The Choice of Exchange Rate Regimes Redux: Complete Literature Review, Theoretical Study
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The Choice of Exchange Rate Regimes Redux: Complete Literature Review, Theoretical Study and Simulation Analysis
Chung-Fu Lai (賴宗福)
佛光大學經濟學系
主要通訊作者：賴宗福
聯絡住址：26247 宜蘭縣礁溪鄉 林美村林尾路一六○號
電話：(03) 9871000 # 23515
電子信箱：[email protected] The Choice of Exchange Rate Regimes Redux: Complete Literature Review, Theoretical Study and Simulation Analysis
Chung-Fu Lai* Department of Economics, Fo Guang University, Taiwan
This paper extends the New Open Economy Macroeconomics (NOEM) model setup of Devereux and Engel (1998) to investigate how consumption home bias, capital mobility, and price-setting behavior affect the consumption volatility, expected level of consumption, and the welfare performance under alternative exchange rate regimes for a country facing foreign monetary shock, then to discuss the issue of exchange rate regime choice. According to the analysis of theoretical derivation and simulation results, the following conclusions were made. Firstly, the variance of domestic consumption is lower in pricing-to-market (PTM) model, and the variance of consumption with producer-currency pricing (PCP) model depends on the degree of capital mobility, the share of tradable goods, and the degree of home bias. Secondly, the fixed exchange rate will dominate floating exchange rate in terms of the expected level of consumption. Thirdly, floating exchange rate is preferable to fixed exchange rate from the perspective of welfare performance, and the higher degree of the home bias and incomplete capital mobility induced a higher level of welfare under alternative exchange rate regimes.
Keywords: home bias, capital mobility, price-setting behavior, exchange rate regimes, new open economy macroeconomics JEL Classification: F33, F41, F55
*Assistant Professor of Department of Economics, Fo Guang University, No.160, Linwei Rd., Jiaosi Shiang, Yilan County 26247, Taiwan, R.O.C. Tel: 886–3–9871000 ext. 23515; E-mail: [email protected].
2 1 Introduction
The openness of capital market and the liberalization of financial transaction are beneficial for the economic development of the country, but the sudden change of flow direction of tremendous capital will shock the stability of the economy under alternative exchange rate regimes. In the environment of full capital mobility, countries that adopt floating exchange rates are worried about the international competitiveness of exporting firms while those adopting fixed exchange rates must afford the opportunity cost of offsetting and accumulating foreign exchange reserve. On the other hand, when the capital flow suddenly stops, countries imposing fixed exchange rates would worry that if they have enough foreign exchange reserve to offset the risk of market speculation, and countries of floating exchange rates will have to afford the relevant costs of depreciation, for example, the increasing prices of imported goods can trigger inflation and increase foreign debt burden. Therefore, understanding the effects of the change of capital mobility in different exchange rate regimes will be helpful in responding to the influence of international capital flow on domestic economy. What is more, the transmission mechanism of the implement of government policies and the change of external environment on economic variables will vary in different exchange rate regimes. In the case of fixed exchange rates, the impact of exogenous changes on economy is transmitted through domestic price index in the long-run while in the case of floating exchange rates, it is through nominal exchange rate, and the non-tradable goods, home bias and pricing-to-market (PTM) are important factors which affect transmission effect. Therefore, knowledge of the influence of these factors in different exchange rate regimes will help relevant government departments make effective policies. The above observations trigger the motivation of this paper. The research on the choice of exchange rate regimes traces back to Friedman
3 (1953), who argued that floating exchange rate system can provide effective insulation from foreign shocks, and Mundell (1960; 1961a; 1961b; 1963) who thought that the insulation function of floating exchange rate would diminish under the circumstance of perfect capital mobility. Hereafter, the issue is gaining more and more attention gradually. Through an overview of previous relevant research, it can be found that the existing literatures mainly concentrate on the influence of the following specific factors on the choice of exchange rate regimes: labor mobility (Mundell, 1961a), the degree of openness (McKinnon, 1963), the diversification of commodity categories (Kenen, 1969), the source of economic shocks (Flood, 1979; Roper and Turnovsky, 1980), the extent of currency substitution (Chen and Tsaur, 1983), shock asymmetry (Bayoumi and Eichengree, 1993), trade intensity (Frankel and Rose, 1998), the price-setting behavior (Devereux and Engel, 1998), the types of expectation (Flood and Marion, 1982), and the capital mobility (Flood, 1979; Ogawa and Sun, 2001). Though there are many relevant researches, few uses complete model to illustrate the impact effects of many different factors under alternative exchange rate systems, which diminish their value as references in policies making. The classic works of Mundell (1960; 1961a; 1961b; 1963) and Fleming (1962) have innovative contributions. Based on Keynes theory, they supposed that there exist some distortions in economy and used the features of price rigidity or price stickiness to analyze the issue of choice of exchange rate regimes. The hypothesis of price stickiness or wage rigidity was widely adopted by the subsequent relevant research. Papers like those written by Turnovsky (1976; 1983), Fischer (1977), Hamada and Sakurai (1978), Flood (1979), Weber (1981), Flood and Marion (1982), Kimbrough (1983), Aizenman and Frenkel (1985) and Glick and Wihlborg (1990). However, most of these papers lack micro-foundations and adopted the ad hoc setting. Therefore, in order to make up the lack of micro-foundations, research on the choice of exchange rate regimes after 1980s started to analyze and compare alterative exchange rate regimes from the viewpoint of welfare maximization. Research includes those made by Lapan and Enders (1980), Helpman (1981), Helpman and Razin (1982), Aizenman (1994), Chin and Miller (1998) and Neumeyer (1998). However, although these researches incorporated micro-
4 foundations, they ignored the important features of price stickiness.1 Accordingly, in recent times, there have been more and more papers researching the choice of exchange rate regimes under the New Open Economy Macroeconomics (NOEM). Basing on the NOEM theory of Obstfeld and Rogoff (1995), Devereux and Engel (1998) tried to build the pricing-to-market model and discussed the advantages and disadvantages of different exchange rate regimes through welfare maximization method under the setting of price stickiness. It was found out that if producers set prices in their currency, there exists trade-off relationship between fixed and floating exchange rates. The variance of domestic consumption is lower under floating exchange rates, but the expected level of consumption is also reduced. While under the fixed exchange rates, though the variance of domestic consumption is higher, the expected consumption is also higher. It was also found under the environment of pricing-to-market, the floating exchange rate is always preferable to the fixed exchange rate. Obstfeld and Rogoff (2002) used a relatively simplified two-period model to analyze the impact of countries facing the productivity shock while the countries separately adopted the floating exchange rate regime, fixed exchange rate regime and monetary union. It is found that among these three kinds of exchange rate regimes, floating exchange rate is the optimal monetary policy since it is self-oriented and is not affected by other countries’ monetary policies, and so there is no need for international policy coordination. While other literatures, such as Devereux et al. (2005), Corsetti (2006), Bergin et al. (2007) and Elekdag and Tchakarov (2007) also emphasizes the importance of micro-foundations and price rigidity in the issue of exchange rate regimes choice.2 In the NOEM framework, controversies on the issue of the choice of exchange rate regimes center on the viewpoint of Friedman (1953), who argued that
1The setting of price stickiness facilitates researchers’ analysis of the adjustment process of economic dynamics. 2 Devereux et al.(2005) explores the effects of monetary policies and price-setting behavior under different kinds of exchange rate regimes; Corsetti (2006) analyzes the degree of openness and the choice of exchange rate regimes. Bergin et al.(2007) researched the effect of exchange rate risk on welfare; Elekdag and Tchakarov (2007) concentrate on the effects of external debt ratio on welfare under different exchange rate regimes.
5 floating exchange rates can weaken expenditure switching effect holding that exchange rates can be completely passed through. He concluded that the floating exchange rate is better than the fixed exchange rate. But the completely exchange rate pass-through he stressed was not supported by Engel (1993) and Parsley and Wei (2001). The empirical results showed that the price hardly responses to exchange rates and the expenditure switching effect is insignificant. Betts and Devereux (1996; 2000) and Devereux and Engel (1998) further believed that local- currency pricing (LCP) is one of the factors that caused the incomplete pass-through of exchange rates. They even incorporated LCP on the basis of NOEM and explored a country’s optimal exchange rate regime when facing productivity shock. The results showed that LCP will weaken the pass-through and expenditure switching effects of exchange rates and the benefits of floating exchange rate system will be substantially diminished. Moreover, the floating exchange rate system can potentially affect price stability, so the fixed exchange rate system is thought as the optimal monetary policy (see Devereux and Engel, 2003). But this conclusion was immediately rebutted by Obstfeld (2006). On the theoretical basis of Devereux and Engel (2003), Obstfeld (2006) integrated non-tradable goods into the NOEM framework, trying to emphasize the incomplete pass-through feature of exchange rates and re-explore the issue of optimal exchange rate regime. The paper found that in the face of productivity shock, floating exchange rate system is the optimal monetary policy for monetary authorities that adopt interest rate rule. He thought that even without the expenditure switching effect, to let the exchange rates float can reserve for interest rates to adjust freely and thus serve as a tool to stabilize the economy. Duarte and Obstfeld (2007) further proved that even for monetary authorities that adopt monetary rule, the optimal monetary policy is still the floating exchange rate regime. Although the above literatures and discussion further developed the NOEM theory, they all ignored the roles of consumption home bias and capital mobility. Under different exchange rate regimes, the transmission channels of foreign shock affect the economy may not be the same, but what is common is that home bias and capital mobility are of remarkable importance in the transmission process. Therefore it would be unsatisfactory if these factors are not
6 discussed in more details. Early researches on issue of consumption home bias mostly centered on the reasons why this bias occur. The so called consumption home bias puzzle means that in the real world, the consumers have the tendency of preferring domestic products, which researchers failed to explain. Obstfeld and Rogoff (2000b) referred to this puzzle as one of the six puzzles in the international economics,3 then the transportation costs (Obstfeld and Rogoff, 2000b; Ried, 2009), the scale and degree of openness (Sutherland, 2005; De Paoli, 2009), non-tradable goods (Stockman and Dellas, 1989; Pesenti and Wincoop, 2002), trade of intermediate input (Hillberry and Hummels, 2002) are considered by scholars as the reasons that cause consumption home bias in the subsequent works, papers of this area mostly supposed that consumption home bias is an endogenous variable while recently researches focused on the impact of consumption home bias behavior on economy and presented the home bias in exogenous form. For example, Pierdzioch (2004) analyzed the impact of monetary shock under different degree of home bias and capital mobility, Hau (2002), Pitterle and Steffen (2004), Kollmann (2004), Sutherland (2005), Leith and Lewis (2006) and Cooke (2010) explored the influence of consumption home bias on exchange rate fluctuations, while De Paoli (2009) discussed the degree of home bias and the welfare effects of monetary policy. Besides, recently the relationship between consumption home bias and the optimal monetary policy is a quite popular topic. Relevant researches includes Faia and Monacelli (2006), Jondeau and Sahuc (2008), Galí and Monacelli (2008) and Wang (2010). It is clear that reasons that cause consumption home bias and its impact belong to two different areas of research. Since no current literature can clearly explain the impact of consumption home bias in the issue of the choice of exchange rate regimes, this paper tend to discuss the latter and regard the home bias as exogenous parameter. NOEM has a history of fifteen years since the time it was proposed by Obstfeld and Rogoff (1995). Since then, numerous scholars has expanded this framework and
3The six puzzles listed by Obstfeld and Rogoff (2000b) respectively are: consumption home bias puzzle, home bias in equity portfolios puzzle, purchasing power parity puzzle, exchange rate disconnect puzzle, the high investment-saving correlation puzzle, the low international consumption correlation puzzle.
7 published their article on related journals. For example, Sutherland (1996) analyzed the effects of transaction costs; Kollmann (1997) expanded and explored the ways of price adjustment; Lane (1997) adjusted NOEM framework into small open economy model; Obstfeld and Rogoff (1998; 2000a) incorporated random disturbance process into the NOEM model; Betts and Devereux (2000) discussed the importance of pricing-to-market; Fender and Yip (2000) analyzed the impact of tariff policies on economic variables; Hau (20007) explained the function of price rigidity and non- tradable goods in the transmission process. Obstfeld and Rogoff (2002) explored the issue of policy coordination; García-Cebro and Varela-Santamaría (2007) analyzed the influence of price fluctuations of international raw material on the exchange rates; Hoffmann and Kempa (2009) studied the impact of different sources of economic disturbance on the goals of monetary policies; Cooke (2010) analyzed the relationship between consumption home bias and exchange rates. Compared to the endless foreign studies, domestic researches published in the national publications are relatively lacking, and therefore could be considered as a new research direction of international economics. Therefore, it will be an innovative breakthrough to focus on all valued issues of current literature and use new methods in international financial field to do research. In view of the importance of the choice of exchange rate regimes issue, lack of analysis on home bias phenomenon in relevant literature of NOEM and the fact that models made by Obstfeld and Rogoff (1995) and Devereux and Engel (1998) all assumed free movement of capital and could not observe the roles of factors like incomplete capital mobility,4 this paper expands the model of Devereux and Engel (1998) and aims to explore the influence of home bias, capital mobility and producers’ price-setting behavior under different exchange rate regimes. This paper is organized into five sections, except for the section of introduction, the content of other sections are as follows: section 2 constructs theoretical framework; section 3 presents the solutions of model, section 4 analyzes the impacts of foreign monetary shock on domestic consumption volatility, expected level of
4In the viewpoint of De Grauwe (2000), capital control has functions of decreasing exchange rate fluctuation, making monetary policies more independent and preventing financial crisis caused by exceeded capital inflow and outflow.
8 consumption and welfare; section 5 is the conclusion and suggestion.
2 Theoretical Framework
This paper is based on the NOEM theory of Obstfeld and Rogoff (1995) and extends it under the model framework of Devereux and Engel (1998). Key assumptions are as follows: (1). Suppose that there are two countries of the same scale, known as home country and foreign country. (2). The numbers of domestic tradable goods modeled as a continuum over the interval [0, 1] while the numbers of foreign tradable goods in the interval (1, 2], and both the numbers of non-tradable goods of these two countries indexed in the interval [0, 1]. In order to distinguish between domestic and foreign variables, all of the following foreign economic variables are marked with an asterisk (*), with subscript H and F respectively representing domestic and foreign products and subscript T and N representing tradable and non-tradable goods. (3). Each individual is both a consumer and a producer. Individuals invest their labor and can produce a unit of heterogeneous tradable and non-tradable goods. Besides, individuals can run company and receive shares of profit. (4). Representative individual is in pursuit of the maximization of expected lifetime utility. The form of expectation is perfect foresight. (5). The government has two kinds of exchange rate regimes to choose from. Monetary authority can change money supply randomly under the floating exchange rate. Under the fixed exchange rate, the domestic monetary authority must alter the domestic monetary policies in order to keep the exchange rate fixed while the foreign monetary authority changes the foreign money supply randomly. (6). Commodity prices have stickiness. Producers set prices prior to monetary shock and will not change them in the short-run. Prices can fully adjust to its steady state position after one period.
9 (7). There are two types of price-setting methods. If producers set prices in terms of their currency, then the prices for home goods paid by foreign consumers changes when the exchange rate alters in response to money supply changes. In the other method, producers set prices in consumers’ currency, that is, home firms set one price for home country consumers in the home currency and another price for foreign counter consumers in the foreign currency. Under the fixed exchange rate regime, the currency in which prices are set is identical since the exchange rate is permanently fixed. (8) Foreign monetary shock is the main source of economic disturbance.
1.1 Representative Individual
Suppose that all individuals have the same preference. Representative individual’s expected lifetime utility is in positive proportion to consumption and real money balances, but is in negative proportion to the labor input.5 The form is as follows:
1 st 1 1 M s U t Et C s V Ls , , , V 0 ;V 0 , (1) 1 1 P st s
where Cs stands for the consumer index of representative individual, M s is
domestic nominal money holdings, Ps is domestic price level M s / Ps is domestic
real money balances, Ls is the amount of labor input, V Ls is function of labor input, is the discount factor, and separately are the elasticity of marginal utility of consumption and real money demand,6 and stand for the importance of real money balances and labor input in utility function, respectively.
5The increase of labor input means the decrease of individual leisure time, which lowers the individual utility. 6The elasticity of marginal utility of consumption (real money demand) is defined as the response degree of marginal utility caused by 1% of the variance of consumption (real money demand).
10 Define the consumer index of representative individual in equation (1) as geometric average of tradable goods consumption ( CT ) and non-tradable goods consumption (C N ):
C C1 C T N , (2) (1 )1 where is the share of the consumption of tradable goods in consumption index with consumption of tradable goods (CT ) including the consumption of domestic and foreign tradable goods (CH and CF ), which is: 1 CT (CH ) (CF ) , (3) where stands for the share of the consumption of domestic tradable goods in tradable goods. 1/ 2 means consumers prefer to domestic tradable goods. Literally is called consumption home bias.
In equation (3), CH stands for representative individual’s consumption of domestic tradable goods while CF is that of foreign tradable goods. The expressions are as follows:
1 1 1 ; (4) CH CH (i) di 0
1 2 1 C C (i) di , (5) F 1 F
The consumption of non-tradable goods ( C N ) is:
1 1 1 , (6) CN CN (i) di 0
In the above three equations, i stands for any goods, is the substitution elasticity
11 between domestic (foreign) products ( >1). Here the substitution elasticity between domestic and foreign tradable goods is 1. As for the foreign side, there is:
* * * 1 CT (CH ) (CF ) .
From the definition of equation (2) and (3), it can derive the price index as follows:
1 P PT PN ; (7)
1 , PT (PH ) (PF ) (8)
where PT and PN respectively stands for the prices of domestic tradable and non- tradable goods, PH and PF are the prices of domestic and foreign tradable goods. The form is as follows:
1 1 1 1 ; (9) PH PH (i) di 0
1 2 1 1 ; (10) PF PF (i) di 1
1 1 1 1 . (11) PN PN (i) di 0
From the above set formulas of consumer and price index, it can derive domestic consumer’s optimal choice of specific domestic tradable goods (CH (i) ),
7 foreign tradable goods ( CF (i) ) and non-tradable goods ( C N (i) ) are:
7From the definition of consumption and price index, we also can derive the domestic consumers’ consumption of domestic and foreign commodities separately as:
12 P (i) P H ; C H (i) C (12) PH PH
P (i) P F ; (13) CF (i) C PF PF
P (i) P N . (14) C N (i) (1 ) C PN PN
Analogously, foreign consumer’s optimal choice of specific domestic tradable goods
* * ( CH (i) ) and foreign non-tradable goods ( CF (i) ) are:
P * (i) P * C * (i) H C * ; (15) H * * PH PH
P* (i) P * C * (i) F C * . (16) F * * PF PF
1.2 Asset Market
As for the setting of asset markets, because the setting made by Devereux and Engel (1998) can not clearly show the impact of imperfect capital mobility, this paper modifies the assumption of free capital movement by Devereux and Engel (1998) and to amend the environment setting of bonds market. This paper assumes that agents of two countries can hold domestic nominal bonds and foreign nominal bonds. The domestic nominal bonds are issued in home currency while foreign nominal bonds in foreign currency. Under the conception of
P P CH C ; CF C PH PF
13 asymmetric transaction costs of Sutherland (1996) and Benigno (2001; 2009), assume that home agents must pay additional transaction costs in order to hold foreign bonds while foreign agents pay no costs for their purchases of home country’s bonds, then copy Benigno (2001)’s approach, set the discount factor of home resident’s purchase of domestic bonds is 1/(1 rt ) and the discount factor of
* the purchase of foreign bonds is 1/((1 rt )()) . Here, () denotes the transaction costs, which can also be regarded as the risk premium of home resident’s holding of foreign bonds. represents the factor that affects the risk premium.8 (0) 1 means that there is no transaction cost and the capital can move freely. () 1 shows that there exist transaction costs and the capital market has imperfect mobility. Since the model is composed of many representative agents, companies and the government, single individual behavior cannot affect the overall economic system. Therefore, in order to simplify the analysis, this paper will regard transaction costs ( ) and its behavior equation ( () ) as an exogenous parameter and avoid setting the specific functional form of. In the subsequent analysis, this paper will give different numerical values and do analysis through simulation methods. The reason of adopting this method is that in this way, the impact of slight changes of capital movement can be easily observed. It is through the setting of additional transaction costs that this paper shows the imperfect substitution nature of domestic and foreign nominal bonds and further introduces the issue of incomplete capital mobility.9
8In literature, there are many factors that affect risk premium. Frankel and Rose (1996), Selaive and Tuesta (2003), Schmitt-Grohé and Uribe (2003), Airaudo (2004) and Benigno (2009) thought that risk premium is affected by the number of foreign bonds hold by home-country residents. Schmitt-Grohé and Uribe (2001), Senhadji (1997; 2003) and Murphy (1991) believed that risk premium is the function of the ratio of external debt to exports. Bhandari (1981) and Frenkel and Rodriguez (1982) found that it is related to net exports. Frenkel et al.(2001) supposed that it is the function of the tax imposed on inflowing capital by home country. Sack (2004), Rudebusch et al.(2007) and Piazzesi and Swanson (2008) held that it is a constant risk premium. 9In general theoretical literature, the setting for incomplete capital mobility is mainly expressed on interest rate parity or the amendment of capital account (such as Arellano, 1982; Flood and Garber, 1984;
14 1.3 Production Function
Suppose labor is the only factor of production, production behavior is:
Y j (i) L j (i) , j H , N . (17)
Equation (17) is the production function of domestic tradable and non-tradable goods. Here the producer’s goal is to set prices to maximize profit function, and the prices must be set prior to domestic and foreign money supply change. Furthermore, this paper aims to explore the pros and cons of fixed and floating exchange rate regimes, and the latter can be divided into two types: producer-currency pricing and pricing-to-market, so totally there are three models: (1). Producer-currency pricing model (PCP model). The producers set prices in terms of their currency. So the prices of foreign goods paid by home consumers and the prices of home goods paid by foreign consumers will change when the exchange rate changes. (2). Pricing-to-market model (PTM model). Producers set prices in consumers’ currency. In this case, the prices are irresponsive to exchange rate changes. (3). Fixed exchange rate system (FER model). Prices are set in advance and the currency in which prices are set is identical since the exchange rate is permanently fixed.
1.4 Budget Constraint
In the PCP model, prices of home goods paid by domestic and foreign consumers are all set in producers’ currency. So the budget constraint that domestic representative individual i faces is:
* Bt (i) St Bt (i) Pt Ct (i) * M t (i) (1 rt ) (1 rt )()
Agénor et al., 1992; Lai and Chang, 1987).
15 * * PH ,t (i)YH ,t (i) YH ,t (i) PN ,t (i)YN ,t (i) Bt 1 (i) St Bt 1 (i) M t 1 (i) Tt (i) , (18)
The left side of the equation (18) represents the spending project of representative individual i in period t , including consumer spending ( Pt Ct ), the discount values
of domestic nominal bonds expenditure (( Bt /(1 rt ) ), foreign nominal bonds
* * expenditure ( St Bt /(1 rt )() ), and money holding ( M t ); the right side of the equation represents the sources of income of representative individual i in period t , including the output revenue of the first two items on the right side of the equation, and incomes of sales of domestic bonds with period t 1 ( Bt1 ) and that of sales of
* foreign bonds ( St Bt1 ), money balances in period t 1 ( M t1 ) and the lump-sum
transferred by government (Tt ). The output revenue includes the domestic market
revenue of domestic tradable goods ( PH ,tYH ,t ), foreign market revenue of domestic
* tradable goods ( PH ,tYH ,t ) and revenue of non-tradable goods ( PN ,tYN ,t ). The
above symbols are defined as follows: PH ,t is the price of domestic tradable goods
in producers’ currency; YH ,t is the sales volume of domestic tradable goods to
* domestic market; YH ,t is that to foreign market. PN ,t is the price of domestic
tradable goods; YN ,t is the output of domestic non-tradable goods; St stands for the nominal exchange rate.
16 In the PTM model, home firms set one price for home country consumers in the home currency and another price for foreign counter consumers in the foreign currency. The budget constraint that home country representative individual i faces is:
* Bt (i) St Bt (i) Pt Ct (i) * M t (i) (1 rt ) (1 rt )()
* * * PH ,t (i)YH ,t (i) St PH ,t (i)YH ,t (i) PN ,t (i)YN ,t (i) Bt 1 (i) St Bt 1 (i) M t 1 (i) Tt (i) , (19)
The difference between (18) and (19) lie in the item of output revenue. In equation
* (19), PH ,t represents the price of domestic tradable goods set in the foreign currency.
In the FER model, if the firm sets prices in producers’ currency, the budget constraint will be the same as in equation (18), if prices are set in consumers’ currency, the budget constraint will be the same as in equation (19).
1.5 Government
Suppose that the government spending is zero, and government transfers the seigniorage revenue to agent in a lump-sum fashion, the budget constraint is:
M t M t1 Tt ,
where M t represents government’s money supply.
3 Solve the Equilibrium Solutions
3.1 Maximization Behavior of Consumer
Insert the profit function of firm into the budget constraint, the corresponding first-
17 order conditions with respect to Ct , M t and Lt respectively for maximizing utility function subject to budget constraint are as follows:
1 P C t t ; Et (20) 1 rt Pt1 Ct1
1 M C t t r 1 ; (21) Pt ( t ) 1 rt
' V Lt Wt Et Ct1 , (22) 1 rt Pt1
Among the above equations, equation (20) is the standard consumption Euler equation, equation (21) is the money demand equation, equation (22) is the labor supply equation. Divide equation (20) by (22), it can derive the optimal wage level as follows:
W t V Lt , (23) Pt Ct
From equation (23) it can see that the trade-off relationship between consumption and leisure. To derive domestic representative consumer’s optimal choice of domestic bonds is the same as showed in equation (20). And the domestic representative consumer’s first-order optimal condition for foreign bonds is:
1 S P C E t1 t t , (24) * t (1 rt ) S t Pt1 Ct1
Equation (24) shows the optimal condition of domestic intertemporal consumption and foreign bonds holding. Similarly, the foreign representative consumer’s optimal choice of foreign bonds is:
18 1 P* C * E t t , (25) * t * * 1 rt Pt1 Ct1
Equation (25) shows the optimal condition of foreign intertemporal consumption and national bonds holding. Combine equation (20) and (24), it can derive the interest rate parity condition when considering the transaction costs:
1 rt St1 * Et ( ) , (26) 1 rt St
Equation (26) shows that factors affecting interest rates difference between countries are exchange rate changes and the capital mobility.10 This equation is also called capital market equilibrium equation, which shows the relationship of domestic and foreign interest rates when capital market is in equilibrium and capital stops moving. Compare equation (24) and (25) and use the method of iterating, it can derive the optimal risk-sharing condition under imperfect capital mobility:
* Ct 1 Ct * , (27) Pt St Pt where C * and P* representatively stand for foreign consumption index and price index. Equation (27) shows the condition for representative consumer holding foreign bonds to have international risk sharing. That is, the discount value of utility
* from consumption that domestic residents get ( S t 1 (Ct 1 / Pt 1 ) /((1 rt 1 )) ) when they spend one dollar to buy foreign bonds will equal to the discount value of
utility from consumption that foreign residents get ( * * * ) (Ct1 / Pt1 ) /(1 rt1 ) when they spend one dollar to buy foreign bonds. This equation illustrates that because of the imperfect capital mobility, the marginal utility generated by the
10In fact, lots of empirical works, like those of Dooley and Isard (1980), Hansen and Hodrick (1980), Spiegel (1990), Frankel (1992) and Montiel (1994), support that capital control leads to the difference in interest rate between two currencies.
19 consumption of domestic products worthy of one unit of home country currency is less than that generated by the consumption of foreign products worthy of one unit of foreign currency.11
3.2 The Maximization Behavior of Producer
We now derive producer’s price-setting behavior under three kinds of models.
3.2.1 PCP Model
In the PCP model, the maximization problem of a representative producer is to maximize equation (1) subject to equation (12), (14), (15), (17) and (18) as
12 constraints. Therefore, to derive the first-order condition with respect to PH ,t (i) , we have:
Pt Et1Ct PH ,t (i) , 1 Et1Ct (i) Ct
When in equilibrium,Ct (i) Ct , it then follows that:
Pt Et1Ct PH ,t 1 , (28) 1 Et1Ct
11Devereux and Engel (1998)’s model assumes that capital can move freely and domestic and foreign bonds are perfect substitute. Thus, for consumers who pursue the maximization of utility, the marginal utility produced by the consumption of domestic commodities worthy of one unit home currency equals to that produced by the consumption of foreign commodities worthy of one unit home currency. The optimal risk sharing condition is given by: * * Ct / Pt Ct / St Pt . 12Under the problem of maximization, because representative agents, while being consumers, run factory, produce goods and get producer profits, there is no difference between getting equilibrium solutions by using profits maximization and by using utility maximization. And because welfare analysis is an important feature in the issue of choice of exchange rate regimes and in the NOEM model, this paper uses utility maximization to explore the optimal price-setting of producers. Refer to Obstfeld (2006) for the same practice.
20 In the PCP model, the law of one price holds.13 Therefore, the price for foreign consumers set by home country producers is:14
* PH ,t PH ,t Et 1 (St ) , (29)
Because of the symmetry of home country and foreign country, the optimal price set by the foreign producer i is:
* * * Pt Et1 Ct PF ,t (i) *1 ; (30) 1 Et1 (Ct )
* PF ,t PF ,t Et1 (St ) , (31)
To get the first-order condition with respect to PN ,t (i) and make use of equilibrium condition, it can derive the price of non-tradable goods as:
Pt Et1Ct PN ,t (i) PN ,t 1 PH ,t . (32) 1 Et1Ct
3.2.2 PTM Model
In the PTM model, representative agent i is under the constraint of equation (12),
(14), (15), (17) and (19), the first-order condition with respect to PH ,t (i) of the maximization of equation (1) is:
Pt Et 1Ct PH ,t (i) PH ,t 1 , 1 Et 1 Ct
13Note that though the law of one price holds, the theory of purchasing power parity does not hold because of the existence of non-tradable goods and consumption home bias. 14Because the exchange rate level with period t is unknown while the price is set prior to period t 1, thus here we insert the expectation symbol. And, the expectation symbol can be removed when transactions actually take place in period t .
21 The equation shows that in the PTM model, the price for home country consumers set by home country producers is the same as in the PCP model (equation (28)).
* To derive the first-order conditions with respect to PH (i) and PN (i) , and make use of equilibrium condition, we respectively have:
* * Pt Et1Ct PH ,t 1 * ; (33) 1 Et1St Ct Ct
Pt Et 1Ct PN ,t 1 PH ,t , 1 Et 1 Ct
Similarly, we have:
* Pt Et1St Ct PF ,t . (34) 1 *1 Et1 Ct Ct
The above three equations are the prices of domestic products for foreign consumers, prices of non-tradable goods and prices of foreign products for home country consumers under the PTM model.
3.2.3 FER Model
In FER model, the producer also has two kinds of price-setting methods to choose from, but because the exchange rate is permanently fixed, so the prices of home products for foreign consumers will not change even under foreign monetary shock.
3.3 Closed-Form Solution
Like the setting of Devereux and Engel (1998), in order to get the closed-form solution, suppose that 1 and V (Lt ) Lt , then the welfare function can be
22 expressed as:
C1 M t t ut ln Lt , (35) 1 Pt
Also assume that the money supply follows a random walk:15 M t Et , (36) M t1 Substitute equation (36) into (21), we have:
1 M 1 r t t , (37) Ct Pt rt
It can be seen from equation (37) that consumption is only the function of real money supply and nominal interest rates. The same apply to the foreign counterpart:
1 M * 1 r * C * t t , (38) t * * Pt rt
Divide equation (37) by (38), and use equation (26), we have:
* * Ct Pt M t rt St1 * * , (39) Ct Pt M t rt St
The optimal risk sharing condition of equation (27) in terms of period t 1 can be expressed as:
Ct1 Pt1 * * , (40) Ct1 St1Pt1
Compare the result of equation (39) and (40) and use equation (20), it can derive:
15It is sure that the above assumptions have closed-form solutions under the three models. Unlike Devereux and Engel (1998) who ignored the central bank might not have independence of monetary policy operation under perfect capital mobility and fixed exchange rate regime, the assumptions of imperfect capital mobility under the analysis framework in this paper seem to be more convictive.
23 r M S t t , (41) t * * rt M t
The equation is one that determinants of the exchange rate, which derived by considering the degree of capital mobility.16
* In equation (41), because the endogenous variables r t and rt have not yet been expressed as the form of exogenous variables or parameters, so the exchange rate level derived is not the final solution. This being the case, make use of
* equilibrium condition of long-run, firstly derive the extent to which r t and rt are effected by exogenous variables from equation (20) and (24),17 and then insert the results back to equation (41), we then have:
(1 ) M S t t * , (42) 1 M t
Equation (42) shows that the fluctuation of exchange rate is affected by domestic money supply relative to foreign money supply and the degree of capital mobility.
3.4 Market Clearing Conditions
Totally there are four markets among models constructed in this paper, namely the labor market, goods market, bonds market and money market. The same goes for the foreign country. In the labor market, the free adjustment of nominal wage makes the labor supply equal to labor demand and labor market is able to achieve equilibrium. In the goods market, the condition of clearing is making demand equal to supply. The market clearing conditions of tradable goods and non-tradable goods are
16If not considering the international risk sharing condition, this exchange rate determination equation will get back to one of monetary approach, which is like the exchange rate determination derived by Frenkel (1976), Mussa (1976) and Kouri (1976) who come up with flexible price and Dornbusch (1976) who put forward with price stickiness. 17Making use of the long-run equilibrium condition, equation (20) and (24) can be written as * 1 rt 1/ and 1 rt 1/() . By shifting terms simply we can derive the results.
24 separately as follows:
P (i) P P* (i) P* Y (i) C (i) C * (i) H ,t t C H ,t t C * ; t H H t * * t PH ,t PH ,t PH ,t PH ,t
P (i) P Y (i) C (i) (1 ) N ,t t C . N N t PN ,t PN ,t
The clearing condition of the asset market is equation (26), which shows the relationship between interest rates of the two countries when capital no longer moves in equilibrium. According Walras’ law, when there are n markets in an economy system, if n 1 markets have reached equilibrium, then market n will certainly reach equilibrium, too. Therefore, if the labor market, goods market and bonds market of the home country have reached equilibrium, the money market will definitely reach clearing state.
4 The Comparison of Different Exchange Rate Regimes
4.1 The Variance of Domestic Consumption Caused by Foreign Monetary Shock
(1). PCP model
Producers set both the prices of products paid by home and foreign consumers in their currency, so the price that foreigners pay for domestic goods and the price that home residents pay for foreign goods will fluctuate when exchange rates change. It can be derived from equation (42) that when the foreign money supply (
25 * M t ) increases by 1%, the exchange rate ( St ) will drop by (1 ) /1
18 * percent. And in the PCP model, the law of one price holds ( PF ,t PF ,t St ),
* when PF ,t is fixed, if the exchange rate ( St ) drops by (1 ) /1
percent, then PF ,t will also decrease by (1 ) /1 percent. Besides,
1 because the form of domestic price index is P PT PN and
1 PT (PH ) (PF ) , so the domestic price index ( P ) will drop by (1)
(1 ) /1 percent accordingly. And it can be deduced from equation (37) that the domestic consumption level (Ct ) will increase by (1)
(1 ) / (1 ) percent.
(2). PTM model
As producers set prices of products for home consumers in home currency and prices of products for foreign consumers in foreign currency and all the prices have been determined in advance, so the shock of foreign money supply will not affect the domestic consumption level. This can be derived from equation (37), that consumption is a function only of domestic real money supply and nominal interest rates.
(3). FER model
* Equation (42) shows that when foreign money supply ( M t ) increases by 1%
and providing that the capital mobility unchanged, domestic money supply ( M t )
18Holds that domestic money supply is fixed.
26 must accordingly increase by 1% in order to keep the exchange rate fixed. While from equation (37) we can see that 1% increase of domestic money supply ( M t )
will lead to 1/ percent increase of domestic consumption level (Ct ).
Note in particular that the interpretation of this paper is the same as that of Devereux and Engel (1998), stressing that in an open economy, foreign shock influence the consumption level is through the channel of exchange rates. The only difference is that this paper assumes incomplete capital mobility and weakens the correlation between the foreign monetary policy changes and domestic interest rates, which seems to be more appropriate than Devereux and Engel (1998)’s way of ignoring the exchange rate channel under the assumption of complete capital mobility. Foreign monetary shock is transmitted to economic variables through the channel of exchange rates and the imperfect mobility of capital will affect the extent of the transmission. This transmission process of exchange rates is what NOEM model emphasizes. As is mentioned in the paper of Mohanty and Turner (2008), with the imperfect mobility of capital, the fluctuation of exchange rates will affect the aggregate demand, expected inflation and personal wealth more easily. Therefore, the channel of exchange rates plays an important role in the transmission process. This paper explores that in an economic system in which the incomplete capital mobility exists, how foreign monetary shock would affect its domestic consumption and welfare level. The interpretation of exchange rates’ transmission channel can also be supported by relevant literatures. Tables 1 shows the variance of domestic consumption caused by 1% increase of foreign money supply in each model.
Table 1: The variance of domestic consumption caused by 1% increase of foreign monetary supply
model consumption volatility
(1 ) (1) PCP % 1
27 PTM 0
1 FER %
Devereux and Engel (1998) found that under the assumption of full capital mobility, the consumption volatility is greater in FER model as compared to PCP and PTM models. This paper extends the assumption of free capital flow, and incorporates the setting of non-tradable goods and consumption home bias into the analysis. It is found that the consumption volatility in FER model is still greater than that in PCP and PTM models,19 and the consumption volatility in the PCP model will be influenced by the degree of capital mobility ( ), the share of consumption of tradable goods in the consumption index ( ) and the extent of home bias ( ). If the capital mobility ( ) increases, the exchange rate pass-through (ERPT) to consumer prices grows and so does the variance of the consumption in the PCP model. Greater share of tradable goods ( ) means greater share of its price in price index. In this situation, exchange rates float will lead to greater price level and variance of consumption. Finally, if the degree of home bias ( ) lowers, the consumption of foreign tradable good will increase, which makes the fluctuation of the prices of foreign goods charged to domestic consumers greater when exchange rates change.
4.2 The Effect of Foreign Monetary Shock on Expected Domestic Consumption Level
Like the foregoing analysis, we assume that the domestic money supply follows
(1 ) 19Because , , 1 , so 1; and 1, hence1 1. Therefore, 1
(1 ) (1) (1 ) (1) 1 1, and . 1 1
28 Et M t / M t1 . Using logarithm function on both sides, we can write the equation as:
~ mt1 mt ln t1 , (43)
where mt is the log of M t and t1 is the random disturbance term of domestic money supply, which follows a normal distribution with the mean is zero and the
2 variance is m .
If define ~ as:
~ 1 2 exp m , 2
Then the log form of money supply is:
1 m m ln 2 v . (44) t1 t 2 m t1 Taking logarithm for equation (37) and (38), we have:
r t ; ct mt pt ln (45) (1 rt )
* * st mt mt ln rt ln rt , (46)
In the above equations, except for interest rates, the variables with lower-case letters denote take logarithm for upper-case letters. With these equations, we can proceed to the effect of foreign monetary shock on the mean of consumption. Refer to Appendix for the derivation process. These results are reported in Table 2.
29 Table 2: The impact of foreign monetary shock on expected domestic consumption (holding that
2 m 0 )
model expected domestic consumption
1 (1 ) 2 1 1 [ (1)] [ (1)]1 2 (1) 2 PCP exp * 2 m 2
1 (1 ) PTM 1 1
1 1 1 1 1 2 exp * 2 m FER 2
If we compare this paper with the conclusion made by Devereux and Engel (1998), we can find that taking the setting of incomplete capital mobility, non- tradable goods and home bias into consideration, the analysis in the issue of choosing the exchange rate regime becomes more complex than that of Devereux and Engel (1998). It takes more than intuition to observe the differences of these exchange rate regimes. This paper intends to adopt numerical simulation method,20 giving parameters values in order to further observe their impact on the consumption level when these values change. Because this paper is based on the NOEM model and makes two economic systems of the same scale as objects for analysis, when selecting parameter values, the paper introduces the empirical data collected by the Lubik and Schorfheide (2005) and Gomes and Sousa (2007). These data are aimed at the United States and the European Union, which are countries of similar scales. This paper is also supplemented by the simulation values or calibration that is usually used in analyzing the U.S. economy in existing NOEM literature to explore the effect of incomplete capital mobility existing in the capital market between the U.S. and EU. Following the empirical results obtained by Hairault and Poriter (1993) aiming
20This paper uses the computer software of Mathematica 7.0 to conduct simulation.
30 at the United States and the setting forms in NOEM literatures of numerous scholars like Sutherland (1996), Senay (1998), Pierdzioch (2004; 2005) and Wang (2010), this paper sets the substitution elasticity between different home commodities ( ) as 6; like Bergin (2003), Lubik and Schorfheide (2005) and Wang (2010), we set the importance of labor supply in the utility function ( ) as 1; and use the setting of Devereux and Engel (2003), Lubik and Schorfheide (2005) and Hoffmann and Kempa (2009), set the elasticity of marginal utility of consumption ( ) to be 2. Besides, when selecting parameter values for the share of tradable goods ( ), in addition to using 0.5 and 0.6 these two values which were deduced by Corestti et al. (2002) and Stockman and Tesar (1995) after they observed the actual data values of the U.S, the paper also simulates the exception of non-tradable goods being absent ( 1). In addition to using 0.6 set by Gomes and Sousa (2007) and 0.85 set by Wang (2010) to simulate in home bias ( ), we also stimulates two special cases, one being the absence of consumption home bias ( 0.5) and the other being the sole consumption of domestic tradable goods ( 1 ). Finally, in the selection of the variable value for transaction costs ( ), this paper uses the empirical value 0.9 set by Gomes and Sousa (2007) that is aimed at the U.S. and the EU to simulate. And in order to explore the effect of different degree of capital mobility (high, medium, low) in the domestic capital market, this paper also adopts 0.8 and 1 these two additional analog values. The main reason why the transaction cost adopts the form is that the effects of different values of transaction cost variables only reflect in the value changes of the whole system and will not affect the final qualitative results. The form of equivalent changes will help analyze the sensibility of the variable of transaction cost. The set values of all parameters are reported in Table 3.
Table 3: The parameters
Description Parameter Value Substitution elasticity between domestic products 6 Importance of labor input in utility function 1 Elasticity of marginal utility of consumption 2
31 Share of the consumption of tradable goods in consumption index 0.5, 0.6, 1
Consumption home bias 0.5, 0.6, 0.85, 1 Transaction costs 0.8, 0.9, 1
Through simulation analysis, this paper validates the conclusion of Devereux and Engel (1998) under the assumption that capital flows freely. Refer to Table 4 for the detailed simulation results.21 Table 4 shows that when in the face of foreign money shock, the expected level of consumption in the FER model would be greater than that under floating exchange rates; and when under the floating exchange rate system, the expected level of consumption in the PCP model will be greater as compared to the PTM model. With respect to the roles that non-tradable goods and consumption home bias play in the analysis of fixed versus floating exchange rates, this paper finds that these two factors do not affect the expected consumption levels in the PTM and FER model.
However, in the PCP model, when 0.5 and 0.6 , the expected consumption level will increase with the higher the degree of consumption home bias ( ). And without regard to the factor of consumption home bias ( 0.5 ), when the share of tradable goods equals to 1 ( 1) or equals to the share of non- tradable goods ( 0.5 ), the expected consumption level is higher in both situations than that when the share of tradable goods is not equal to the share of non- tradable goods ( 0.6 ). This is because when the share of tradable goods and the share of non-tradable goods are not equal, foreign monetary shock will have asymmetric impact on domestic consumption level, in which situation the expected
21The paper written by Devereux and Engel (1998) can be seen as a special case of the condition of 1 in this paper.
32 consumption level reaches its lowest level. When 1, the expected consumption level is in the decline if consumption home bias ( ) is between 0.5 and 0.6, and it increases again when the bias is between 0.6 and 1. Table 5 and Table 6 show the impact of foreign monetary shock on the expected consumption level under the assumption of incomplete capital mobility. In this case, the expected consumption level in the FER model is still higher than that in the PCP and PTM model, so the fixed exchange rate is better than the floating exchange rate. Although this derivation is mostly in accordance with the conclusion derived under the assumption that capital can move freely, we should pay attention to the two points. The first one is that the expected consumption level in the PCP and the FER model under incomplete capital mobility is higher than that under complete capital mobility, and with the lower the mobility degree, the expected consumption level increases. The other point is that when the degree of capital mobility is lower ( 0.8 ), if 0.6 and is between 0.5 and 0.6, the expected consumption level will decrease, the expected consumption level will increase while is between 0.6 and 1. And when 1 and is between 0.5 and 0.85, expected consumption will decrease, the expected consumption will increase while is between 0.85 and 1.
Table 4: The effect of foreign monetary shock on the expected consumption (
2 dE(C) / d(exp( * )) ): the case of complete capital mobility ( ) m 1
0.5 0.6 0.85 1
PCP 0.401 0.402 0.410 0.417
33 PTM 0 0 0 0 0.5 FER 0.472 0.472 0.472 0.472
PCP 0.408 0.401 0.409 0.417 0.6 PTM 0 0 0 0
FER 0.472 0.472 0.472 0.472
PCP 0.404 0.400 0.405 0.417 1 PTM 0 0 0 0
FER 0.472 0.472 0.472 0.472
Table 5: The effect of foreign monetary shock on the expected consumption: the degree of capital
mobility is higher ( 0.9 )
0.5 0.6 0.85 1
PCP 0.406 0.408 0.411 0.417 0.5 PTM 0 0 0 0
FER 0.497 0.497 0.497 0.497
PCP 0.406 0.406 0.411 0.417 0.6 PTM 0 0 0 0
FER 0.497 0.497 0.497 0.497
PCP 0.415 0.405 0.408 0.417 1 PTM 0 0 0 0
FER 0.497 0.497 0.497 0.497
Table 6: The effect of foreign monetary shock on the expected consumption: the degree of capital
mobility is lower ( 0.8 )
0.5 0.6 0.85 1
PCP 0.412 0.412 0.413 0.417 0.5 PTM 0 0 0 0
FER 0.528 0.528 0.528 0.528
PCP 0.414 0.412 0.413 0.417 0.6 PTM 0 0 0 0
34 FER 0.528 0.528 0.528 0.528
PCP 0.427 0.418 0.412 0.417 1 PTM 0 0 0 0
FER 0.528 0.528 0.528 0.528
4.3 The Effect of Foreign Monetary Shock on Domestic Welfare Level
Following the general setting of Obstfeld and Rogoff (1995) and Devereux and Engel (1998), we assume that 0 and 1, then the expected utility function can be simplified as:
E(C1 ) E(u ) t E(L ) . t 1 t
Substitute the expected consumption level and expected output level in each
2 model into the above equation, and assume that m 0 , we can separately get the expected utility in these three models:
(1). PCP model
The expected utility in the PCP model is:
1 [ (1 )](1) 1 1 1 1 [ (1 )](1 )[1 (1 )( (1))] 2 E(u ) exp * . t 1 22 m
(47)
(2). PTM model
The expected utility in the PTM model is:
35 1 [ (1 )](1 ) 1 1 1 1 1 2 E(u ) (1) 1 (1)exp * . t 2 m 1 2
(48)
(3). FER model
In the FER model, the expected utility is:
1 1 1 1 1 1 1 2 E(u ) exp * . (49) t 2 m 1 2
Use the same simulation method and set the same parameter values as those in the above section, we can simulate the impact of foreign monetary shock on the expected utility in each model as Table 7, Table 8 and Table 9 shows. It can be seen from these three tables that when in the face of foreign monetary shock, domestic welfare level drops. In Table 7, in the special case of 1, the conclusion of Devereux and Engel (1998) can be verified, namely the expected utility in the PCP and PTM models are higher than that in the FER model. This paper also discovers that with the increase of the share of tradable goods ( ), the expected utility in the PCP model declines while that in the PTM model increases. And the expected utility in the PCP and PTM models both rise with the increase of degree of home bias ( ) while that in the PER model stays the same despite of the change of the share of tradable goods ( ) and the degree of home bias ( ). Table 8 and Table 9 show the result under incomplete capital mobility, which is almost the same as that under the perfect mobility. Only in the three models will the expected utility rise with the increase of imperfect mobility of capital.
Table 7: The effect of foreign monetary shock on expected utility: the case of 1
0.5 0.6 0.85 1
PCP -2.088 -2.068 -2.028 -2.008
36 PTM -1.809 -1.655 -1.267 -1.034 0.5 FER -2.275 -2.275 -2.275 -2.275
PCP -2.108 -2.084 -2.032 -2.008 0.6 PTM -1.757 -1.613 -1.252 -1.034
FER -2.275 -2.275 -2.275 -2.275
PCP -2.205 -2.155 -2.052 -2.008 1 PTM -1.551 -1.448 -1.190 -1.034
FER -2.275 -2.275 -2.275 -2.275
Table 8: The effect of foreign monetary shock on the expected utility: the case of 0.9
0.5 0.6 0.85 1
PCP -2.061 -2.047 -2.020 -2.008 0.5 PTM -1.787 -1.637 -1.262 -1.034
FER -2.158 -2.158 -2.158 -2.158
PCP -2.076 -2.058 -2.023 -2.008 0.6 PTM -1.731 -1.593 -1.245 -1.034
FER -2.158 -2.158 -2.158 -2.158
PCP -2.148 -2.110 -2.037 -2.008 1 PTM -1.511 -1.417 -1.181 1.034
FER -2.158 -2.158 -2.158 -2.158
Table 9: The effect of foreign monetary shock on the expected utility: the case of 0.8
0.5 0.6 0.85 1
PCP -2.031 -2.023 -2.012 -2.008 0.5 PTM -1.730 -1.618 -1.256 -1.034
FER -2.035 -2.035 -2.035 -2.035
PCP -2.039 -2.029 -2.012 -2.008 0.6 PTM -1.701 -1.570 -1.240 -1.034
FER -2.035 -2.035 -2.035 -2.035
PCP -2.085 -2.061 -2.018 -2.008
37 PTM -1.467 -1.385 -1.169 1.034
1 FER -2.035 -2.035 -2.035 -2.035
4.4 Interpretation
On the basis of Obstfeld and Rogoff (1995) and Devereux and Engel (1998) model , this paper investigates the choice of exchange rate regimes from the perspective of welfare maximization and except proving the conclusion of Devereux and Engel (1998) again, this paper further shows the roles that consumption home bias, incomplete capital mobility and different price-setting behavior play in this issue. Through theoretical derivation and simulated analysis of results, we can understand the effects of foreign monetary shock on the fluctuation of domestic consumption, expected consumption and consumer utility in different economic system under different exchange rate regimes. In this section, the effects of changes of these parameters are reported in Table 10, Table 11 and Table 12, after which the interpretation follows.
2 2 Table 10: The effect of parameter changes on d / d(exp( * )) c m
Variance of consumption PCP ＋ － ＋
PTM ○ ○ ○
FER ○ ○ ○
Note: ＋ denotes positive affect, － denotes negative affect, ○ denotes no effect.
Table 11: The effect of parameter changes on dE(C) / d(exp( 2 )) m*
Expected level of consumption PCP － ＋ －
38 PTM ○ ○ ○
FER ○ ○ －
Note: see the note of table 10.
dE(u) / d(exp( 2 )) Table 12: The effect of parameter changes on m*
Welfare level PCP － ＋ －
PTM ＋ ＋ －
FER ○ ○ －
Note: see the note of table 10.
Sorting out the above conclusions, we can find that the choice of exchange-rate regime is mainly affected by the degree of exchange rate pass-through (ERPT) and capital mobility. In our paper, there are three factors that affect ERPT, namely the non-tradable goods, home bias and pricing-to-market behavior. Through influencing the degree of ERPT, these three factors further affect the choice of fixed and floating exchange rate regimes. It can be seen from Table 10 that, if we evaluate exchange rates in terms of the variance of consumption, because in the PTM and FER model the price does not respond to exchange rate changes, the degree of the economic openness ( ), consumption home bias ( ) and capital mobility ( ) makes no differences in the ERPT process. But in the PCP model, exchange rate variability will influence prices and then further affect the degree of consumption variance. Therefore, the more open the economy ( ) is, the more consumption will be affected; the higher the degree of consumption home bias ( ) is, the less consumption will be affected. What’s more, PTM insulates domestic consumption from exchange rate fluctuations. In this case, floating exchange rates dominate fixed exchange rates. From the perspective of expected consumption, exchange rates will not change under the FER model, so the expected consumption will reach its highest level
39 because of agent’s mentality that the expected transaction is stable; the reason why the expected consumption in the PCP model is higher than that in the PTM model is that the price discrimination imposed by producers weakens the agent’s expectation for the stability of transactions. It can be found from Table 11 that in the PCP model, when the economy opens deeper to the outside world ( increases), the agent will expect higher possibility of exchange rate fluctuation and this sense of uncertainty will lower the expected consumption level. However, increased home bias ( increases) will weaken the sense of uncertainty caused by exchange rate variance, so the expected consumption level will rise; consumption is irresponsive to exchange rate volatility in the PTM model, therefore, the degree of economic openness ( ), home bias ( ) and capital mobility ( ) are of no effect. In the comparison of welfare levels, the expected utility in the PCP and PTM models will be higher than that in the FER model, which is mainly because of the improved independence of monetary policies under floating exchange rates. And from Table 12, we can see that it is more difficult to maintain the stability of exchange rates as the degree of economic openness deepens ( increases). In this case, the welfare level under floating exchange rates (PCP and PTM models) will be higher than that under fixed exchange rates (FER model), the impact of the variance of exchange rates on economy will decline with the increase of degree of home bias ( increases). Also the welfare level in the PCP model will rise while that in the PTM model will drop. Finally, in terms of the role of capital mobility, generally countries with low degree of capital mobility will prefer floating exchange rates in order to maintain the independence of domestic monetary policies. This can be observed from Table 8 and Table 9, which suggest that the benefits of floating exchange rates will increase with the decline of capital mobility. Moreover, it can be derived from Table 11 and 12 that incomplete capital mobility will lower the possibility of drastic fluctuation of exchange rates, therefore the expected consumption level in the three models will rise and so is the welfare level.
5 Conclusions and Suggestions
40 Obstfeld and Rogoff (1995) stimulated the produce of New Open Economy Macroeconomics in the 1990s. Subsequent researches indeed have enriched the international finance field, but the factors of home bias and incomplete capital mobility, though existing in real society widely, are always ignored. Especially, it would be narrow if the importance of capital mobility fails to be expressed in the analysis of the choice of fixed versus floating exchange rates. Therefore, this paper tries to explore the roles that home bias, capital mobility and the type of commodity pricing arrangement play in different exchange rate regimes on the basis of New Open Economy Macroeconomics. This paper extends on the basis of Devereux and Engel (1998) model and from the perspective of welfare maximization, it explores the effects of foreign monetary shock on the consumption volatility, expected consumption and welfare level in different economic systems under different exchange rate regimes, correcting the imperfections of the literature of Devereux and Engel (1998). This paper not only manages to show the role of non-tradable goods in the issue of the choice of exchange rate regimes, but also further explain the effects of home bias and capital mobility on this issue. The following are the key conclusions of this paper. (1). In terms of the variance of consumption, the PTM model sees the lowest variance degree while in the PCP model, the variance degree is affected by the extent of capital mobility, the share of the consumption of tradable goods in the consumption index and the degree of home bias. (2). From the expected consumption viewpoint, fixed exchange rates dominate floating exchange rates. (3). From the perspective of welfare level, the expected utility in the PCP and the PTM model will be higher than in the FER model and will rise with the increase of the degree of home bias and imperfect mobility of capital. Finally, it is through setting the parameter values of home bias and the proportion of PTM that this paper carries out the analysis, which can be seen as one of its constraints. In the subsequent research, it is advisable to explore home bias and the behavior of PTM in endogenous form and incorporate the factors that cause the change of parameters of home bias and the behavior of PTM, like the existence of
41 trade costs and intermediate goods, in order to find out if these factors will affect the choice of optimal exchange rate regimes.
Appendix
Derivation of Expected Consumption and Utility
It follows from equation (37) that:
C M r t t t Pt , 1 rt
Substituting it in equation (28), we have:
1 1 Et1 (Ct )Et1 (M t ) Cov(Ct , M t ) rt PH ,t 1 , (A1) 1 Et1 (Ct ) 1 rt
Taking logarithm for both sides, then we have:
2 rt pH ,t mt1 ln() m (1 ) mc ln , (A2) 1 1 rt
where mc is the covariance of mt and ct in the information set at period t 1,
2 m is the variance of mt .
An analogous equation holds for the foreign country:
* * * * 2 rt p m ln( ) * (1 ) * * F ,t t1 m m c ln * . (A3) 1 1 rt
And, equation (44), (45), (46), (A2) and (A3) all hold in each model.
Besides, substituting equation (8) into equation (7), using PH ,t PN ,t and taking logarithm for both sides, we can then deduce the domestic price level as:
42 pt 1 (1)p H ,t (1)p F ,t , (A4)
Likewise, the foreign price level is: * * * pt 1 (1)p H ,t (1)pF ,t .
1. PCP model
The log form of the law of one price can be written as:
* pH ,t pH ,t st ; (A5)
* pF ,t pF ,t st . (A6)
Inserting equation (A2) and (A6) into equation (A4), we have:
2 rt * pt 1 (1 )mt1 ln m (1 ) mc ln (1 )( p F ,t st ) . 1 1 rt
Again inserting equation (A3) and (46) into the above formula, we then have:
2 rt pt 1 (1)mt1 ln m (1 ) mc ln 1 1 rt
* * * 2 ri * * (1)mt 1 ln * (1 ) * ln mt mt ln rt ln rt , m m c 1 * 1 ri
It is given by equation (44) that: 1 m m ln 2 v . t t1 2 m t
Likewise, for the foreign counterpart, there is:
43 * * * 1 2 * m m ln * v . (A7) t t1 2 m t
Inserting the above equations into each other, we have:
1 2 * 1 2 rt m p 1 (1 ) (1 ) (1 ) * (1 ) * ln t t t m mc t m m c 2 2 1 1 rt
rt ln 1 (1 ) * (1 ) , (1 rt ) (1 rt )
Substitute the results back to equation (45):
1 2 * 1 2 rt c = 1 (1) v (1 ) (1) * (1 ) * ln t t m mc t m m c 2 2 1 1 rt
1 (1 ) * (1 ) (1 rt ) (1 rt ) ln , (A8) 1 rt It is given by equation (A8) that:
1 (1 ) 2 ; mc m
(1) 2 * * , m c m
Then inserting the above two equations back to equation (A8), we can derive:
2 2 1 (1) (1) * 1 (1 ) 2(1 ) (1) 2 (1 ) 2 (1 ) (1 ) 2 ct vt vt 2 m 2 m* 2 2
1 (1) * (1) 1 rt 1 (1 rt ) (1 rt ) ln ln , (A9) 1 1 rt 1 rt
44 It can be deduced from equation (A9) that the domestic and foreign monetary shock will affect the variance of consumption and further influence the welfare. That is:
2 2 2 1 (1 ) 2 (1 ) 2 * , (A10) c 2 m 2 m
Use equation (26). The expected consumption level is then given by:
1 (1 ) 2 2 [ (1 )] [ (1 )] 1 2 (1 ) c 1 1 2 E(C) exp(Ec ) exp * , 2 m 2 2
(A11) The expected utility can be derived as:
1 (1 )1 (1 ) 1 1 E(C 1 ) 1 1 1 1
1 (1)(1 ) 1 (1)(1 ) 2 (1)(1 )(1 1 (1)(1 )) 2 exp * 2 m 2 m , (A12) 2 2
In the PCP model, law of one price holds. Use equation (7) and (8) and insert the optimal price level for producers (equation (28), (29), (30) and (32)) and the expected consumption level (equation (A11)) of PCP model into the goods market equilibrium condition, we can derive the expected output level through symmetric analysis:
1 (1 ) (1 ) E(Y ) 1 1
(1 )1 (1 )( 1 (1 )(1 ) 2 (1 ) (1)1 1 (1 )(1 ) 2 exp * . 2 m 2 m 2 2
2. PTM model
45 Substitute the optimal risk sharing condition (equation (27)) into equation (33). Equation (33) can be re-written as:
* * * Pt Et 1 (Ct ) PH ,t = *1 , (A13) 1 Et1 (Ct )
Likewise, we have:
Pt Et1 (Ct ) PF ,t 1 , (A14) 1 Et1 (Ct )
Inserting equation (28) and (A14) into the definition equation of domestic price index (equation (7) and (8)), and using equation (26), we can get that:
1 (1 ) (1 ) (1 ) Pt Et1 (Ct ) Pt PH ,t PF ,t 1 , (A15) 1 Et1 (Ct ) or
E (C1 ) (1 ) E (C ) . (A16) t1 t 1 t1 t
Taking logarithm for both sides of equation (A16), we have:
(1 ) 2 1 2 2 , (1 )Et1 (ct ) c ln (1)ln Et1 (ct ) c 2 1 2
Transposing terms of the above equation, we then have:
1 (1 ) 2 2 E (c ) ln ln c , (A17) t1 t 1 2
It follows from equation (45) that:
1 2 2 , (A18) c 2 m
46 Comparing equation (A18) and (A10), we can find that the effect of domestic monetary shock on the variance of domestic consumption in PCP model is greater than that in PTM. Insert equation (A18) into equation (A17):
1 (1 ) 2 2 Et1 (ct ) ln ln m , (A19) 1 22
The expected consumption level is given by:
1 (1 ) 2 E(C) exp(Ec 2 / 2) 1 1 exp 2 , (A20) c 2 m 2
Using equation (A16) and (A20), we can derive the expected utility:
1 (1) (1 ) 1 1 1 1 1 1 E(C ) exp 2 , (A21) 2 m 1 1 2
It follows from equation (A1) and (A15) that:
(1 ) 1 PH ,t Pt ;
* 1 (1 ) * PH ,t Pt ,
Substituting the above two equations into goods market equilibrium condition and using equation (A20), we can deduce the expected output level as:
E(Y)
1 (1) (1 ) (1)1 (1 ) 1 1 (1 ) 2 (1 ) 2 1 (1 ) exp (1 ) exp * 2 m 2 m . 2 2
(A22)
47 3. FER model
Like Devereux and Engel (1998), assuming the fixed exchange rate is normalized to 1 ( st 0 ), then we can write equation (46) as:
* * mt mt ln rt ln rt 0 , (A23)
It can be seen from the above equation that when in the face of foreign monetary shock, the monetary authorities can keep exchange rates fixed by adjusting the monetary policies and the adjustment extent depends on the degree of capital mobility. From equation (45) and (A23), we have:
1 2 * * * , mc m c m
* * Inserting the above equation into (A2), and because pH ,t pH ,t and pF ,t pF ,t in FER model, we can get:
1 r * p p p * 2 ln t , H ,t F ,t t mt1 m* * * (A24) 1 1 rt
Substitute the above equation back into (45) and use (26):
1 * 2 2 1 ct t * ln , (A25) 22 m 1
Because in FER model,
2 1 2 * , (A26) c 2 m
So the expected consumption level can be derived as:
48 1 1 2 1 1 1 E(C) expEc / 2 2 . (A27) c exp * 2 m 2
The expected utility is:
1 1 1 E(C 1 ) 1 1 1 1 2 . (A28) exp * 2 m 1 1 2
The expected output level is:
1 1 E(Y ) 1 1 1 2 . exp * 2 m 2
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