testing for the LOP or international agricultural price integration is to regress domestic on world prices. In a log-linear specification, the regression coefficient represents the price transmission elasticity, also referred to as the “pass-through” coefficient, which is hypothesized to have the value of 1 in case of perfectly integrated markets. Empirical evidence on pass-through is generally mixed. Using a large number of agriculture products from the Food and Agriculture Organisation, Mundlak and Larson (1992) find the majority of world
6 price variations are transmitted to and constitute a dominant component of domestic prices changes. Goldberg and Knetter (1997) and Abbott (2010), on the other hand, detect incomplete, or less than unity, pass-through from foreign to US price levels, partly due to the US being a world price-maker. According to Burstein and Gopinath (2014), low pass-through in the agricultural sector of developed countries may result from most international transactions being priced in these countries’ currencies. Jabara and Schwartz (1987) document that changes in the
US-Japan exchange rate were passed through fully and rapidly during the 1970s when the dollar declined against the yen, while there was a much lower pass-through in the appreciation period of the 1980s.4 One suspects the more exchange-rate shocks are perceived to be permanent, the greater the likelihood of a close-to-unity pass-through coefficient. Adopting an optimal-pricing framework to test for PPP, Feenstra and Kendall (1997) find support the notion that during the
1980s, exporters adjust their prices by less than the full change in the exchange rate, and such behaviour appears to explain a significant portion of the deviations from the PPP.
4 Additionally, there is some evidence that in the 1980s, the price response was asymmetric: Japanese exporters and importers exploited the temporary decrease in the value of the dollar to extract quota rents by further increasing yen prices, giving rise to a low pass-through coefficient. But when the dollar appreciates, the pass-through coefficient is not significantly different from 1. This is possibly because exporters’ do not have much incentive for changing prices in the presence of an inelastic destination demand and when the risk of loss of market share is small. From Japanese importers’ point of view, monopolistic power allows them to absorb favourable exchange-rate changes into margins.
This type of incomplete and asymmetric pass-through behaviour is typical of food and agriculture markets, as in the recent cases of Japanese meat (Miljkovic and Zhuang, 2011), US beer (Hellerstein, 2008) and US cocoa bean
(Luckstead, 2018), for example. Forbes et al. (2018) find that exchange rate pass-through is low in response to domestic demand shocks and high in response to domestic monetary policy shocks. Another reason for a less-than- unitary pass-through is the tendency of exchange rates to “overshoot” economic fundamentals in the short-run (see, e.g., Bjørnland, 2009; Dornbusch, 1980; Frankel, 2008; and Hatzenbuehler, 2016).
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Related to the above is the growing literature of international retail pricing strategies, which emphasises price discrimination as a source of deviations from the LOP.5 In particular, variable mark-ups are found to play an important role in price determination of some identical items sold globally. Using a rich dataset from multinational apparel retailer and transport service providers, Simonovska (2015) finds that in affluent countries where the price elasticity of demand is relatively low, firms tend to exert considerable pricing power and charge systematically higher mark-ups, thus creating substantial deviations from the LOP. For US beer market, Hellerstein (2008) document that changes in manufacturers’ and retailers’ mark-ups explain about 50 percent of the incomplete transmission of exchange rates to prices. Using high- frequency price data on millions of items sold online, Cavallo et al. (2014), Cavallo et al. (2018) and Cavallo and Rigobon (2016) find support for strong price equalisation, but only among countries within the same currency union. However, the lack of price deviations is not always a result of arbitrage pressure induced by free trade, but could also be influenced by firms’ price- setting strategies. For example, large US retailers are estimated to forgo substantial profits by charging nearly uniform prices across stores in spite of heterogeneous competition levels and consumer demography, according to DellaVigna and Gentzkow (2017). These authors explore possible motivations for such a pricing strategy, including advertisements that promote the same price to a wide area, avoidance of price war with competitors, and the most likely factor – the reduction of costly managerial effort related to price monitoring.
In cross-country studies of the LOP the influence of exchange rates on prices comes to the forefront. Thus, to conclude this section, and as a preface to our tests of the LOP in subsequent sections, we shall consider some simple examples. If the prices of a Big Mac (BM) hamburger in
5 Other sources of deviations include the costs of distribution, trade policy interventions, insulating price policies, price stickiness and international oil price shocks (Jabara and Schwartz, 1987).
8 different countries, converted to US dollars using market exchange rates, satisfy the LOP there would be no dispersion as they would be completely equalised. Clearly, this is not the case in panel A of Figure 2.1, where the standard deviation (SD) of prices is 100 e0.35 1 42 percent.
Yet panel A also shows that the dispersion of BM prices is still somewhat less than that of the prices of the whole consumption basket (as measured by the cost-of-living index) in the same set of countries, where the SD is about 50 percent; and substantially less than the dispersion of incomes (GDP per capita), with an SD of 188 percent. The far left plot in panel B reveals a surprisingly close relation between BM prices in local currency units and exchange rates: The slope coefficient here is 0.95, not too far from the LOP value of 1.6 The relationship is weaker in the middle plot for the price level (slope = 0.90), and weaker still for GDP in the right-hand side plot (slope = 0.75). As price levels contain substantial elements of nontraded goods, we would not expect them to exhibit as close a relation to exchange rates as do the BM prices, as indicated by a the smaller slope coefficient and the larger standard error of the regression. GDPs would appear to be even less tradable, with a still smaller slope coefficient and larger standard error of the regression. These three cases clearly illustrate the importance of “tradability” to the validity of the LOP: The more tradeable the good (the less the nontraded components), the smaller the deviations from the LOP, other things being the same.
3. Food Prices
Let pic be the price of item i in country c in local currency units (LCUs) and Sc be the exchange rate for the currency of c, defined as the cost in LCUs of $US1. Define the world price
6 This coefficient was referred to above as the pass-through coefficient.
9 of i, measured in $US, as p, so that pS is the world price in LCUs. Under the “strong” i ic
version of the LOP, prices are equalized absolutely, that is, pic p i S c . According to the “weak”
kic kic version of this law, prices are proportional: pic e p i Sc , where e pic p i S c 1 k ic is
a “wedge” factor. The strong version of the LOP corresponds to kic 0. In a time-series context, the wedge is usually taken to be a constant over time, while in a cross-country (or cross- commodity) setting, the wedge is constant over countries (or commodities). For domestic prices, we use unpublished data from the 2011 round of the International Comparison Program (ICP) on
198 food items in 175 countries, which are average retail prices paid by consumers (World Bank,
2013, unpublished).7 For the world price of a good, we use a cross-country weighted average of its prices, with weights reflecting relative importance.8 Panel A of Figure 3.1 contains two distributions of the deviations, one layered on top of the other. The lightly shaded one is for the
ICP. Importantly, there is substantial dispersion as the logarithmic standard deviation of the deviations is 0.55, or 100 e0.55 1 73 percent, from the third element in the first column of panel C1. One might imagine that with price dispersion of this order of magnitude, there must be major barriers that prevent arbitrage.9
7 For details of these data, see Appendix A1.
8 Ideally, information on the relative importance at the product level should be used, but as this is not available we thus use the next best alternative, viz., information from one level higher pertaining to the corresponding basic heading. For details, see Appendix A2.
9 It is worth repeating that the prices are those of consumer goods, many of which contain large nontraded components, the prices of which are difficult or impossible to arbitrage across countries. Add to that the additional barriers such as transport costs, costs implicit in complying with health and safety regulations and the usual explicit taxes and charges that many governments impose on imported goods, and it becomes easier to understand the price dispersion.
10
The solid line in panel A of Figure 3.1 represents the density of the deviations, kict , associated with annual producer prices from the Food and Agriculture Organization (FAO) of
158 food and agricultural items in 133 countries, over the 24-year period 1991 – 2014 (FAO, online).10 For the world price of each commodity, we follow Mundlak and Larson (1992) and use a weighted average of export prices, with weights reflecting the relative importance of the exporters of that commodity.11 It can be seen from the first element of the first column of panel
C2 that the mean price difference now is 0.27, which may not be considered to be too large in view of recent estimates of trade costs (Anderson and van Wincoop, 2004). But the dispersion is very high, as the standard deviation is 100 e0.86 1 136 percent and the tails of the distribution are longer than those of the ICP: The cumulative probability plot in panel B shows that 40 percent of total ICP deviations lie within the range [ 0.3, 0.3] , while the corresponding figure for the FAO is 25 percent.12 The smaller dispersion of the ICP prices is perhaps surprising, as the FAO prices refer to producer prices while those of the ICP are paid by consumers. As the
FAO prices are possibly closer to those actually used in international trade transactions, prime facie we might expect them to be more closely linked across countries, and less dispersed than their ICP counterparts. On the other hand, unlike the ICP’s processed food items purchased by final consumers, many of the agricultural commodities of the FAO are exported in substantially unprocessed form and subject to the more volatile economic conditions of world markets. The
10 These are prices “received by farmers…as collected at the point of initial sale (prices paid at the farm-gate)”
(FAO, online).
11 For details, see Appendix A2.
12 From the last two columns of panel C, 99 percent of the truncated observations for the FAO (96,769/97,274) and
ICP (23,116/23,171) are in the range [ 3, 3] ; while only 32 percent for FAO (30,752/97,274) and 44 percent for ICP
(10,192/23,171) are in the range [ 0.3, 0.3].
11 volatility of world prices may lead to large swings in the terms of trade and slower, less stable growth of commodity-exporting countries, which tend to be developing economies (Jacks et al.,
2011; and Loayza et al., 2007). The volatility of world agricultural markets, coupled with less stable growth of producing countries, may account for much of the cross-country dispersion of prices.
There is an interesting pattern in the dispersion of the deviations that is related to the above point about the markets for consumer goods and agricultural commodities and their developing-economy producers. Figure 3.2 shows volatility falls significantly as countries become richer, but there is a distinct difference between the ICP and the FAO responses: A doubling of per capita income is associated with a decrease of about 2.1 log2 1.5 percentage points in standard deviation of the ICP deviations, while for the FAO, the decrease is twice that at about 4.3 log2 3 percentage points. This highlights the relative tranquillity of consumer prices in comparison to the prices of commodities.
Using the FAO prices, column 2 of Table 3.1 reveals that the standard deviation of kict starts off at about 1 in the early 1990s and then decreases to 0.8 in 2013. This 20-percent decrease in price variability suggests markets may have become more integrated over time, which is indirect evidence of reduced trade barriers. Does the dispersion of kict mainly come from differences in prices of the same commodities across countries, or simply from different commodities having different deviations? Columns 3 and 4 of Table 3.1 shed light on this with a variance decomposition. On average, a little over two-thirds of the variance comes from price differences of the same commodity, while only about a third comes from price differences between commodities. A similar question can be posed using countries as the base of comparison, viz., how large are the price differences in the same countries compared with the
12 differences between countries? As seen from columns 5 and 6, the between-country effect dominates the total variance in most years, which is possibly a surprising result.
Finally, we use the FAO data to present preliminary patterns of the raw dependence of
* prices on exchange rates with. Let logrict logp ict logp it be the domestic price of good i
relative to the world price and (h)logr ict logr ict logr ic,t-h be its change over h years. Part (i) of
panel A of Figure 3.3 is a scatterplot of (1)log r ict against (1)logS ct , the change in the exchange rate for a 1-year horizon. For a given country, there is one change in the rate each year, whereas there is a price change for each of the multiple items. This is reflected by the several clusters of observations that form near-vertical lines. However, there is still a strong positive relationship between prices and exchange rates with a slope of the regression line of 0.91. The relatively low
R2 of 0.23 is a partial result of the high frequency of near-zero changes in exchange rates over the
1-year horizon (15 percent of the observations), which can also be seen from the concentration of probability mass around zero in the corresponding contour plot in panel B. Note also that the
majority of values of (1)logS ct are positive, indicating that, on average, most currencies depreciate with respect to the $US during the period. For horizons of 5, 10 and 20 years, the proportion of the near-zeros decreases, the slope coefficients move closer to unity, and R2 increases [see parts (ii) to (iv) of panel A]. There seems to be a high degree of pass-through of currency to price changes, but as there is considerable dispersion around the regression lines, there is a considerable chance of deviations from the LOP.13 It is to be emphasised this evidence has only a preliminary status, and a more formal investigation follows.
13 In Appendix A5, we show that these observations persist when compressing the sample using country and commodity averages.
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4. Cross-Sectional Evidence
Most tests of the law of one price involve time-series data; in contrast, the tests in this section are carried out across countries for each item, and across items for each country. Here we use the International Comparison Program (ICP) price data discussed in the previous section.
Cross-Country Regressions
As discussed previously, the price of item i in country c ( pic ) is linked to the world price
* kic * pi and the exchange rate Sc according to pic e p i S c where kic is the (logarithmic)
* deviation from parity. For a given item i, pi is the same across countries and taking the deviation to be constant across countries to be denoted by ,this leads to a log-linear ki cross-country regression for item i:
(4.1) logpic i i logS c ic ,
* where log p is the intercept; is the exchange-rate elasticity or the pass-through i i ki i
coefficient; and ic is a disturbance term. Under the LOP, i 1.
Equation (4.1) is estimated across countries for c 1, ,C 175 observations for item i; i and this regression is repeated for each of the i = 1,…,198 food items. The 198 estimates of the
14 elasticity i are plotted in the top row of panel A of Figure 4.1. The mean and median are 0.96 and 0.97, respectively, and the majority are not too far away from 1, the value implied by the
LOP. From the cumulative distribution on the left-hand side of the second row of panel A, about
58 percent of the estimates are within the range 1±0.05. As can be seen from the bottom row, there is, however, considerable dispersion among the estimates, which range from 0.81 (for sweet potatoes) to 1.06 (lemonade), and their standard deviation is 0.05. It must also be acknowledged
14 The actual estimates are reported in Appendix A4.
14 that a number of coefficients are significantly different from unity (from the right-hand side of second row of panel A, 65 percent), contradicting the LOP. But there does not seem to be any particular pattern to the estimates, other than the important property that the elasticities are clearly centred on a value close to unity.
The above tests use consumer prices that typically contain substantial elements of packaging and retailing components that are mostly non-traded goods/services. For this reason, it might be plausibly argued that the LOP rejections are surprisingly modest. This position cannot be stated too firmly, however, due to the number of elasticities significantly different from unity.
Cross-Commodity Regressions
For a given country c the exchange rate Sc is constant. Taking the deviation to now be a constant across commodities denoted by , the cross-commodity version of equation (4.1) is kc
(4.2) logpic c c logp i ic ,
where logS is an intercept; c is the elasticity of domestic prices with respect to world c c kc
prices, which is also a type of pass-through coefficient, with c 1 under the LOP; and ic is a
disturbance. Equation (4.2) is estimated for each country with data on Nc 198 items and the estimated slope coefficients are given in the top row of panel B of Figure 4.1.15 These estimates are somewhat lower than previously -- the mean and median are 0.92 and 0.93 – and the standard deviation is now about twice as large at 0.11.
The middle and bottom rows of panel B of Figure 4.1 show that the proportion of the elasticities falling in the range 1±0.05 is now smaller at 27 percent (previously 58 percent in a cross-country setting); and that 53 percent are significantly different from unity (less than before, when this percentage was 65). Again, there is no clear pattern in the estimates across countries
15 See Table A4.2 of Appendix A4 for the estimates.
15
(see the bottom row). The above approach for world prices is only approximate and certainly imperfect: Any measurement error would lead to a downward bias in the estimated elasticities.
That the estimates are, on average, not so far from unity in this case is perhaps also surprising.
5. Are LOP Deviations Stationary?
The previous section analysed the law of one price with a cross section of countries/commodities for one year, using the ICP data. We now augment this with tests that add a time dimension, and consider the FAO prices across countries, commodities and time. Another difference is that previously prices paid by consumers were used, while the FAO prices refer to those received by producers. The tests of this section shed light on the dynamics of prices and exchange rates and reveal whether or not deviations from the LOP die out over time, as rates and prices align with one another.
Cross-Country Analysis
If the law of one price holds in the long run, any initial deviations are eliminated in subsequent years, that is, the deviations are stationary (around a long-run mean). We thus test for
* the stationarity of LOP deviations, kict logp ict logp it logS ct , using a panel autoregressive model:
Hc (5.1) kict c c t c k ic,t 1 c,h k ic,t h ict , c1,,C;t1,,T. i i h1
The deterministic drift and trend terms are allowed to vary across countries. Although we make no attempt to explicitly control for commodity-specific factors, such as transport costs, import tariffs and other impediments to the equalization of prices, the intercepts and deterministic terms
may account for some of these effects. The null hypothesis is H0c : 0 c 1, ,Ci . The
alternative is HAc : 0 for at least one c; that is, deviations are mean-reverting in at least one
16
country. Significant negative values of c provide evidence against the null hypothesis, implying mean-reversion. We use the modified “inverse normal method” proposed by Hartung (1999) and modified by Choi (2001) to combine the p-values of the individual cross-sectional statistics and
16 test for stationarity of the whole panel. The lag order Hc is determined by the Akaike information criterion.
Among the major advantages of this approach are: (i) The allowance for country-specific intercepts, trends and slope coefficients; and (ii) the number of time periods can vary across countries, that is, the panel can be unbalanced. Additionally, the test is applicable when the number of countries is large relative to the number of time periods (a so-called “short” panel).
For each commodity, we estimate model (5.1) and test for stationarity with Hartung (1999)’s Z*- stat, which has a standard normal distribution under the null. The top part of panel A of Figure
5.1 contains the Z*-stat values. The mean is 3.23 and in more than 80% of cases (commodities) the values are smaller than the 5-percent critical value of 1.64 (using a one-tail test). Thus, for about three-quarters of commodities we reject the null of a panel unit root.
The half-life of deviations for country c is log 0.5 logβ1c (Enders, 2015). Since
there are Ci equations/countries in a panel corresponding to item i, we compute the mean half- live (across countries) for each item and panel A of Figure 5.2 plots the results. As can be seen, the mean half-life is approximately one year, with a standard deviation of 0.75 years.
Accordingly, on average, prices adjust fairly quickly to eliminate shocks to the LOP.
Cross-Commodity Analysis
We reformulate model (5.1) into a cross-commodity form:
16 A more detailed discussion of this approach is provided in Appendix A6.
17
Hi (5.2) kict i i t iic,t1 k i,h k ic,th ict , i1,,N,t1,,T, c c h1 where each panel now refers to a country. Panel B of Figure 5.1 summarises the stationarity tests.
The commodity Z*-stats have a mean of -3.44 and a standard deviation of 1.91. Similar to the previous results, the deviations are stationary in about 80 percent of cases (countries). The corresponding half-lives, presented in panel B of Figure 5.2, are similar to before. The half-lives are much shorter than those from the first-generation literature with its “glacial” adjustment speeds of the deviations from the PPP (Rogoff, 1996). The faster speed of adjustment is consistent with recent studies using panel approaches.17 A possible explanation lies in our use of actual commodity prices, while the prior studies use price indices that are some type of average of a number of prices and can include substantial service components. Because of the averaging and the inclusion of non-traded goods, price indices are likely to be stickier than actual commodity prices, which possibly conceal the true adjustment path. We further analyse this path in the next section.
To conclude this section, we note that the LOP implies prices and exchange rates are co- integrated. Therefore, as an alternative to testing the stationarity of LOP departures, we perform panel co-integration tests proposed by Kao (1999), Pedroni (2004) and Westerlund (2007).18
Though some of the densities of the p-values under the null of no co-integration exhibit long right tails, most have a mass around zero. Thus, in agreement with the panel unit test results, no co-
17 See, among others, Bahmani-Oskooee and Wu (2018), Breitung and Candelon (2005), Pesaran (2007), and
Westerlund and Blomquist (2013).
18 We first carry out panel unit-root tests for prices and exchange rates (in Appendix A6) and find they are integrated of order 1. Then, for each of the 124 commodities and 126 countries, we perform 16 co-integration tests, a total of 16
(124+126) = 4,000.
18 integration can be rejected at conventional significance levels for the majority of commodities and countries. See Appendix A7 for details.
6. The Adjustment Path
The previous section examined the mean-reversion nature of deviations of prices from parity and the deviations were found to have an average half-life of one year. To shed more light on the shorter-term dynamics, in this section we use quarterly data on a single small, open economy with a large agricultural export sector, namely Australia.
It is reasonable to expect the prices of Australian wheat, its largest agricultural export, and the exchange rate to be endogenously determined, consistent with the “commodity currency” literature (see, e.g., Chen and Rogoff, 2003, Chen et al., 2010 and Clements and Fry, 2008).
* Denote the price of Australian wheat in quarter t by pt and the corresponding US price by pt .
* Define the relative price as logrt log p t p t . We control for variations in aggregate price
levels by deflating by CPIs and so define logrt logr t logR t ,where
log Rt log CPI AU,t CPI US,t , and logSt logS t logR t , where St is the USD/AUD exchange
4 rate. We consider the bivariate VAR model: ytΣ, h 1 A h y t h u t where yt log r t ,logS t ,
19 Ah ,h 1, ,4 are 22 matrices of coefficients and ut is a white-noise error vector. As shown in Appendix A7, the two variables are co-integrated, and so the VAR model can be expressed in error-correction form:
3 (6.1) ΔΔ,yt Πy t 1 Γ h y t h u t h1
19 As there is neither trending nor drifting behaviour, we do not include deterministic terms. The lag length is determined to be 4 by the Akaike information criterion. For an examination of generalisations of the VAR model, see
Appendix A8.
19
4 4 where Π I Σh 1 A h αβ and ΓAhΣ j h 1 j . Co-integration means that the error correction
term βy t1 is stationary, or deviations from the LOP are short-lived. Panel A of Figure 6.1 presents the generalised impulse response functions (Pesaran and Shin, 1996, 1998; hereafter, the
GIRFs) following an initial 3.4% shock to the exchange rate (a depreciation of the AUD).20 As can be seen from the far-right plot, LOP deviations are insignificant after the fourth quarter, confirming stationarity.
The GIRFs deal with the impact of an unanticipated shock to the exchange rate. These functions indicate the effects of, say, a sudden collapse of the country’s currency. Another class of effects also of interest is the impact of a sustained under/over-valued exchange rate, which can be studied by changing the error correction term (hereafter, the ECT) of the VECM model.21 We
3 rewrite model (6.1) as: ΔΣΔ,yt α β y t 1 h 1 Γ h y t h u t where α is the vector of adjustment
speeds and β β12 ,β is the co-integrating vector with β11 . Suppose there is an inherited
departure from parity, so the ECT βy t 1k t 1 0. The subsequent adjustment path can be simulated using the following 7-step procedure:
1. Estimate the above VECM and denote the estimated parameters by αˆ , βˆ and Γˆ .
2. The VAR(4) means the VECM is of third-order, so that three initial values of y are needed. Set
these initial values equal to the in-sample values p,p 1,p 2 , and denote them by:
y0p y log r p ,logS p ; y 1p1 y log r p1 ,logS p1 ; y 2p2 y log r p2 ,logS p2 .
20 Appendix A8 provides details on the construction of the GIRFs.
21 An example of such a sustained disequilibrium of exchange rates is the “dollar effect”, which refers to the persistent misalignment of some currencies against the USD.
20
ˆ 3. For h = 0, 1, 2, define the normalised initial deviations as yyh hιk h / ι β , where ι 1, 1
ˆ ˆ and khh βy . As βy h 0, the subsequent simulations do not reflect the effects of the initial
three quarters.
4. Set the first simulated value of the change in the level of the variables, Δyt , to Δyˆ 3 0, x ,
where x equals the standard deviation of the residuals of the VAR exchange-rate equation. The
first simulated level of y t is yˆˆ3 y 2Δ. y 3
ˆˆ ˆ ˆ3 ˆ ˆ 5. Set the simulated value of Δyt in the next quarter to ΔΣΔ,y4 α β y 3 h 1 Γ h y 4 h so that
yˆ4 y ˆ 3Δ. y ˆ 4 Recursively implement step 4 and obtain 12 subsequent simulated values of y t ,
yˆ tt 1, ,12, to represent the time path over a 12-quarter period following the initial
change in logS of x.
6. Repeat steps 2 – 5 for all possible initial values yp , p 1, ,T 2. This yields
p p yˆ t t 1, ,12;p 1,...,T 2 . Then for each t, average the simulated series yˆ t over p
to again neutralise the effects of initial values. Compute the corresponding Δyˆ tt .
What makes these simulated paths different to the GIRFs? The GIRFs answer the question “if one variable is shocked, how does the system, including the ECT, react?” without any assumption about the initial state of the ECT. In contrast, the above procedure answers the question “if the ECT is initially at its steady-state value of zero, and is subsequently thrown out of equilibrium, how does each variable react to restore the steady state?” Both approaches lead to an examination of the “reaction” of the system following a change, but the nature of the change and its interpretation are different. First, as stated previously, while the shocks underlying the
GIRFs are unexpected, the changes in the above approach can be interpreted as expected.
Secondly, and relatedly, for the GIRFs, shocks are transmitted via the error terms, which feed
21 into changes in the variables. In our simulations, however, the levels of variables, not the errors, are changed directly. Third, an operational distinction between the two approaches relates to the meaning of the time “horizon”. For the GIRFs, the horizon refers to hypothetical time points following the shock. These could refer to either future periods, periods within the sample or, conceivably, even periods before the sample; the precise time identification is left unspecified by the GIRFs. In the simulations, in contrast, the periods always refer to actual times in the future.
When initial values are chosen to be at the end of the sample, the resulting time paths can be viewed as out-of-sample forecasts, conditional on the assumed change, x.
Panel B of Figure 6.1 presents the simulated time path of the changes in prices and the
ˆ exchange rate,Δyˆ t t 1, ,12 , and that of LOP deviations, Δk t , corresponding to x 0.034, an initial 3.4% undervaluation of the Australian dollar. “Time 0” here refers to t = 1 in the above procedure, so that the initial period coincides with the quarter when the change x
ˆ ˆ occurs, consistent with the GIRFs. The change in the deviation at time 0, is Δk0 β 0, x , and
ˆ ˆ since the co-integrating vector is β 1, 1.24 , Δk0 1.24 0.034, or about -4%. Thus, domestic prices initially fall relative to world prices. These initial changes can be seen from the middle and far-right plots of panel B. Adjustment towards equilibrium is rapid, beginning in quarter 1 when domestic prices rise by about 2.5% and as the exchange rate is unchanged, the
LOP departure is also about 2.5%. Subsequently, the exchange rate remains more or less unchanged, prices stabilise, and the deviations mirror the behaviour of prices.
Comparing the two sets of results, it is clear that the GIRF adjustment paths are more volatile than those of the simulations. This reflects the unexpected nature of the exchange-rate shock underlying the GIRFs, while there is a sustained misalignment in the simulations. In both cases, however, the adjustment of prices and the exchange rate is quite rapid and convergence to
22 long-run values occurs within five quarters. In restoring the LOP, a notable difference is the nature of the adjustment path. Following the unexpected shock, panel A of Figure 6.1 reveals the adjustment burden seems approximately evenly divided between changes in prices and the currency value: The initial depreciation is mostly “neutralised” in quarters 2-3 by a subsequent appreciation and a fall in domestic prices; and the LOP departures have a damped oscillatory over/undershooting pattern. In contrast, from panel B, the sustained misalignment leads to a large offsetting change in prices in the quarter immediately following, and, thereafter, the price changes converge monotonically to zero. Thus in this sense, prices do most of the adjusting in this case.
7. Summary, Implications and Qualifications
The equalisation of prices of the same product in different countries is known as the law of one price (LOP), but it is well-appreciated this holds under apparently demanding conditions.
The usual reasons preventing or blunting the arbitrage process underlying the LOP are trade barriers of all kind (quantitative restrictions on trade, explicit tariffs and subsidies, health and safety regulations, etc.), as well as variations in price mark-ups (from the cost of imports to consumer prices, for example). A further difficulty is most products contain service components; and the prices of many types of services cannot be arbitraged due to their nontraded nature
(examples are wholesale and retail margins).
Notwithstanding the stringent requirements, we found considerable support for the LOP for food and agricultural products, and without any attempt to control for commodity-specific and country-specific factors. These results were obtained in three basic ways. First, retail prices from the International Comparisons Program (World Bank, 2013, unpublished) were used in cross- country and cross-commodity regressions for a substantial number of food items and countries.
Second, producer prices over time, countries and products from the Food and Agriculture
23
Organisation (2018) were employed in panel unit-roots tests. Third, a vector error-correction approach was used for wheat prices in Australia and the US to examine in detail the dynamics of the adjustment process of prices and exchange rates. We found that variations in the exchange rate were relatively more important than wheat prices in bringing about the LOP. Even though price disparities can be substantial and persistent in the short run, our results indicate they mostly mean-revert toward the LOP over time. The implication is that policies attempting to divorce domestic agricultural prices from their world counterparts will, more often than not, be likely to have a troubled history.
Our findings are subject to two important qualifications. First, for the majority of countries and products, the LOP holds, yet there are still some major departures. We do not claim the LOP holds in the short run, but only as a long-run tendency in the sense that departures from parity are stationary. Second, it should be acknowledged that we have not analysed in any detail the cross-sectional heterogeneity of the speed of adjustment. This speed may depend on the magnitude of the LOP deviations, since the larger the deviations, the stronger is the incentive to arbitrage them away. Once the deviations fall below a certain level, however, price correction may not be as strong due to the role of trade costs in reducing the incentive to buy low and sell high. Therefore, within a certain band, it is possible for prices to follow a random walk with no clear mean-reverting orientation. The existence of such a “band of no-arbitrage” is investigated with a threshold autoregressive model in a separate paper by Vo (2018).
The reconciliation of our results supporting the LOP with the law’s restrictive prerequisites probably lies in our first qualification regarding the time needed for prices and exchange rates to make the required adjustments. It takes time for prices to be arbitraged across countries because of three reasons. First, there can be difficulties in collecting reliable market information and for participants to be convinced price divergences are worthwhile acting upon,
24 especially when driven by currency movements (are they likely to reverse direction?). Second, overcoming trade costs is also likely to be time consuming (if, for example, local agents have to be engaged to deal with importing-country regulations). Third, devising innovative ways to deal with costly nontraded components (such as bypassing the traditional retail model with on-line sales technologies) can incur significant trial-and-error learning costs, further adding to delays.
In summary, the law of one food price tends to hold for many commodities and countries
(but not all) in the long run, not the shorter term.
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30
Figure 1.1 Disparate Food Prices, 2011
A. Food Prices Lower in Richer Countries (Price of Food Relative to Cost-of-living)
100 × log y = -12.3x + const 80 80 (1.8)
40 40
0 0
-40 -40 GDP per capita -80 -80 ($US, log scale) 2,500 17,500 122,500 7.82 9.82 11.82 B. Food Prices Higher in Richer Countries
B1. Food Prices in $US B2. Big Mac Prices in $US
y = 20.0x + const y = 30.7x + const
7.82 9.82 11.82 80 7.82 9.82 11.82 80 (3.4) 80 80 (7.2)
40 40 40 40
0 0 0 0
-40 -40 -40 -40
-80 -80 -80 -80 2,500 17,500 122,500 2,500 17,500 122,500 C. Food Prices Roughly Constant
Prices of a Particular Brand of Beer in $US
7.82 9.86 80 80 y = 2.9x + const (4.7)
40 40
0 0
-40 -40
-80 -80 2,500 17,500 122,500
Notes: 1. All data refer to 2011. 2. Panel A: The vertical axis refers to100 logP logP , where is a food price index for country c c 1, ,126 and is a F,c c PF,c Pc cost-of-living index (see Appendix A1 for details). Both indices are in local currency units (LCU). 100 logP logP logS , 3. Panel B: (i) Left-hand side plot: The vertical axis refers to F,c F,US c where PF,US is the food price index for the
US and Sc is the market exchange rate for c (the LCU cost of $US1). (ii) Right-hand side plot: The vertical axis refers to 100 logp logp logS , BM,c BM,US c where pBM,c and pBM,US are the prices of a Big Mac in c (c = 1,…,51) and in the US. 100 logp logp logS , 4. Panel C: The vertical axis refers to i,c i,US c where pi,c and pi,US are the price of a particular brand of beer in c (c = 1,…,116) and in the US. 5. In each panel, the horizontal axis is GDP per capita (in $US, based on PPP exchange rates). Solid lines are the OLS regression lines. Heteroscedasticity-robust standard errors in parentheses. Sources: International Comparison Program (World Bank, 2013, unpublished). Big Mac prices are from http://www.economist.com/content/big- mac-index
31
Figure 2.1 Prices and Exchange Rates: Three Illustrations
A. Price Distributions ($US, logged, demeaned)
Big Macs (SD = 0.35)
Cost-of-living index (SD = 0.41)
GDP per capita (SD = 1.06)
-5.0 -2.5 0.0 2.5 5.0
B. Prices and Exchange Rates (Local currency prices and market exchange rates)
Log Big Mac Prices Log Cost-of-living Index Log GDP per capita 20 20 20 y = 0.95 x + const y = 0.90 x - const (0.01) (0.01) SEE = 0.33 SEE = 0.35
9 9 9 y = 0.75 x - const (0.05) SEE = 0.89
Log MER -2 -2 -2 -2 5 12 -2 5 12 -2 5 12
Notes: 1. Data refer to 55 countries in 2011. 2. Panel A: The standard deviation (SD) of the logs of the BM prices is 0.35; price indices, 0.41; and GDP per capita, 1.06. In percentage terms, these are 42%, 50% and 188%, respectively. 3. Panel B: The horizontal axis refers to the log of market exchange rates (MERs).The plot on the far left is a scatter of the log of Big Mac prices against the logarithm of MERs. This is followed by scatters of the log of the cost-of-living indices (see Appendix A1 for details) and the log of per capita GDPs, against the log MERs. In each plot, the solid line is the OLS regression line. Heteroskedasticity-robust standard errors in parentheses. SEE denotes the standard error of the regression. Sources: Big Mac prices are from http://www.economist.com/content/big-mac-index. Data underlying the cost-of-living indices, GDP and MERs are from the International Comparison Program (World Bank, 2013, unpublished).
32
Figure 3.1 Domestic Relative to World Prices
A. Histograms (De-meaned) B. Cumulative Distributions
Relative frequency (%) Probability (%) 25 1001 Difference 20 ICP ICP 15 FAO 25% FAO 10 40%
5 Log Log 0 relative 0 relative -3 0 3 price -3 -0.3 0 0.3 3 price
±0.3 C. Filtered Data
Percentage of tail observations excluded Truncation ranges 0% 10% 20% 30% 40% 50% [-3,3] [-0.3,0.3]
C1. ICP Mean 0.16 0.15 0.15 0.15 0.15 0.14 0.15 0.02 Median 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.02 SD 0.55 0.41 0.34 0.28 0.23 0.19 0.54 0.17 Min -2.61 -0.72 -0.51 -0.37 -0.27 -0.19 -2 -0.3 Max 2.77 1.1 0.85 0.69 0.58 0.49 2 0.3 Obs. included 23,171 20,853 18,537 16,219 13,903 11,585 23,116 10,192 Obs. excluded 0 2,318 4,634 6,952 9,268 11,586 55 12,979
C2. FAO
Mean -0.27 -0.26 -0.25 -0.25 -0.24 -0.24 -0.26 -0.02 Median -0.23 -0.23 -0.23 -0.23 -0.23 -0.23 -0.22 -0.03 SD 0.86 0.62 0.51 0.42 0.34 0.27 0.82 0.17 Min -7.73 -1.73 -1.36 -1.1 -0.91 -0.75 -3 -0.3 Max 8.31 1.05 0.72 0.52 0.37 0.24 3 0.3 Obs. included 97,274 87,546 77,818 68,092 58,364 48,636 96,769 30,752 Obs. excluded 0 9,728 19,456 29,182 38,910 48,638 505 66,522
Notes: * 1. For the ICP data, the price of commodity i in country c, relative to the world price, is kic log p ic log p i logS c , where p and p* denote the domestic price and world price, respectively, and S denotes the exchange rate. These ic i c data refer to the prices of 198 food commodities in 175 countries in 2011. * 2. For the FAO data, the relative price of commodity i in country c in year t is kict logp ict logp it logS ct . These data refer to the prices of 133 food and agriculture commodities in 158 countries in 1991 – 2013. 3. Panel A: Data are de-meaned, logged and outliers omitted. 4. Panel C: The last column corresponds to the range [-0.3, 0.3] of the cumulative distribution plots in panel B.
33
Figure 3.2 Price Dispersion and Income
A. ICP B. FAO
y = -2.11 log(x) + constant y = -4.31 log(x) + constant (0.4) (1.17) SD×100 SEE = 5.8 SEE = 17.9 75 5.70 6.70 7.70 8.70 9.70 10.70 160 5.70 6.70 7.70 8.70 9.70 10.70
65 120
55 80
45 Income 40 ($ per capita, log 35 scale) 0 300 3,000 30,000 300 3,000 30,000
Notes: All data refer to 2011. The price of commodity i in country c, relative to the world price, is * * k log p log p logS, i 1, , N , where p and p denote the domestic price and world price, respectively, and S denotes ic ic i c c ic i c
Nc 2 the exchange rate. Price dispersion is measured by the standard deviation (SD), c1N c i 1k ic k c , where
Nc kc 1 N c i 1 k ic is the country mean.
1. Panel A: Income is measured as explog Mcc log P , where Mc is the total consumption expenditure of c, and logP Σ131 w logp is its cost-of-living index, with w the budget share of good j c j 1 j jc j
j 1, ,131 food and non-food basic headings and p jc is the PPP price of j. Data are from ICP (World Bank, 2013, unpublished). 2. Panel B: Income is the GDP per capita (in $US, at PPP, in 2010 constant prices) obtained from FAO (2018). 3. In each panel, the solid line is the OLS regression line. Heteroskedasticity-robust standard errors in parentheses. SEE is the standard error of estimation.
34
Figure 3.3 Price and Exchange-Rate Changes over Different Horizons Horizon: (i) 1-year (ii) 5-year (iii) 10-year (iv) 20-year A. Scatterplots
B. Density contours
Notes: * 1. logrict logp ict logp it is the price of commodity i in country c at year t (in local currency units, LCUs), relative to the world price (in $US). Thus,
(h)logr ict logr ict logr ic,t-h (t h + 1, ,T ic ; h 1, 5, 10, 20 ) is the h-year change in relative price and (h)logS ct logS ct logS c,t-h is the corresponding change in the exchange rate. To facilitate presentation, only values in the range 1,4 and are shown. 2. Panel A: The solid line is the 45° line and the dashed line indicates the OLS regression line. The number of observations is indicated by n. 3. Panel B: The outer most contours encompass 95% of the observations. Light (dark) areas indicate higher (lower) densities.
35
Figure 4.1 Exchange-Rate Elasticities of Prices, 198 Items, 175 Countries, 2011 A. Cross-Country Regressions B. Cross-Commodity Regressions logpic i i logS c ic , c 1, ,C i countries consuming i (i = 1, ,198) logpic c c logp i ic , i 1,..., N c food items in c (c 1, ,175)
40 Mean = 0.96 40 Mean = 0.92 Median = 0.97 Median = 0.93 30 SD = 0.05 SD = 0.11 Min = 0.81 Min = 0.54 20 20 Max = 1.06 Max = 1.16 10
Histogramof Slopes 0 0 0.8 0.84 0.88 0.92 0.96 1 1.04 1.08 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Slopes Slopes Absolute t-values for H:0iβ1 Absolute t-values for H:0cβ1 1 1 1 1 0.97 0.8 0.78 0.757 0.60 0.39 0.47 0.35
0 0 0 0 0.8 0.9 0.95 1.0 1.05 1.1 0.6 0.8 0.95 1.0 1.05 1.2 Cumulative Distributions 0.0 2.0 4.0 6.0 8.0 10.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0
Bottom 10 Middle 10 Top 10 Bottom 10 Middle 10 Top 10 1.2 1.2
1.1
1.1 1.0 0.9 1.0 0.8
0.9 0.7 0.6
0.8 0.5
Togo
Maize Onion
Egypt Nepal
Toffee
Jordan
Mango
Papaya
Poland
Ireland
Turkey Cyprus
Croatia
Nigeria Algeria
Tunisia
Spinach
Portugal
Sea Sea Bass
Anguilla Slovenia
Avocado
Morocco Moldova
Bermuda
Spaghetti
Macaroni
Lao PDRLao
Lemonade
Montserrat
Beef, Fillet
Sour Sour cream
Philippines
Bangladesh
Brown sugar
SintMaarten
New Zealand
Grapes, green
Bahamas, The
Ranked Items/Countries
SweetPotatoes
Czech Republic
Ginger (Mature)
Tinned pineapple
St. St. Kitts and Nevis
Red wine, table wine
Eggplant(aubergine)
Antiguaand Barbuda
Tomatopaste (Large)
VirginIslands, British
WheatSemolina (Suji)
St. St. Vincent& Gren. the
Strawberry/ApricotJam
Frozen chipped potatoes
Cassava - Manioc - Yuka Tinned sweetcorn/Maize
Brown- riceFamily Pack
Medium size chicken eggs TinnedButton Mushrooms
Coffee Roasted 100%Arabica Notes: pic is the price of item i in country c, in local currency units (LCU); Sc is the exchange rate of c (the LCU price of $US1); and pi is the world consumption price of item i. Data are from the World Bank (2011, unpublished).
36
Figure 5.1 Unit Root Tests, 124 Food and Agriculture Items, 126 Countries, 1991 – 2013 A. Cross-Country Regressions B. Cross-Commodity Regressions
Hc Hi kict c tk cic,t1 h1c,h k ic,th ict ; c1,,C i producing countries kict i t iic,t1 k h1i,h k ic,th ict ; i 1, , N c products * * Z -stat tests H0c : 0 c Z -stat tests H0i : 0 i Histogram Cumulative Distribution Histogram Cumulative Distribution ∗ Z∗-stat Z -stat 20 1 20 1
Mean = -3.23 Mean = -3.44 stats
- Median = -3.13 Median = -3.28 0.8 0.83 SD = 1.91 SD = 1.91 Min = -9.93 Min = -8.37 Max = 0.94 Max = 0.96 10 10
-1.64
Distributions of Z* -1.64 ∗
Histograms and Cumulative 0 0 Z -stat 0 0 Z*-stat -10 -8 -6 -4 -2 0 -9 -7 -5 -3 -1 1 -9 -7 -5 -3 -1 -9 -7 -5 -3 -1 1
Z∗-stat Z∗-stat 2 Bottom 10 Middle 10 Top 10 2 Bottom 10 Middle 10 Top 10
0 0
-2 -2
-4 -4
-6 -6 -8 -8 -10
-10
Rye Jute
Figs
Oats
Fiji
Iran
Maize
Peru
Barley
Mali
Cloves
Apples
India
Latvia
Apricots
Jordan Congo
France
Poland
Beeswax
Yemen
Nuts, nes
Iceland Bolivia
Coconuts
Tunisia
Rapeseed
Tomatoes
Ecuador
Ranked Items/Countries
Namibia
Hungary
Malaysia
Meat, duck
Peas,green
Barbados
Indonesia
Onions,dry Meat, horse
Tajikistan
Meat, rabbit
Oilseedsnes
Grain,mixed Gooseberries
Macedonia
Mustard seed
Saint Lucia Saint
Kazakhstan
El Salvador El
Puerto Rico Puerto
Switzerland
Netherlands
Saudi Arabia Saudi
Sunflower seed
United States United
Rubber, natural
Plums andsloes
Eggs,hen,in shell
Nutmeg, mace and… Meat, goose & fowl
Chillies andpeppers, dry
* Notes: The underlying variable is the deviation from the LOP: kict logp ict logp it logS ct , where pict is the price of item i in country c at time t (in local currency units); pit is the world price of item i (in $US); and S ct is the nominal exchange rate of c.
37
Figure 5.2 Speed of Adjustment of Prices, 124 Food and Agriculture Items, 126 Countries, 1991 – 2013 A. Cross-Country Regressions B. Cross-Commodity Regressions H Hc For each country c: k t k i k ; i 1, ,N . For each commodity i: kict c tk cic,t1 h1c,h k ic,th ict ; c1,,C i ict i iic,t1 h1i,h ic,th ict c C N Average half-life: HL 1 C Σi HL , where HL log 0.5 logβ1 c i c 1 c ccAverage half-life: HL 1 NcΣ i 1 HL i , where HLii log 0.5 logβ1 Histogram Cumulative Distribution Histogram Cumulative Distribution
50 1 40 1
Mean = 1.07 Mean = 1.00 Median = 0.97
lives Median = 0.88 - SD = 0.75 SD = 0.53 Min = 0.24 Min = 0.36 25 Max = 7.32 20 Max = 4.45
Distributionof half 0 HL (years)r 0 HL (years) 0 HL (years) 0 HL (years) Histogramand Cumulative 0.2 0.9 1.7 2.4 0.24 1.24 2.24 0.4 1.2 2.0 0.3 1.3 2.3
HL (years) HL (years) 8 5 Bottom 10 Middle 10 Top 10 Bottom 10 Middle 10 Top 10
6 4 3 4 2 2 1
0 0
Tea
Rye
Figs
Peru
Mali
India
Chile
Israel
Spain
Olives
Congo
Lentils
Guinea Yemen
Algeria Estonia
Malawi
Linseed
Gambia Albania
Papayas
Burundi
Ecuador
Cherries
Portugal
Uruguay
Beeswax
Romania
Plantains
Suriname
Honduras
Viet Nam Viet
Singapore
Asparagus
Pineapples
Artichokes
Spices, nes Spices,
Philippines
Blueberries
Kyrgyzstan
Cranberries
Meat, horse Meat,
Onions, dry Onions,
Switzerland
Canary seed Canary
Ranked Items/Countries
Persimmons
Beans, green Beans,
Cook Islands Cook
Grain, mixed Grain,
New Zealand New
Burkina Faso Burkina
Sweet potatoes Sweet
Lemons and limes and Lemons
Nutmeg, mace and… mace Nutmeg,
Carrots and turnips and Carrots
Dominican Republic Dominican
Vegetables, fresh nes fresh Vegetables,
Anise, badian, fennel,… badian, Anise, Eggs, other bird, in shell bird, other Eggs, Chillies and peppers, dry peppers, and Chillies
* Notes: The underlying variable is the deviation from the LOP: kict logp ict logp it logS ct , where pict is the price of item i in country c at time t (in local currency units); pit is the world price of item i (in $US); and S ct is the exchange rate of c.
38
Figure 6.1 Quarterly Effects of Exchange-Rate Change, Australia
Wheat Price Exchange Rate Deviation from LOP
A. Generalized Impulse Responses (Unexpected shock to exchange rate)
Response (%) 7 14 7 14 14 7 1.8% 3.4%
7 7 0 7 0 0
Horizon (quarters) -2.4%
-7 0 -7 0 -7 0 0 1 2 12 0 1 2 12 0 1 2 12
B. Simulations (Undervalued currency)
Change per quarter (%) 7 14 7 14 7 14 3.4%
7 7 0 7 0 0 0% Time (quarters) -4%
0 -7 -7 0 -7 0 0 1 2 12 0 1 2 12 0 1 2 12
3 Notes: These results are based on a bivariate VAR(4) model in VECM form: ΔΣΔyt α β y t 1 h 1 Γ h y t h u t . The “wheat price” is the domestic (Australian) relative to the world (US) price of wheat; the exchange rate is the AUD/USD spot rate; and the relative price and exchange rate are deflated by the ratio of Australia’s CPI to that in the US. The initial shock to the exchange rate is 3.4%, the standard deviation of the residuals of the VAR exchange-rate equation. 1. In each panel, the curve in the middle of the shaded band refers to the point estimates brought about by the change in the exchange rate at time zero of 3.4%. The band indicates the 95% confidence interval based on 10,000 bootstrap samples obtained from the procedure of Lütkepohl (2005); see Appendix A8 for details. 2. Panel A: These are generalised impulse response functions proposed by Pesaran and Shin (1996, 1998). (i) Far-left and middle plots: The vector of responses of the price and exchange rate to the exchange-rate shock at y 2 horizon h is f (h) φιhΣu σ h 0, ,T , where φh is derived from the VAR coefficient matrix; Σu is the
22nd covariance matrix of the residuals; ι 0, 1 ; and σ 0.034 is the 2 diagonal element of Σu . (ii) Far-right plot: The response of the LOP deviation is fk (h) βfˆ y (h), where βˆ is the estimated co-integrating vector and f y (h) is as defined in (i) above. 3. Panel B: See text for details of the simulation procedure. Source: Wheat prices are quarterly averages of prices in Australia and the US (averaged across 5 grades of wheat), from USDA (2018). Exchange-rate and CPI data are from FRED (2018). The sample period is 1987Q1 – 2018Q4.
39
Table 3.1 Price Dispersion and Components Logarithmic Components of Dispersion (percent) Year standard deviation Commodities Countries
t Within Between Within Between (1) (2) (3) (4) (5) (6) 1991 1.01 63.9 36.1 53.7 46.3 1992 1.01 69.6 30.4 52.9 47.1 1993 0.97 67.2 32.8 47.3 52.7 1994 1.13 73.1 26.9 62.5 37.5 1995 0.94 65.6 34.4 39.3 60.7 1996 0.88 67.2 32.8 39.1 60.9 1997 0.89 68.1 31.9 35.7 64.3 1998 0.91 68.1 31.9 37.9 62.1 1999 0.92 67.6 32.4 33.2 66.8 2000 0.91 68.7 31.3 32.0 68.0 2001 0.90 68.9 31.1 32.0 68.0 2002 0.90 67.4 32.6 31.7 68.3 2003 0.90 69.7 30.3 32.6 67.4 2004 0.88 67.9 32.1 32.1 67.9 2005 0.87 69.8 30.2 32.0 68.0 2006 0.89 67.4 32.6 32.3 67.7 2007 0.84 67.0 33.0 32.6 67.4 2008 0.83 66.9 33.1 33.0 67.0 2009 0.85 67.0 33.0 29.6 70.4 2010 0.94 67.5 32.5 53.6 46.4 2011 0.93 66.7 33.3 57.1 42.9 2012 0.90 68.3 31.7 57.2 42.8 2013 0.80 70.4 29.6 37.4 62.6 Mean 0.91 68.0 32.0 40.3 59.7 SD 0.07 1.8 1.8 10.2 10.2
Notes: * 1. Let kict logp ict logp it logS ct be the price of item i in country c and year t, relative to the world price (or the
logarithmic deviation from the law of one price). The mean and variance of kict over items and countries are 2 NC 2 N C kt 1/[N C] i 1 c 1 k ict and t 1/ [N C] i 1 c 1 k ict k tt . For each item i in year t, the mean and
2 C 2C variance over countries are ki t 1/ C c 1 k ict and it 1/ C c 1 k ict k ii tt . The variance over items is
2 2N 1/ N k k . It can be shown that 2 N 2 2 , that is, the total variance is the sum of t i 1 ii tt t t 1/ N i 1 it t within- and between-commodity components. 2 2. Column 2: This contains the square root of the total variance: t . 3. Column 3: This is the within-commodity fraction of total variance: N 2 2 100 1/ N i 1 it / t .
22 4. Column 4: This is the between-commodity fraction of total variance: 100 tt / . 5. Columns 5 and 6: Analogous to columns 3 and 4, using a country basis, these columns contain the within- and between- country components of the total variance. 6. The above decompositions hold exactly for balanced panels, and only approximately with our unbalanced data. See Appendix A3 for details.
SUPPLEMENTARY MATERIALS
A-1 Appendices for “THE LAW OF ONE FOOD PRICE”
A1. DATA DESCRIPTION
ICP Data The dataset from the International Comparison Program (hereafter, ICP) contains retail prices from global surveys and expenditures from national accounts (World Bank, 2013). There are three main levels of commodity aggregation: There are products, basic headings (listed in Table A1.1) and aggregated categories. The published version of the data refers to the aggregated categories, while the unpublished version, provided to us by the World Bank, contains data for 182 countries on the first two levels. These two levels form the basis of our analyses in the main text: The disaggregated prices are used in the cross-sectional analyses of Sections 3 and 4, while the basic heading data are used to construct the cost-of- living and food price indices of Figures 1.1 and 2.1, as well as the price dispersion measure used in Figure 3.2. We made the following adjustments to the data: i. Product-level: We have average prices, but not expenditures, for 1,244 disaggregated products. Of these, 198 are food, which are listed in Table A1.2. As Russia, Sudan and Egypt are dual participants in the ICP, we keep each country only once by using the entries that contain more observations. Cuba and Bonaire are also omitted as they have incomplete data. Additionally, average prices are unavailable for Iran and Georgia. This leaves 182 – 3 – 2 – 2 = 175 unique countries. Finally, 257 products were removed as they were represented in less than 30 countries. The final sample consists of 1,244 – 257 = 987 products, 198 foods and 789 non-foods, in 175 countries. If no prices were missing, there would be 987 175 172,725 valid observations. But as 81,266 are missing, there are 172,725 – 81,266 = 91,459 product × country observations remaining. ii. Basic-heading level: Total consumption is defined as the sum of the first 132 of the basic headings listed in Table A1.1.1 We consider the first 32 as food items. We make two adjustments to these data. As above, we first remove duplicate entries for Russia, Sudan and Egypt and omit Cuba and Bonaire. Second, we combine some
1 This follows the ICP’s definition of “Actual Household Consumption”, which is the total value of the individual consumption expenditures of households, non-profit institutions serving households, and general government at purchasers’ prices. SUPPLEMENTARY MATERIALS
A-2 commodities. For example, many West Asia countries have little to no PPP real expenditure per capita on pork due to religious reasons. We partially “solve” this by combining the “Pork” and “Lamb, mutton and goat” groups; so food now consists of 31 basic headings. To maintain internal consistency when we combine groups, expenditures (in both domestic currency units and in US dollars, that is, real expenditures) are summed over the sub-components, whilst the purchasing power parity of the combination is the ratio of nominal to real expenditures.2 Our final sample contains 182 (the starting number of countries) – 3 (duplicates) – 2 (Cuba and Bonaire) – 22 (small consumption) = 155 countries. One limitation of the ICP data is that the 31 basic headings exclude food consumed away from home, which is important in some high-income countries.
ICP Food Prices and Income After the above adjustments, we are left with 31 food basic headings and 131 consumption basic headings. Define wi as the budget share of good i (the proportion of total consumption expenditure devoted to i), so that if the 31 food items are the first 31 goods, the
31 budget share of food as a group is WF i 1 w i . If pi is the price of category i, the relative price of food can then be defined as
P 31w 131 logFi logP logP logp w logp . F i i i PWi 1F i 1 This relative price is the difference between the conditional budget-share weighted logarithmic mean of the prices of the food items, log PF , and the log of the cost-of-living
131 index, logP w logp . Table A1.3 contains, in columns 3 and 7, the food relative i1 ii price and as can be seen, there is a distinct tendency for food to become cheaper as income rises.3 The relative price of food is plotted against income in panel A of Figure 1.1, while the
2 Using a minimum cut-off of $0.01, the following 22 countries are omitted: Algeria, Angola, Bangladesh, Brunei Darussalam, Burundi, Egypt, Ethiopia, Iran, Kuwait, Lao PDR, Malawi, Maldives, Mauritania, Myanmar, Nicaragua, Pakistan, Palestinian Territory, Saudi Arabia, Sudan, Tanzania, Togo and Yemen. 3 For example, on average for the poorest quartile of countries, the relative price of food is 36.3 percent, while this falls to 13.7 for the richest quartile. This means that, on average, food is about 20 percent cheaper in the richest countries as compared to the poorest. If the relative price of food in country c is x,c then a representative basket of food costs expxcc 1 x times the cost of a representative basket of all goods, with x0c for c = the US as a normalization. The relative cost of food in country c as compared to that in another country d, where the relative price is x,d is exp xc exp x d exp x c x d . For countries in the top and bottom income quartiles, the averages are xc 0.137 and xd 0.363; consequently, the cost difference is exp 0.137 0.363 0.798. Thus, food is 20.2 percent cheaper in the top quartile. Using the approximation that for small z, expz 1 z, SUPPLEMENTARY MATERIALS
A-3 cost-of-living index is plotted in Figure 2.1. Columns 4 and 8 of Table A1.3 contain a
31 2 measure of dispersion of food prices across items, i 1w i / W F log p i log P F . Food prices have a tendency to be less dispersed in richer countries, as shown in Figure 3.2. FAO Data Producer price data from the Food and Agriculture Organisation (FAO) are used in Sections 3 and 5 of the paper. This entails the combination of two large data sets from the FAO (2018): (i) Annual domestic producer prices on 208 food and agricultural items in 162 countries over the 24-year period 1991 – 2014. (ii) The export quantities and values of 387 items from 181 countries over the period 1986 – 2013. These export data are used in the derivation of the world production prices (see Appendix A2 below for more details). When combining these datasets, we omit items with no observations, leaving 133 items, in 158 countries, from 1991 to 2013; this yields 97,274 product × country × year observations. For the computation of the ratios between price changes and exchange rate changes (used in Appendix A5), we omit years when there is no change in either variables, resulting in 82,187 observations. We also make two further adjustments to the data used in the cross-country regressions: (i) We only include items with data of at least two producers, who have at least 15 years of observations each. (ii) Cross-sectional units with non-consecutive observations (i.e., with gaps between years) are also omitted. This leaves a sample of 124 items, covering 158 countries, from 1991 to 2013, with a total of 79,171 observations. Similarly, for the cross-item regressions, we only use countries which produce at least two items, and have at least 15 years of data (with no gaps) for each of these products. The resulting sample consists of 126 countries and 133 items from 1991 to 2013, yielding a total of 78,350 observations. These final samples form the basis of the export weights when computing the law of one price deviations with the FAO data, discussed in Appendix A2. Table A1.4 lists all adjustments made to ICP and FAO data throughout this paper.
the approximate cost difference is 1 xcd x 1 0.137 0.363 0.774, implying that food is approximately 22.6 percentage cheaper. The approximation error is 22.6 20.2 2.4 percentage points, which is not particularly small and reflects the large difference between the top and bottom quartiles. SUPPLEMENTARY MATERIALS
A-4 A2. THE LOP DEVIATIONS
The deviations from the law of one price (LOP) were discussed in Section 3. This appendix presents a further examination of the statistical attributes of the deviations. The
* deviation for good i is defined as kic logp ic logp i logS c , where pic is the price of item i
in country c in local currency units (LCUs), pi is the world price measured in $US and Sc is the exchange rate for the currency of c, defined as the cost in LCUs of $US 1. The world price
of i in LCUs is pSic . We proxy the world price with a weighted average price, with weights reflecting relative importance of each country in international trade of i. Let Ci denote the set of countries in which product i (i = 1,…, 198) is consumed and let real consumption of i in country cCi be q.ic Food products are aggregated into G < n = 31 food basic headings, denoted by X , g 1, ,G. Measuring in US dollars so units are comparable, Qq g gc iXg ic is the consumption of group g in c,C QQ is world consumption of i and i g cCi gc w Q Q is country c’s share, with w 1. The world price of i is then defined as gc gc g cCi gc a weighted geometric mean of the country prices:
p logp w logic , i X , i 1, ,198. i cCi gc g Sc This means that items in the same group receive the same weight. While this approach is not perfect, in the absence of direct information on individual items’ consumption and on world prices, it is a reasonable working approximation. A similar approach is adopted for the FAO data: Let xict be the value of export of commodity i i 1, ,133 from country c
C c 1, ,158 in year t, measured in $US, so that Xxct c 1 ict is the “world” total trade in the commodity and wict x ict X ct is country c’s share. The world price of i in t is defined as
x *C pict log pit c 1 w ict log , i 1, ,133, Sct
x where pit denotes the corresponding export price in c, in local currency units, and Sc is country c’s exchange rate against the $US. Figure A2.1 gives some details on the dispersion of the deviations. A selection of the cross-country standard deviations (SD) for ICP items are given in the top plot of panel A. Irish whiskey and cream liqueur have the lowest SD, perhaps reflecting these are fairly SUPPLEMENTARY MATERIALS
A-5 standardised products. Additionally, international travellers are known to actively arbitrage price differences for spirits.4 Then come dried mung bean and apple juice. These commodities have SDs of 20-30 percent, which interestingly is of the same order of magnitude as that of Big Mac hamburgers (as shown in Figure 2.1 of the main text).5 Dried shrimp, chilies and bean curd are at the other end of the distribution with the highest dispersion, possibly reflecting the role of differing varieties. Evidently, even these high-dispersion commodities are more tradable (as measured by their SDs) than GDPs (again in Figure 2.1), which is quite reasonable. The bottom plot of panel A contains the countries with the lowest and highest dispersion – the differences in dispersion between the low- and high-dispersion countries are smaller than the low-high differences for the commodities. This pattern is also true for FAO prices, as can be seen in panel B of the same figure, although dispersion tends to be greater for FAO as these data contain mostly unprocessed products subject to volatile world market conditions. We shall investigate the differences between the cross-item and cross-country sources of dispersion in Appendix A3 below. The first row in panel A of Figure A2.2 gives a frequency distribution of the ICP deviations for all commodities and countries. The mean is about 16 percent and the distribution seems to be reasonably symmetric. Importantly, there is substantial dispersion as the logarithmic standard deviation is 0.55, or more than 50 percent; and from the cumulative distribution on the right of the panel, only 40 percent of observations lie in the range [-0.3, +0.3]. The second row shows that if we average over commodities, there is some compression -- the dispersion of the country means is considerably lower, at about 27%, and about 65% of the observations now lie in the range [-0.3, +0.3]. Somewhat more compression emerges in the third row when commodity means are used. Panel B of Figure A2.2 presents the distributions for the FAO deviations. In the first row, the full sample mean is -0.27, which is probably not too excessive, but the standard deviation is high at 0.86 and the tails long with only about 25 percent of the observations lying in the range [-0.3, 0.3]. The second and third rows of this panel plot, for all years, the distribution of the country means, k1 N k , and the commodity means, kk1 C ctN i 1 ict ii ttC c 1 ict where N and C denote the total number of items and countries, respectively. The variance of the country mean (which measures the country effect) is 0.582 0.34, while that of the commodity mean (the commodity effect) is 0.532 0.28. This points to the dominance of the
4 It should also be noted that these prices come mostly from richer countries. 5 The agreement between the minimum-dispersion ICP commodities and Big Macs would seem reassuring, if only because The Economist magazine regards the Big Mac as an example of an “idealised” good that is the same the world over, well suited for PPP-exchange-rate calculations. SUPPLEMENTARY MATERIALS
A-6 country effect, something that is further elaborated on in the next appendix.6 In agreement with Figure A2.1, Figure A2.2 also shows that the FAO deviations are more dispersed than the ICP’s.
A3. VARIANCE DECOMPOSITIONS
The deviation from the LOP is, in essence, a relative price, the price of the good at home in terms of its cost abroad (with both prices expressed in terms of local currency units). In this appendix, we use the FAO data to investigate the source of variation in these relative prices LOP deviations. Assuming for simplicity a balanced structure for each panel, the mean and variance of the deviations, over all countries and commodities, at time t are
2 NC 2 N C kt 1/[N C] i 1 c 1 k ict and t 1/ [N C] i 1 c 1 k ict k tt . These are termed the grand mean and variance at time t. Denote the mean of these grand variances the “overall grand
2 T 2 variance”: 1/ T t 1 t . Is it the variability among commodities or countries that contribute most to the grand variance? In the following we answer this question using two
2 types of decompositions of t .
A Commodity-Based Decomposition
Consider the deviation of commodity i in the C countries, ki1t , ,k iCt . The mean and
2 C 2 C variance are: ki t 1/C c 1 k, ict i t 1/C c 1 k ict k ii tt . The dispersion of the deviations
22 N2 of all N commodities is the mean of i t,..., n t , that is, 1/ Ni 1 i t . The conventional label
2 for this mean might be the “within-commodity variance”. But as it refers to differences across countries of the prices of the same commodity when expressed in the same currency, the more dispersion across countries, the larger is this measure. Accordingly, it is more useful to refer to this mean as the “cross-country” component of the variance, to be denoted by
2 N 2 1,t 1/ N i 1 i t . The corresponding “between-commodity variance” is the dispersion of the commodity means around the grand mean, which shall be referred to as the “cross-
2 2N commodity” variance: 2,t 1/ N i1 k iitt k tt , where
NNC ktt 1/ N i 1 k ii tt 1/ N C i 1 c 1 k ict is the grand mean. Using the above concepts, it can be easily shown that the grand variance is made up of the cross-country and cross-commodity components:
2 2 2 (A3.1) t 1,t 2,t .
6 The greater variance of the cross-country component is largely due to extreme values in both tails. SUPPLEMENTARY MATERIALS
A-7 A Country-Based Decomposition
Next, consider the price of each of the N commodities in country c, k1ct , ,k Nct . The
2 N 2 N mean and variance are: kct 1/N i 1 k, ict ct 1/N i 1 k ict k cctt . The mean of the C
22 variances, 1t,..., Ct , is the within-country dispersion of prices. As this measures the variability of prices across commodities, we shall call this the cross-commodity variance,
2 C 2 1,t 1/ C c 1 ct . The dispersion of the country means around the grand mean is the country
2 2C k 1/C CNC k 1/NC k. effect: 2,t 1/ C c 1 k ct k tt , where t c 1 cctt i 1 c 1 ict Again, the grand variance can then be decomposed into (new) commodity and country effects:
2 2 2 (A3.2) t 1,t 2,t . Both types of decomposition above yield measures of the commodity and country effects. Due to the differing basis underlying each decomposition, in general the effects are not the same. However, equations (A3.1) and (A3.2) imply that the differences between the two types of variances coincide:
2 2 2 2 (A3.3) 1,t 1,t 2,t 2,t 0. Since the panels we use are unbalanced, equations (A3.1)-(A3.3) hold only approximately.
2 2 2 2 Table 3.1 of the main text presents, for each year, the square roots of t , 1,t , 2,t , 1,t and
2 2,t .
A4. CROSS-SECTIONAL TESTS
Tables A4.1 and A4.2 present the detailed estimation results for the cross-sectional tests of the LOP. These are discussed in Section 4 of the main text.
A5. PRICE CHANGES AND EXCHANGE-RATE CHANGES
As a complement to the material in Section 3, this appendix presents a preliminary analysis of the relationship between price changes and exchange-rate changes, using the FAO data. Let pict be the LCU price of commodity i (i 1, ,133) in country (c 1, ,158) and year t (t 1, ,23). The corresponding log-change is logpict logp ict logp ic,t-1 (t 2, ,23) .
* * Define the price in c relative to the world price pit as logrict logp ict logp it . The 1-year
* logarithmic change of relative prices is logrict logr ict logr ic,t-1 logp ict logp it , with log rict 0 meaning that the domestic price rises relative to the world price. Similarly, SUPPLEMENTARY MATERIALS
A-8 let Sct be the LCU price of one US dollar and logSct logS ct logS c,t-1 be the log-change in the exchange rate (so that logSct 0 means the domestic currency depreciates). As documented in panel C of Figure 3.1, the FAO data contain 97,274 commodity- country-year observations. We make two adjustments to these data: (i) We omit items with a single producer and countries with a single product; and (ii) omit years when either
logrict 0 or logSct 0. This leaves 82,187 observations. As there are still many outlying observations, we trim the data according to extreme values of the ratio logrict / logS ct .
These extremes are determined by the parameter ω, which is the size of a censor window defined as the proportion of the total number of observations discarded. Figure A5.1 presents the histogram of the ratios using the censorship rules of ω = 15% (i.e., the most extreme 7.5% values in the two tails are excluded). A blow-up of this histogram is also provided by restricting the range to [-1, 3]. For the LOP to hold, the ratios logrict / logS ct should be centred around 1. The table at the bottom of Figure A5.1 shows that the ratios are centred at somewhat below 1, but these results refer to a one-year horizon only. The first two rows of Table A5.1 provide the 2-by-2 contingency table for exchange rate changes and price changes over the 1-year horizon. If the LOP holds, there should be a tendency for the elements on the diagonal to exceed the corresponding off-diagonals, and this pattern is observed in the table. The column and row totals of the table reveal that currencies depreciate relative to the dollar more frequently than they appreciate (58,196 depreciations vs. 33,084 appreciations), and prices increase more often than decrease (56% vs 44%). The χ 2 value for the hypothesis independence far exceeds the critical value. Similar patterns emerge in latter parts of the table referring to changes over 5-, 10- and 20-year horizons. Panel A Figure 3.3 of the text contains scatter plots the scatterplot of h-year changes in the relative prices, (h)log r ict , against the corresponding exchange-rate changes, (h)logS ct , using the full, uncensored sample (97,274 observations). For a given country, there is a certain value of (h)logS ct for each horizon. When this is related to a number of price changes (h)log r ict over the same horizon, the result is a series of points resembling a vertical line in the scatter. Such a pattern is evident in panel A of Figure 3.3. Consequently, it may be desirable to “compress” the information represented by (h)log r ict by averaging across items:
Nct (h)logr ct 1/ N ct i=1 (h) logr ict (t h + 1, ,T ic ) , where Nct denotes the number of items SUPPLEMENTARY MATERIALS
A-9 produced by c at time t. Panel A of Figure A5.2 gives the results. This is a clear picture of the relationship between price and exchange-rate changes, and the main implication from Figure 3.3 remains unchanged: The LOP works better at longer horizons, as indicated by the slope coefficient moving closer to unity and the improved goodness-of-fit.
A6. PANEL UNIT ROOTS
In this appendix we report the detailed results of the panel unit root tests and co- integration tests discussed in Section 5. We start by testing for a cross-country panel unit root using:
Hc (A6.1) Δkict α c γ c t β c k ic,t 1 c,h Δk ic,t h ε ict , c 1,...,C i ;t 1,...,T i , h1 which has half-life HLcc log(0.5) / log(β 1) . Since there are Ci equations/countries in the panel for item i, we define the mean and standard deviation of half-lives, across countries, as
C 2 i Ci μHL (1/ C i )Σ c 1 HL c and σHL (1/ C i )Σ c 1 HL c μ HL . There are several ways to test for a panel unit roots. The standard inverse normal method, according to Choi (2001), uses the combination of significance levels derived from individual unit-root test statistics as follows: Let Gc be the one-sided unit-root test statistic for country c (this is an ADF test statistic in our case, but it could be any unit root test). The asymptotic p-value for is pc F G c 1 F G c , where F denotes the continuous
C distribution of under the null. The combined test statistic is Z 1/ C i Φp1 , icc1 where Φ is the standard normal cumulative distribution function. Here the countries’ p-
1 values are combined to define the so-called “probits”: tcc Φ p . Each probit has a standard normal distribution by construction, hence the term “inverse-normal method”. With the assumption of independent cross-sectional disturbances, Choi (2001) shows that Z follows an asymptotic standard normal distribution under the null. However, cross-sectional dependence would seem to be important in agriculture markets where common shocks to prices (such as a surge in demand) frequently occur. The dominant role of the US dollar in world markets means that a shock to that currency would possibly be transmitted to prices across countries, giving rise to further cross-sectional dependence. Ignoring such dependence could lead to size distortion and reduce much of the gain in power associated with the panel approach (O’Connell, 1998). Additionally, cross- sectional dependence can result in misleading inference and inconsistent estimators (Phillips SUPPLEMENTARY MATERIALS
A-10 and Sul, 2007). For panels with the cross-sectional dimension (N) smaller than the time series (T) dimension, the error cross-correlation can be modelled using the SURE framework. However, standard tests are not applicable in “short” panels where N is larger than T (Pesaran, 2015). A solution to this problem for short panels is suggested by Hartung (1999), who pointed out that dependency in the original test statistics Gc can be characterized by a certain correlation structure among the probits t c . He assumes a constant correlation structure of the and derives a consistent estimator together with a weighted inverse-normal test statistic, denoted as “ Z* -stat”, which is distributed N(0,1) under the null. Demetrescu et al. (2006) show that when the original statistics have a multivariate normal distribution, this method is robust to violation of the constant correlation assumption. The authors also point out that even when normality does not hold, -stat has a superior performance when there exist medium to strong correlations, relative to tests that ignore cross-sectional dependence. In our application, we first test for cross-sectional dependence using Pesaran’s (2004) tests, and only apply Hartung’s correction procedure when the null of independence is rejected at the 5% level of significance. Table A6.1 presents the cross-country panel regression results, while Table A6.2 gives the parallel cross-commodity results. These results form the basis of Figures 5.1 and 5.2 in the text.
A7. CO-INTEGRATION
The LOP implies prices and exchange rates are co-integrated. Therefore, as an alternative to testing the stationarity of LOP departures (as in Section 5 of the main text), in this appendix we perform panel co-integration tests proposed by Kao (1999), Pedroni (2004) and Westerlund (2007).
First, we re-define the relative price of good i as kict log r ict log S ct , where
* log rict log p ict log p it . Before testing for possible co-integration of log rict and log Sct , we test for unit roots in each of these series. For completeness, we use both our main statistic (see Section A6) and two other tests that allow for individual unit root processes and unbalanced panels, i.e., the Im et al. (2003) and the Fisher-type Phillip-Perron tests (Maddala and Wu, 1999).7 Panel A of Table A7.1 describes key characteristics of these three unit root tests. Cross-country panel unit root test results are presented in Table A7.2. As can be seen,
7 However, the latter two tests do not account for cross-sectional dependence, which could lead to lower test power. We mitigate the effect of cross-sectional correlation by de-meaning the data before applying any tests. SUPPLEMENTARY MATERIALS
A-11 for the majority of commodities we cannot reject the null of a panel unit root for both of these series at the 1% level of significance. Table A7.3 gives similar conclusions about the unit root behaviour of prices in most countries in our sample.8 With these results, we can rewrite equation (A6.1) in VEC form:9
HHcc (A7.1) logrict α c γ c t θ c logr ic,t-1 η c logS c,t-1 θ c,h logr ic,t-h κ c,h logS c,t-h e ct . h=1 h=1
If the speed-of-adjustment coefficient θc is negative, there is error-correction, which in turn implies co-integration. Westerlund (2007) proposes four statistics to test H0c : θ 0. These tests can be grouped into two categories based on the exact specification of the alternative hypothesis.10 On the one hand, we have the “group-mean” statistics, for which rejection of the null is taken as evidence of co-integration for at least one country, i.e., HAc : θ0 for at least one c. These are constructed as:
1 CCθˆˆ 1 T θ Gc ; G c c , τθˆ CCc=1SE θˆ c=1 θ1 c c
θˆ ˆ θ ˆ where c and SEθc are the least-squares estimate of c and its standard error; θ1c is a
H semi-parametric estimate of θ 1 1c θ ; and T is the number of observations for c. c h=1 c,h c On the other hand, we have the “panel” statistics, for which rejection of the null is taken as evidence of co-integration for the panel as a whole, i.e., HAc : θ 0 c. These statistics are: ˆ θ ˆ Pτθ ; P Tθ, SEθˆ
ˆ ˆ where θ is a type of cross-sectional average of θc and T is the cross-sectional average of Tc . Panel C of Table A7.1 documents the characteristics of the four tests.11
8 With the cross-commodity tests, we can only examine the stationarity of prices, since for a given country the exchange rate does not vary across items. 9 As in the text, the lag order Hc is selected by the Akaike information criterion, and does not exceed 2 in all cases. 10 Westerlund (2007) argues that if we estimate θc by simply pre-specifying ηc , the resulting test statistics will not be free of nuisance parameters. Alternatively, we can re-parameterized equation (A7.1) and write the error- correction term as θc logr ic,t-1 ω c logS c,t-1 , where ωc θ c η c . Since ωc is unrestricted and the co-integrating vector is implicitly estimated under the alternative, it is possible to construct valid test statistics based on the least-squares estimate of θc . 11 One of the major strengths of the tests based on equation (A7.1) is their flexibility. In particular, they allow for a large degree of heterogeneity, both in the long- and short-run parts of the error-correction model (see, e.g., Persyn and Westerlund, 2008). To account for possible cross-sectional dependence, we obtain robust critical values through a bootstrap procedure, as suggested by Westerlund (2007). SUPPLEMENTARY MATERIALS
A-12
Table A7.4 reports the p-values for these tests. While the Z-statistics ( G τ and Pτ ) overwhelmingly reject the null, the normalized types ( Gθ and Pθ ) support no co-integration for many commodities. We also use the tests developed by Kao (1999) and Pedroni (2004), which rather than relying on structural dynamics, adopt Engle and Granger (1987)’s residual- based approach.12 Panel B of Table A7.1 documents the characteristics of these tests. From Table A7.5 we can see that again, the evidence on co-integration is mixed. Overall, the Pedroni tests provide stronger support for co-integration than Kao’s. Nevertheless, compared with the Westerlund’s tests, these tests suffer from low power if there is violation of the common factor restriction assumption, that is, the long-run parameters for the variables in their levels are equal to their short-run counterparts for the variables in differences (see, e.g., Banerjee et al., 1998 and Persyn and Westerlund, 2008). As another robustness check, we weight these p-values by export shares, and find that the weighted mean p-values are mostly smaller than the unweighted means. See the 5th- and 6th-to-last rows of Table A7.5. The higher unweighted means imply that items with low trade volumes “pull” the centre of gravity of the densities away from zero, leading to false acceptance of no co-integration. For the cross-commodity tests, we use the following model:
HHii ** logrict α i + γ i t θ i logr ic,t-1 η i logp i.t-1 θ i,h logr ic,t-h κ i,h logp i,t-h e ict , h=1 h=1 from which similar group-mean and panel test statistics can be constructed. Table A7.6 shows the test results. Again, the results from t-stat based and support co-integration, but those of and do not. However, as Westerlund et al. (2015) point out, interpreting tests of the null of no co-integration requires care. In particular, rejection according to the group- mean statistics does not imply that all cross-sectional units are co-integrated. For further checks, we complement these tests with the ones proposed by Kao (1999) and Pedroni (2004). As can be seen from the bottom of Table A7.7, there is stronger support for co-integration here than in the cross-country case, in the sense of greater differences between the weighted and unweighted mean p-values. To summarise the co-integration tests, Figure A7.1 presents the density distributions of the p-values for commodities and countries, pooled across all tests. While there are long tails, both plots have a mass around zero, which points to co-integration: The lower-than-1%
12 We thank Timothy Neal for kindly assisting us with his Stata code (Neal, 2014) that implements Pedroni’s (2004) tests. SUPPLEMENTARY MATERIALS
A-13 mass means the null of no co-integration can be rejected at the 1% level for most countries and for most items.
A8. THE ADJUSTMENT PATH
This appendix provides details of the construction of the generalised impulse response functions (hereafter, the GIRFs) and the bootstrap confidence intervals for the GIRFs and the simulated time paths discussed in Section 6 of the text. The following discussion primarily draws on Cheung et al. (2004) and Pesaran and Shin (1996, 1998).
For a commodity i in country c, consider the Hc -lag vector auto-regression
[VAR( Hc )] representation of equation (A6.1):
Hc (A8.1) yt A h y t h u t ; t = 1, 2, ,T, h1 where yt log r t ,logS t ; Ahch 1, ,H are 22 coefficient matrices; and ut is a 2- dimensional white-noise process, with mean Eu0t and time invariant positive definite covariance matrix Euutt Σu . As for the majority of countries, prices and exchange rates co-integrated (Appendix A7), the error-correction term kt 1 βy t 1 is stationary. Among many others, Cheung et al. (2004) impose the long-run LOP restriction on kt , which implies co-integrating vector β [1, 1] . To compute the GIRFs, we opt instead to use the ˆ ˆ estimated value of β [1, β] . As y t is first-difference stationary, Δyt can be expressed as an infinite moving average:
(A8.2) Δ,yt φu h t h h0
h1 where φh B hΣ m 0 φ m with B0φI 0 2 ( I2 is a two-dimensional identity matrix).
Hc BBAh Σ m 1 m h m is the “cumulative effect” matrix. For the GIRFs, we use the subscript to denote the impulse (shocked) variable, and superscript for the response variable. Thus, for example, for a price shock, the response at
S P horizon h of the exchange rate is fP (h) and that of the price is fP (h) . It can be shown that the
13 GIRF of Δyt with respect to a unit innovation in variable j is:
13 When there are contemporaneous correlations between the components of the error process ut , we cannot shock one variable while keeping the other fixed. A popular solution is to orthogonalize of shocks with the SUPPLEMENTARY MATERIALS
A-14 φιΣ fSP (h),f (h) ΕΔ|y u σ,ΣΕΔ|Σ y hju , j j tht,j jjuu th σ jj
th where σ jj is the j diagonal element of Σu , φh is obtained from equation (A8.2) and ι j is a selection vector that has 1 as its element and zero elsewhere. In words, the above GIRF measures the effects on Δyth of a shock to the equation. The response of the co-
KSPˆ integrating relation (denoted by K) to a unit shock to variable j is fj (h) β f(h),f j j (h),
KPSˆ KPSˆ viz., fSSS (h) f (h) β f (h) and fPPP (h) f (h) β f (h). We adopt the residual-based bootstrap method of Lütkepohl (2000, 2005) to compute confidence intervals for the GIRFs with a 6-step procedure:
1. Estimate the bivariate VAR( Hc ) model (A8.1) and denote the estimated coefficient ˆ matrices by Ahch 1, ,H and the residual vector by uˆ t . 1T 2. Compute the de-meaned residuals: uuˆ t t 1, ,T where uu T Σt 1ˆ t , and * generate bootstrap residuals ut by randomly drawing with replacement T observations from the de-meaned residuals. To preserve the contemporaneous correlations, this involves drawing 21 vectors of residuals. H 3. Compute the bootstrap sample recursively as y***c Aˆ y u t = 1, , T . th1 h t h t The initial values y***,,, y y are chosen to be the same as the first H t Hcc t H 1 t 1 c actual observations on y.
4. Re-estimate the parameter matrices Ah based on the bootstrap sample. 5. Re-compute the GIRFs, with the shock size and co-integrating vector equal to those derived from the original VAR estimates. 6. Repeat steps two to five 10,000 times and compute the 2.5 and 97.5 percentiles of the GIRFs at each horizon. These percentiles constitute the 95% confidence intervals (CIs). Note that the original shock sizes (derived from the covariance matrix of the VAR) and co-integrating vector are kept constant in all simulations. The CIs in panel A of Figure 6.1 of the text use the above approach. For the CIs for the simulated time paths in panel B of that figure, we follow the above procedure up to step 4 to generate 10,000 bootstrap samples. Then instead of re-computing the GIRFs, we re-apply the 6-step procedure described in Section 6; and the CIs for the simulated paths are then constructed in a manner similar to step 6 above.
Choleski decomposition of Σu . The disadvantage is that the impulse responses depend on the ordering of variables. The generalized impulse responses proposed by Pesaran and Shin (1998) avoid the problem by allowing each variable to be affected by its own historical path, as well as the others’. SUPPLEMENTARY MATERIALS
A-15 APPENDIX REFERENCES Banerjee, A., J. Dolado and R. Mestre (1998). “Error-Correction Mechanism Tests for Co- integration in a Single-Equation Framework.” Journal of Time Series Analysis 19: 267– 83. Cheung, Y. W., K. S. Lai and M. Bergman (2004). “Dissecting the PPP Puzzle: The Unconventional Roles of Nominal Exchange Rate and Price Adjustments.” Journal of International Economics 64:135-50. Choi, I. (2001). “Unit Root Tests for Panel Data.” Journal of International Money and Finance 20: 249-72. Demetrescu, M., U. Hassler and A.-I. Tarcolea (2006). “Combining Significance of Correlated Statistics with Application to Panel Data.” Oxford Bulletin of Economics and Statistics 68: 647-62. Engle, R., and C. Granger (1987). “Co-Integration and Error Correction: Representation, Estimation and Testing”. Econometrica 55(2): 251-76. FAO (2018). Food and Agriculture Organization of the United Nations. Available at: http://www.fao.org/faostat/en/#data/ Im, K. S., M. H. Pesaran and Y. Shin (2003). “Testing for Unit Roots in Heterogeneous Panels.” Journal of Econometrics 115: 53-74. Kao, C. (1999). “Spurious Regression and Residual-Based Tests for Co-integration in Panel Data.” Journal of Econometrics 90: 1-44. Lütkepohl, H. (2000). “Bootstrapping Impulse Responses in VAR Analyses.” Proceedings in Computational Statistics 14th Symposium held in Utrecht, The Netherlands. Pp. 109- 119. Physica: Heidelberg. (2005). New Introduction to Multiple Time Series Analysis. New York: Springer-Verlag. Maddala, G. S., and S. Wu (1999). “A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test.” Oxford Bulletin of Economics and Statistics 61: 631-52. Neal, T. (2014). “Panel Co-integration Analysis with xtpedroni.” Stata Journal 14: 684-92. O’Connell, P. G. (1998). “The Overvaluation of Purchasing Power Parity.” Journal of International Economics 44: 1-19. Pedroni, P. (1999). “Critical Values for Co-integration Tests in Heterogeneous Panels with Multiple Regressors.” Oxford Bulletin of Economics and Statistics 61: 653-70. (2004). “Panel Co-integration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis”. Econometric Theory 20: 597–625. Pesaran, M. H. (2004). “General Diagnostic Tests for Cross Section Dependence in Panels.” Cambridge Working Papers in Economics 0435. Faculty of Economics, University of Cambridge. (2015). “Testing Weak Cross-sectional Dependence in Large Panels.” Econometric Reviews 34: 1089-117. and Y. Shin (1996). “Co-integration and Speed of Convergence to Equilibrium.” Journal of Econometrics 71: 117-43. (1998). “Generalized Impulse Response Analysis in Linear Multivariate Models.” Economics Letters 58: 17-29. , Y. Shin and R. P. Smith (1999). “Pooled Mean Group Estimation of Dynamic Heterogeneous Panels.” Journal of the American Statistical Association 94: 621-34. Persyn, D., and J. Westerlund (2008). “Error Correction-Based Co-integration Tests for Panel Data.” Stata Journal 8: 232-41. Phillips, P. C. B., and D. Sul (2007). “Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence.” Journal of Econometrics 137: 162– 88. Westerlund, J. (2007). “Testing for Error Correction in Panel Data.” Oxford Bulletin of Economics and Statistics 69: 709-48. , K. Thuraisamy and S. Sharma (2015). “On the Use of Panel Co-integration Tests in Energy Economics.” Energy Economics 50: 359-63. World Bank (2013, unpublished). 2011 International Comparison Program Data for Researchers. Washington, DC: World Bank. SUPPLEMENTARY MATERIALS
A-16 Figure A2.1 Relative Price Dispersion A. ICP B. FAO
SD (× 100) 120 Bottom 10 Middle 10 Top 10 200
60 100
0 0 Tea
Commodities
Oats
Hops
Maize
Mullet
Grapes
Apples
Tilapia
Mango
Linseed
Spinach
Cassava
Triticale
Superior…
Olive oil Olive
Flavored…
Rapeseed
Kola nuts Kola
Cassava -… Cassava
Kiwi fruit Kiwi
Cinnamon…
Meat, goat Meat,
Silk-worm…
Cornflakes…
Long grain… Long
Spices, nes Spices,
Short pasta Short Cottonseed
Beef, Fillet Beef,
Veal breast… Veal
Sour cream Sour
Apple juice Apple
White sugar White
Bean Curd -… Curd Bean
Corned beef Corned
Red snapper Red
Oilseeds nes Oilseeds
Strawberries
Meat, turkey Meat,
Green/Mung…
Cauliflowers…
Grain, mixed Grain, Gooseberries
Cashew nuts,… Cashew
Irish whiskey… Irish paste… Tomato
Dried Shrimp Dried
Cherries, sour Cherries,
Anise, badian,… Anise,
Nutmeg, mace… Nutmeg,
Chilies (Long) Chilies
Honey, natural Honey,
Natural honey,… Natural
Domestic Beer… Domestic
Sweet potatoes Sweet
Whole chicken Whole
Sweet Potatoes Sweet
Bambara beans Bambara
Tea bags, black bags, Tea Plums and sloes and Plums
120 200
60 100
0 0
Countries
Italy
Mali
Haiti
Chile
Japan
Malta
Egypt
Latvia
France
Ireland
Turkey
Cyprus
Austria
Estonia
Canada Estonia Nigeria Tunisia
Sweden Senegal
Bahrain
Burundi
Rwanda Burundi
Ecuador
Djibouti
Ethiopia
Ethiopia
Namibia
Belgium
Denmark
Denmark
Suriname
Lithuania
Indonesia Mongolia
Botswana
Tajikistan
Singapore
Turks and… Turks
Singapore
Nicaragua
Swaziland
Zimbabwe
Costa Rica Costa
Azerbaijan
Bosnia and… Bosnia
Kyrgyzstan
El Salvador El
Cabo Verde Cabo
Madagascar
Egypt, Arab… Egypt,
Iran (Islamic… Iran
Saudi Arabia Saudi
Gambia, The Gambia,
Venezuela, RB Venezuela,
Sudan (former) Sudan
Central African… Central
St. Kitts and Nevis and Kitts St. Brunei Darussalam Brunei
Notes: * * - Panel A: For the ICP data, the price of commodity i in country c, relative to the world price, is k log p log p logS , where p and p denote the domestic price and world price, ic ic i c ic i
Ni 2 Ni respectively, and Sc denotes the exchange rate. The SD for each item i is i1N i c 1k ic k i , where ki 1 N i c 1 k ic is the cross-country mean. The SD for each country
Nc 2 Nc c is c1N c i 1k ic k c , where kc 1 N c i 1 k ic is the cross-item mean. * NTii 2 - Panel B: For the FAO data, the relative price of commodity i in country c in year t is kict log p ict log p it logS ct . The SD for each item i is i 1 N i T i c1t1ict k k i ,
NTii NTcc 2 where ki 1 N i T i c 1 t 1 k ict is the cross-country mean, averaged over time. The SD for each country c is c 1 N c T c i1t1ict k k c , where
NTcc kc 1 N c T c i 1 t 1 k ict is the cross-item mean. SUPPLEMENTARY MATERIALS
A-17 Figure A2.2 Distribution of Relative Prices A. ICP B. FAO Histogram Cumulative Distribution Histogram Cumulative Distribution
5,000 Mean = 0.16 1 25,000 Mean = -0.27 1 Median = 0.14 Median = -0.23 4,000 20,000 0. SD = 0.55 SD = 0.86
3,000 Min = -2.61 0.6 15,000 Min = -7.73 Max = 2.77 Max = 8.31 2,000 10,000 0.
Countries 1,000 0.2 5,000 0 0 0 0 All Commodities and -0.3 0.3 -3 -1 -0.3 0. 1 3 -2.4 -1.6 -0.8 0 0.8 1.6 2.4 -2.0 -1.0 0.0 1.0 2.0 -7.80 -3.80 0.20 4.20 8.20 50 Mean = 0.17 1 600 1 Median = 0.15 Mean = -0.21 40 SD = 0.27 Median = -0.25 0.8 Min = -0.51 0.69 400 SD = 0.58 30 Max = 0.90 Min = -6.71 Max = 6.69 20 200 0.4 10 0.04
Country Means 0 0 0 0 -1.0 -0.5 -0.3 0.0 0.3 0.5 1.0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 -3 -2 -1 0 1 2 3 < -3 -2 -1 0 1 2 > 3 -0.3 0.3 50 1 600 1 Mean = 0.16 Mean = -0.35 Median = 0.13 0.8 40 Median = -0.33 SD = 0.23 SD = 0.53 0.73 400 Min = -0.39 Min = -3.14 30 Max = 0.93 Max = 1.82 0.5
20 200 10 0.02 Commodity Means 0 0 0 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.5 -0.3 0.0 0.3 0.5 1.0 -3.2 -2.4 -1.6 -0.8 0 0.8 1.6 -3 -2 -1 -0.3 0 0.3 1 2
Notes: The country (commodity) means are computed across commodities (countries). * 1. Panel A: The ICP data cover 198 food commodities in 175 countries, 2011. The relative price of commodity i in country c is kic log p ic log p i logS c . * 2. Panel B: The FAO data cover 133 food and agriculture commodities in 158 countries, 1991 – 2013. The relative price of commodity i in country c in year t is kict logp ict logp it logS ct . 3. The ICP and FAO plots in the first row are combined and replicated in Figure 3.1 of the main text.
SUPPLEMENTARY MATERIALS A-18
Figure A5.1. Ratio of Changes in Prices to Exchange Rates, 1-year Horizon
logrict / logS ct Censorship rule: Censorship rule: 15% observations excluded -1≤ ∆ log rict /∆ log Sct ≤ 3
Mean = 0.84 Mean = 0.88 Median = 0.77 Median = 0.84 SD = 4.04 SD = 1.01 Min = -12.02 Min = -1 Max = 13.95 Max = 3 Obs = 69,859 Obs = 37,788
-12.0 -4.2 3.6 11.3 -1.00 0.33 1.67 3.00 Percentage of tail observations excluded Truncation range 0% 5% 15% 25% 35% 45% 50% [-1 , 3] (1) (2) (3) (4) (5) (6) (7) (8) Mean 6.12 0.77 0.84 0.83 0.81 0.79 0.79 0.88 Median 0.77 0.77 0.77 0.77 0.77 0.77 0.77 0.84 SD 2,312.98 10.13 4.04 2.58 1.82 1.33 1.13 1.01 Min -107,929.15 -63.78 -12.02 -5.74 -3.25 -1.93 -1.47 -1.00 Max 414,692.11 57.52 13.95 7.65 5.09 3.66 3.16 3.00 Obs included 82,187 78,077 69,859 61,639 53,421 45,203 41,093 37,788 Obs included 0 4,110 12,328 20,548 28,766 36,984 41,094 44,399
Notes: The figure presents the distribution of logrict / logS ct . The left panel corresponds to the sample with 15% of the observations excluded. The right panel corresponds to the range -1 to 3. Summary statistics of the two filtered samples are given in columns 3 and 8 of the table.
SUPPLEMENTARY MATERIALS A-19 Figure A5.2. Average Price Changes and Exchange Rate Changes for Various Horizons Horizons: (i) 1-year (ii) 5-year (iii) 10-year (iv) 20-year A. Scatterplots
B. Density contours
Notes: * 1. logrict logp ict logp it is the local price of i in country c for year t relative to the world price. (h)logr ict logr ict logr ic,t-h (t h + 1, ,T ic ; h 5, 10, 20) is the h-year change in
Nct relative prices. (h)logS ct logS ct logS c,t-h is the corresponding change in the exchange rates. (h)logr ct 1/ N ct i1(h) logr ict is the average price change over all items. To
facilitate presentation, only values in the range of 1 (h) logr ct 4 and 1 h logSct 4 are shown. 2. Panel A: The solid line is the 45° line and the dashed line indicates the OLS regression line. 3. Panel B: The outer most contours represent 95% of the observations. Light (dark) areas indicate higher (lower) densities.
SUPPLEMENTARY MATERIALS A-20
Figure A7.1 Distributions of p-values, Tests for Co-integration
A. Commodities B. Countries Frequency 1,200 1,200
Mean = 0.12 Mean = 0.11 Median = 0.00 Median = 0.00 SD = 0.2 SD = 0.21 600 600 # Obs = 1,984 # Obs = 2,016
p-values 0 0 0.0 0.2 0.3 0.5 0.0 0.2 0.3 0.5 Notes: This figure presents the density distribution of p-values from all co-integration test results (i.e., from both the first and second sets presented in Tables A7.4 – A7.7). There are 16 tests for the null of no co-integration, viz., Kao’s (1999)
modified Dickey-Fuller ( DFρ ), Dickey-Fuller ( DFt ), augmented Dickey-Fuller ( ADFt ), unadjusted Modified Dickey-Fuller * * DFρ and unadjusted Dickey-Fuller DFt ; Pedroni’s (2004) panel Zν , panel ρ Zρ , panel t (non-parametric) Zt ,
* * panel t (parametric) Zt , group rho Zρ , group t (non-parametric) Zt and group t (parametric) Z;t and Westerlund’s
(2007) panel t Pτ , panel α Pα , group t Gτ and group α Gα . See Table A7.1 and appendix text for details.
SUPPLEMENTARY MATERIALS
A-21 Table A1.1 ICP Basic Headings No. ICP Basic Heading No. ICP Basic Heading 1. Rice 78. Combined passenger transport 2. Other cereals, flour and other products 79. Other purchased transport services 3. Bread 80. Postal services 4. Other bakery products 81. Telephone and telefax equipment 5. Pasta products 82. Telephone and telefax services 6. Beef and veal 83. Audio-visual, photo.and information processing equipment 7. Pork 84. Recording media 8. Lamb, mutton and goat 85. Repair of audio-visual, photo. And info. Processing equipment 9. Poultry 86. Major durables for outdoor and indoor recreation 10. Other meats and meat preparations 87. Maint. & repair of other major durables for recreation & culture 11. Fresh, chilled or frozen fish and seafood 88. Other recreational items and equipment 12. Preserved or processed fish and seafood 89. Garden and pets 13. Fresh milk 90. Veterinary and other services for pets 14. Preserved milk and other milk products 91. Recreational and sporting services 15. Cheese 92. Cultural services 16. Eggs and egg-based products 93. Games of chance 17. Butter and margarine 94. Newspapers, books and stationery 18. Other edible oils and fats 95. Package holidays 19. Fresh or chilled fruit 96. Education 20. Frozen, preserved or processed fruit and fruit-based prod. 97. Catering services 21. Fresh or chilled vegetables other than potatoes 98. Accommodation services 22. Fresh or chilled potatoes 99. Hairdressing salons and personal grooming establishments 23. Frozen, presser. Or processed veg. and veg.-based products 100. Appliances, articles and products for personal care 24. Sugar 101. Prostitution 25. Jams, marmalades and honey 102. Jewellery, clocks and watches 26. Confectionery, chocolate and ice cream 103. Other personal effects 27. Food products nec 104. Social protection 28. Coffee, tea and cocoa 105. Insurance 29. Mineral waters, soft drinks, fruit and vegetable juices 106. Financial Intermediation Services Indirectly Measured (FISIM) 30. Spirits 107. Other financial services 31. Wine 108. Other services nec 32. Beer 109. Final cons. Exp. Of resident households in the rest of the world 33. Tobacco 110. Final cons. Exp.of non-resident households in the eco. Territory 34. Narcotics 111. Individual consumption expenditure by NPISHs 35. Clothing mats, articles of clothing & clothing accessories 112. Housing 36. Garments 113. Pharmaceutical products 37. Cleaning, repair and hire of clothing 114. Other medical products 38. Shoes and other footwear 115. Therapeutic appliances and equipment 39. Repair and hire of footwear 116. Out-patient medical services 40. Actual and imputed rentals for housing 117. Out-patient dental services 41. Maintenance and repair of the dwelling 118. Out-patient paramedical services 42. Water supply 119. Hospital services 43. Miscellaneous services relating to the dwelling 120. Compensation of employees 44. Electricity 121. Intermediate consumption 45. Gas 122. Gross operating surplus 46. Other fuels 123. Net taxes on production 47. Furniture and furnishings 124. Receipts from sales 48. Carpets and other floor coverings 125. Recreation and culture 49. Repair of furniture, furnishings and floor coverings 126. Education benefits and reimbursements 50. Household textiles 127. Compensation of employees 51. Major household appliances whether electric or not 128. Intermediate consumption 52. Small electric household appliances 129. Gross operating surplus 53. Repair of household appliances 130. Net taxes on production 54. Glassware, tableware and household utensils 131. Receipt from sales 55. Major tools and equipment 132. Social protection 56. Small tools and miscellaneous accessories 133. Compensation of employees 57. Non-durable household goods 134. Intermediate consumption 58. Domestic services 135. Gross operating surplus 59. Household services 136. Net taxes on production 60. Pharmaceutical products 137. Receipts from sales 61. Other medical products 138. Fab. Metal products, except machinery & equipment 62. Therapeutic appliances and equipment 139. General purpose machinery 63. Medical Services 140. Special purpose machinery 64. Dental services 141. Electrical and optical equipment 65. Paramedical services 142. Other manufactured goods nec 66. Hospital services 143. Motor vehicles, trailers and semi-trailers 67. Motor cars 144. Other road transport 68. Motor cycles 145. Other transport equipment 69. Bicycles 146. Residential buildings 70. Animal drawn vehicles 147. Non-residential buildings 71. Fuels and lubricants for personal transport equipment 148. Civil engineering works 72. Maintenance and repair of personal transport equipment 149. Other products 73. Other services in respect of personal transport equipment 150. Opening value of inventories 74. Passenger transport by railway 151. Closing value of inventories 75. Passenger transport by road 152. Acquisitions of valuables 76. Passenger transport by air 153. Disposals of valuables 77. Passenger transport by sea and inland waterway 154/155. Exports/Imports of goods and services Source: World Bank (2013, unpublished).
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Table A1.2 ICP Food Products
No. Product No. Product No. Product 1. Long grain rice – Parboiled 67. Squid 133. Ginger (Mature) 2. Long grain rice – Non-Parboiled 68. Red snapper 134. Garlic (White) 3. Long grain rice – Family Pack 69. Sea Crab 135. Brown Potatoes 4. Jasmine Rice 70. Tilapia 136. Sweet Potatoes 5. Basmati Rice 71. Black Pomfret 137. Cassava – Manioc – Yuka 6. White rice, 25% broken 72. Mullet 138. Dried white beans 7. White rice, medium Grain 73. Canned sardine with skin 139. Tinned white beans in tomato sauce 8. Brown rice – Family Pack 74. Canned tuna without skin 140. Green Olives (with stones) 9. Short-grained rice 75. Canned mackerel fillet in veg. oil 141. Potato chips 10. Cornflakes [Specified brand] 76. Smoked salmon 142. Frozen chipped potatoes 11. Wheat flour, not self-rising 77. Dried Shrimp 143. Tomato paste (Small) 12. Wheat semolina (Suji) 78. Milk, un-skimmed Pasteurized 144. Tomato paste (Large) 13. Oats, rolled 79. Milk, un-skimmed UHT 145. Tinned green peas 14. Maize Flour White 80. Milk, low-fat, Pasteurized 146. Tinned sweet corn/Maize 15. Couscous 81. Milk, condensed 147. Lentils, Dry 16. Baguette 82. Milk, powdered 148. Green/Mung Beans, dried 17. White bread 83. Yoghurt, plain 149. Tinned Button Mushrooms 18. Whole wheat bread 84. Sour cream 150. White sugar 19. Roll 85. Cheese, Cheddar 151. Brown sugar 20. Sliced white bread 86. Cream cheese 152. Strawberry/Apricot Jam 21. Pita bread 87. Cheese, processed 153. Pineapple Jam 22. Sandwich biscuits/cookies 88. Cheese, Camembert Type 154. Orange marmalade 23. Chocolate cake (Individual serving) 89. Cheese, Gouda Type 155. Natural honey, Mixed blossoms 24. Chocolate cake (Whole) 90. Bean Curd – Tofu 156. Chocolate bar 25. All-butter croissant 91. Large size chicken eggs 157. Ice cream, Cornetto-type 26. Butter biscuits 92. Medium size chicken eggs 158. Chewing gum 27. Flavored biscuits/cookies sweet 93. Butter, unsalted 159. Fruit drops (Hard candies) 28. Salted crackers 94. Salted Butter 160. Ice cream, packed 29. Short pasta 95. Margarine, regular fat 161. Toffee 30. Spaghetti 96. Sunflower oil 162. Mayonnaise 31. Dried Noodles 97. Olive oil 163. Cooking salt 32. Instant Noodles 98. Palm oil 164. Tomato ketchup 33. Vermicelli (Angel Hair) 99. Soybean oil 165. Black Pepper, ground 34. Macaroni 100. Peanut oil 166. Thin Soya Sauce 35. Beef, fillet 101. Vegetable oil 167. Curry Powder 36. Beef, rump steak 102. Apple, Red Delicious 168. Chicken Ext. (bouillon/stock cube) 37. Beef, center brisket 103. Banana, Standard 169. Baking powder 38. Beef, for stew or curry 104. Grapes, green 170. Baby food 39. Beef with bones 105. Grapefruit 171. Chili sauce 40. 100% Beef, minced 106. Orange 172. Chili powder 41. Veal chops 107. Papaya 173. Baby cereals 42. Veal breast (non-refrigerated), with bones 108. Pineapple 174. Cocoa Powder, Tin 43. Pork, loin chop 109. Lemon 175. Instant coffee [Specified brand] 44. Pork, fillet 110. Mango 176. Coffee Roasted 100% Arabica 45. Pork, shoulder 111. Watermelon 177. Coffee Roasted 100% Robusta 46. Pork, ribs 112. Apple, Typical Local Variety 178. Tea bags, black 47. Lamb whole leg 113. Peach 179. Tea, green 48. Lamb chops 114. Melon 180. Tea, black 49. Mutton mixed cut 115. Tinned pineapple 181. Mineral water 50. Goat mixed cut/with bones (non-refrigerated) 116. Dried almonds 182. Carb. S.Drink [Spec. brand] (Small) 51. Whole chicken – Broiler 117. Roasted groundnuts/peanuts 183. Carb. S.Drink [Spec. brand] (Large) 52. Whole chicken 118. Mixed Fruits in Syrup 184. Apple juice 53. Chicken breast without skin 119. Dried dates 185. Orange juice 54. Chicken legs 120. Cucumber 186. Lemonade 55. Live chicken 121. Bell pepper 187. Vodka 56. Chicken breast with skin and bones 122. Carrots 188. Whisky 57. Pork ham, pressed 123. Onion 189. Gin [Specified Brand] 58. Bacon, smoked 124. Maize 190. Irish whiskey & cream liquer [Spec. brand] 59. Beef liver 125. Round tomato, loose 191. Superior Light/White Rum 60. Corned beef 126. Green cabbage 192. Red wine, table wine 61. Canned chicken 127. Lettuce 193. Red wine, Bordeaux Supérieur 62. Carp 128. Avocado 194. White wine, table wine 63. Mackerel, un-cleaned 129. Eggplant (aubergine) 195. Sparkling wine 64. Sea Bass 130. Cauliflower 196. Domestic Canned Beer 65. Whole Shrimps 131. Spinach 197. Domestic Beer Bottle 66. Shrimps 132. Chilies (Long) 198. Beer [Specified brand] Notes: Listed in this table are the 198 food products, out of the total 987 products. Source: World Bank (2013, unpublished).
SUPPLEMENTARY MATERIALS
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Table A1.3 Income and Food Prices in 155 Countries in 2011
Food (×100) Food (×100) Income Income Country Relative Price Country Relative Price US = 100 US = 100 price SD price SD (1) (2) (3) (4) (5) (6) (7) (8) 1. Bermuda 110.7 8.4 27.6 40. Anguilla 47.3 30.0 29.9 2. United States 100.0 0.0 0.0 41. Bahrain 47.2 20.2 43.9 3. Cayman Islands 95.3 35.0 28.6 42. Czech 43.4 16.9 21.3 4. Hong Kong 88.1 24.1 30.2 43. Bahamas 43.1 27.6 32.7 5. Norway 87.7 23.1 26.1 44. Trini. & Tob. 42.6 51.7 31.8 6. Luxembourg 85.2 -20.9 30.6 45. Poland 40.9 14.4 22.9 7. Switzerland 82.0 -7.6 43.3 46. Slovakia 40.3 20.6 21.8 8. UAE 77.2 10.1 32.7 47. Barbados 39.0 35.5 39.4 9. Sweden 76.3 0.7 23.9 48. Lithuania 38.6 19.7 24.3 10. Germany 75.1 1.1 31.2 49. Oman 37.5 30.0 36.8 11. Australia 74.6 7.2 19.8 50. St. Kitts & Nevis 37.2 60.1 30.8 12. Austria 74.5 7.2 29.6 51. Croatia 36.5 34.9 19.8 13. Denmark 73.6 1.6 26.8 52. Hungary 36.4 30.3 26.5 14. Canada 73.5 18.5 15.1 53. Russia 35.6 38.0 24.5 15. Iceland 72.9 15.6 29.2 54. Chile 35.5 32.8 29.9 16. Finland 72.5 2.2 24.9 55. Estonia 35.5 24.3 20.8 17. France 72.0 1.7 32.9 56. Turkey 34.9 41.5 34.0 18. Belgium 71.2 -1.2 28.6 57. Montserrat 34.5 51.7 42.1 19. United Kingdom 70.3 -7.1 19.4 58. Uruguay 34.3 33.3 29.5 20. Netherlands 70.3 -11.8 26.7 59. Seychelles 33.7 39.6 52.7 21. Singapore 70.0 30.3 36.6 60. Latvia 33.6 29.6 25.8 22. Taiwan 68.1 42.8 31.5 61. Antigua & Barb. 32.3 58.2 35.1 23. Aruba 66.9 41.2 26.5 62. Montenegro 29.7 29.5 27.2 24. Macao 65.4 28.9 33.2 63. Kazakhstan 29.7 36.6 28.1 25. Japan 65.4 29.4 34.2 64. Mexico 29.4 12.9 20.6 26. Ireland 63.1 7.8 19.4 65. Mauritius 28.2 31.6 39.1 27. Italy 62.0 7.9 25.5 66. Malaysia 27.7 31.5 34.2 28. Cyprus 60.7 20.3 22.7 67. Virgin Islands 27.5 17.2 31.6 29. New Zealand 60.5 18.3 20.0 68. Panama 27.1 36.8 37.4 30. Spain 57.5 -0.7 20.1 69. Belarus 26.8 41.4 40.0 31. Israel 55.6 22.1 31.4 70. Romania 26.5 25.6 28.1 32. Sint Maarten 55.4 35.7 26.1 71. Bulgaria 25.9 33.3 30.1 33. Greece 55.1 13.3 29.7 72. Serbia 25.6 35.6 32.1 34. Curaçao 53.9 28.2 23.1 73. Brazil 24.9 4.7 30.3 35. Malta 51.4 26.6 17.3 74. Costa Rica 24.4 35.6 34.5 36. Portugal 49.1 1.1 25.4 75. Grenada 24.2 42.3 43.0 37. Slovenia 48.8 12.5 23.8 76. Jordan 24.0 58.2 41.1 38. South Korea 48.8 57.6 33.0 77. Dominican Rep. 22.9 29.3 30.9 39. Qatar 48.6 -11.8 40.4 78. Dominica 22.8 47.9 45.8 Mean 62.8 13.7 27.5 Mean 29.8 33.1 32.1 Mean Income ($ p.c.) 25,974 Mean Income ($ p.c.) 12,341 (continued on next page)
SUPPLEMENTARY MATERIALS
A-24
Table A1.3 Income and Food Prices in 155 countries in 2011 (continued)
Food (×100) Food (×100) Income Income Country Relative Price Country Relative Price US = 100 US = 100 price SD price SD (1) (2) (3) (4) (5) (6) (7) (8) 79. St. Vin. & Gren. 21.7 52.3 36.1 118. Bolivia 8.9 35.0 33.6 80. Macedonia 21.7 26.3 29.6 119. Honduras 8.6 27.7 34.2 81. Thailand 21.4 32.6 39.5 120. Kyrgyzstan 7.8 56.7 38.8 82. South Africa 20.9 28.9 30.7 121. Vietnam 7.7 34.6 48.3 83. Colombia 20.6 28.8 37.9 122. India 7.2 29.8 45.5 84. St. Lucia 20.3 45.0 33.4 123. São Tomé & P. 6.8 25.1 51.9 85. Bosnia & Herz. 20.3 35.4 23.3 124. Cambodia 5.7 31.8 52.5 86. Turks & Caicos 20.1 17.1 30.2 125. Ghana 5.7 64.6 38.3 87. Venezuela 19.3 44.2 35.7 126. Lesotho 5.6 44.5 28.8 88. Ukraine 18.8 42.2 28.7 127. Tajikistan 5.6 27.7 48.6 89. Tunisia 18.6 44.5 49.3 128. Nigeria 5.2 55.8 35.9 90. Peru 18.3 30.3 37.7 129. Kenya 5.0 60.8 42.1 91. Azerbaijan 18.3 25.7 39.4 130. Djibouti 4.7 30.0 44.9 92. Belize 18.2 71.5 42.7 131. Cameroon 4.6 13.3 62.8 93. El Salvador 17.7 38.4 28.5 132. Côte d’Ivoire 4.6 24.5 48.6 94. Ecuador 17.3 31.3 32.3 133. Senegal 4.3 29.6 56.9 95. Jamaica 16.7 44.5 26.3 134. Nepal 4.3 28.3 47.7 96. Sri Lanka 16.7 38.9 55.0 135. Zambia 3.9 27.1 46.5 97. Albania 16.7 21.8 29.0 136. Uganda 3.8 41.5 54.5 98. Namibia 15.9 57.7 33.2 137. Congo, Rep. 3.5 54.3 42.8 99. Botswana 15.7 46.0 29.2 138. Haiti 3.5 27.7 39.9 100. Armenia 14.8 35.6 37.2 139. Gambia 3.3 53.5 54.2 101. Mongolia 14.7 53.6 60.2 140. Sierra Leone 3.3 54.4 48.7 102. Iraq 14.5 52.8 39.7 141. Chad 3.1 30.7 56.3 103. Georgia 14.5 56.4 46.8 142. Benin 2.9 37.9 56.7 104. Gabon 14.2 35.5 50.4 143. Rwanda 2.9 39.0 76.8 105. Guatemala 14.1 33.7 32.6 144. Zimbabwe 2.7 30.9 42.7 106. Swaziland 13.4 40.0 46.9 145. Madagascar 2.7 11.6 53.0 107. Fiji 13.3 17.3 42.8 146. Guinea-B. 2.2 12.4 53.2 108. Paraguay 12.9 22.9 23.7 147. Mali 2.2 18.8 52.0 109. Moldova 12.6 34.0 34.4 148. Mozambique 1.8 38.4 51.3 110. Eq. Guinea 12.6 44.4 49.6 149. Liberia 1.8 50.6 53.7 111. Suriname 12.3 34.4 37.4 150. Burkina Faso 1.8 32.1 56.2 112. Indonesia 12.3 29.3 47.6 151. Comoros 1.8 27.1 58.1 113. Philippines 11.7 23.8 40.4 152. C. Africa 1.6 28.1 57.0 114. Cape Verde 11.6 38.1 34.2 153. Guinea 1.5 54.4 67.4 115. China 11.2 31.0 46.2 154. Niger 1.5 47.3 46.1 116. Morocco 10.9 52.1 42.0 155. Congo, D.R. 0.9 43.2 44.0 117. Bhutan 10.0 38.8 51.2 Mean 14.5 37.9 38.2 Mean 3.7 36.3 49.2 Mean Income ($ p.c.) 6,010 Mean Income ($ p.c.) 1,525 Notes: Countries are ranked in terms of per capita income and are divided into 4 quartiles. The US is the reference country. 1. Columns (2) and (6): Income is defined as an index of real total consumption per capita with US = 100. More precisely, income is explog M log P , where M is the total consumption expenditure defined as the sum of expenditure by households, non-profits serving households and individual government on 131 food and non-food items, and logP Σ131 w logp is the cost-of-living index, with w the budget share of good i (the proportion of total i 1 i i i p consumption expenditure devoted to i) and i its PPP price. 2. Columns (3) and (7): Food is defined as the sum of 31 food items, including alcoholic beverages. The relative price of
food is log PFF P logP logP, the difference between the conditional budget-share weighted logarithmic mean of 31 the prices of the food items, logPF Σ i 1 w i logp i , and the cost-of-living index. wi w i W F is the share of i within 31 food (known as the “conditional budget-share”) and WwF i 1 i is the budget share of food as a group.
31 2 3. Columns (4) and (8): The within-food price standard deviation (SD) is i 1w i log p i log P F .
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Table A1.4 Data Adjustments Data Types Attributes Adjustments Made (§. denotes section # Countries # Items Years Covered number in the main text) (1) (2) (3) (4) (5) ICP 1. Basic heading prices and 155 31 2011 Omit dual participants (Russia, expenditures Sudan and Egypt) and countries with incomplete data (Cuba, Boraine, Iran and Georgia). Omit non-food basic headings. 2. Retail product prices (§.3, 175 198 2011 Omit dual participants (Russia, §.4) Sudan and Egypt) and countries with incomplete data (Cuba, Boraine, Iran and Georgia). Omit products that are represented in less than 30 countries. FAO 3. Producer prices 162 208 1991 – 2014 4. Export prices and volumes 181 387 1986 – 2013 5. Matched data 158 133 1991 – 2013 6. Data to study deviations 158 133 1991 – 2013 Omit items and countries with no (§.3) annual observations. 7. Data to test for cross- 158 124 1991 – 2013 Omit items that are represented in country unit roots (§.5) less than 30 country-years and in countries with gaps. 8. Data to test for cross-item 126 133 1991 – 2013 Omit countries that are unit roots (§.5) represented in less than 30 commodity-years and with items with gaps. Notes: All data are at annual frequency. All panels are two-way unbalanced (i.e., the number of producers for each produce is not the same in each year). The number of sections where the corresponding data are used are given in column (1). Sources: ICP data are provided by World Bank (2013, unpublished). FAO data are retrieved from http://www.fao.org/faostat/en/#data.
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Table A4.1 Slope Coefficients, Cross-Country Regressions, 198 Food Items
log pic i i log S c ic , c 1, ,C i consuming countries; i 1,...,198
Item Slope t-stat Obs Item Slope t-stat Obs (1) (2) (3) (4) (5) (6) (7) (8) 1. Long grain rice – Parboiled 0.90 5.80 121 63. Mackerel, un-cleaned 0.91 4.22 92 2. Long grain rice – Non-Parboiled 0.93 5.65 95 64. Sea Bass 0.83 6.67 64 3. Long grain rice – Family Pack 1.01 0.37 59 65. Whole Shrimps 0.92 3.88 69 4. Jasmine Rice 1.02 1.24 60 66. Shrimps 0.94 4.82 131 5. Basmati Rice 0.96 2.40 119 67. Squid 0.90 5.22 84 6. White rice, 25% broken 0.94 3.12 59 68. Red snapper 0.91 3.62 39 7. White rice, Medium Grain 0.93 4.22 66 69. Sea Crab 0.96 1.73 46 8. Brown rice – Family Pack 0.97 1.44 48 70. Tilapia 0.93 3.90 73 9. Short-grained rice 0.92 5.15 66 71. Black Pomfret 0.90 4.32 30 10. Cornflakes [Specified brand] 1.02 2.49 161 72. Mullet 0.88 4.78 33 11. Wheat flour, not self-rising 1.00 0.02 166 73. Canned sardine with skin 0.94 4.90 161 12. Wheat Semolina (Suji) 1.05 1.66 60 74. Canned tuna without skin 0.99 1.23 161 13. Oats, rolled 1.00 0.31 141 75. Canned mackerel fillet in vegetable oil 0.99 0.61 111 14. Maize Flour White 0.98 1.19 75 76. Smoked salmon 0.93 2.71 75 15. Couscous 1.00 0.07 46 77. Dried Shrimp 0.95 1.15 51 16. Baguette 0.90 5.82 124 78. Milk, un-skimmed Pasteurized 1.01 0.66 151 17. White bread 0.94 3.13 118 79. Milk, un-skimmed UHT 1.02 2.44 158 18. Whole wheat bread 0.95 3.05 138 80. Milk, low-fat, Pasteurized 1.01 0.60 147 19. Roll 0.91 3.67 88 81. Milk, condensed 0.95 3.28 75 20. Sliced White bread 0.95 3.67 158 82. Milk, powdered 1.00 0.41 114 21. Pita bread 0.95 1.53 52 83. Yoghurt, plain 0.98 1.59 157 22. Sandwich biscuits/cookies 0.98 1.45 155 84. Sour cream 1.04 1.33 108 23. Chocolate cake (Individual serving) 0.96 2.15 68 85. Cheese, Cheddar 1.01 0.97 110 24. Chocolate cake (Whole) 0.93 4.22 96 86. Cream cheese 1.02 1.44 149 25. All-butter croissant 0.96 2.88 141 87. Cheese, processed 1.00 0.04 161 26. Butter biscuits 0.96 2.85 150 88. Cheese, Camembert Type 1.02 1.28 96 27. Flavored biscuits/cookies sweet 0.98 1.34 160 89. Cheese, Gouda Type 1.01 0.84 124 28. Salted crackers 0.96 2.57 140 90. Bean Curd – Tofu 0.95 0.72 32 29. Short pasta 1.02 1.54 138 91. Large size chicken eggs 0.98 1.88 153 30. Spaghetti 0.97 3.07 171 92. Medium size chicken eggs 0.97 2.33 108 31. Dried Noodles 0.96 2.25 102 93. Butter, unsalted 0.98 2.60 164 32. Instant Noodles 0.95 2.96 141 94. Salted Butter 0.98 2.53 160 33. Vermicelli (Angel Hair) 1.03 1.70 128 95. Margarine, regular fat 0.99 0.88 168 34. Macaroni 0.97 2.22 118 96. Sunflower oil 1.01 1.20 151 35. Beef, Fillet 0.87 6.70 155 97. Olive oil 1.00 0.27 167 36. Beef, Rump steak 0.94 3.73 156 98. Palm oil 0.99 0.33 58 37. Beef, Center brisket 0.92 6.72 134 99. Soybean oil 1.00 0.24 94 (continued on next page)
SUPPLEMENTARY MATERIALS
A-27 Table A4.1 Slope Coefficients, Cross-Country Regressions, 198 Food Items (continued)
log pic i i log S c ic , c 1, ,C i consuming countries; i 1,...,198
Item Slope t-stat Obs Item Slope t-stat Obs (1) (2) (3) (4) (5) (6) (7) (8) 38. Beef, for stew or curry 0.95 3.70 73 100. Peanut oil 0.99 0.38 45 39. Beef with bones 0.93 5.02 116 101. Vegetable oil 0.95 4.31 148 40. 100% Beef, minced 0.96 4.24 161 102. Apple, Red Delicious 0.96 2.84 112 41. Veal chops 0.97 1.36 61 103. Banana, Standard 0.90 7.38 173 42. Veal breast (non-refrig.), w/ bones 0.91 5.28 74 104. Grapes, green 1.03 1.77 126 43. Pork, loin chop 0.94 5.26 138 105. Grapefruit 0.92 4.64 100 44. Pork, fillet 0.95 3.56 134 106. Orange 0.93 4.65 169 45. Pork, shoulder 0.96 2.21 60 107. Papaya 0.85 8.44 96 46. Pork, ribs 0.96 3.17 150 108. Pineapple 0.89 6.53 159 47. Lamb whole leg 0.90 6.35 132 109. Lemon 0.91 5.77 160 48. Lamb chops 0.91 5.44 129 110. Mango 0.85 6.39 93 49. Mutton mixed cut 0.95 2.86 64 111. Watermelon 0.91 4.99 162 50. Goat mixed cut non-refri. w/ bones 0.92 4.27 59 112. Apple, Typical Local Variety 1.01 0.32 108 51. Whole chicken – Broiler 1.00 0.47 144 113. Peach 0.99 0.60 104 52. Whole chicken 1.00 0.43 149 114. Melon 0.91 3.90 99 53. Chicken breast without skin 0.96 2.87 150 115. Tinned pineapple 1.05 3.82 120 54. Chicken legs 0.98 2.11 159 116. Dried almonds 1.01 0.57 58 55. Live chicken 1.00 0.28 65 117. Roasted groundnuts/peanuts 0.92 4.74 118 56. Chicken breast with skin and bones 1.00 0.04 96 118. Mixed Fruits in Syrup 0.99 0.51 106 57. Pork ham, pressed 0.95 3.09 109 119. Dried dates 0.98 1.43 98 58. Bacon, smoked 0.98 1.73 115 120. Cucumber 0.90 6.35 172 59. Beef liver 0.97 2.04 113 121. Bell pepper 0.93 3.48 160 60. Corned beef 1.00 0.16 63 122. Carrots 0.96 2.40 172 61. Canned chicken 1.02 0.70 47 123. Onion 0.97 2.18 170 62. Carp 0.89 7.09 90 124. Maize 0.82 7.65 92 125. Round tomato, loose 0.88 7.21 169 162. Mayonnaise 0.97 2.40 124 126. Green cabbage 0.93 3.51 119 163. Cooking salt 1.00 0.09 162 127. Lettuce 0.91 5.86 158 164. Tomato ketchup 1.02 1.67 166 128. Avocado 0.84 7.78 93 165. Black Pepper, ground 0.92 4.55 144 129. Eggplant (aubergine) 0.87 6.72 163 166. Thin Soya Sauce 0.93 3.51 148 130. Cauliflower 0.96 1.89 155 167. Curry Powder 1.00 0.13 71 131. Spinach 0.86 5.80 131 168. Chicken Extract (bouillon/stock cube) 0.92 4.46 117 132. Chilies (Long) 0.90 3.68 115 169. Baking powder 0.96 2.70 102 133. Ginger (Mature) 0.97 1.40 80 170. Baby food 0.98 1.19 117 134. Garlic (White) 0.98 1.22 134 171. Chili sauce 1.02 0.80 75 135. Brown Potatoes 0.95 2.98 164 172. Chili powder 1.00 0.01 81 136. Sweet Potatoes 0.81 9.47 110 173. Baby cereals 0.99 0.76 152 137. Cassava – Manioc – Yuka 0.82 5.86 49 174. Cocoa Powder, Tin 1.01 1.04 144 138. Dried white beans 0.96 2.63 100 175. Instant coffee [Specified brand] 0.96 4.00 170 139. Tinned white beans tomato sauce 1.01 0.43 112 176. Coffee Roasted 100% Arabica 0.96 2.46 134 140. Green Olives (with stones) 1.00 0.07 136 177. Coffee Roasted 100% Robusta 0.99 1.06 100 141. Potato chips 0.95 3.68 162 178. Tea bags, black 0.98 1.87 160 142. Frozen chipped potatoes 1.03 2.53 120 179. Tea, green 0.93 3.34 77 143. Tomato paste (Small) 0.95 3.86 155 180. Tea, black 0.93 2.20 70 144. Tomato paste (Large) 1.03 2.43 59 181. Mineral water 0.97 1.98 168 145. Tinned green peas 1.02 1.96 129 182. Carbonated Soft Drink (Small) 0.98 1.69 166 146. Tinned sweet corn/Maize 1.06 5.28 139 183. Carbonated Soft Drink (Large) 1.01 0.57 168 147. Lentils, Dry 1.01 0.67 132 184. Apple juice 1.02 2.58 130 148. Green/Mung Beans, dried 0.96 3.00 30 185. Orange juice 1.02 2.22 128 149. Tinned Button Mushrooms 1.05 2.90 73 186. Lemonade 1.06 3.03 66 150. White sugar 0.99 1.17 161 187. Vodka 0.95 3.19 154 151. Brown sugar 0.97 1.48 89 188. Whisky 0.97 2.79 155 152. Strawberry/Apricot Jam 0.97 2.80 170 189. Gin [Specified Brand] 0.98 1.98 97 153. Pineapple Jam 0.99 0.71 106 190. Irish whiskey & cream liq. [Specified] 1.01 0.60 55 154. Orange marmalade 1.00 0.33 116 191. Superior Light/White Rum 0.96 2.79 125 155. Natural honey, Mixed blossoms 0.98 1.83 156 192. Red wine, table wine 1.04 2.12 154 156. Chocolate bar 0.97 2.44 117 193. Red wine, Bordeaux Supérieur 1.03 1.00 48 157. Ice cream, Cornetto-type 0.97 1.75 141 194. White wine, table wine 1.03 1.29 127 158. Chewing gum 0.95 3.59 154 195. Sparkling wine 0.98 1.39 131 159. Fruit drops (Hard candies) 0.94 4.03 135 196. Domestic Canned Beer 0.97 2.48 130 160. Ice cream, packed 0.98 1.41 145 197. Domestic Beer Bottle 0.94 5.16 151 161. Toffee 0.97 1.74 106 198. Beer [Specified brand] 0.98 2.58 152 Summary Statistics Mean 0.96 2.78 117 Median 0.97 2.45 123 SD 0.05 1.98 39 Min 0.81 0.01 30 Max 1.06 9.47 173
Notes: Food items are arranged in the order in which they appear in the ICP data. “Slope” refers to the estimated coefficient
i and the t-statistic is for H0i : 1 . “Obs” is the number of observations in each regression, that is, the number of C . countries i
SUPPLEMENTARY MATERIALS
A-28 Table A4.2 Slope Coefficients, Cross-Commodity Regressions, 175 Countries logpic c c logp i ic , i 1,...,N c food items consumed in c; c 1, ,175
Country Slope t-stat Obs Country Slope t-stat Obs (1) (2) (3) (4) (5) (6) (7) (8) 1. Bermuda 0.70 4.76 118 88. Thailand 0.98 0.50 127 2. Cayman Islands 0.76 4.17 127 89. Azerbaijan 1.01 0.27 154 3. United States 0.92 2.10 109 90. Belize 0.87 2.22 115 4. Hong Kong SAR, China 1.00 0.10 134 91. St. Lucia 0.83 3.17 122 5. Norway 0.95 1.04 115 92. Albania 1.01 0.20 115 6. Luxembourg 0.91 1.85 127 93. Colombia 0.78 3.93 78 7. Switzerland 1.01 0.16 127 94. Bosnia and Herzegovina 0.99 0.36 124 8. Taiwan, China 0.98 0.61 130 95. Algeria 1.16 2.96 130 9. Singapore 1.04 0.75 139 96. El Salvador 0.86 2.41 111 10. United Arab Emirates 0.99 0.32 196 97. South Africa 0.87 2.90 130 11. Aruba 0.78 4.47 130 98. Tunisia 1.15 2.61 130 12. Germany 0.99 0.22 128 99. Sri Lanka 1.02 0.35 114 13. Sweden 0.97 0.69 124 100. Peru 0.91 1.92 110 14. Iceland 1.00 0.06 116 101. Mongolia 0.81 3.32 122 15. Austria 0.94 1.24 122 102. Turks and Caicos Islands 0.74 4.66 104 16. Australia 0.90 2.25 117 103. Jamaica 0.79 4.72 132 17. Denmark 0.89 2.36 126 104. Ecuador 1.02 0.34 69 18. Macao SAR, China 0.96 0.94 136 105. Equatorial Guinea 0.74 2.64 63 19. Canada 0.91 2.32 110 106. Namibia 0.83 3.77 181 20. Finland 0.98 0.39 110 107. Moldova 0.93 1.62 158 21. France 0.92 1.75 129 108. Botswana 0.82 4.73 149 22. Belgium 0.97 0.65 128 109. Iraq 1.09 2.17 157 23. United Kingdom 0.99 0.30 130 110. Gabon 0.89 2.27 167 24. Netherlands 1.02 0.40 120 111. Guatemala 0.89 2.66 127 25. Curaçao 0.74 5.35 128 112. Swaziland 0.87 3.40 146 26. Japan 0.81 3.10 97 113. Paraguay 0.83 3.45 121 27. Ireland 0.93 1.54 130 114. Kyrgyzstan 0.96 0.86 137 28. Sint Maarten 0.73 5.17 119 115. Fiji 0.99 0.33 102 29. Cyprus 0.94 1.92 127 116. Maldives 0.75 3.44 86 30. Italy 0.95 1.32 132 117. Philippines 0.94 1.51 146 31. New Zealand 0.94 1.22 102 118. Indonesia 1.03 0.74 139 32. Kuwait 0.95 1.09 175 119. Palestinian Territory 1.10 2.28 178 33. Spain 0.91 2.45 130 120. Suriname 0.77 4.72 133 34. Malta 0.96 1.09 133 121. Morocco 1.11 2.47 176 35. Greece 0.98 0.54 133 122. Cape Verde 0.80 5.03 165 36. Israel 1.02 0.65 121 123. Nicaragua 0.82 3.21 110 37. Anguilla 0.68 7.12 130 124. China 1.04 0.99 146 38. Korea, Rep. 1.02 0.35 108 125. Tajikistan 1.05 1.21 125 39. Bahrain 0.99 0.30 187 126. Vietnam 1.05 1.16 128 40. Qatar 0.96 0.90 168 127. Angola 0.82 2.92 61 41. St. Kitts and Nevis 0.68 6.41 120 128. Bhutan 1.02 0.34 103 42. Portugal 0.93 1.82 126 129. Bolivia 0.90 2.19 112 43. Slovenia 0.94 1.61 129 130. Pakistan 1.04 0.78 113 44. Saudi Arabia 0.96 0.94 180 131. Honduras 0.86 2.60 105 45. Trinidad and Tobago 0.89 2.18 130 132. Myanmar 1.01 0.16 115 46. Belarus 1.07 1.30 133 133. Yemen 0.94 0.96 132 47. Bahamas, The 0.67 6.16 109 134. São Tomé and Principe 0.91 2.01 147 48. Brunei Darussalam 0.92 1.44 131 135. India 0.99 0.24 160 49. Czech Republic 1.10 2.75 131 136. Lao PDR 0.93 1.11 104 50. Lithuania 1.01 0.17 125 137. Cambodia 0.98 0.55 133 51. Seychelles 0.90 2.02 169 138. Ghana 0.79 5.33 184 52. Poland 1.10 2.79 129 139. Bangladesh 1.15 3.02 124 53. Russian Federation 1.07 1.52 110 140. Lesotho 0.87 3.30 164 54. Slovakia 1.03 0.88 124 141. Nigeria 0.73 6.95 183 55. Montserrat 0.54 7.17 108 142. Sudan 0.81 3.33 125 56. Antigua and Barbuda 0.68 4.96 86 143. Kenya 1.02 0.41 143 57. Turkey 1.15 3.53 123 144. Nepal 1.14 2.89 97 58. Hungary 1.00 0.05 126 145. Djibouti 0.97 0.53 153 59. Barbados 0.76 4.03 130 146. Côte d’Ivoire 0.92 1.63 175 60. Chile 0.96 0.95 120 147. Senegal 0.88 2.76 161 61. Oman 1.03 0.61 147 148. Cameroon 0.89 2.39 176 62. Croatia 0.94 1.56 130 149. Mauritania 0.85 2.69 122 63. Estonia 1.01 0.36 124 150. Uganda 1.03 0.63 168 64. Latvia 1.00 0.03 125 151. Haiti 0.80 1.80 47 65. Uruguay 0.82 3.97 86 152. Zambia 0.87 2.71 147 66. Montenegro 1.01 0.24 117 153. Congo, Rep. 0.87 3.40 176 67. Kazakhstan 1.02 0.58 155 154. Sierra Leone 0.87 2.72 166 68. Mexico 1.04 1.07 122 155. Gambia, The 0.88 2.63 169 69. Mauritius 0.98 0.31 146 156. Chad 0.92 1.50 102 70. Bulgaria 0.97 0.74 131 157. Togo 0.93 1.45 168 71. Malaysia 0.96 0.94 151 158. Rwanda 1.00 0.08 150 72. Grenada 0.75 5.12 125 159. Benin 0.88 2.24 134 (continued on next page)
SUPPLEMENTARY MATERIALS
A-29 Table A4.2 Slope Coefficients, Cross-Commodity Regressions, 175 Countries (continued) logpic c c logp i ic , i 1,...,N c food items consumed in c; c 1, ,175
Country Slope t-stat Obs Country Slope t-stat Obs (1) (2) (3) (4) (5) (6) (7) (8) 73. Romania 0.99 0.36 127 160. Madagascar 0.83 3.40 170 74. Panama 0.81 3.89 118 161. Zimbabwe 0.85 4.10 172 75. Serbia 1.03 0.80 131 162. Malawi 0.84 3.14 154 76. Egypt, Arab Rep. 1.12 2.18 153 163. Ethiopia 1.08 1.59 134 77. Venezuela, RB 0.82 2.62 108 164. Guinea-Bissau 0.82 4.45 178 78. Jordan 1.16 3.56 189 165. Mali 0.85 3.17 175 79. Ukraine 1.04 1.17 149 166. Liberia 0.77 4.73 176 80. Brazil 0.84 3.76 123 167. Guinea 0.99 0.11 122 81. Virgin Islands, British 0.62 6.60 103 168. Tanzania 0.88 2.60 158 82. Dominican Republic 0.86 2.67 104 169. Mozambique 0.88 2.97 176 83. Armenia 1.01 0.21 155 170. Burkina Faso 0.95 0.82 124 84. Macedonia, FYR 0.98 0.47 112 171. Central African Republic 0.83 2.92 137 85. Costa Rica 0.91 1.93 116 172. Comoros 0.84 2.77 124 86. Dominica 0.80 3.31 114 173. Burundi 1.06 0.99 146 87. St. Vincent and the Grenadines 0.71 5.32 109 174. Niger 0.92 1.48 134 175. Congo, Dem. Rep. 0.89 2.40 168 Summary Statistics Mean 0.92 2.15 132 Median 0.93 1.92 129 SD 0.11 1.66 26 Min 0.54 0.03 47 Max 1.16 7.17 196
Notes: Countries are arranged by decreasing GDP per capita. “Slope” refers to the estimated coefficient c and the t- statistic is for H0c : 1. “Obs” is the number of observations in each regression, that is, the number of items Nc .
Table A5.1 Contingency Table for Price Changes and Exchange Rate Changes
Percentage of observations Horizons ER depreciation ER appreciation Total (1) (2) (3) Price increase 63 43 56 Price decrease 37 57 44 A. 1-year Total (Obs) 100 (58,196) 100 (33,084) 100 (91,280) 2 statistic (p-value) 3,476 (0.00) Price increase 72 40 61 Price decrease 28 60 39 B. 5-year Total (Obs) 100 (44,956) 100 (24,123) 100 (69,079) statistic (p-value) 7,063 (0.00) Price increase 77 37 63 Price decrease 23 63 37 C. 10-year Total (Obs) 100 (28,170) 100 (16,076) 100 (44,246) statistic (p-value) 7,053 (0.00) Price increase 85 34 73 Price decrease 15 66 27 D. 20-year Total (Obs) 100 (4,974) 100 (1,581) 100 (6,555) statistic (p-value) 1,595 (0.00) Notes: 1. The first three rows in columns (1) – (3) of each panel present the percentages of the total numbers of observations (which are in parentheses in every 3rd row) with price/exchange-rate configurations indicated by the corresponding rows and columns. See text of Appendix 5 for details. 2 2. The statistics testing the null of independence between logSct and logrict are provided in the last row of each horizon-specific panels, together with their p-values in parentheses.
SUPPLEMENTARY MATERIALS
A-30 Table A6.1 Cross-Country Tests for Panel Unit Root of LOP Deviations, 124 Food and Agriculture Items, 1991-2013
Hc kict c c t cic,t1 k h1c,h k ic,th ict , c 1,...,C i ;t 1,...,T i
p- p- Item Obs Producers Z*-stat α μ σ Item Obs Producers Z*-stat value β HL HL value (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) 1. Anise, badian, fennel, coriander 46 2 -1.94 0.03 0.14 -0.72 0.55 0.15 46. Grapefruit (inc. pomelos) 526 25 -2.09 0.02 -0.5 -0.61 1.29 2.36 2. Apples 1,307 61 -5.68 0.00 -0.46 -0.76 0.74 0.59 47. Grapes 1,141 54 -1.49 0.07 -0.56 -0.63 1.03 1.04 3. Apricots 751 36 -7.91 0.00 -0.77 -1.06 0.73 0.66 48. Honey, natural 1,102 54 -2.67 0.00 0.5 -0.75 0.67 0.35 4. Artichokes 277 13 -1.37 0.09 -0.26 -0.62 0.99 0.88 49. Hops 273 13 -2.27 0.01 -0.24 -0.64 1.21 1.96 5. Asparagus 406 19 -2.64 0.00 -0.33 -0.64 1.57 0.99 50. Jute 126 6 -0.39 0.35 -0.39 -0.64 0.89 0.72 6. Avocados 489 23 -3.89 0.00 -0.52 -0.71 1.12 1.02 51. Kiwi fruit 157 8 -1.18 0.12 -0.07 -0.74 0.73 0.31 7. Bananas 962 46 -4.35 0.00 -0.13 -0.7 1.19 1.06 52. Leeks, other alliaceous vegetables 241 13 -3.81 0.00 -0.07 -0.86 0.79 0.82 8. Barley 1,484 69 -3.35 0.00 0.03 -0.9 0.69 0.63 53. Lemons and limes 826 40 -4.48 0.00 -0.36 -0.74 0.96 0.78 9. Beans, dry 1,241 60 -5.28 0.00 0.13 -0.76 0.95 0.87 54. Lentils 546 27 -3.7 0.00 -0.03 -0.75 0.95 0.57 10. Beans, green 960 46 -3.44 0.00 -0.4 -0.65 0.97 1.84 55. Lettuce and chicory 955 45 -4.21 0.00 -0.35 -0.71 0.93 0.95 11. Beeswax 127 6 0.94 0.83 -0.28 -0.39 0.37 1.86 56. Linseed 320 16 -2.02 0.02 0.05 -0.94 0.58 0.32 12. Blueberries 81 4 -0.98 0.16 -0.83 -0.66 0.98 0.54 57. Maize 2,044 96 -7.6 0.00 0.21 -0.84 0.86 0.78 13. Broad beans, horse beans, dry 359 17 -4.77 0.00 0.38 -0.87 0.87 0.89 58. Maize, green 220 10 -2.51 0.01 -0.5 -0.55 1.22 1.05 14. Buckwheat 219 11 -4.45 0.00 -0.04 -0.96 0.72 0.51 59. Mangoes, mangosteens, guavas 507 25 -2.63 0.00 -0.55 -0.65 1.31 0.93 15. Cabbages and other brassicas 1,715 81 -5.56 0.00 -0.68 -0.75 1.11 1.36 60. Meat, cattle 1,339 63 -3.97 0.00 -0.23 -0.6 1.23 0.97 16. Canary seed 98 5 -2.8 0.00 -0.19 -0.82 0.53 0.28 61. Meat, chicken 1,318 62 -4.11 0.00 0.27 -0.63 1.32 1.73 17. Carrots and turnips 1,643 78 -4.87 0.00 -0.33 -0.71 0.99 0.8 62. Meat, duck 260 12 -3.02 0.00 -0.14 -0.63 1.36 1.18 18. Cashew nuts, with shell 207 10 -2.85 0.00 -0.91 -0.69 1.28 0.94 63. Meat, game 66 3 -3.35 0.00 -0.48 -0.78 0.99 0.05 19. Cauliflowers and broccoli 991 46 -5.03 0.00 -0.45 -0.76 1.03 0.95 64. Meat, goat 815 37 -0.86 0.19 0.01 -0.56 1.16 0.81 20. Cherries 864 41 -3.49 0.00 -0.78 -0.74 0.96 1.04 65. Meat, goose and guinea fowl 125 6 -3.05 0.00 0.21 -0.87 1.1 1 21. Cherries, sour 399 19 -4.51 0.00 -0.57 -0.77 0.7 0.45 66. Meat, horse 283 13 -0.19 0.43 -0.04 -0.47 2.1 2.12 22. Chestnut 177 8 -0.74 0.23 -0.48 -0.57 0.93 0.56 67. Meat, pig 1,329 61 -5.04 0.00 -0.17 -0.67 1.01 0.76 23. Chick peas 458 22 -2.85 0.00 0.04 -0.96 0.62 0.61 68. Meat, rabbit 273 13 -3.33 0.00 -0.19 -0.73 1.43 1.78 24. Chillies and peppers, dry 138 7 -0.23 0.41 -0.07 -0.55 5.27 9.81 69. Meat, sheep 1,212 56 -4.11 0.00 0.02 -0.64 1.3 1.13 25. Chillies and peppers, green 1,035 49 -3.75 0.00 -0.66 -0.68 1.29 2.27 70. Meat, turkey 322 16 -1.36 0.09 0.13 -0.66 1.04 0.6 26. Cloves 40 2 0.16 0.56 0.33 -0.41 1.3 0.04 71. Melons, other (inc.cantaloupes) 720 34 -4.3 0.00 -0.3 -0.67 1.16 0.92 27. Cocoa, beans 414 19 -4.65 0.00 -0.15 -0.74 1.21 1.77 72. Milk, whole fresh cow 1,981 93 -2.43 0.01 -0.27 -0.66 1.02 0.76 28. Coconuts 404 19 -0.62 0.27 -0.53 -0.5 1.37 0.69 73. Millet 591 30 -2.93 0.00 -0.37 -0.89 0.65 0.53 29. Coffee, green 637 29 -4.2 0.00 -0.25 -0.72 1.21 0.77 74. Mushrooms and truffles 546 26 -1.47 0.07 -0.34 -0.63 1.07 0.77 30. Cotton lint 204 10 -4.34 0.00 -0.27 -1 0.87 0.81 75. Mustard seed 189 9 -3.29 0.00 -0.05 -0.78 1.05 1.2 31. Cottonseed 223 11 -1.66 0.05 -0.16 -0.71 0.88 0.78 76. Nutmeg, mace and cardamoms 62 3 -0.01 0.50 0.16 -0.52 1.48 1.47 32. Cranberries 46 2 -1.31 0.10 0.28 -0.74 0.51 0.08 77. Nuts, nes 101 5 -3.13 0.00 -0.63 -0.81 1.18 1.11 33. Cucumbers and gherkins 1,583 75 -4.66 0.00 -0.45 -0.67 1.04 0.71 78. Oats 1,164 54 -7.77 0.00 -0.04 -0.89 0.63 0.43 34. Currants 267 13 -2.01 0.02 -0.36 -0.76 0.78 0.35 79. Oil, palm 187 9 -2.91 0.00 0.64 -0.68 0.84 0.46 35. Dates 256 12 -1.64 0.05 -0.22 -0.62 1.47 1.4 80. Oilseeds nes 50 3 -0.55 0.29 -0.91 -0.71 0.58 0.22 36. Eggplants (aubergines) 666 32 -4.73 0.00 -0.96 -0.77 0.91 0.65 81. Olives 466 22 -0.83 0.20 -0.48 -0.55 0.96 0.4 37. Eggs, hen, in shell 2,057 100 -5.71 0.00 0 -0.7 1.32 3.59 82. Onions, dry 1,623 77 -9.93 0.00 -0.14 -1.01 0.55 0.4 38. Eggs, other bird, in shell 53 3 -4.68 0.00 -1.95 -0.94 0.35 0.03 83. Onions, shallots, green 534 26 -2.95 0.00 -0.23 -0.91 0.69 0.41 39. Figs 424 20 -3.08 0.00 -0.56 -0.72 1.54 2.28 84. Oranges 1,174 56 -4.47 0.00 -0.33 -0.69 1.05 0.8 40. Flax fibre and tow 176 9 -0.74 0.23 -1.8 -0.7 0.61 0.27 85. Papayas 439 20 -1.94 0.03 -0.83 -0.6 1.51 2.05 41. Fruit, fresh nes 228 12 -2.98 0.00 -1.12 -0.75 1.29 0.84 86. Peaches and nectarines 857 41 -4.5 0.00 -0.53 -0.79 1.33 2.21 42. Garlic 1,076 52 -4.84 0.00 0.16 -0.81 0.71 0.42 87. Pears 1,080 51 -5.24 0.00 -0.37 -0.76 1 1.02 43. Ginger 283 15 -4 0.00 -0.16 -0.88 0.6 0.31 88. Peas, dry 730 35 -2.1 0.02 0.2 -0.75 0.82 0.7 44. Gooseberries 154 8 0.04 0.51 0.51 -0.51 1.07 0.41 89. Peas, green 837 39 -3.27 0.00 -0.24 -0.67 0.99 0.55 45. Grain, mixed 39 2 -3.23 0.00 -2.15 -1.49 0.24 - 90. Pepper (piper spp.) 203 10 -1.67 0.05 -0.38 -0.71 0.86 0.45 (continued on next page)
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A-31
Table A6.1 Cross-Country Tests for Panel Unit Root of LOP Deviations, 124 Food and Agriculture Items, 1991-2013 (continued)
Hc kict c c t cic,t1 k h1c,h k ic,th ict , c 1,...,C i ;t 1,...,T i
p- p- Item Obs Producers Z*-stat α μ σ Item Obs Producers Z*-stat value β HL HL value (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) 91. Persimmons 62 3 -0.87 0.19 -0.52 -0.76 0.51 0.32 111. Sugar beet 847 41 -1.33 0.09 -0.29 -0.61 0.92 0.35 92. Pineapples 658 31 -1.21 0.11 -0.48 -0.49 7.32 29.09 112. Sunflower seed 793 38 -8.97 0.00 -0.22 -1.04 0.67 0.8 93. Pistachios 137 6 -4.26 0.00 0.27 -1.01 1.21 0.54 113. Sweet potatoes 930 44 -2.41 0.01 -0.22 -0.46 1.93 1.34 94. Plantains 489 23 -3.89 0.00 -0.48 -0.65 0.97 0.68 114. Tangerines & mandarins 599 29 -4.1 0.00 -0.41 -0.73 0.82 0.47 95. Plums and sloes 922 44 -6.43 0.00 -0.81 -0.89 0.93 1.37 115. Tea 367 17 -2.47 0.01 -0.87 -0.54 1.57 2.32 96. Poppy seed 105 5 -2.55 0.01 0.41 -0.81 0.64 0.24 116. Tobacco, unmanuf 1,121 56 -1.93 0.03 -0.48 -0.56 1.31 0.84 97. Potatoes 2,139 100 -3.46 0.00 -0.07 -1.05 0.59 0.6 117. Tomatoes 2,094 98 -5.85 0.00 -0.62 -0.72 1.03 1.09 98. Pumpkins, squash and gourds 822 39 -4.69 0.00 -0.74 -0.73 0.9 0.82 118. Triticale 318 16 -2.86 0.00 -0.22 -0.81 0.7 0.61 99. Quinces 387 19 -1.81 0.04 -0.39 -0.75 1 1.07 119. Vanilla 61 3 -0.85 0.20 -1.22 -0.61 1.09 1.15 100. Rapeseed 740 35 -6.17 0.00 0.03 -0.77 0.75 0.45 120. Vegetables, fresh nes 421 22 -3.68 0.00 -0.5 -0.77 0.95 1.13 101. Roots and tubers, nes 142 7 -2.15 0.02 0.04 -0.77 0.8 0.25 121. Walnuts, with shell 540 26 -4.16 0.00 -0.2 -0.78 1.15 0.91 102. Rubber, natural 193 9 -0.61 0.27 -0.51 -0.59 0.86 0.36 122. Watermelons 969 47 -5.63 0.00 -0.37 -0.77 1.09 0.86 103. Rye 843 40 -3.34 0.00 0.36 -0.95 0.5 0.28 123. Wheat 1,719 80 -3.98 0.00 0.09 -0.87 0.74 0.53 104. Sesame seed 524 25 -1.59 0.06 -0.11 -0.74 0.79 0.48 124. Wool, greasy 851 41 -5.06 0.00 -0.69 -0.73 0.84 0.51 105. Silk-worm cocoons, reelable 129 7 -0.86 0.20 -0.97 -0.76 0.72 0.28 Total 79,171 106. Sorghum 973 46 -4.09 0.00 0.33 -0.95 0.67 0.56 Mean 638 30 -3.23 0.06 -0.31 -0.74 1.07 1.17 107. Soybeans 1,054 49 -3.39 0.00 0.28 -0.88 0.73 0.72 Median 498 24 -3.28 0.00 -0.29 -0.73 0.97 0.78 108. Spices, nes 54 3 -3.58 0.00 -0.31 -1.05 2.15 - SD 522 25 1.91 0.13 0.44 0.15 0.75 2.72 109. Spinach 642 32 -5.04 0.00 -0.53 -0.8 0.92 1.21 Min 39 2 -9.93 0.00 -2.15 -1.49 0.24 0.03 110. Strawberries 1,002 49 -3.82 0.00 -0.55 -0.72 1.23 1.27 Max 2,139 100 0.94 0.83 0.64 -0.39 7.32 29.09 Notes:
* * 1. The deviation from LOP is kic,t logp ict logp it logS ct , where pict is the price (in local currency units) of commodity i in country c in year t, pit is the world price of i (in $US) and Sct is the exchange rate of c (the domestic currency cost of $US1).
2. Each commodity i is represented by a panel of Ci producing countries. The panels are unbalanced. “Obs” denotes the total number of country-year observations for each commodity, and “Producers” denotes the number of producing countries/equations in each panel. We exclude commodities that are represented by less than 30 country-years. The Z* -stat is the inverse-normal statistic that tests
Hc H0c : 0 c in kict c c t cic,t1 k h1c,h k ic,th ict , c 1,...,C i ;t 1,...,T i .
2 Ci Ci 3. α and β denote the cross-country mean of c and c , respectively. μHL (1/ C i )Σ c 1 HL c and σHL (1/ C i )Σ c 1 HL c μ HL are the cross-country mean and standard deviation of the half-lives
corresponding to producers of i, where HLcc log(0.5) / log(β 1) the half-like for c. We omit the small number of countries where βc 1. The half-life estimates are plotted in panel A of Figure 5.2. of the text. .
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A-32 Table A6.2 Cross-Commodity Tests for Panel Unit Root of LOP Deviations, 126 Countries, 1991-2013
Hi kict i i t iic,t1 k h1i,h k ic,th ict , i 1,...,N c ; t 1,...,T c
Country Obs Products Z*-stat p-value α β μHL σHL Country Obs Products Z*-stat p-value α β μHL σHL (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) 1. Albania 586 30 -1.64 0.05 0 -0.63 2.35 6.13 46. Ghana 290 14 -2.18 0.01 -0.16 -0.8 1.22 2.19 2. Algeria 445 22 -1.91 0.03 -0.15 -0.83 0.53 0.29 47. Greece 1,422 65 -3.6 0.00 0.06 -0.65 1.18 1.32 3. Ant. & Barb. 80 5 -1.6 0.06 0.68 -0.65 0.73 0.37 48. Guinea 110 6 -1.16 0.12 0.15 -0.65 0.88 0.39 4. Argentina 638 29 -4.33 0.00 -0.23 -0.67 1.5 2.88 49. Honduras 387 22 -1.86 0.03 -0.59 -0.61 1.84 1.22 5. Armenia 679 40 -4.22 0.00 -0.82 -0.9 0.74 0.61 50. Hungary 1,289 57 -7.33 0.00 -0.7 -0.85 0.74 0.47 6. Australia 1,397 65 -3.59 0.00 -0.27 -0.84 0.8 0.73 51. Iceland 308 15 -0.92 0.18 0.64 -0.63 0.92 0.48 7. Austria 1,189 53 -6.32 0.00 0.05 -0.77 1.03 0.8 52. India 288 17 -3.23 0.00 -0.43 -0.95 0.47 0.21 8. Azerbaijan 620 31 -2.58 0.00 -1.14 -0.69 0.91 0.7 53. Indonesia 661 30 -3.15 0.00 -0.59 -0.65 1.1 0.91 9. Bangladesh 723 33 -4.74 0.00 -0.7 -0.75 0.79 0.6 54. Iran 962 46 -6.68 0.00 -0.25 -0.68 0.78 0.53 10. Barbados 184 8 -1.01 0.16 0.68 -0.52 1.21 0.3 55. Ireland 291 13 -1.66 0.05 -0.03 -0.56 1.15 0.85 11. Belarus 450 23 -1.19 0.12 -0.39 -0.67 0.73 0.37 56. Israel 1,071 51 -5.5 0.00 -0.13 -0.76 0.88 0.63 12. Bhutan 108 6 -3.01 0.00 -1.2 -0.92 0.75 0.52 57. Italy 718 38 -1.66 0.05 -0.06 -0.73 0.69 0.44 13. Bolivia 1,171 53 -0.89 0.19 -0.27 -0.49 1.66 1.43 58. Jamaica 656 29 -4.97 0.00 0.38 -0.65 1.03 0.72 14. Bosn. & Herz. 598 34 -1.86 0.03 -0.41 -0.86 0.63 0.5 59. Japan 970 44 -2.69 0.00 0.97 -0.81 0.67 0.55 15. Brazil 354 16 -3.03 0.00 -0.23 -0.7 1.42 1.1 60. Jordan 966 43 -7.19 0.00 -0.67 -0.84 0.77 0.72 16. Bulgaria 671 42 -4.26 0.00 -0.83 -0.97 0.74 0.42 61. Kazakhstan 450 23 -3.12 0.00 -0.8 -0.71 0.96 0.43 17. Burkina Faso 80 5 -3.87 0.00 -0.02 -1.03 0.39 0.03 62. Kenya 563 27 -3.32 0.00 -0.23 -0.64 1.05 0.81 18. Burundi 427 21 -1.33 0.09 -0.03 -0.67 0.87 0.8 63. Kyrgyzstan 408 26 -2.15 0.02 -1.24 -1.11 0.37 0.16 19. Cote d'Ivoire 352 18 -4.48 0.00 -0.52 -0.72 0.83 0.61 64. Lao 177 10 -5.85 0.00 -0.52 -0.77 1.07 0.28 20. Cabo Verde 378 20 -2.51 0.01 1.07 -0.97 0.84 0.52 65. Latvia 616 31 -6.55 0.00 -0.47 -0.86 0.58 0.3 21. Cambodia 155 8 -1.27 0.10 -0.22 -0.64 1.23 0.71 66. Lebanon 828 45 -2.54 0.01 -0.4 -0.86 0.67 0.49 22. Cameroon 231 11 -5.27 0.00 -0.39 -0.72 1.01 0.42 67. Lithuania 344 17 -5.92 0.00 -0.65 -0.87 0.65 0.32 23. Canada 1,072 49 -3.41 0.00 -0.42 -0.78 0.74 0.54 68. Madagascar 233 12 -2.69 0.00 -0.3 -0.71 1.07 1 24. Chile 1,064 49 -1.67 0.05 -0.37 -0.56 1.97 2.27 69. Malawi 144 8 -4.11 0.00 0.54 -1.15 0.45 0.25 25. China 1,431 66 -2.88 0.00 -0.48 -0.61 1.29 1.15 70. Malaysia 426 20 -3.1 0.00 -0.2 -0.69 1.42 2.15 26. Colombia 604 27 -2.66 0.00 -0.15 -0.61 1.02 0.53 71. Mali 209 11 -3.06 0.00 -0.15 -0.81 2.49 3.7 27. Congo 407 19 -1.15 0.12 -0.26 -0.45 1.83 1.21 72. Malta 597 31 -6.44 0.00 0.22 -1.03 0.97 0.81 28. Cook Islands 56 3 -1.27 0.10 -0.55 -0.86 0.36 0.13 73. Mauritius 480 21 -4.68 0.00 0 -0.73 1.04 1.01 29. Costa Rica 289 13 -1.84 0.03 -0.33 -0.7 1 0.76 74. Mexico 2,078 92 -2.12 0.02 -0.29 -0.71 0.77 0.53 30. Croatia 962 50 -5.78 0.00 -0.15 -0.89 0.9 1.26 75. Mongolia 250 12 -1.32 0.09 -0.21 -0.77 0.65 0.36 31. Cyprus 1,422 63 -4.71 0.00 0.16 -0.7 1.22 1.05 76. Morocco 542 26 -5.34 0.00 -0.02 -0.85 0.75 0.78 32. Czech 959 46 -5.56 0.00 -0.46 -0.79 0.83 0.5 77. Mozambique 122 8 -1.65 0.05 -0.99 -1.05 0.68 0.18 33. Denmark 658 29 -5.8 0.00 0.01 -0.76 0.83 0.56 78. Namibia 75 5 -0.55 0.29 -0.07 -0.79 0.58 0.36 34. Dominican Republic 800 35 -5.42 0.00 -0.29 -0.74 0.87 0.55 79. Nepal 391 19 -3.68 0.00 -0.03 -0.81 0.68 0.58 35. Ecuador 713 32 0.96 0.83 -0.51 -0.28 3.07 2.02 80. Netherlands 528 24 -3.13 0.00 -0.06 -0.8 0.72 0.44 36. Egypt 984 44 -1.55 0.06 -0.27 -0.53 1.15 0.62 81. New Zealand 510 26 -4.45 0.00 -0.26 -0.82 0.88 0.86 37. El Salvador 605 27 -3.28 0.00 -0.22 -0.79 0.8 0.39 82. Nicaragua 275 14 -5.56 0.00 0.15 -0.87 0.6 0.35 38. Estonia 504 23 -2.3 0.01 -0.35 -0.88 0.55 0.31 83. Niger 289 15 -1.49 0.07 -0.65 -0.55 1.2 0.65 39. Ethiopia 437 23 -1.43 0.08 -0.4 -0.85 0.56 0.35 84. Nigeria 430 19 -1.42 0.08 0.76 -0.61 0.8 0.36 40. Fiji 320 20 -3.08 0.00 -0.16 -0.88 1.29 1.04 85. Norway 814 38 -6.28 0.00 0.27 -0.86 0.92 1.17 41. Finland 474 21 -1.6 0.05 0.12 -0.52 1.09 0.53 86. Palestine 593 35 -5.36 0.00 -0.14 -0.96 0.82 0.74 42. France 1,046 46 -6.59 0.00 -0.12 -0.84 0.93 1.08 87. Pakistan 548 28 -2.07 0.02 -0.22 -0.82 0.71 0.39 43. Gambia 101 5 -2.37 0.01 0.85 -0.76 0.5 0.24 88. Panama 425 19 -2.71 0.00 0.16 -0.66 1.15 0.68 44. Georgia 312 18 -4.05 0.00 -0.13 -0.95 0.81 0.67 89. Paraguay 270 14 -3.67 0.00 0 -0.89 1.27 1.02 45. Germany 779 35 -5.91 0.00 -0.01 -0.8 1 1.44 90. Peru 1,433 69 -1.1 0.13 -0.36 -0.54 4.45 20.76 (continues on next page)
SUPPLEMENTARY MATERIALS
A-33 Table A6.2 Cross-Commodity Tests for Panel Unit Root of LOP Deviations, 126 Countries, 1991-2013 (continued)
Hi kict i i t iic,t1 k h1i,h k ic,th ict , i 1,...,N c ;t 1,...,T c
p- p- Country Obs Products Z*-stat μ σ Country Obs Products Z*-stat value α β HL HL value (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) 91. Philippines 955 43 -4.53 0.00 -0.35 -0.72 2.51 5.17 112. Switzerland 943 41 -6.64 0.00 0.46 -0.79 0.84 0.56 92. Poland 864 38 -8.37 0.00 -0.67 -0.89 0.79 0.77 113. Tajikistan 41 2 -0.56 0.29 -0.06 -0.56 1.22 1.18 93. Portugal 1,033 46 -5.82 0.00 -0.2 -0.76 0.85 0.52 114. Thailand 674 32 -4.67 0.00 -0.56 -0.78 1.07 0.74 94. Puerto Rico 693 32 -3.22 0.00 0 -0.59 1.21 1.28 115. Macedonia 814 38 -7.25 0.00 -0.32 -0.89 0.81 0.66 95. Republic of Korea 729 39 -1.65 0.05 0.47 -0.81 0.78 0.38 116. Togo 199 9 -6.07 0.00 -0.26 -0.97 0.75 0.42 96. Republic of Moldova 660 33 -4.78 0.00 -1.05 -1.06 0.57 0.26 117. Trinidad and Tobago 268 12 -1.61 0.05 -0.47 -0.66 0.75 0.25 97. Romania 917 45 -1.63 0.05 -0.52 -0.83 0.52 0.33 118. Tunisia 844 37 -6.56 0.00 -0.27 -0.83 0.66 0.51 98. Russian Federation 805 39 -1.92 0.03 -0.84 -0.74 0.71 0.33 119. Turkey 1,532 69 -4.8 0.00 -0.3 -0.71 0.92 0.92 99. Rwanda 412 19 -1.83 0.03 0.03 -0.55 1.47 1.69 120. Ukraine 751 39 -3.51 0.00 -1.2 -0.93 0.64 0.32 100. Saint Lucia 289 17 -3.12 0.00 0.33 -0.75 1.33 0.84 121. United Kingdom 770 35 -3.73 0.00 0.01 -0.66 1.07 0.84 101. Saudi Arabia 211 13 -0.76 0.22 0.03 -0.65 1.08 0.66 122. United States 1,667 76 -6.65 0.00 -0.28 -0.77 0.97 0.77 102. Senegal 344 17 -2.11 0.02 -0.42 -0.65 0.99 0.93 123. Uruguay 846 37 -5.02 0.00 -0.16 -0.69 0.84 1.03 103. Singapore 100 6 -2.62 0.00 -0.47 -0.89 0.89 0.41 124. Venezuela 962 43 -1.48 0.07 -0.46 -0.6 1.04 0.67 104. Slovakia 1,065 54 -3.41 0.00 -0.42 -0.68 0.84 1.63 125. Viet Nam 207 9 -1.62 0.05 -0.3 -0.52 1.87 2.51 105. Slovenia 827 38 -4.55 0.00 -0.11 -0.91 0.76 0.54 126. Yemen 953 43 -0.24 0.41 -0.02 -0.4 1.77 0.89 106. South Africa 1,316 59 -5.06 0.00 -0.51 -0.76 0.81 0.58 Total 78,350 107. Spain 1,643 72 -5.79 0.00 -0.1 -0.7 0.88 0.71 Mean 630 30 -3.44 0.04 -0.21 -0.76 1.00 0.99 108. Sri Lanka 834 38 -2.89 0.00 -0.18 -0.62 1.18 1 Median 595 29 -3.13 0.00 -0.23 -0.76 0.88 0.63 109. Sudan (former) 172 9 -4.1 0.00 -0.41 -0.95 1.09 0.65 SD 400 18 1.91 0.10 0.42 0.15 0.53 1.95 110. Suriname 633 31 -2.23 0.01 0.71 -0.96 0.41 0.22 Min 41 2 -8.37 0.00 -1.24 -1.15 0.36 0.03 111. Sweden 456 21 -4.89 0.00 -0.07 -0.83 0.69 0.47 Max 2,078 92 0.96 0.83 1.07 -0.28 4.45 20.76 Notes: These results parrellel those of Table A6.1 See notes to that table.
SUPPLEMENTARY MATERIALS
A-34 Table A7.1 Key Features of Panel Tests for Unit Roots and Co-integration
Allowing for panel-specific… Authors’ original Null Alternative Full titles of statistics References AR Co-integrating nomenclatures hypothesis hypothesis parameters? vectors? (1) (2) (3) (4) (5) (6) (7) A-Panel unit root tests
1. t-bar NT t-bar Im et al. (2003) All panels At least one Yes - 2. Fisher-type PP (Inverse-normal) Z Maddala and Wu (1999), Choi (2001) contain unit panel is Yes - 3. Fisher-type ADF (Inverse-normal) Z* Choi (2001), Demetrescu et al. (2006) roots stationary Yes - B. Residual-based co-integration tests
4. Modified Dickey-Fuller DFρ Kao (1999) No All panels are No No co-integration co-integrated 5. Dickey-Fuller DFt No No
6. Augmented Dickey-Fuller ADFt No No 7. Unadjusted Modified Dickey-Fuller * No No DFρ 8. Unadjusted Dickey-Fuller * No No DFt
9. Panel Zν Pedroni (1999, 2004) No All panels are No Yes co-integration co-integrated 10. Panel ρ Zρ No Yes
11. Panel t (non-parametric) Zt No Yes 12. Panel t (parametric) * No Yes Zt 13. Group rho Yes Yes Zρ 14. Group t (non-parametric) Yes Yes Zt 15. Group t (parametric) * Yes Yes Zt C. Fisher-type co-integration tests 16. Panel t Westerlund (2007), All panels are Yes Yes Pτ No Persyn and Westerlund (2008) co-integrated 17. Panel α Pθ co-integration Yes Yes
18. Group t G τ Some panels are Yes Yes co-integrated 19. Group α Gθ Yes Yes Notes: For all tests, cross-sectional correlation is mitigated by de-meaning the data. All tests allow for unbalanced panels, and panel-specific constants and time trends, except for those of Kao (1999), which only allow for panel-specific constants.
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A-35 Table A7.2 Cross-Country Tests for Panel Unit Roots (p-values)
log ric,t logSct Item Item t Z Z* (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 1. Anise, badian, … 0.78 0.99 0.86 0.85 0.99 0.96 66. Meat, horse 0.00 0.00 0.49 0.00 0.00 0.00 2. Apples 0.00 0.00 0.00 0.05 0.70 0.07 67. Meat, pig 0.00 0.00 0.17 0.00 0.00 0.05 3. Apricots 0.00 0.00 0.15 0.00 0.01 0.00 68. Meat, rabbit 0.01 0.59 0.99 0.08 0.94 1.00 4. Artichokes 0.00 0.00 0.76 0.00 0.00 0.00 69. Meat, sheep 0.00 0.00 0.05 0.00 0.00 0.00 5. Asparagus 0.00 0.03 0.95 0.00 0.00 0.01 70. Meat, turkey 0.26 0.99 0.66 0.40 0.99 0.25 6. Avocados 0.00 0.00 0.78 0.01 0.31 0.80 71. Melons, other 0.00 0.00 0.88 0.01 0.78 0.38 7. Bananas 0.00 0.01 0.36 0.00 0.21 0.97 72. Milk, whole fresh cow 0.00 0.00 0.07 0.02 0.69 0.48 8. Barley 0.00 0.00 0.18 0.01 0.27 0.99 73. Millet 0.00 0.00 0.09 0.00 0.00 0.00 9. Beans, dry 0.00 0.00 0.57 0.39 0.99 1.00 74. Mushrooms and truffles 0.00 0.00 0.97 0.01 0.73 0.19 10. Beans, green 0.00 0.00 0.95 0.00 0.84 0.10 75. Mustard seed 0.00 0.10 0.94 0.24 0.94 0.54 11. Beeswax 0.77 0.99 0.90 0.60 0.97 0.99 76. Nutmeg, mace … 0.23 0.71 0.92 0.38 0.92 1.00 12. Blueberries 0.03 0.17 0.08 0.00 0.00 0.00 77. Nuts, nes 0.02 0.21 0.19 0.04 0.24 0.71 13. Broad beans, … 0.02 0.87 1.00 0.19 0.99 1.00 78. Oats 0.00 0.00 0.20 0.00 0.05 0.03 14. Buckwheat 0.00 0.00 0.63 0.00 0.00 0.96 79. Oil, palm 0.24 0.81 0.88 0.85 1.00 0.95 15. Cabbages and … 0.00 0.00 0.23 0.00 0.00 0.18 80. Oilseeds nes 0.17 0.06 0.21 0.86 0.97 0.00 16. Canary seed 0.04 0.41 0.00 0.13 0.67 0.00 81. Olives 0.00 0.19 0.11 0.02 0.13 0.00 17. Carrots and turnips 0.00 0.00 0.81 0.00 0.00 1.00 82. Onions, dry 0.00 0.00 0.00 0.00 0.00 0.17 18. Cashew nuts, with shell 0.01 0.19 0.36 0.00 0.00 0.00 83. Onions, shallots, green 0.00 0.00 1.00 0.44 1.00 1.00 19. Cauliflowers … 0.00 0.00 0.12 0.00 0.00 1.00 84. Oranges 0.00 0.00 0.91 0.00 0.14 0.00 20. Cherries 0.00 0.00 0.36 0.00 0.14 0.00 85. Papayas 0.00 0.04 0.15 0.06 0.02 0.76 21. Cherries, sour 0.00 0.00 0.00 0.00 0.00 0.40 86. Peaches and nectarines 0.00 0.00 0.58 0.17 0.99 0.03 22. Chestnut 0.07 0.58 0.91 0.99 1.00 1.00 87. Pears 0.00 0.00 0.01 0.26 1.00 0.18 23. Chick peas 0.00 0.32 0.25 0.16 1.00 1.00 88. Peas, dry 0.00 0.00 1.00 0.00 0.00 0.97 24. Chillies and peppers, dry 0.05 0.77 0.99 0.00 0.06 0.93 89. Peas, green 0.00 0.00 0.64 0.00 0.27 0.02 25. Chillies and … 0.00 0.00 1.00 0.17 0.24 1.00 90. Pepper (piper spp.) 0.17 0.89 0.95 0.12 0.86 1.00 26. Cloves 0.48 0.92 0.98 0.21 0.68 0.93 91. Persimmons 0.01 0.00 0.09 0.07 0.36 0.49 27. Cocoa, beans 0.00 0.00 0.23 0.00 0.00 0.00 92. Pineapples 0.00 0.00 0.35 0.15 0.58 0.98 28. Coconuts 0.00 0.04 0.42 0.82 1.00 0.42 93. Pistachios 0.00 0.00 0.54 0.00 0.00 0.59 29. Coffee, green 0.00 0.01 0.00 0.05 0.35 0.00 94. Plantains 0.00 0.00 0.16 0.00 0.00 0.00 30. Cotton lint 0.00 0.00 0.10 0.00 0.00 0.00 95. Plums and sloes 0.00 0.00 0.00 0.06 0.84 0.00 31. Cottonseed 0.00 0.00 0.00 0.05 0.43 0.00 96. Poppy seed 0.00 0.01 0.66 0.09 0.02 0.99 32. Cranberries 0.25 0.66 0.75 0.32 0.61 0.76 97. Potatoes 0.00 0.00 0.00 0.00 0.00 0.35 33. Cucumbers and gherkins 0.00 0.00 0.00 0.00 0.00 0.95 98. Pumpkins, squash … 0.00 0.00 0.01 0.01 0.84 0.79 34. Currants 0.00 0.00 0.00 0.00 0.00 0.10 99. Quinces 0.00 0.00 0.36 0.11 0.83 0.31 35. Dates 0.00 0.35 0.89 0.00 0.03 0.05 100. Rapeseed 0.00 0.00 0.86 0.00 0.05 0.96 36. Eggplants (aubergines) 0.00 0.00 0.34 0.00 0.00 0.00 101. Roots and tubers, nes 0.01 0.15 0.00 0.68 1.00 0.65 37. Eggs, hen, in shell 0.00 0.00 0.00 0.00 0.32 0.00 102. Rubber, natural 0.69 1.00 1.00 0.09 0.40 0.07 38. Eggs, other bird, in shell 0.13 0.60 0.52 0.26 0.81 0.93 103. Rye 0.00 0.00 0.00 0.00 0.00 0.00 39. Figs 0.00 0.02 0.64 0.16 0.99 0.11 104. Sesame seed 0.00 0.00 0.66 0.00 0.00 1.00 40. Flax fibre and tow 0.00 0.00 0.79 0.00 0.01 1.00 105. Silk-worm cocoons… 0.04 0.53 0.00 0.06 0.46 0.30 41. Fruit, fresh nes 0.00 0.00 0.43 0.00 0.00 1.00 106. Sorghum 0.00 0.00 0.98 0.00 0.34 0.17 42. Garlic 0.00 0.00 0.28 0.00 0.00 0.91 107. Soybeans 0.00 0.00 0.00 0.03 0.85 0.02 43. Ginger 0.00 0.10 0.83 0.00 0.14 0.87 108. Spices, nes 0.16 0.68 0.63 0.46 0.95 0.75 44. Gooseberries 0.00 0.00 0.18 0.00 0.00 0.58 109. Spinach 0.00 0.01 0.99 0.00 0.07 0.77 45. Grain, mixed 0.70 0.97 0.90 0.59 0.90 0.57 110. Strawberries 0.00 0.00 0.50 0.53 0.99 0.35 46. Grapefruit … 0.00 0.00 0.13 0.00 0.00 0.00 111. Sugar beet 0.00 0.00 0.00 0.00 0.00 0.00 47. Grapes 0.00 0.00 0.04 0.00 0.01 0.00 112. Sunflower seed 0.00 0.00 0.93 0.70 0.97 1.00 48. Honey, natural 0.00 0.00 0.00 0.00 0.00 0.36 113. Sweet potatoes 0.00 0.00 0.22 0.04 0.43 0.99 49. Hops 0.00 0.00 0.43 0.00 0.00 0.57 114. Tangerines, mandarins 0.00 0.00 0.08 0.00 0.39 0.08 50. Jute 0.00 0.00 0.00 0.00 0.00 0.00 115. Tea 0.00 0.11 0.12 0.59 0.94 1.00 51. Kiwi fruit 0.00 0.00 0.17 0.00 0.00 0.77 116. Tobacco, unmanufactured 0.38 1.00 1.00 1.00 1.00 1.00 52. Leeks, other alliaceous 0.00 0.00 0.26 0.00 0.00 0.89 117. Tomatoes 0.00 0.00 0.53 0.01 0.28 0.99 53. Lemons and limes 0.00 0.00 0.67 0.00 0.00 0.00 118. Triticale 0.00 0.00 0.18 0.00 0.00 0.00 54. Lentils 0.00 0.07 0.77 0.33 0.97 0.19 119. Vanilla 0.05 0.24 0.99 0.00 0.00 0.29 55. Lettuce and chicory 0.00 0.00 0.73 0.00 0.50 1.00 120. Vegetables, fresh nes 0.00 0.00 0.00 0.00 0.00 0.13 56. Linseed 0.00 0.00 0.96 0.00 0.00 0.98 121. Walnuts, with shell 0.00 0.00 0.65 0.00 0.00 0.73 57. Maize 0.00 0.00 0.34 0.00 0.00 0.96 122. Watermelons 0.00 0.00 0.76 0.00 0.00 0.00 58. Maize, green 0.00 0.00 0.06 0.02 0.09 0.66 123. Wheat 0.00 0.00 0.44 0.00 0.00 0.00 59. Mangoes, mangosteens 0.00 0.00 0.81 0.00 0.00 0.38 124. Wool, greasy 0.00 0.00 0.02 0.00 0.00 0.01 60. Meat, cattle 0.00 0.00 0.00 0.00 0.00 0.00 Mean 0.05 0.14 0.46 0.12 0.35 0.47 61. Meat, chicken 0.00 0.00 0.85 0.00 0.00 1.00 Median 0.00 0.00 0.39 0.00 0.11 0.38 62. Meat, duck 0.00 0.00 0.98 0.00 0.00 0.99 SD 0.15 0.29 0.37 0.24 0.40 0.42 63. Meat, game 0.00 0.00 0.01 0.11 0.55 0.00 Max 0.78 1.00 1.00 1.00 1.00 1.00 64. Meat, goat 0.00 0.00 0.91 0.00 0.00 0.11 Min 0.00 0.00 0.00 0.00 0.00 0.00
* Notes: Prices are defined as logric,t logp ict logp it , where pict is the price (in local currency units) of commodity i in country c in year * * t, pit is the world price of i (in $US). logSct is the logarithm of the exchange rate of c (the domestic currency cost of $US1). t , Z and Z denote the panel unit root test statistics used by Im et al. (2003), Maddala and Wu (1999) and Demetrescu et al. (2006), respectively (see Table A7.1 for details).
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A-36 Table A7.3 Cross-Commodity Tests for Panel Unit Roots (p-values) * log pict log p Country Country ct t Z Z* Z (1) (2) (3) (4) (5) (6) (7) (8) 1. Albania 0.00 0.00 0.18 67. Lithuania 0.00 0.00 0.03 2. Algeria 0.00 0.00 0.03 68. Madagascar 0.17 0.70 0.08 3. Antigua and Barbuda 0.17 0.70 0.08 69. Malawi 0.00 0.00 0.12 4. Argentina 0.00 0.00 0.12 70. Malaysia 0.00 0.00 0.87 5. Armenia 0.00 0.00 0.87 71. Mali 0.00 0.00 0.02 6. Australia 0.00 0.00 0.02 72. Malta 0.00 0.00 0.00 7. Austria 0.00 0.00 0.00 73. Mauritius 0.00 0.00 0.20 8. Azerbaijan 0.00 0.00 0.20 74. Mexico 0.00 0.00 0.94 9. Bangladesh 0.00 0.00 0.94 75. Mongolia 0.00 0.04 0.83 10. Barbados 0.00 0.04 0.83 76. Morocco 0.00 0.00 0.00 11. Belarus 0.00 0.00 0.00 77. Mozambique 0.00 0.00 0.93 12. Bhutan 0.00 0.00 0.93 78. Namibia 0.00 0.01 1.00 13. Bolivia 0.00 0.01 1.00 79. Nepal 0.00 0.00 0.36 14. Bosnia and Herzegovina 0.00 0.00 0.36 80. Netherlands 0.00 0.00 0.28 15. Brazil 0.00 0.00 0.28 81. New Zealand 0.00 0.00 0.01 16. Bulgaria 0.00 0.00 0.01 82. Nicaragua 0.00 0.00 0.97 17. Burkina Faso 0.00 0.00 0.97 83. Niger 0.00 0.00 0.85 18. Burundi 0.00 0.00 0.85 84. Nigeria 0.00 0.00 0.05 19. Cabo Verde 0.00 0.00 0.05 85. Norway 0.00 0.00 0.21 20. Cambodia 0.00 0.00 0.21 86. Occupied Palestinian Territory 0.01 0.21 0.69 21. Cameroon 0.01 0.21 0.69 87. Pakistan 0.00 0.06 0.08 22. Canada 0.00 0.06 0.08 88. Panama 0.00 0.00 0.18 23. Chile 0.00 0.00 0.18 89. Paraguay 0.00 0.00 1.00 24. China 0.00 0.00 1.00 90. Peru 0.00 0.00 0.91 25. Colombia 0.00 0.00 0.91 91. Philippines 0.00 0.00 0.71 26. Congo 0.00 0.00 0.71 92. Poland 0.01 0.79 0.98 27. Cook Islands 0.01 0.79 0.98 93. Portugal 0.04 0.23 0.03 28. Costa Rica 0.04 0.23 0.03 94. Puerto Rico 0.00 0.00 0.05 29. Croatia 0.00 0.00 0.05 95. Republic of Korea 0.00 0.00 0.05 30. Cyprus 0.00 0.00 0.05 96. Republic of Moldova 0.00 0.00 0.07 31. Czechia 0.00 0.00 0.07 97. Romania 0.00 0.00 0.31 32. Cote d'Ivoire 0.00 0.00 0.31 98. Russian Federation 0.00 0.00 0.36 33. Denmark 0.00 0.00 0.36 99. Rwanda 0.00 0.00 0.55 34. Dominican Republic 0.00 0.00 0.55 100. Saint Lucia 0.00 0.00 0.09 35. Ecuador 0.00 0.00 0.09 101. Saudi Arabia 0.00 0.00 0.02 36. Egypt 0.00 0.00 0.02 102. Senegal 0.00 0.00 0.00 37. El Salvador 0.00 0.00 0.00 103. Singapore 0.00 0.00 0.00 38. Estonia 0.00 0.00 0.00 104. Slovakia 0.00 0.00 0.00 39. Ethiopia 0.00 0.00 0.00 105. Slovenia 0.00 0.00 0.99 40. Fiji 0.00 0.00 0.99 106. South Africa 0.00 0.00 0.22 41. Finland 0.00 0.00 0.22 107. Spain 0.00 0.00 0.31 42. France 0.00 0.00 0.31 108. Sri Lanka 0.00 0.00 0.01 43. Gambia 0.00 0.00 0.01 109. Sudan (former) 0.00 0.00 0.32 44. Georgia 0.00 0.00 0.32 110. Suriname 0.00 0.00 0.01 45. Germany 0.00 0.00 0.01 111. Sweden 0.00 0.00 0.28 46. Ghana 0.00 0.00 0.28 112. Switzerland 0.00 0.00 0.06 47. Greece 0.00 0.00 0.06 113. Tajikistan 0.01 0.20 0.41 48. Guinea 0.01 0.20 0.41 114. Thailand 0.00 0.01 0.74 49. Honduras 0.00 0.01 0.74 115. Macedonia 0.00 0.00 0.03 50. Hungary 0.00 0.00 0.03 116. Togo 0.00 0.00 0.42 51. Iceland 0.00 0.00 0.42 117. Trinidad and Tobago 0.00 0.00 0.08 52. India 0.00 0.00 0.08 118. Tunisia 0.00 0.45 1.00 53. Indonesia 0.00 0.45 1.00 119. Turkey 0.00 0.00 0.01 54. Iran 0.00 0.00 0.01 120. Ukraine 0.00 0.04 0.99 55. Ireland 0.00 0.04 0.99 121. United Kingdom 0.00 0.00 0.08 56. Israel 0.00 0.00 0.08 122. United States of America 0.00 0.00 0.18 57. Italy 0.00 0.00 0.18 123. Uruguay 0.00 0.00 0.11 58. Jamaica 0.00 0.00 0.11 124. Venezuela 0.00 0.00 0.00 59. Japan 0.00 0.00 0.00 125. Viet Nam 0.00 0.00 0.01 60. Jordan 0.00 0.00 0.01 126. Yemen 0.00 0.00 0.18 61. Kazakhstan 0.00 0.00 0.18 Summary Statistics 62. Kenya 0.00 0.00 0.51 Mean 0.00 0.03 0.32 63. Kyrgyzstan 0.00 0.00 0.00 Median 0.00 0.00 0.18 64. Lao 0.00 0.00 0.79 SD 0.02 0.11 0.34 65. Latvia 0.00 0.00 0.04 Min 0.00 0.00 0.00 66. Lebanon 0.00 0.00 0.18 Max 0.17 0.79 1.00 Notes: See notes to Table A7.2.
SUPPLEMENTARY MATERIALS
A-37 Table A7.4 Cross-Country Tests for Co-integration (p-values)
Item G τ Gθ Pτ Pθ Item (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1. Anise, badian, fennel, coriander 0.01 0.00 0.01 0.00 66. Meat, horse 0.09 0.49 0.07 0.01 2. Apples 0.00 0.01 0.00 0.00 67. Meat, pig 0.00 0.00 0.00 0.00 3. Apricots 0.00 0.04 0.00 0.00 68. Meat, rabbit 0.00 0.93 0.03 0.74 4. Artichokes 0.00 0.84 0.00 0.15 69. Meat, sheep 0.00 0.38 0.00 0.19 5. Asparagus 0.00 0.66 0.00 0.11 70. Meat, turkey 0.00 0.48 0.00 0.00 6. Avocados 0.00 0.62 0.00 0.37 71. Melons, other (inc.cantaloupes) 0.00 0.95 0.00 0.84 7. Bananas 0.00 0.90 0.00 0.08 72. Milk, whole fresh cow 0.00 0.26 0.00 0.61 8. Barley 0.00 0.00 0.00 0.09 73. Millet 0.00 0.01 0.00 0.00 9. Beans, dry 0.00 0.01 0.00 0.00 74. Mushrooms and truffles 0.00 0.05 0.00 0.03 10. Beans, green 0.00 0.16 0.00 0.81 75. Mustard seed 0.00 0.08 0.91 0.96 11. Beeswax 0.12 0.67 0.26 0.44 76. Nutmeg, mace and cardamoms 0.13 0.67 0.37 0.62 12. Blueberries 0.03 0.88 0.06 0.29 77. Nuts, nes 0.08 0.84 0.02 0.28 13. Broad beans, horse beans, dry 0.00 0.01 0.41 0.60 78. Oats 0.00 0.00 0.00 0.00 14. Buckwheat 0.00 0.00 0.00 0.00 79. Oil, palm 0.00 0.58 0.00 0.11 15. Cabbages and other brassicas 0.00 0.00 0.00 0.00 80. Oilseeds nes 0.00 0.09 0.00 0.00 16. Canary seed 0.00 0.45 0.01 0.26 81. Olives 0.05 1.00 0.02 0.55 17. Carrots and turnips 0.00 0.00 0.00 0.00 82. Onions, dry 0.00 0.00 0.00 0.00 18. Cashew nuts, with shell 0.00 0.30 0.00 0.01 83. Onions, shallots, green 0.00 0.32 0.00 0.19 19. Cauliflowers and broccoli 0.00 0.17 0.00 0.00 84. Oranges 0.00 0.80 0.00 0.50 20. Cherries 0.00 0.34 0.00 0.00 85. Papayas 0.00 0.34 0.00 0.13 21. Cherries, sour 0.00 0.81 0.00 0.04 86. Peaches and nectarines 0.00 0.13 0.00 0.00 22. Chestnut 0.25 0.82 0.06 0.31 87. Pears 0.00 0.02 0.00 0.00 23. Chick peas 0.00 0.07 0.00 0.93 88. Peas, dry 0.00 0.01 0.03 0.73 24. Chillies and peppers, dry 0.31 0.57 0.96 0.97 89. Peas, green 0.00 0.03 0.00 0.16 25. Chillies and peppers, green 0.00 0.50 0.00 0.01 90. Pepper (piper spp.) 0.00 0.92 0.37 0.67 26. Cloves 0.29 0.87 0.59 0.67 91. Persimmons 0.13 0.64 0.05 0.28 27. Cocoa, beans 0.00 0.35 0.33 0.82 92. Pineapples 0.00 0.98 0.00 0.76 28. Coconuts 0.00 0.88 0.00 0.39 93. Pistachios 0.00 0.00 0.01 0.71 29. Coffee, green 0.00 0.57 0.30 0.90 94. Plantains 0.00 0.99 0.00 0.90 30. Cotton lint 0.00 0.01 0.00 0.00 95. Plums and sloes 0.00 0.00 0.00 0.00 31. Cottonseed 0.00 0.77 0.02 0.80 96. Poppy seed 0.01 0.21 0.01 0.03 32. Cranberries 0.09 0.52 0.07 0.25 97. Potatoes 0.00 0.00 0.00 0.00 33. Cucumbers and gherkins 0.00 0.43 0.00 0.00 98. Pumpkins, squash and gourds 0.00 0.82 0.00 0.00 34. Currants 0.00 0.14 0.00 0.00 99. Quinces 0.00 0.08 0.00 0.00 35. Dates 0.00 0.70 0.17 0.45 100. Rapeseed 0.00 0.00 0.00 0.16 36. Eggplants (aubergines) 0.00 0.54 0.00 0.03 101. Roots and tubers, nes 0.00 0.57 0.00 0.62 37. Eggs, hen, in shell 0.00 0.00 0.00 0.00 102. Rubber, natural 0.00 0.39 0.00 0.00 38. Eggs, other bird, in shell 0.03 0.78 0.00 0.39 103. Rye 0.00 0.00 0.00 0.00 39. Figs 0.00 0.24 0.00 0.00 104. Sesame seed 0.00 0.84 0.00 0.51 40. Flax fibre and tow 0.00 0.76 0.52 0.65 105. Silk-worm cocoons, reelable 0.02 0.31 0.05 0.27 41. Fruit, fresh nes 0.00 0.55 0.00 0.28 106. Sorghum 0.00 0.02 0.00 0.00 42. Garlic 0.00 0.00 0.00 0.04 107. Soybeans 0.00 0.00 0.00 0.07 43. Ginger 0.00 0.85 0.00 0.55 108. Spices, nes 0.00 0.79 0.00 0.08 44. Gooseberries 0.63 0.85 0.36 0.27 109. Spinach 0.00 0.38 0.00 0.01 45. Grain, mixed 0.00 0.01 0.00 0.00 110. Strawberries 0.00 0.18 0.00 0.00 46. Grapefruit (inc. pomelos) 0.00 0.78 0.00 0.18 111. Sugar beet 0.00 0.91 0.00 0.00 47. Grapes 0.00 0.57 0.00 0.00 112. Sunflower seed 0.00 0.00 0.00 0.00 48. Honey, natural 0.00 0.00 0.00 0.69 113. Sweet potatoes 0.00 1.00 0.00 0.60 49. Hops 0.01 0.68 0.00 0.30 114. Tangerines and mandarins 0.00 0.37 0.00 0.00 50. Jute 0.48 0.83 0.08 0.35 115. Tea 0.27 0.86 0.09 0.46 51. Kiwi fruit 0.17 0.83 0.00 0.45 116. Tobacco, unmanufactured 0.00 0.99 0.07 0.34 52. Leeks, other alliaceous vegetables 0.00 0.49 0.00 0.21 117. Tomatoes 0.00 0.11 0.00 0.05 53. Lemons and limes 0.00 0.81 0.00 0.40 118. Triticale 0.00 0.00 0.00 0.00 54. Lentils 0.00 0.15 0.00 0.57 119. Vanilla 0.56 0.76 0.62 0.66 55. Lettuce and chicory 0.00 0.20 0.00 0.08 120. Vegetables, fresh nes 0.00 0.26 0.00 0.60 56. Linseed 0.00 0.10 0.00 0.32 121. Walnuts, with shell 0.00 0.00 0.00 0.01 57. Maize 0.00 0.00 0.00 0.02 122. Watermelons 0.00 0.72 0.00 0.02 58. Maize, green 0.00 0.16 0.00 0.00 123. Wheat 0.00 0.00 0.00 0.01 59. Mangoes, mangosteens, guavas 0.00 0.82 0.01 0.45 124. Wool, greasy 0.00 0.50 0.00 0.08 60. Meat, cattle 0.00 0.64 0.00 0.01 Summary Statistics 61. Meat, chicken 0.00 0.29 0.00 0.42 Mean 0.04 0.42 0.06 0.26 62. Meat, duck 0.64 0.88 0.30 0.36 Median 0.00 0.39 0.00 0.14 63. Meat, game 0.13 0.45 0.01 0.06 SD 0.11 0.35 0.16 0.29 64. Meat, goat 0.00 0.85 0.00 0.55 Min 0.00 0.00 0.00 0.00 65. Meat, goose and guinea fowl 0.00 0.42 0.00 0.33 Max 0.64 1.00 0.96 0.97 Notes: This table reports the p-values of Westerlund’s (2007) tests for panel co-integration. Columns 2, 3, 7 and 8 show the results for the group-mean statistics, and , which test for H:0cθ (the ECT coefficient) 0 against H:Acθ0 for at least one c.
Columns 5, 6, 9, 10 show the results for the panel statistics, Pτ and Pθ , which test for H:0cθ0 against H:Acθ 0 c.
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A-38
Table A7.5 Second Set of Cross-Country Tests for Co-integration (p-values) Kao (1999) Pedroni (2004) Item * * * DF DF Z Z Z * ρ t ADF DFρ DFt ν ρ t Zt Zρ Zt Zt (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 1. Anise, badian, fennel, coriander 0.00 0.01 0.00 0.00 0.01 0.40 0.33 0.11 0.37 0.40 0.17 0.40 2. Apples 0.00 0.00 0.00 0.00 0.00 0.21 0.00 0.00 0.00 0.01 0.00 0.00 3. Apricots 0.00 0.00 0.22 0.00 0.00 0.21 0.00 0.00 0.00 0.00 0.00 0.00 4. Artichokes 0.26 0.44 0.31 0.00 0.00 0.36 0.09 0.00 0.04 0.40 0.00 0.08 5. Asparagus 0.02 0.00 0.00 0.49 0.15 0.39 0.00 0.00 0.02 0.30 0.00 0.00 6. Avocados 0.20 0.32 0.17 0.00 0.00 0.14 0.01 0.00 0.04 0.36 0.00 0.12 7. Bananas 0.10 0.00 0.25 0.00 0.00 0.40 0.00 0.00 0.26 0.35 0.00 0.39 8. Barley 0.00 0.00 0.00 0.00 0.00 0.04 0.00 0.00 0.29 0.40 0.00 0.33 9. Beans, dry 0.00 0.00 0.00 0.00 0.00 0.04 0.00 0.00 0.01 0.37 0.00 0.00 10. Beans, green 0.38 0.06 0.01 0.00 0.00 0.39 0.00 0.00 0.00 0.32 0.00 0.00 11. Beeswax 0.33 0.16 0.22 0.25 0.13 0.05 0.05 0.00 0.39 0.26 0.00 0.40 12. Blueberries 0.00 0.00 0.00 0.00 0.00 0.40 0.40 0.17 0.40 0.29 0.23 0.25 13. Broad beans, horse beans, dry 0.42 0.04 0.02 0.00 0.00 0.12 0.07 0.00 0.00 0.39 0.00 0.02 14. Buckwheat 0.00 0.00 0.00 0.00 0.00 0.25 0.00 0.00 0.03 0.23 0.00 0.00 15. Cabbages and other brassicas 0.00 0.00 0.34 0.00 0.00 0.24 0.00 0.00 0.00 0.00 0.00 0.02 16. Canary seed 0.00 0.00 0.00 0.00 0.00 0.37 0.11 0.00 0.00 0.38 0.00 0.17 17. Carrots and turnips 0.01 0.00 0.47 0.00 0.00 0.40 0.00 0.00 0.00 0.00 0.00 0.00 18. Cashew nuts, with shell 0.03 0.01 0.01 0.00 0.00 0.18 0.23 0.00 0.14 0.39 0.01 0.36 19. Cauliflowers and broccoli 0.00 0.00 0.27 0.00 0.00 0.38 0.00 0.00 0.00 0.05 0.00 0.00 20. Cherries 0.11 0.00 0.44 0.00 0.00 0.24 0.00 0.00 0.24 0.07 0.00 0.05 21. Cherries, sour 0.00 0.00 0.35 0.00 0.00 0.38 0.00 0.00 0.03 0.18 0.00 0.33 22. Chestnut 0.26 0.08 0.37 0.00 0.00 0.37 0.08 0.00 0.03 0.38 0.02 0.14 23. Chick peas 0.00 0.00 0.00 0.00 0.00 0.09 0.03 0.00 0.00 0.40 0.00 0.01 24. Chillies and peppers, dry 0.43 0.45 0.20 0.23 0.22 0.31 0.36 0.02 0.38 0.28 0.07 0.31 25. Chillies and peppers, green 0.42 0.28 0.00 0.00 0.00 0.34 0.00 0.00 0.09 0.04 0.00 0.07 26. Cloves 0.27 0.38 0.30 0.27 0.38 0.38 0.40 0.36 0.17 0.33 0.40 0.03 27. Cocoa, beans 0.46 0.45 0.17 0.08 0.12 0.38 0.07 0.00 0.24 0.39 0.00 0.40 28. Coconuts 0.35 0.35 0.14 0.00 0.00 0.30 0.13 0.00 0.07 0.35 0.00 0.00 29. Coffee, green 0.34 0.07 0.23 0.01 0.00 0.32 0.03 0.00 0.00 0.40 0.00 0.05 30. Cotton lint 0.00 0.00 0.03 0.00 0.00 0.25 0.00 0.00 0.33 0.04 0.00 0.40 31. Cottonseed 0.00 0.00 0.00 0.00 0.00 0.39 0.05 0.00 0.12 0.38 0.00 0.03 32. Cranberries 0.29 0.26 0.05 0.25 0.24 0.31 0.36 0.18 0.05 0.39 0.24 0.07 33. Cucumbers and gherkins 0.00 0.00 0.28 0.00 0.00 0.30 0.00 0.00 0.20 0.16 0.00 0.27 34. Currants 0.00 0.00 0.00 0.00 0.00 0.36 0.05 0.00 0.00 0.40 0.00 0.08 35. Dates 0.00 0.00 0.01 0.00 0.00 0.23 0.26 0.00 0.00 0.39 0.00 0.01 36. Eggplants (aubergines) 0.12 0.01 0.38 0.00 0.00 0.39 0.00 0.00 0.02 0.03 0.00 0.40 37. Eggs, hen, in shell 0.00 0.00 0.00 0.00 0.00 0.15 0.00 0.00 0.19 0.34 0.00 0.36 38. Eggs, other bird, in shell 0.09 0.17 0.06 0.00 0.00 0.34 0.15 0.00 0.00 0.36 0.00 0.01 39. Figs 0.00 0.00 0.00 0.00 0.00 0.35 0.00 0.00 0.38 0.20 0.00 0.23 40. Flax fibre and tow 0.00 0.01 0.04 0.00 0.00 0.32 0.27 0.00 0.39 0.39 0.00 0.40 41. Fruit, fresh nes 0.09 0.01 0.46 0.00 0.00 0.32 0.05 0.00 0.13 0.33 0.00 0.11 42. Garlic 0.00 0.00 0.00 0.00 0.00 0.08 0.02 0.00 0.10 0.20 0.00 0.01 43. Ginger 0.33 0.07 0.00 0.00 0.00 0.20 0.36 0.00 0.28 0.16 0.01 0.40 44. Gooseberries 0.12 0.13 0.09 0.01 0.04 0.39 0.36 0.13 0.01 0.27 0.32 0.40 45. Grain, mixed 0.02 0.09 0.08 0.00 0.02 0.22 0.26 0.04 0.02 0.39 0.06 0.01 46. Grapefruit (inc. pomelos) 0.00 0.00 0.07 0.00 0.00 0.21 0.00 0.00 0.03 0.22 0.00 0.33 47. Grapes 0.00 0.00 0.00 0.00 0.00 0.29 0.00 0.00 0.40 0.40 0.00 0.11 48. Honey, natural 0.00 0.00 0.00 0.00 0.00 0.31 0.20 0.00 0.00 0.04 0.00 0.07 49. Hops 0.03 0.02 0.01 0.00 0.00 0.33 0.20 0.00 0.35 0.34 0.01 0.35 50. Jute 0.00 0.00 0.01 0.00 0.00 0.37 0.20 0.03 0.09 0.40 0.10 0.26 51. Kiwi fruit 0.06 0.00 0.01 0.00 0.00 0.29 0.08 0.00 0.16 0.39 0.00 0.35 52. Leeks, other alliaceous vegetables 0.03 0.00 0.01 0.00 0.00 0.15 0.02 0.00 0.40 0.30 0.00 0.12 53. Lemons and limes 0.03 0.00 0.07 0.00 0.00 0.34 0.00 0.00 0.03 0.21 0.00 0.34 54. Lentils 0.00 0.00 0.01 0.00 0.00 0.35 0.05 0.00 0.02 0.36 0.00 0.30 55. Lettuce and chicory 0.03 0.00 0.16 0.00 0.00 0.37 0.00 0.00 0.00 0.09 0.00 0.05 56. Linseed 0.00 0.00 0.00 0.00 0.00 0.24 0.00 0.00 0.11 0.32 0.00 0.26 57. Maize 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.00 0.00 58. Maize, green 0.01 0.00 0.13 0.00 0.00 0.33 0.26 0.00 0.00 0.37 0.00 0.00 59. Mangoes, mangosteens, guavas 0.00 0.00 0.03 0.00 0.00 0.37 0.02 0.00 0.04 0.37 0.00 0.12 60. Meat, cattle 0.00 0.00 0.00 0.00 0.00 0.19 0.00 0.00 0.33 0.38 0.00 0.13 61. Meat, chicken 0.01 0.00 0.00 0.00 0.00 0.34 0.02 0.00 0.38 0.27 0.00 0.27 62. Meat, duck 0.07 0.00 0.00 0.00 0.00 0.05 0.19 0.02 0.00 0.39 0.07 0.00 63. Meat, game 0.19 0.32 0.24 0.13 0.28 0.38 0.05 0.00 0.29 0.27 0.00 0.26 64. Meat, goat 0.43 0.04 0.21 0.00 0.00 0.29 0.00 0.00 0.03 0.38 0.00 0.00 65. Meat, goose and guinea fowl 0.28 0.24 0.24 0.00 0.00 0.26 0.13 0.00 0.05 0.39 0.00 0.00 (continued in next page)
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Table A7.5 Second Set of Cross-Country Tests for Co-integration (continued) (p-values) Kao (1999) Pedroni (2004) Item * * * DF DF Z Z Z * ρ t ADF DFρ DFt ν ρ t Zt Zρ Zt Zt (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 66. Meat, horse 0.08 0.05 0.26 0.05 0.04 0.34 0.40 0.11 0.07 0.19 0.20 0.08 67. Meat, pig 0.00 0.00 0.00 0.00 0.00 0.39 0.00 0.00 0.00 0.39 0.00 0.05 68. Meat, rabbit 0.38 0.19 0.43 0.01 0.02 0.34 0.13 0.00 0.00 0.39 0.00 0.00 69. Meat, sheep 0.14 0.00 0.32 0.00 0.00 0.23 0.04 0.00 0.18 0.15 0.00 0.40 70. Meat, turkey 0.00 0.00 0.00 0.00 0.00 0.34 0.11 0.00 0.12 0.40 0.00 0.33 71. Melons, other (inc.cantaloupes) 0.00 0.00 0.01 0.00 0.00 0.38 0.01 0.00 0.00 0.39 0.00 0.00 72. Milk, whole fresh cow 0.02 0.00 0.25 0.00 0.00 0.40 0.00 0.00 0.00 0.35 0.00 0.02 73. Millet 0.00 0.00 0.00 0.00 0.00 0.17 0.00 0.00 0.00 0.17 0.00 0.04 74. Mushrooms and truffles 0.04 0.00 0.47 0.00 0.00 0.40 0.07 0.00 0.00 0.37 0.00 0.01 75. Mustard seed 0.06 0.07 0.01 0.02 0.05 0.34 0.32 0.00 0.27 0.37 0.00 0.33 76. Nutmeg, mace and cardamoms 0.02 0.05 0.01 0.02 0.05 0.40 0.40 0.36 0.30 0.29 0.40 0.32 77. Nuts, nes 0.25 0.43 0.18 0.00 0.02 0.40 0.12 0.00 0.00 0.39 0.00 0.03 78. Oats 0.00 0.00 0.00 0.00 0.00 0.15 0.00 0.00 0.00 0.38 0.00 0.00 79. Oil, palm 0.00 0.00 0.02 0.00 0.00 0.36 0.17 0.00 0.38 0.39 0.00 0.39 80. Oilseeds nes 0.28 0.32 0.01 0.06 0.14 0.39 0.07 0.00 0.00 0.20 0.00 0.00 81. Olives 0.00 0.00 0.00 0.00 0.00 0.39 0.34 0.01 0.03 0.14 0.12 0.00 82. Onions, dry 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 83. Onions, shallots, green 0.00 0.06 0.00 0.00 0.00 0.05 0.00 0.00 0.09 0.34 0.00 0.05 84. Oranges 0.42 0.00 0.26 0.00 0.00 0.33 0.00 0.00 0.04 0.22 0.00 0.38 85. Papayas 0.07 0.05 0.29 0.00 0.00 0.12 0.00 0.00 0.09 0.22 0.00 0.40 86. Peaches and nectarines 0.00 0.00 0.05 0.00 0.00 0.28 0.00 0.00 0.02 0.00 0.00 0.26 87. Pears 0.00 0.00 0.07 0.00 0.00 0.22 0.00 0.00 0.00 0.00 0.00 0.07 88. Peas, dry 0.00 0.00 0.00 0.00 0.00 0.22 0.09 0.00 0.37 0.23 0.00 0.35 89. Peas, green 0.03 0.00 0.02 0.00 0.00 0.38 0.00 0.00 0.00 0.16 0.00 0.00 90. Pepper (piper spp.) 0.27 0.11 0.07 0.00 0.00 0.30 0.36 0.01 0.39 0.25 0.07 0.07 91. Persimmons 0.19 0.04 0.28 0.00 0.00 0.18 0.10 0.01 0.34 0.32 0.02 0.20 92. Pineapples 0.20 0.03 0.47 0.00 0.00 0.22 0.21 0.00 0.13 0.22 0.00 0.00 93. Pistachios 0.00 0.00 0.02 0.00 0.00 0.40 0.01 0.00 0.00 0.17 0.00 0.00 94. Plantains 0.03 0.00 0.18 0.00 0.00 0.40 0.03 0.00 0.32 0.38 0.00 0.03 95. Plums and sloes 0.00 0.00 0.17 0.00 0.00 0.32 0.00 0.00 0.00 0.00 0.00 0.00 96. Poppy seed 0.16 0.11 0.18 0.00 0.02 0.40 0.19 0.01 0.39 0.39 0.02 0.11 97. Potatoes 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 98. Pumpkins, squash and gourds 0.02 0.00 0.14 0.00 0.00 0.37 0.00 0.00 0.00 0.01 0.00 0.00 99. Quinces 0.04 0.00 0.26 0.00 0.00 0.40 0.00 0.00 0.00 0.10 0.00 0.07 100. Rapeseed 0.01 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.02 0.00 0.17 101. Roots and tubers, nes 0.15 0.01 0.12 0.00 0.00 0.31 0.33 0.00 0.00 0.32 0.00 0.04 102. Rubber, natural 0.36 0.49 0.44 0.18 0.35 0.21 0.26 0.02 0.14 0.34 0.06 0.32 103. Rye 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.10 0.00 0.00 104. Sesame seed 0.01 0.00 0.02 0.00 0.00 0.15 0.00 0.00 0.00 0.21 0.00 0.08 105. Silk-worm cocoons, reelable 0.35 0.08 0.00 0.09 0.02 0.39 0.40 0.15 0.00 0.24 0.30 0.00 106. Sorghum 0.00 0.00 0.00 0.00 0.00 0.08 0.00 0.00 0.00 0.01 0.00 0.03 107. Soybeans 0.00 0.00 0.00 0.00 0.00 0.09 0.00 0.00 0.00 0.15 0.00 0.00 108. Spices, nes 0.24 0.44 0.05 0.00 0.00 0.35 0.22 0.00 0.22 0.39 0.00 0.10 109. Spinach 0.07 0.42 0.11 0.00 0.00 0.17 0.00 0.00 0.30 0.22 0.00 0.40 110. Strawberries 0.00 0.00 0.00 0.00 0.00 0.32 0.00 0.00 0.03 0.39 0.00 0.19 111. Sugar beet 0.00 0.00 0.00 0.00 0.00 0.20 0.07 0.00 0.07 0.26 0.00 0.38 112. Sunflower seed 0.00 0.00 0.00 0.00 0.00 0.25 0.00 0.00 0.00 0.00 0.00 0.00 113. Sweet potatoes 0.17 0.00 0.00 0.00 0.00 0.22 0.15 0.00 0.01 0.11 0.00 0.39 114. Tangerines, mandarins 0.00 0.00 0.00 0.00 0.00 0.29 0.00 0.00 0.00 0.33 0.00 0.00 115. Tea 0.00 0.00 0.22 0.00 0.00 0.28 0.10 0.00 0.27 0.37 0.00 0.22 116. Tobacco, unmanufactured 0.12 0.13 0.45 0.01 0.03 0.38 0.39 0.00 0.06 0.00 0.19 0.18 117. Tomatoes 0.00 0.00 0.39 0.00 0.00 0.22 0.00 0.00 0.00 0.01 0.00 0.06 118. Triticale 0.03 0.00 0.00 0.00 0.00 0.32 0.00 0.00 0.10 0.19 0.00 0.05 119. Vanilla 0.06 0.09 0.22 0.06 0.09 0.36 0.32 0.10 0.40 0.39 0.16 0.40 120. Vegetables, fresh nes 0.02 0.00 0.23 0.00 0.00 0.35 0.00 0.00 0.01 0.27 0.00 0.07 121. Walnuts, with shell 0.00 0.00 0.02 0.00 0.00 0.20 0.00 0.00 0.14 0.16 0.00 0.20 122. Watermelons 0.00 0.00 0.01 0.00 0.00 0.36 0.00 0.00 0.04 0.18 0.00 0.10 123. Wheat 0.00 0.00 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.13 0.00 0.00 124. Wool, greasy 0.01 0.00 0.42 0.00 0.00 0.39 0.00 0.00 0.00 0.37 0.00 0.13 Mean 0.09 0.06 0.12 0.02 0.02 0.28 0.09 0.02 0.11 0.25 0.03 0.14 Trade share-weighted mean 0.05 0.02 0.08 0.00 0.01 0.23 0.04 0.00 0.11 0.22 0.01 0.14 Median 0.01 0.00 0.02 0.00 0.00 0.32 0.02 0.00 0.03 0.29 0.00 0.08 SD 0.13 0.12 0.14 0.07 0.06 0.11 0.13 0.05 0.14 0.14 0.08 0.15 Max 0.46 0.49 0.47 0.49 0.38 0.40 0.40 0.36 0.40 0.40 0.40 0.40 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Notes: This table reports the p-values of 12 tests for panel co-integration as proposed by Kao (1999) and Pedroni (2004). The null is that all panels exhibit no co-integration, while the alternative is all panels are co-integrated. See Table A7.1 for details.
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Table A7.6 Cross-Commodity Tests for Co-integration (p-values)
Country G τ Gθ Pτ Pθ Country (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1. Albania 0.00 0.04 0.00 0.00 67. Lithuania 0.00 0.00 0.00 0.04 2. Algeria 0.00 0.04 0.00 0.00 68. Madagascar 0.04 0.89 0.42 0.73 3. Ant. & Barb. 0.06 0.92 0.97 0.92 69. Malawi 0.00 0.12 0.00 0.01 4. Argentina 0.00 0.92 0.00 0.85 70. Malaysia 0.00 0.55 0.00 0.07 5. Armenia 0.00 0.52 0.00 0.00 71. Mali 0.00 0.70 0.00 0.04 6. Australia 0.00 0.00 0.00 0.00 72. Malta 0.00 0.00 0.00 0.00 7. Austria 0.00 0.00 0.00 0.00 73. Mauritius 0.00 0.31 0.00 0.05 8. Azerbaijan 0.00 0.00 0.03 0.00 74. Mexico 0.00 0.00 0.00 0.00 9. Bangladesh 0.00 0.89 0.00 0.00 75. Mongolia 0.00 0.47 0.01 0.57 10. Barbados 0.49 0.97 0.08 0.70 76. Morocco 0.00 0.00 0.00 0.00 11. Belarus 0.00 0.78 0.00 0.26 77. Mozambique 0.00 0.99 0.02 0.16 12. Bhutan 0.00 0.68 0.00 0.21 78. Namibia 0.03 0.92 0.01 0.63 13. Bolivia 0.00 1.00 0.00 0.77 79. Nepal 0.00 0.53 0.00 0.01 14. Bosn. & Herz. 0.00 0.62 0.00 0.09 80. Netherlands 0.00 0.01 0.00 0.00 15. Brazil 0.00 0.25 0.05 0.85 81. New Zealand 0.00 0.04 0.00 0.00 16. Bulgaria 0.00 0.03 0.00 0.02 82. Nicaragua 0.00 1.00 0.04 1.00 17. Burkina Faso 0.15 0.85 0.25 0.47 83. Niger 0.00 0.75 0.00 0.46 18. Burundi 0.00 0.97 0.00 0.12 84. Nigeria 0.00 0.00 0.00 0.00 19. Cote d'Ivoire 0.00 0.79 0.00 0.08 85. Norway 0.00 0.00 0.00 0.02 20. Cabo Verde 0.00 0.10 0.00 0.01 86. Palestine 0.00 0.99 0.00 0.65 21. Cambodia 0.00 0.52 0.08 0.62 87. Pakistan 0.00 0.15 0.00 0.00 22. Cameroon 0.36 0.60 0.33 0.57 88. Panama 0.00 0.98 0.58 0.96 23. Canada 0.00 0.02 0.00 0.00 89. Paraguay 0.00 0.16 0.00 0.03 24. Chile 0.00 0.22 0.00 0.00 90. Peru 0.00 0.46 0.00 0.28 25. China 0.00 0.92 0.00 0.21 91. Philippines 0.00 0.00 0.00 0.00 26. Colombia 0.00 0.03 0.00 0.00 92. Poland 0.00 0.00 0.00 0.00 27. Congo 0.00 0.11 0.00 0.00 93. Portugal 0.00 0.00 0.00 0.00 28. Cook Islands 0.00 0.88 0.01 0.51 94. Puerto Rico 0.00 0.99 0.16 0.91 29. Costa Rica 0.00 0.80 0.00 0.10 95. Republic of Korea 0.00 0.12 0.00 0.03 30. Croatia 0.00 0.01 0.00 0.00 96. Republic of Moldova 0.00 0.00 0.00 0.00 31. Cyprus 0.00 0.06 0.00 0.00 97. Romania 0.00 0.00 0.00 0.00 32. Czech 0.00 0.00 0.00 0.00 98. Russian Federation 0.00 0.00 0.00 0.00 33. Denmark 0.00 0.00 0.00 0.00 99. Rwanda 0.00 0.98 0.00 0.49 34. Dominican Republic 0.00 0.33 0.00 0.01 100. Saint Lucia 0.00 1.00 0.76 0.99 35. Ecuador 1.00 1.00 1.00 1.00 101. Saudi Arabia 0.25 1.00 0.01 0.39 36. Egypt 0.00 0.43 0.00 0.12 102. Senegal 0.00 0.15 0.00 0.00 37. El Salvador 0.00 0.56 0.00 0.09 103. Singapore 0.00 0.74 0.00 0.39 38. Estonia 0.00 0.00 0.00 0.00 104. Slovakia 0.00 0.00 0.00 0.00 39. Ethiopia 0.07 1.00 0.05 0.67 105. Slovenia 0.00 0.00 0.00 0.00 40. Fiji 0.00 0.81 0.00 0.17 106. South Africa 0.00 0.00 0.00 0.00 41. Finland 0.00 0.94 0.20 0.85 107. Spain 0.00 0.00 0.00 0.00 42. France 0.00 0.00 0.00 0.00 108. Sri Lanka 0.00 1.00 0.00 0.66 43. Gambia 0.00 0.19 0.00 0.04 109. Sudan (former) 0.00 0.00 0.00 0.00 44. Georgia 0.00 0.62 0.00 0.00 110. Suriname 0.00 1.00 0.00 0.67 45. Germany 0.00 0.00 0.00 0.00 111. Sweden 0.00 0.19 0.00 0.01 46. Ghana 0.02 0.98 0.00 0.66 112. Switzerland 0.00 0.00 0.00 0.00 47. Greece 0.00 0.09 0.00 0.00 113. Tajikistan 0.01 0.47 0.03 0.41 48. Guinea 0.00 1.00 0.46 0.82 114. Thailand 0.00 0.03 0.00 0.00 49. Honduras 0.00 1.00 0.38 0.88 115. Macedonia 0.00 0.00 0.00 0.00 50. Hungary 0.00 0.00 0.00 0.00 116. Togo 0.00 0.10 0.00 0.00 51. Iceland 0.00 0.24 0.00 0.03 117. Trinidad and Tobago 0.01 0.80 0.00 0.31 52. India 0.00 0.99 0.18 0.93 118. Tunisia 0.00 0.16 0.00 0.00 53. Indonesia 0.00 0.01 0.00 0.01 119. Turkey 0.00 0.00 0.00 0.00 54. Iran 0.00 1.00 0.00 0.94 120. Ukraine 0.00 0.00 0.00 0.00 55. Ireland 0.06 0.65 0.03 0.27 121. United Kingdom 0.00 0.96 0.03 0.97 56. Israel 0.00 0.06 0.00 0.00 122. United States 0.00 0.94 0.00 0.14 57. Italy 0.00 0.08 0.00 0.00 123. Uruguay 0.00 0.00 0.00 0.00 58. Jamaica 0.00 0.96 0.00 0.85 124. Venezuela 0.00 0.93 0.00 0.23 59. Japan 0.00 0.55 0.00 0.01 125. Viet Nam 0.99 1.00 0.95 0.98 60. Jordan 0.00 0.59 0.00 0.00 126. Yemen 0.03 1.00 0.95 0.98 61. Kazakhstan 0.00 0.00 0.00 0.00 Summary Statistics 62. Kenya 0.00 0.96 0.00 0.46 Mean 0.03 0.44 0.07 0.25 63. Kyrgyzstan 0.00 0.01 0.00 0.03 Median 0.00 0.32 0.00 0.03 64. Lao 0.01 0.84 0.01 0.55 SD 0.14 0.41 0.20 0.35 65. Latvia 0.00 0.00 0.00 0.00 Min 0.00 0.00 0.00 0.00 66. Lebanon 0.00 1.00 0.17 1.00 Max 1.00 1.00 1.00 1.00 Notes: This table reports the p-values of the four tests for panel co-integration as proposed by Westerlund (2007).
Columns 2, 3, 7 and 8 are the group-mean statistics, and , which test for H:0iθ (the ECT coefficient) = 0 against
H:0iθ0 for at least one i. Columns 4, 5, 9, 10 are the panel statistics, Pτ and Pθ , which test for H:0iθ0 against
H:0iθ 0 i .
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A-41
Table A7.7 Second Set of Cross-Commodity Tests for Co-integration (p-values)
Kao (1999) Pedroni (2004) Country * DF DF * Z Z Z * * ρ t ADF DFρ DFt ν ρ t Zt Zρ Zt Zt (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 1. Albania 0.00 0.00 0.00 0.00 0.00 0.17 0.29 0.00 0.00 0.24 0.00 0.01 2. Algeria 0.02 0.00 0.01 0.00 0.00 0.36 0.01 0.00 0.00 0.39 0.00 0.26 3. Antigua and Barbuda . . . 0.40 0.40 0.19 0.15 0.34 0.19 0.03 0.17 0.16 4. Argentina 0.00 0.00 0.00 0.00 0.00 0.34 0.01 0.00 0.34 0.39 0.00 0.30 5. Armenia 0.24 0.16 0.01 0.00 0.00 0.02 0.00 0.00 0.08 0.39 0.00 0.40 6. Australia 0.00 0.00 0.00 0.00 0.00 0.39 0.00 0.00 0.00 0.00 0.00 0.00 7. Austria 0.29 0.00 0.00 0.00 0.00 0.24 0.00 0.00 0.00 0.19 0.00 0.00 8. Azerbaijan 0.15 0.00 0.09 0.11 0.00 0.31 0.15 0.00 0.00 0.17 0.00 0.00 9. Bangladesh 0.20 0.03 0.07 0.00 0.00 0.20 0.00 0.00 0.00 0.21 0.00 0.20 10. Barbados . . . 0.00 0.00 0.22 0.16 0.01 0.05 0.39 0.04 0.09 11. Belarus 0.00 0.00 0.00 0.00 0.00 0.09 0.00 0.00 0.39 0.01 0.00 0.03 12. Bhutan 0.07 0.12 0.18 0.03 0.03 0.37 0.05 0.00 0.27 0.34 0.00 0.00 13. Bolivia 0.14 0.17 0.08 0.00 0.00 0.35 0.08 0.00 0.16 0.14 0.00 0.02 14. Bosnia and Herzegovina 0.02 0.00 0.46 0.00 0.00 0.10 0.00 0.00 0.09 0.37 0.00 0.00 15. Brazil 0.27 0.16 0.44 0.00 0.00 0.13 0.00 0.00 0.00 0.22 0.00 0.01 16. Bulgaria 0.44 0.00 0.48 0.00 0.00 0.08 0.02 0.00 0.38 0.34 0.00 0.36 17. Burkina Faso 0.22 0.29 0.34 0.00 0.03 0.22 0.34 0.00 0.24 0.33 0.04 0.40 18. Burundi 0.33 0.47 0.19 0.01 0.04 0.29 0.01 0.00 0.38 0.38 0.00 0.22 19. Cabo Verde 0.05 0.03 0.35 0.00 0.00 0.32 0.05 0.00 0.33 0.40 0.00 0.40 20. Cambodia 0.38 0.05 0.34 0.00 0.00 0.20 0.04 0.00 0.02 0.40 0.00 0.18 21. Cameroon 0.17 0.13 0.12 0.01 0.04 0.15 0.21 0.00 0.05 0.36 0.02 0.01 22. Canada 0.01 0.00 0.01 0.00 0.00 0.39 0.36 0.06 0.23 0.29 0.08 0.08 23. Chile 0.01 0.00 0.23 0.00 0.00 0.38 0.00 0.00 0.00 0.00 0.00 0.00 24. China 0.04 0.01 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.00 0.00 0.00 25. Colombia 0.10 0.00 0.07 0.00 0.00 0.35 0.00 0.00 0.00 0.38 0.00 0.00 26. Congo 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 0.01 0.03 0.00 0.00 27. Cook Islands 0.05 0.08 0.16 0.35 0.44 0.04 0.09 0.00 0.00 0.32 0.00 0.00 28. Costa Rica 0.35 0.11 0.47 0.13 0.05 0.07 0.39 0.00 0.03 0.36 0.00 0.03 29. Croatia 0.00 0.00 0.00 0.00 0.00 0.33 0.00 0.00 0.00 0.05 0.00 0.00 30. Cyprus 0.00 0.00 0.06 0.00 0.00 0.06 0.00 0.00 0.00 0.05 0.00 0.00 31. Czechia 0.00 0.00 0.20 0.00 0.00 0.40 0.00 0.00 0.00 0.05 0.00 0.00 32. Cote d'Ivoire 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 0.29 0.18 0.00 0.35 33. Denmark 0.00 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.07 0.00 0.00 34. Dominican Republic 0.20 0.00 0.43 0.00 0.00 0.34 0.00 0.00 0.00 0.06 0.00 0.00 35. Ecuador . . . 0.31 0.00 0.35 0.00 0.03 0.00 0.00 0.00 0.00 36. Egypt 0.00 0.00 0.00 0.00 0.00 0.03 0.01 0.00 0.28 0.39 0.00 0.38 37. El Salvador . . . 0.00 0.00 0.08 0.00 0.00 0.01 0.32 0.00 0.17 38. Estonia 0.00 0.00 0.00 0.00 0.00 0.39 0.00 0.00 0.00 0.02 0.00 0.00 39. Ethiopia 0.00 0.00 0.00 0.00 0.00 0.22 0.02 0.00 0.04 0.40 0.00 0.05 40. Fiji 0.05 0.25 0.00 0.00 0.00 0.40 0.33 0.00 0.00 0.14 0.00 0.00 41. Finland 0.11 0.00 0.00 0.00 0.00 0.39 0.26 0.00 0.03 0.15 0.02 0.12 42. France 0.00 0.00 0.18 0.00 0.00 0.36 0.00 0.00 0.00 0.00 0.00 0.00 43. Gambia 0.00 0.00 0.07 0.00 0.00 0.39 0.00 0.00 0.01 0.12 0.00 0.03 44. Georgia 0.04 0.00 0.21 0.00 0.00 0.39 0.01 0.00 0.02 0.36 0.00 0.00 45. Germany 0.00 0.00 0.00 0.00 0.00 0.37 0.00 0.00 0.00 0.01 0.00 0.00 46. Ghana 0.13 0.01 0.09 0.00 0.00 0.40 0.02 0.00 0.34 0.37 0.00 0.12 47. Greece 0.01 0.00 0.07 0.00 0.00 0.38 0.00 0.00 0.23 0.26 0.00 0.11 48. Guinea 0.36 0.18 0.30 0.00 0.01 0.29 0.17 0.00 0.29 0.39 0.00 0.07 49. Honduras 0.00 0.00 0.07 0.00 0.00 0.38 0.11 0.00 0.08 0.33 0.00 0.07 50. Hungary 0.00 0.00 0.01 0.00 0.00 0.26 0.00 0.00 0.00 0.00 0.00 0.00 51. Iceland 0.00 0.00 0.00 0.00 0.00 0.38 0.01 0.00 0.00 0.32 0.00 0.21 52. India 0.10 0.00 0.00 0.00 0.00 0.15 0.37 0.00 0.01 0.13 0.00 0.00 53. Indonesia 0.01 0.01 0.30 0.00 0.00 0.00 0.00 0.00 0.01 0.30 0.00 0.00 54. Iran 0.00 0.00 0.00 0.00 0.00 0.38 0.00 0.00 0.00 0.35 0.00 0.38 55. Ireland 0.01 0.00 0.02 0.00 0.00 0.19 0.27 0.01 0.31 0.35 0.01 0.40 56. Israel 0.23 0.01 0.14 0.00 0.00 0.31 0.00 0.00 0.00 0.04 0.00 0.00 57. Italy 0.00 0.00 0.01 0.00 0.00 0.37 0.00 0.00 0.31 0.37 0.00 0.24 58. Jamaica 0.00 0.00 0.05 0.00 0.00 0.19 0.02 0.00 0.21 0.37 0.00 0.34 59. Japan 0.09 0.01 0.00 0.00 0.00 0.09 0.00 0.00 0.00 0.12 0.00 0.00 60. Jordan 0.00 0.00 0.11 0.00 0.00 0.39 0.00 0.00 0.00 0.00 0.00 0.00 61. Kazakhstan 0.00 0.02 0.05 0.00 0.02 0.11 0.02 0.00 0.38 0.39 0.00 0.37 62. Kenya 0.00 0.00 0.00 0.00 0.00 0.21 0.01 0.00 0.24 0.34 0.00 0.31 63. Kyrgyzstan 0.01 0.00 0.13 0.00 0.00 0.26 0.08 0.00 0.00 0.32 0.00 0.05 64. Lao 0.27 0.36 0.07 0.33 0.42 0.33 0.04 0.00 0.00 0.35 0.00 0.01 65. Latvia 0.00 0.00 0.00 0.00 0.00 0.19 0.00 0.00 0.25 0.12 0.00 0.31 (continued in next page)
SUPPLEMENTARY MATERIALS
A-42 Table A7.7 Second Set of Cross-Commodity Tests for Co-integration (continued) (p-values)
Kao (1999) Pedroni (2004) Country * DF DF * Z Z Z * * ρ t ADF DFρ DFt ν ρ t Zt Zρ Zt Zt (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 66. Lebanon 0.11 0.00 0.13 0.00 0.00 0.01 0.02 0.00 0.22 0.31 0.00 0.02 67. Lithuania 0.00 0.00 0.01 0.00 0.00 0.25 0.00 0.00 0.00 0.24 0.00 0.40 68. Madagascar 0.13 0.02 0.01 0.00 0.00 0.39 0.14 0.00 0.38 0.39 0.00 0.28 69. Malawi 0.02 0.00 0.04 0.00 0.00 0.25 0.11 0.00 0.00 0.39 0.00 0.00 70. Malaysia 0.01 0.00 0.11 0.00 0.00 0.40 0.00 0.00 0.03 0.28 0.00 0.07 71. Mali 0.32 0.35 0.43 0.00 0.00 0.27 0.01 0.00 0.00 0.39 0.00 0.01 72. Malta 0.00 0.00 0.17 0.00 0.00 0.16 0.00 0.00 0.29 0.02 0.00 0.24 73. Mauritius 0.21 0.01 0.01 0.00 0.00 0.40 0.00 0.00 0.00 0.04 0.00 0.00 74. Mexico 0.00 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.05 0.00 0.00 75. Mongolia 0.00 0.00 0.00 0.00 0.00 0.36 0.19 0.00 0.31 0.38 0.00 0.19 76. Morocco 0.00 0.00 0.01 0.00 0.00 0.40 0.00 0.00 0.00 0.25 0.00 0.06 77. Mozambique 0.00 0.00 0.00 0.00 0.00 0.40 0.39 0.01 0.16 0.20 0.06 0.12 78. Namibia 0.00 0.02 0.11 0.00 0.02 0.18 0.40 0.06 0.40 0.32 0.05 0.38 79. Nepal 0.02 0.00 0.00 0.00 0.00 0.28 0.05 0.00 0.03 0.40 0.00 0.05 80. Netherlands 0.00 0.00 0.07 0.00 0.00 0.40 0.00 0.00 0.01 0.02 0.00 0.05 81. New Zealand 0.00 0.00 0.28 0.00 0.00 0.11 0.00 0.00 0.01 0.07 0.00 0.37 82. Nicaragua 0.00 0.00 0.00 0.00 0.00 0.15 0.02 0.00 0.39 0.38 0.00 0.37 83. Niger 0.19 0.50 0.02 0.09 0.05 0.07 0.23 0.00 0.00 0.30 0.00 0.03 84. Nigeria 0.00 0.00 0.00 0.00 0.00 0.23 0.00 0.00 0.00 0.19 0.00 0.00 85. Norway 0.11 0.27 0.38 0.00 0.00 0.40 0.00 0.00 0.00 0.09 0.00 0.00 86. Occupied Palestinian Territory . . . 0.00 0.00 0.00 0.01 0.00 0.26 0.39 0.00 0.00 87. Pakistan 0.38 0.06 0.08 0.00 0.00 0.21 0.00 0.00 0.01 0.21 0.00 0.06 88. Panama . . . 0.00 0.00 0.04 0.24 0.00 0.09 0.26 0.02 0.09 89. Paraguay 0.10 0.01 0.17 0.00 0.00 0.29 0.02 0.00 0.00 0.40 0.00 0.39 90. Peru 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.40 0.00 0.02 91. Philippines 0.00 0.00 0.05 0.00 0.00 0.28 0.00 0.00 0.00 0.00 0.00 0.00 92. Poland 0.00 0.00 0.00 0.00 0.00 0.27 0.00 0.00 0.00 0.00 0.00 0.00 93. Portugal 0.04 0.00 0.14 0.00 0.00 0.19 0.00 0.00 0.00 0.00 0.00 0.00 94. Puerto Rico . . . 0.00 0.00 0.07 0.39 0.01 0.40 0.05 0.15 0.28 95. Republic of Korea 0.28 0.01 0.09 0.00 0.00 0.08 0.04 0.00 0.01 0.26 0.00 0.31 96. Republic of Moldova 0.00 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.10 0.00 0.26 97. Romania 0.00 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.40 0.00 0.00 0.08 98. Russian Federation 0.00 0.00 0.00 0.00 0.00 0.09 0.00 0.00 0.01 0.01 0.00 0.07 99. Rwanda 0.03 0.00 0.00 0.00 0.00 0.35 0.01 0.00 0.18 0.30 0.00 0.01 100. Saint Lucia . . . 0.00 0.00 0.02 0.39 0.00 0.35 0.09 0.09 0.30 101. Saudi Arabia 0.24 0.49 0.33 0.01 0.01 0.15 0.36 0.02 0.00 0.05 0.15 0.00 102. Senegal 0.35 0.09 0.05 0.00 0.00 0.38 0.01 0.00 0.22 0.32 0.00 0.33 103. Singapore 0.12 0.42 0.02 0.00 0.00 0.34 0.22 0.00 0.09 0.39 0.00 0.38 104. Slovakia 0.00 0.00 0.00 0.00 0.00 0.28 0.00 0.00 0.34 0.20 0.00 0.08 105. Slovenia 0.05 0.00 0.38 0.00 0.00 0.40 0.00 0.00 0.00 0.00 0.00 0.00 106. South Africa 0.00 0.00 0.33 0.00 0.00 0.20 0.00 0.00 0.00 0.00 0.00 0.00 107. Spain 0.00 0.00 0.00 0.00 0.00 0.32 0.00 0.00 0.00 0.01 0.00 0.00 108. Sri Lanka 0.14 0.04 0.08 0.00 0.00 0.17 0.00 0.00 0.00 0.35 0.00 0.00 109. Sudan (former) 0.14 0.01 0.11 0.00 0.00 0.39 0.00 0.00 0.00 0.03 0.00 0.01 110. Suriname 0.00 0.00 0.00 0.00 0.00 0.15 0.00 0.00 0.00 0.00 0.00 0.36 111. Sweden 0.04 0.00 0.04 0.00 0.00 0.40 0.02 0.00 0.00 0.39 0.00 0.00 112. Switzerland 0.04 0.29 0.00 0.00 0.00 0.18 0.00 0.00 0.00 0.00 0.00 0.00 113. Tajikistan 0.41 0.30 0.37 0.00 0.00 0.39 0.11 0.00 0.33 0.29 0.00 0.13 114. Thailand 0.34 0.01 0.25 0.00 0.00 0.35 0.00 0.00 0.00 0.13 0.00 0.00 115. Macedonia 0.00 0.00 0.02 0.00 0.00 0.11 0.00 0.00 0.00 0.00 0.00 0.00 116. Togo 0.05 0.00 0.00 0.00 0.00 0.30 0.02 0.00 0.00 0.26 0.00 0.00 117. Trinidad and Tobago 0.26 0.22 0.13 0.00 0.02 0.27 0.00 0.00 0.16 0.22 0.00 0.39 118. Tunisia 0.00 0.00 0.03 0.00 0.00 0.22 0.00 0.00 0.00 0.00 0.00 0.00 119. Turkey 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.13 0.00 0.00 120. Ukraine 0.00 0.00 0.00 0.00 0.00 0.39 0.00 0.00 0.05 0.10 0.00 0.03 121. United Kingdom 0.39 0.18 0.12 0.00 0.00 0.01 0.04 0.00 0.30 0.39 0.00 0.40 122. United States of America . . . 0.00 0.00 0.00 0.00 0.00 0.00 0.17 0.00 0.15 123. Uruguay 0.00 0.00 0.00 0.00 0.00 0.30 0.00 0.00 0.00 0.01 0.00 0.00 124. Venezuela 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.29 0.00 0.01 125. Viet Nam 0.00 0.00 0.06 0.00 0.00 0.24 0.17 0.01 0.28 0.39 0.06 0.06 126. Yemen 0.00 0.00 0.00 0.00 0.00 0.02 0.01 0.00 0.00 0.38 0.00 0.00 Mean 0.08 0.05 0.10 0.01 0.01 0.25 0.06 0.00 0.10 0.21 0.01 0.11 Trade share-weighted mean 0.05 0.02 0.09 0.00 0.00 0.23 0.03 0.00 0.05 0.16 0.00 0.08 Median 0.01 0.00 0.04 0.00 0.00 0.27 0.00 0.00 0.01 0.23 0.00 0.03 SD 0.12 0.11 0.13 0.06 0.06 0.13 0.11 0.03 0.14 0.15 0.03 0.14 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 0.44 0.50 0.48 0.40 0.44 0.40 0.40 0.34 0.40 0.40 0.17 0.40 Notes: This table reports the p-values of 12 tests for panel co-integration as proposed by Kao (1999) and Pedroni (2004). The null is that all panels exhibit no co-integration, while the alternative is all panels are co-integrated. For cases indicated by a dot (.), data are insufficient to reliably compute some test statistics.