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James Bullard is assistant vice president at the Federal Reserve Bank of St. Louis. The author thanks Patrick Coe, Mark Crosby, Mark Fisher, Phillip Jefferson, John Keating, Bob King, Chris Otrok, Bob Rasche, Trish Pollard, John Seater, Apostolos Serletis, Dan Thornton, and David Rapach for helpful comments and suggestions. Nick Meggos and Stephen Majesky provided research assistance.

firm conclusion about whether monetary Testing Long- injections had important real effects, in the short run or in the long run. In addition, Run Monetary many of the empirical tests that were devised ran into important criticisms that Neutrality seemed to invalidate their conclusions. These criticisms were based, at least in Propositions: part, on questionable handling or interpre- tation of the time-series properties of the Lessons from data. In recent years, however, economists have devised new tests of long-run mone- the Recent tary neutrality, as well as related neutrality- type propositions. A fair amount of litera- Research ture has been written on the subject, and the purpose of this paper is to review this literature.1 James Bullard The next section provides more detail concerning the background behind the onetary economists long have current empirical tests of neutrality propo- thought that government injections sitions. In the following sections, some of M of money into a macroeconomy the recent research using the newer set of have a certain neutral effect. The main tests is reviewed, and a few related papers idea is that changes in the money stock are discussed along with the results authors eventually change nominal prices and have found using somewhat different nominal wages, ultimately leaving impor- methodologies. The final section offers tant real variables, like real output, real some comments about directions for consumption expenditures, real wages, future research. and real interest rates, unaffected. Since economic decision making is based on real factors, the long-run effect of injecting SOME BACKGROUND money into the macroeconomy is often What is Long-Run Neutrality? described as neutral—in the end, real vari- ables do not change and so economic deci- In discussing long-run monetary sion making is also unchanged. How long neutrality, economists typically refer to a such a process takes, and what might hap- specific, hypothetical experiment that nor- pen in the meantime, are hotly debated mally is not observed directly in actual questions. But relatively few economists economies. The experiment is a one-time, debate the merits of long-run neutrality. permanent, unexpected change in the level Indeed, long-run neutrality is instead of the money stock. If, for instance, the taken as a given, almost an axiom, a money stock was $5 billion one day, and logical consequence of suppositions had been $5 billion for a long time, then made in economic theory. what would the effect be of suddenly 1 Not all papers dealing with neu- Curiously, during most of the postwar changing it to $6 billion and keeping it trality issues—an enormous period the empirical evidence on long-run there for a long time? According to the amount of literature—can be monetary neutrality has been in a state of quantity theory of money, prices should surveyed here. Instead, atten- flux. No doubt this is in part because it is rise eventually in proportion to the tion is restricted to those that difficult to look at the data generated by increase in the money stock, and all real use the newer techniques dis- the world’s economies and come to any variables, perhaps after some transition cussed later.

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time, would return to their original values Empirical tests that convincingly docu- and stay there until some further distur- mented departures from long-run monetary bance comes along. This is long-run neutrality therefore would be quite surprising monetary neutrality. (or quite suspect!) to monetary economists. In the hypothetical experiment, it is There is a second hypothetical experi- important that the new level of the money ment, related to the first, that more closely stock be maintained for some, possibly resembles the types of monetary policy long, period of time, to allow the transi- actions we see in actual economies. This tion effects to vanish. Theoretically, the experiment says that the government ini- change in the money stock has to be “per- tially maintains a certain growth rate for manent.” In the world’s economies, we the money stock for a long period of time. observe a high degree of persistence in At some date, that growth rate is adjusted many macroeconomic variables, but it is unexpectedly to some new rate, say, from generally difficult to tell the difference 3 percent to 5 percent on an annual basis, between “highly persistent” and “perma- and is kept there for another long period nent.” In the empirical work surveyed of time. What effect should this have on below we will see the use of many tests— important real variables like the capital- unit root diagnostic tests—intended to labor ratio, real output, real consumption categorize macroeconomic variables into expenditures, and real interest rates? If those that have been subject to permanent the answer is that after a long period of shocks and those that have not. It is impor- time, nothing would happen to the real tant to bear in mind, however, that these variables, we have what is referred com- tests may not accurately distinguish between monly to as long-run monetary superneu- the two cases—statistically speaking, the trality. Here again, one might expect an tests have limited power. The tests are used important transition period (commonly because they offer the best available method known as “the short run”) when the econ- for making the distinction between highly omy is adjusting to the new rate of persistent and permanent changes, but they monetary growth. Quite a lot could are far from perfect. happen to real variables during this adjust- In the hypothetical experiment, it is also ment period. But the neutrality and important that the change be unexpected, superneutrality propositions discussed because if the economy’s participants knew in this paper mainly concern long-run, that the money stock was going to increase, limiting effects. and therefore, that prices were about to Perhaps surprisingly, there are many increase, they might start changing their plausible analyses that suggest that depar- present behavior. For example, they might tures from long-run monetary superneu- buy consumption goods today, before the trality might be consistent with standard price increase takes effect. Prices then might economic theory. It is, in fact, relatively begin to rise in advance of the money stock easy to produce such theories. Moreover, change. This complicates the story, and these departures could go either way; that hence, we will think in terms of unantici- is, a permanently higher rate of monetary pated changes in the money stock level. growth might eventually either raise or In the discussion below, this will be lower the level of economic activity, or approximated by the notion of a “perma- change other important real variables in 2 The phrase “standard economic nent shock” to the money supply. either a positive or negative direction.3 assumptions” means maintain- In the world of monetary theory, nearly Accordingly, whereas long-run neutrality ing assumptions that markets all models based on standard economic is taken almost as an axiom of monetary clear at all times and that all assumptions embody some form of mone- economics, long-run superneutrality is agents behave rationally. tary neutrality.2 Most likely this is because far more circumspect. An empirical test 3 For a description of these monetary theorists generally think long-run that convincingly showed departures departures, see the survey by monetary neutrality is sensible, and, there- from long-run superneutrality would Orphanides and Solow (1990). fore, they build it into their models. not be too surprising, since this result

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58 N OVEMBER/DECEMBER 1999 is consistent with a number of existing Thus permanent effects on the level of a economic theories.4 variable need not imply permanent effects It is important to note that whether on the growth rate of that variable. Conse- the level of real output rises or falls, or quently, a natural question to ask is whe- whether other real variables change in a ther permanent changes in the monetary particular direction in response to a per- growth rate affect a country’s rate of econ- manent increase in the money growth rate, omic growth; that is, is money superneu- does not have any particular connotations tral with respect to economic growth? for social welfare. In many theories, infla- Many researchers in recent years have in tion distorts a Pareto optimal equilibrium, fact investigated questions of this type so that as a long-run proposition the popu- (mostly with methodology outside the lation in the economy generally prefers focus of this survey). There is much less lower rates of money growth accompanied theory concerning this issue, but some of by lower rates of inflation. Different theo- the results I discuss later will have some ries make different predictions in this regard, bearing on this topic. however, and to sort these out one would have to consider various theories and their Prima Facie Evidence. In his Nobel underlying assumptions in some detail. Lecture, Lucas (1996) addresses the topic Since this would take us too far astray, social of monetary neutrality, both in the short welfare will not be addressed in this survey. run and the long run, and discusses theo- There is another side to the superneu- retical developments that might reconcile trality question. Fischer (1996) suggests the perceived short-run effects of an increase that the reason the central banks of the in the money supply with long-run mone- world’s industrialized economies have tary neutrality. Lucas mentions several avidly pursued long-run price stability is pieces of evidence as constituting the main because in the long run, inflation has dis- reasons that he would like a satisfactory tortionary effects that adversely impact a theory of the real effects of monetary policy real variable, or a group of real variables, to address. Among these, he cites Friedman that people care about. If monetary growth and Schwartz (1963) who argue that all causes inflation, and inflation has distor- major recessions in the United States tionary effects, then long-run monetary between 1867 and 1960 were preceded superneutrality should not hold in the by substantial contractions in the money data. On the contrary, a permanent shock supply, suggesting that monetary policy to the rate of monetary growth should have mistakes were a primary contributor to some long-run effect on the real economy; business cycle downturns during this why else should we worry about it? Care period. Lucas states that severe monetary needs to be taken, however, in defining contraction seemed to play an important which variables are supposed to be affected role especially during the Great Depression and which are not—this is an area of some of 1929-33. But he also cites work by Sar- confusion in the literature.5 In the current gent (1986) who argues that huge reduc- paper we will try to avoid this problem tions in the rate of monetary expansion through use of the language “superneutrality —reductions much larger than anything 4 The situation described is with respect to variable x.” experienced in the post-Civil War United summarized by Canova (1994, The above discussion has referred to States—did not lead to any unusually large p. 123), who states, “... there changes in real variables, meaning changes reduction in real output in the hyperinfla- are very few available models in the level of the variable, especially so tionary post-World War I European econ- which display superneutrality, with respect to the level of real output. Of omies. These reductions were carried out while most existing models, course, real output in industrialized econ- in conjunction with monetary reform. both in the neoclassical and omies generally grows over time. A shift The hyperinflations ended abruptly when neoKeynesian tradition, possess in the level would be a one-time movement, credible reform was announced. But these neutrality of money.…” say from 100 to 90, whereupon the variable citations are subsidiary to Lucas’s (1996, 5 See Marty (1994) for a would resume growing at its previous rate. p. 668) main contention, that there is clear discussion.

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Figure 1 theories can claim empirical success at the level exhibited in figure 1? ... The kind of Money Growth and Inflation monetary neutrality shown in this figure Inflation needs to be a central feature of any mone- 100% tary or macroeconomic theory that claims empirical seriousness.” ° While Figure 1 is impressive, one 45 should be careful to note that these results 80 are different from the stories about long-run monetary neutrality and superneutrality outlined above. Evidently, the average rate 60 of money growth is correlated highly with the average rate of inflation in a country. But the story about long-run monetary neutrality is about a permanent, unexpected 40 change in the level of the money stock in a single country, and the ultimate impact of such a change. And, the story about 20 superneutrality concerns the long-run effect of a permanent, unexpected change in the rate of monetary expansion. Taking averages over long periods of time, while 0 20 40 60 80 100% informative at some level, masks the infor- Money Growth mation about such events, to the extent Postwar average rates of money growth versus average inflation rates in 110 countries. Obser- they might have occurred in the data. To vations near the 45 degree line, which is not fitted to the data, are consistent with the quantity study long-run neutrality more directly, theory. This figure is from McCandless and Weber (1995). the time-series evidence on inflation and monetary growth for individual countries needs to be considered. Can we isolate evidence—even “decisive confirmation”— permanent, or at least highly persistent, that long-run monetary neutrality holds. changes in the money stock (or the mone- Figure 1 shows the evidence that tary growth rate), which are then corre- Lucas (1996) cites. This figure, from lated with persistent changes in the price McCandless and Weber (1995), plots the level (or the rate of inflation) and simulta- average rates of monetary growth against neously are uncorrelated with permanent average rates of inflation for 110 countries. movements in important real variables? The averages are taken over 30 years, That is the challenge of testing monetary 1960-90. Monetary growth is measured neutrality propositions. as the annual growth rate of M2 for a country, and inflation is measured as the Time-Series Evidence.Some tests of long- annual rate of increase in the consumer run monetary neutrality during the 1960s price index for a country. The 45-degree simply regressed the level of real output line is not fit to the data, but instead repre- on a distributed lag of observations on the sents a theoretical presumption based on money stock. In reaction to this practice, the quantity theory, that the rate of infla- Sargent (1971) and Lucas (1972) argued tion should correspond to the rate of money that such evidence was circumspect for two growth (adjusted for the real output growth related reasons. One is that Sargent and rate in a particular economy).McCandless Lucas built simple and plausible reduced- and Weber report a simple correlation of form models of the macroeconomy in .95 between money growth and inflation which long-run monetary neutralityheld based on this data. Lucas (1996, p. 666) by construction, but which also would asks “... how many specific economic produce data such that, if the standard

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60 NOVEMBER/DECEMBER1999 practice was applied, the researcher would the Lucas-Sargent critique and required conclude that long-run monetary neutrality little macroeconomic structure. failed. Thus, any evidence based on the (then) standard methodology was difficult to interpret. TESTING NEUTRALITY The second reason—the one that is at PROPOSITIONS the heart of the methods used in the recent Recent Tests Based (Mostly) research—was that the story of monetary neutrality involves permanent changes in on U.S. Data the level of the money stock, and that one Fisher and Seater (1993) work in terms cannot effectively test such a theory with- of bivariate systems, with a measure of out evidence that the actual money stock money as one of the variables. Adopting has been subject to a permanent change. their notation, let m be the natural loga- The idea of permanent changes in econ- rithm of the nominal money stock M. Let omic variables is statistically modeled as a y be a second variable, expressed in either unit root in the autoregressive representa- real or nominal terms, which is the loga- tion of a time series; a time series with a rithm of a variable like the price level or unit root has quite different properties real output, and where the variable itself from a stationary series.6During the early is Y.7 Denote the order of integration of a 1970s when Lucas and Sargent first wrote variable by 〈x〉, so that if x is integrated of about this topic, the implications of unit order l, we write 〈x〉 = l. Sometimes we roots in economic time series were only also will use the phrase “x is I (l)” to beginning to be appreciated. Later, in an describe the order of integration. Denote influential paper, Nelson and Plosser a difference operator by ⌬, so that ⌬y indi- (1982) argued that many U.S. macroe- cates the approximate growth rate of the conomic time series were best characterized variable Y. Fisher and Seater study the by a unit root in their univariate, autoregres- following system sive representations. Their results brought the issue of how to handle these nonsta- ∆ m = ∆ y + tionary time series to the fore in macro- (1) a(L) mt b(L) yt ut econometrics, and led to econometric 6 One could use other methods methodologies that respected the potential to statistically model a perma- ∆ y = ∆ m + for nonstationarity in important macroeco- (2) d(L) yt c(L) mt wt nent shift in the level or growth nomic variables. rate of a monetary variable. The nonstationarity in economic vari- One could, for instance, posit a ables was viewed as something of a head- where a(L), b(L), c(L) and d(L) are lag discrete shift in the mean of the variable at a given date, T, and ache for much of macroeconometrics. But polynomials, and a0 = d0 = 1 and b0 and c0 one could then check to see in a remarkable turn of events, it actually are unrestricted. The error vector (ut,wt)' was a boon to testing neutrality proposi- is iid with zero mean and covariance ∑. how other variables responded tions. As Lucas and Sargent had argued, Now let x ≡ ∆im and z ≡ ∆j y , with i, j to such a permanent move- t t t t ment. Nothing here is ruling one needs permanent changes in the money = 0 or 1. Fisher and Seater define a certain out such an approach, but the stock as part of the historical record to test long-run derivative (LRD) that is central to literature surveyed in this paper the proposition of long-run neutrality in a their findings. The LRD is a change in z focuses on unit-root characteri- time-series setting. But permanent shocks with respect to a permanent change in x, zations of variables of interest are exactly what macroeconomic time given by as measures of whether these series provide. ∂ ∂ series have permanent compo- ≡ zt+k / ut This was exactly the line pursued by (3) LRDz,x lim , nents or not. k→∞ ∂ ∂ xt+k / ut Fisher (1988) and Fisher and Seater 7 To simplify the discussion in this (1989, 1993), and also in a series of papers section, interest rates are left ∂ ∂µ ≠ by King and Watson (1992, 1994, 1997). provided limk→∞ xt+k / t 0, otherwise out here, even though they are These authors provided new tests of long- the LRD is undefined. Fisher and Seater included in Fisher and Seater’s run neutrality propositions that respected then define long-run neutrality and long-run (1993) framework.

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superneutrality in this framework, and for efforts that, because of the time they were each, discuss four cases that depend on the written, did not take such explicit account order of integration of the variables.8 of the time-series properties of the data. First of all, money is long-run neutral They interpret the evidence in Anderson with respect to y if LRDy,m= 1 when y is a and Karnovsky (1972), Kormendi and nominal variable, or if LRDy,m= 0 when y Meguire (1984), Lucas (1980), and is a real variable. The four cases are: Geweke (1986) mostly as consistent with 1) 〈m〉 < 1. Here the LRD is not defined long-run neutrality and not very informa- because there have been no permanent tive about long-run superneutrality. They shocks to the level of the money stock, also provide some evidence of their own. and the data are uninformative concerning They use the Friedman and Schwartz long-run monetary neutrality. 2) 〈m〉 ≥ 〈y〉 (1982) data on money, prices, nominal + 1 ≥ 1. Here the LRD is zero because income, and real income from 1867 to while there have been permanent shocks 1975 in the United States. All variables are to the level of the money stock, there have viewed as I(1), making tests of long-run been none to y. If y is a nominal variable, neutrality possible. With respect to nom- long-run neutrality is violated, otherwise it inal income and prices, long-run monetary holds. 3) 〈m〉 = 〈y〉 ≥ 1. This case admits neutrality holds in this data, but with tests of long-run neutrality, in an effort to respect to real output, long-run monetary find out if the permanent shocks to the neutrality fails. level of the money stock are correlated with As mentioned earlier, evidence of the the permanent shocks to the variable y. failure of long-run monetary neutrality is 4) 〈m〉 = 〈y〉 –1 ≥ 1. This case is more either surprising or suspect among mone- complicated. A necessary condition for tary theorists; the Fisher and Seater finding long-run neutrality is that the permanent was no exception. In a note, Boschen and shock to money does not change the Otrok (1994) re-estimate the systems growth rate of y. studied by Fisher and Seater, again using Secondly, money is long-run superneu- the Friedman and Schwartz (1982) data, tral with respect to y if LRDy, ∆m= 0. The but now updating the time series through cases are 1) 〈∆m〉 < 1. Here the LRD is not 1992. They split the data set into two sub- defined because there have been no perma- samples, 1869-1929 and 1940-92. They nent shocks to the growth rate of the money find that long-run neutrality holds in both stock, and the data are uninformative con- of the subsamples using the Fisher and cerning long-run monetary superneutrality. Seater methodology. They conclude that 2) 〈∆m〉 ≥ 〈y〉 + 1 ≥ 1. The LRD is zero there may have been something special because while there have been permanent about the financial disruption during the shocks to the growth rate of the money Great Depression era that causes the test to stock, there have been none to y. Long-run fail when that period is included. superneutrality holds. 3) 〈∆m〉 = 〈y〉 ≥ 1. Haug and Lucas (1997) comment fur- This case admits tests of long-run superneu- ther on these findings. They reason that, trality, in an effort to find out if the perma- since Canada did not experience bank fail- 8 In an appendix, Fisher and nent shocks to the level of the money stock ures during the Great Depression, the Seater (1993) argue that coin- are correlated with the permanent shocks evidence on long-run neutrality using tegration plays no role in their to the variable y. 4) 〈∆m〉 = 〈y〉 –1 ≥ 1. Canadian data might provide further bivariate tests of neutrality or Here LRD∆y, ∆m= 0 is testable; that is, one evidence that something unusual happened superneutrality. This does not can determine whether a permanent in the United States during this period. imply that one could not devise other, similar tests based on change in the growth rate of money is Their data set includes real national cointegration, as (in fact) has associated with a permanent change in income and the M2 money supply from been done. See, for instance, the growth rate of y. 1914-94. They argue that pre-1914 data is the Boschen and Mills (1995) Fisher and Seater (1993) use these inappropriate for this purpose because paper reviewed later in this results to analyze previous research efforts changes in the money supply were not section. testing long-run neutrality propositions, exogenous in Canada at that time. They

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62 N OVEMBER/DECEMBER 1999 conclude, based on augmented Dickey- the order of integration of the variables Fuller (ADF) tests, that both time series are involved when devising tests of neutrality I(1). And, according to the Fisher and propositions. They study a “final form” Seater (1993) methodology, long-run mone- model tary neutrality with respect to real output ∆ = µ +θ ε η +θ ε m cannot be rejected using the entire Canadian (4) yt y yη (L) t ym (L) t sample period. Haug and Lucas interpret this finding as independent support for the ∆ = µ +θ ε η +θ ε m arguments of Boschen and Otrok (1994). (5) mt m mη (L) t mm (L) t Olekalns (1996) similarly explored an alternative data set, 94 years of annual where y is the logarithm of real output, ε m Australian data. The downturn of the 1930s the ␪ coefficients are lag polynomials, t is was less severe in Australia. Olekalns uses a serially independent, zero mean shock to εη the Fisher and Seater methodology, and two money, and t is a vector of nonmonetary measures of money, M1 and M3, along with shocks that affect output. King and Watson real gross domestic product. All variables show that are reasonably described as I(1) according θ (1) to ADF tests. Olekalns finds that long-run (6) γ = ym ym θ ( ) monetary neutrality cannot be rejected mm 1 using the narrower money measure. How- ever, using the broader money measure, is the long-run elasticity of real output long-run neutrality can be rejected for with respect to permanent shocks to the this data set, and the rejection carries even money stock. Thus, long-run neutrality when dummy variables are used to control here is analogous to the Fisher and Seater for the Depression period as well as the definition: ␥ym = 0. Again, long-run neutral- WWII period. Olekalns concludes that ity can be investigated only if there have results can be sensitive to the measure been permanent shocks to the money stock. of money used. Importantly, King and Watson (1997) A recent paper by Coe and Nason (1999) emphasize identification issues. They ana- also contributes to this literature. They use lyze long-run neutrality propositions the Fisher and Seater (1993) test for long-run across a range of possible identifications neutrality, and they employ the same U.S. of their bivariate system, in an effort to data as Fisher and Seater, except that they understand the robustness of various con- update the data through 1997. When Coe clusions to differing assumptions. They and Nason use a broad measure of the rewrite the equations (4) and (5) as money stock (as Fisher and Seater did), they p ∆ = λ ∆ + ∑ α ∆ replicate the Fisher and Seater rejection of (7) yt ym mt j,yy yt− j 9 Coe and Nason also study the long-run monetary neutrality with respect to j=1 p asymptotic power properties of real output. But when they replace the broad + ∑ α ∆ + ε η j,ym mt− j t the Fisher and Seater long-hori- money measure with the monetary base, they j=1 zon regression test, and they can no longer reject long-run neutrality. conclude that the test has low p They also consider about a century of data ∆ = λ ∆ + ∑ α ∆ power against alternative (8) mt my yt j,my yt− j from the United Kingdom, and fail to reject j=1 hypotheses of monetary non- p neutrality. For small samples, long-run neutrality using either broad or + ∑ α ∆ + ε m j,mm mt− j t Monte Carlo experiments reveal narrow measures of money. Coe and Nason j=1 conclude that the Fisher and Seater rejection poor size-adjusted power espe- cially at longer horizons. Coe of long-run neutrality is not robust to a and they assume that and Nason conclude based on η change in either the measure of money or (ε m ε ) = this portion of their analysis 9 cov t , t 0. the country of study. that the Fisher and Seater An important work in this literature, They note that there are several plausible approach to testing long-run King and Watson (1997) also use bivariate ways to complete their identification of the monetary neutrality may not be systems, and they also take careful note of system. One could assume ␭ym = 0, or that informative.

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Figure 2

Inflation and Unemployment λ A. 95% Confidence Interval for ␥ym as a Function of my 6

4 m

y 2 ␥ 0

—2 —0.6—0.20.2 0.61.01.41.82.2 λmy λ B. 95% Confidence Interval for ␥ym as a Function of ym 6

4 m

y 2 ␥

0

—2 —10—8—6 —4—202 λym

C. 95% Confidence Interval for ␥ym as a Function of ␥my 10

6 m

y 2 ␥ —2

—6 —5—4 —3 —2—10123 ␥my

D. 95% Confidence Ellipse when ␥ym = 0 1.5

0.5 m y

λ —0.5

—1.5

—2.5 —0.4—0.2 0.0 0.20.40.60.8 λmy

The evidence on long-run monetary neutrality according to King and Watson (1997). The panels show how the point estimate of ␥ changes under the differing identifying restrictions, with the dotted lines indicating 95% confidence intervals. The bottom panel y m λ λ displays a 95% confidence ellipse for ym and my under the identifying restriction ␥ym = 0.

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␭my= 0; this means that the impact elasticity involving ␭ym and ␥my. They also estimate of one variable on the other is zero. Alter- 95-percent confidence intervals for ␭my, natively, one could simply assume long-run ␭ym, and ␥my using the identifying assump- monetary neutrality by imposing ␥ym = 0. tion that long-run neutrality holds, ␥ym =0, And finally, one could assume that ␥ym = 1 in order to see if the confidence intervals where ␥my is the long-run elasticity of money produced contain the most reasonable with respect to a permanent shock to real values for these parameters. All of this output. King and Watson (1997, p.77) evidence comes down in favor of long-run argue that this last assumption is consistent neutrality, which is consistent with the with stable prices in an economy with con- findings of Fisher and Seater (1993) and stant velocity. Boschen and Otrok (1994), because the Because King and Watson wish to sample period here covers the postwar investigate the robustness of neutrality United States.10 This evidence is summa- results to alternative identifying assump- rized in Figure 2. tions, they use all four of these possibilities. The superneutrality of money is inves- Furthermore, they allow a wide variety of tigated using a bivariate system with money values for each elasticity, not just the zeroes growth (replacing the level of the money and ones of the previous paragraph. Thus, stock) and real output, and the hypothesis the identifying assumptions are that either is that the long-run elasticity of the level of one of the impact elasticities is known to output to a permanent change in the growth be a certain value, or that one of the long- rate of money, ␥y, ∆m , is zero. The evidence run elasticities is known to be a certain on this question turns out to be mixed, in value. They then turn to estimation and that for some identification schemes that report results considering a number of King and Watson consider reasonable, the neutrality propositions. The quarterly hypothesis that ␥y, ∆m =0 can be rejected at data are for the United States and cover the 5-percent level. Moreover, the effect the sample period from 1949:1 to 1990:4; can go either way: a permanently higher except for systems with unemployment, rate of money growth tending to in which case the sample period is from permanently increase the level of real 1950:1 to 1990:4. The lag length p is set output, or to decrease the level of real to six, although they experiment with output. For instance, if the identifying values of four and eight at some points. assumption is ␭∆m, y =0 (which King and Based on unit-root diagnostic tests, King Watson again interpret as a short-run and Watson conclude that all the series money demand elasticity), then the esti- involved can reasonably be viewed as I(1), mated value of ␥y, ∆m is positive and statis- so that tests of neutrality propositions tically significant, while if the identifying can be executed. assumption is that ␭∆m, y =.6, then the esti- King and Watson (1997) first investi- mated value of ␥y, ∆m is negative and statis- 10 Jefferson (1997) also investi- gate the long-run neutrality of money in tically significant. As mentioned earlier, gates monetary neutrality ques- the context of a bivariate system using real theories exist that are consistent with tions using the King and output and money (M2). They begin by both possibilities. Watson (1997) methodology, estimating a value for ␥ym using the identi- King and Watson go on to investigate except that he considers mea- sures of both inside money fying assumption that ␭my is known. They a neutrality proposition associated with find that a 95-percent confidence interval the early 20th century economist Irving (defined as nominal checkable deposits, or M2 less currency) for ␥ym contains zero (and so supports Fisher. The proposition is that nominal long-run monetary neutrality) so long as interest rates move one-for-one with and outside money (defined as the monetary base). He uses ␭ ␭ my > 1.4. If we interpret my the parameter permanent changes in inflation, leaving nearly a century of data from as a short-run elasticity of money demand, the real interest rate unaffected. Using a the United States and finds ≤ ≤ a reasonable range is .1 ␭my .6, so that system with consumer price index some departures (under some the evidence is consistent with long-run inflation, π, playing the role of the money identifying restrictions) from neutrality. King and Watson complete sim- variable, and the nominal interest rate on long-run neutrality when inside ilar calculations for identifying assumptions three-month Treasury bills, R, playing the money is used.

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role of the output variable, King and results on neutrality for a wide variety of Watson (1997) investigate the hypothesis identification schemes, they do so only for that ␥Rπ =1; that is, the long-run elasticity bivariate systems, and they note the possi- of the nominal interest rate with respect to bilities for exposure to omitted variable a permanent inflation shock is one. The bias. One of the few multivariate studies evidence here again turns out to depend available using techniques related to those on the identification scheme. When statis- of Fisher and Seater (1993) for testing tically significant differences from the neutrality is by Boschen and Mills (1995). standard Fisher relation occur, they occur They use the notion of permanent shocks in a negative direction, with nominal to the level of the money stock to test interest rates rising less than one-for-one long-run monetary neutrality in the U.S. with perma-nent shocks to inflation. In data. They use a relatively high dimensional other words, real interest rates are lowered system, and they organize their research permanently by permanent, positive shocks around the idea that, if long-run neutrality to the inflation rate. King and Watson find does not hold, there would be a nonsta- that identifying the model by assuming tionary component of real output that is ␥Rπ =1, and then estimating 95-percent determined by long-term movements in confidence intervals for the remaining the money stock. They study a vector error parameters, leads to the conclusion that correction model (VECM) representation

there are reasonable configurations of k−1 ∆ = µ + ∑ Γ ∆ + Π + ε parameters that are consistent with the (9) Xt i Xt−i Xt−k t, Fisher hypothesis. Nevertheless, the main i=1 conclusion is that nominal interest rates where X' ≡ (y, m,υ)', and y is aggregate do not adjust fully to permanent inflation output, υ is a vector of real shocks, m is a shocks, and this conclusion holds across a vector of monetary shocks, and ε is nor- large set of identification schemes. mally distributed, iid, and has mean zero. Finally, King and Watson turn to esti- Interest centers on the long-run impact mating the slope of a long-run Phillips coefficient matrix ∏ that describes the curve; that is, the long-run response of long-run relationships in the model. For unemployment to permanent shocks in the each cointegrating relationship, this matrix inflation rate. This particular test is dis- will have a nonzero row. If there is a coin- cussed in more detail in another paper, tegrating relationship between the mone- King and Watson (1994). The bivariate tary variables and output, then these varia- system now includes the CPI inflation rate bles contribute to the trend shifts in output, in the role of the nominal variable, and the and long-run neutrality is violated.11 unemployment rate in the role of the real Boschen and Mills (1995) use quarterly variable. The hypothesis is that the long- U.S. data from 1951:4 to 1990:4. They run Phillips curve is vertical, which means include variables describing productivity, ␥uπ =0 in this framework. King and Watson real oil prices, weighted foreign real GDP report that a statistically significant (nega- of major U.S. trading partners, real govern- tive) slope for the long-run Phillips curve ment purchases, taxes, labor supply, the can be obtained only if the identifying M1 money stock, the M2 money stock, assumption is that ␥πu>2.3, or alternatively and the nominal three-month Treasury bill that ␥uπ< –0.7. In particular, if either of rate. They use augmented Dickey-Fuller these two impact elasticities are zero, then tests as diagnostics for the presence of a vertical long-run Phillips curve cannot be nonstationarity in these data; they found rejected. King and Watson conclude that a (sometimes weak) evidence of a unit root reasonable estimate of the long-run Phillips in all the series. They test for cointegrating curve based on this data is either vertical relationships among the blocks of real and 11For a related approach and or at least “very steep.” nominal variables, and then between the analysis, see Hoffman and While King and Watson’s strong suit is nominal and real variables, as a means of Rasche (1996), Chapter 7. that they can investigate the robustness of testing for long-run monetary neutrality.

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Based on these tests, Boschen and Mills cases he uses the I(1) aggregates to test for conclude that long-run monetary neutrality neutrality and the I(2) aggregates to test holds during the postwar period in the U.S. for superneutrality. The remaining series This result confirms the findings that Fisher on output, inflation, interest rates, and and Seater (1993), Boschen and Otrok unemployment rates, for the most part, (1994), and King and Watson (1997) can be reasonably interpreted as I(1). reported regarding long-run monetary neu- Weber then turns to tests of long-run trality in the postwar U.S. data. This result monetary neutrality in these countries, also provides the best available evidence using the same wide variety of possible that omitted variable bias did not contami- identifying assumptions that King and nate the previous results on this question. Watson used. His general finding is that for broader monetary aggregates, such as M2 or M3, a wide variety of identifying Recent Tests Using restrictions are consistent with (fail to International Data reject) long-run monetary neutrality in the So far, we have results that conform to G7 economies during the postwar era. For the suggestions of King and Watson and narrower measures of money, the range of Fisher and Seater only for U.S. data—cer- identifying restrictions consistent with tainly a natural place to start but not the long-run monetary neutrality is much true extent of the available evidence. As a smaller. Confidence ellipses for ␭ym and first effort at generalization, Weber (1994) ␭my under the identifying assumption that explicitly set out to apply the King and money is long-run neutral, ␥ym=0, include Watson testing procedures to G7 econo- the plausible region of the space where ␭ym mies: Canada, France, Germany, Italy, <0, (the short-run impact of money on Japan, the United Kingdom, and the output is positive) and ␭my >0 (money United States. The data is quarterly, from reacts countercyclically to output in the the postwar era, but the particular years short run). This is true across the G7 vary across countries. economies for both narrow and broad Weber begins with a battery of unit- measures of money. root diagnostics—using a much more Superneutrality is examined using a elaborate procedure than the papers bivariate VAR in differenced money growth discussed so far—in an effort to make and differenced real output. In general, careful statements about the evidence for long-run superneutrality with respect to the presence of a unit root in the time the level of real output is rejected for a series. For each country, he uses several wide variety of identifying restrictions different measures of the money stock, in across the G7 economies. part to confront the question of whether Considering the question of whether the results are sensitive to how money is the long-run Phillips curve is vertical, defined. The combination of several diag- Weber proceeds using the changes in infla- nostic tests and many different time series tion and unemployment in his bivariate produces a plethora of results that are not VAR. For six of the seven G7 economies, all the same. As a general rule, however, the hypothesis that ␥uπ =0 cannot be narrower monetary aggregates tended to rejected except in cases of rather extreme be I(1), while broader aggregates tended to identifying assumptions. The exception is be I(2). Strictly speaking, according to the Italy, where this hypothesis can be rejected methodology outlined above, if money is readily. Weber also considers a “reverse” I(2) then superneutrality can be tested, hypothesis, with causality running from whereas neutrality cannot. In response to unemployment to inflation. In this case this situation, Weber takes two approaches: the hypothesis ␥πu =0 can be rejected easily In some cases, he performs neutrality tests across the non-Italian economies. For anyway and warns the reader to interpret Italy this hypothesis is rejected only for the results with caution, while in other extreme identification schemes. Weber

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Figure 3 Long-Run Response of the Level of Output To a Permanent Increase in Inflation 4.5

3.5

2.5

1.5 e

0.5

—0.5

—1.5

—2.5 Germany USA Cyprus Finland Ireland Portugal Iceland Chile Austria Japan Australia UK Spain Costa Rica Mexico Argentina

Country

Countries ordered from lowest to highest average inflation in sample. Horizontal lines represent point estimates. Vertical lines represent 90 percent confidence bounds. The point estimate of the long-run response of the level of real output to a permanent inflation shock is generally positive for the low inflation countries but zero or negative for high inflation countries. This figure is reproduced from Bullard and Keating (1995) and is reprinted with permission by the Journal of Monetary Economics. speculates that wage indexation in Italy the evidence is much more favorable for during much of this period accounts for a Fisher relation, ␥rπ=1, to hold. The gen- the differences between Italy and the other eral finding in the previousliterature (see industrialized economies. for instance, Lothian, 1985, for 20 OECD Finally, Weber goes on to test the countries) is that nominal interest rates Fisher relation for the G7 economies using adjust less than one-for-one with inflation. a bivariate VAR in differenced inflation and While Weber considered G7 differenced nominal interest rates. He economies, Bullard and Keating (1995) finds that for Germany, a Fisher relation consider virtually all of the countries in can be rejected for a wide variety of identi- the world where enough data existed to fying restrictions, although some important formulate tests of long-run neutrality benchmark restrictions do not lead to propositions in the spirit of Fisher and rejection. For the United States, Weber Seater (1993) and King and Watson (1997). confirms the findings of King and Watson In working with a large number of countries, (1997) that nominal interest rates do not data availability and quality impinge adjust one-for-one with permanent shocks significantly on the analysis. Accordingly, to inflation. Even stronger evidence in this Bullard and Keating restrict attention to direction is found for the United Kingdom. countries that produce at least moderately But for Japan, Canada, Italy, and France, high quality data (according to published

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68 N OVEMBER/DECEMBER 1999 assessments) and have at least 25 years of The main results for the Group A consecutive annual observations (quarterly countries are as follows: The long-run data often is not available). This leaves response of the level of output to a perma- them with 58 countries. Bullard and Keating nent inflation shock was positive and focus their analysis on one particular version statistically significant for four countries, of a neutrality proposition: the effect of a negative and statistically significant for permanent shock to inflation on the level one country, and not statistically different of output. If money is long-run neutral— from zero for the remainder. The point and the evidence reported in this survey estimate of this long-run response generally suggests that this is a reasonable assump- declined as the in-sample average inflation tion—then this can be viewed as a test rate increased, as shown in Figure 3. of monetary superneutrality with respect The Group B countries, which possess to the level of real output. Moreover, prob- permanent inflation shocks but no perma- lems with the definition of money within nent output shocks, provide prima facie and across countries are avoided. evidence of superneutrality. The Group C Bullard and Keating also begin with a countries are uninformative because they battery of unit-root diagnostic tests for the do not possess permanent inflation shocks. real output and GDP deflator time series Altogether, the results appear to be consis- they use. They divide countries into tent with superneutrality for most of the groups based on the results of these tests, countries that are informative. according to whether a country can be However, as Figure 3 indicates, and characterized as having experienced as is borne out by the associated impulse- permanent shocks to inflation or not, and response functions, low-inflation countries similarly for the level of real output. appear to react very differently to permanent Countries that experienced permanent inflation shocks than high-inflation coun- shocks to inflation and also to the level of tries.12 In particular, for low-inflation output are candidates for a test based on a countries the point estimate of the long- bivariate VAR; there were 16 countries in run response is generally positive, while this group, dubbed Group A. There were for high-inflation countries it is zero or also nine Group B countries for which negative. This suggests that averaging evidence of a unit root in inflation was results from low and high-inflation coun- found, but evidence of a unit root in tries may be misleading. output was lacking. A large number of Bullard and Keating also comment countries, 31, showed no evidence of perma- on the prospects for permanent inflation nent shocks in the inflation series, and were shocks to permanently alter rates of growth put into Group C. The two remaining of real output in this sample. According countries were special cases. to ADF and other diagnostic tests for unit Bullard and Keating (1995) then ran a roots, real output growth rates are stationary two-variable VAR for the Group A countries, in nearly all countries that experienced in differenced inflation and differenced permanent shocks to inflation. This is direct output. They committed to the long-run evidence for superneutrality with respect identifying restriction that money is long- to output growth rates. This result does run neutral, ␥πy=0 in the King and Watson not seem like one that is likely to change 12 Other aspects of the impulse- (1997) notation, and did not attempt to with data sets or countries, since the sta- response functions had natural search over alternative identifying restric- tionarity of real output growth is likely to interpretations according to con- tions. They used the techniques of Blan- remain under most conceivable criteria.13 ventional wisdom, and also chard and Quah (1989) to decompose All of the Bullard and Keating data are were generally consistent shocks into permanent and transitory for postwar economies. Serletis and Krause across countries. components, and consequently they consi- (1996) use the Backus and Kehoe (1992) 13 This result conflicts with other dered the impulse-response functions of data set, which includes more than 100 evidence from the cross-country reactions of the two variables to both years of annual observations on real output, growth regression literature, permanent and transitory shocks. prices, and money for Australia, Canada, such as Barro (1996).

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Denmark, Germany, Italy, Japan, Norway, Both Serletis and Krause (1996) and Serletis Sweden, the United Kingdom, and the and Koustas (1998) fail to reject long-run United States.14 They test for unit roots neutrality even when this period is included using the procedures of Zivot and Andrews (under a range of plausible identification (1992), and they conclude that money is schemes in the latter case). However, reasonably described as I(1) except in Serletis and Koustas (1998) in fact reject Germany and Japan where it is I(0); these long-run neutrality under the Fisher and latter two countries are therefore uninfor- Seater (1993) identifying restriction (␥my = mative on neutrality questions in this data 0), but they do not reject under other, set. Serletis and Krause (1996) find that possibly more plausible, identifying restric- output is I(0) for Australia, Canada, Den- tions. Of course, differences in results could mark, Italy, the United Kingdom, and the also be due to differences in the data sets United States. These countries, therefore, employed. Similar comments can be made provide direct evidence in favor of long- concerning the results of Olekalns (1996) run neutrality with respect to output. using a near-century of Australian data. Serletis and Krause use the Fisher and Crosby and Otto (1999) move away Seater (1993) regression test to produce from the money-inflation-output nexus estimates for the remaining money-price discussed in many of the papers so far, in or money-output combinations. These order to analyze the long-run connection results generally support a hypothesis of between inflation and the capital stock long-run monetary neutrality. using the methods of Fisher and Seater The same data set is used by Serletis (1993) and King and Watson (1997). and Koustas (1998), who apply the King Crosby and Otto consider a bivariate VAR and Watson methodology to study long- with inflation playing the role of the nom- run neutrality and superneutrality issues inal variable, and the capital stock playing over a range of plausible identifying restric- the role of the real variable. They use the tions. They use only the money and real long-run identifying restriction that shocks output series, and apply a battery of tests to to the capital stock do not have permanent determine the integration properties of the effects on the rate of inflation, which is data. Except for the money series for Italy, similar to the long-run restriction sometimes which is I(2), they conclude that all series employed in the papers discussed earlier. are I(1) and hence provide a reasonable They construct an annual capital stock 14 Some data are missing, dataset with which to test long-run mone- series for 64 countries using postwar data, notably 1914-24 and 1939-49 tary neutrality (superneutrality for Italy).15 with differing sample periods for different for Germany and 1941-51 for The results state that it is generally difficult countries. Their unit-root diagnostics Japan. Also missing are 1915- to reject long-run monetary neutrality in (ADF tests) indicate that 34 of these coun- 20 for Denmark, and 1940-45 this dataset under plausible identifying tries have both permanent shocks to for Norway. restrictions. An exception is the United inflation and to the capital stock. For 15 These results on orders of inte- Kingdom, when the identifying restriction these countries they test superneutrality ≤ ≤ gration are somewhat different is that 0 ␭my .6. Superneutrality of with respect to the capital stock using from those of the previous money with respect to real output in the their bivariate VAR. The Crosby and Otto paragraph, even though the Italian data can be rejected under plausible estimates indicate that a permanent infla- data set is the same, because identifying restrictions. tion shock has no statistically significant Serletis and Koustas (1998) The Serletis and Krause (1996) and Ser- long-run impact on the capital stock for a use different (and more stan- letis and Koustas (1998) results may appear large majority of the countries. Departures dard) procedures to test for the to impinge on the Fisher and Seater (1993) from this result are generally on the posi- presence of unit roots than Serletis and Krause (1996). and Boschen and Otrok (1994) findings for tive side, with a permanent inflation shock In section four of their paper, the United States, namely that the results tending to raise the stock of capital in a Serletis and Koustas (1998) for long-run monetary neutrality in the country. Crosby and Otto argue that these discuss the differences when United States over the last century depend results are robust to a number of changes the Zivot and Andrews (1992) critically on inclusion or removal of the in their analysis, including an alternative methodology is used. Great Depression years from the sample. identifying restriction.

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A real variable of interest to many Rapach (1999a) is the first author to economists is productivity. In an attempt consider a trivariate VAR in this literature. to understand the long-run relationship His variables are the inflation rate, the between inflation and productivity, nominal interest rate, and the level of real Sbordone and Kuttner (1994) devote a output. The data is from the postwar portion of their analysis to bivariate VAR period for 14 industrialized (OECD) coun- methodology similar to that used by King tries, where continuous observations on all and Watson (1997). They use data from three variables are available starting from the postwar United States, and they the 1960s and extending to the mid-1990s.16 conclude that both series are reasonably Rapach (1999a) uses long-run identifying characterized as I(1). Sbordone and restrictions following Blanchard and Quah Kuttner use the King and Watson (1997) (1989); he needs three for the trivariate approach to identification, setting impact system. Rapach first extends the often- multipliers and long-run multipliers to used monetarist restriction that permanent various values in an effort to learn about shocks to interest rates and output cannot the sensitivity of the results to alternative have permanent effects on the inflation identification schemes. Under many of rate. Rapach’s third restriction, also moti- these schemes, the long-run impact of a vated by theoretical considerations, is that permanent, positive shock to inflation on permanent shocks to output (“permanent productivity is negative. If the identifica- technology shocks”) leave the real interest tion scheme is the monetarist one—the rate unchanged. Since the long-run long-run impact of a permanent shock to response of inflation to a permanent tech- productivity on inflation is zero—then the nology shock is already set to zero, this last estimated effect of a permanent inflation restriction is accomplished by making the shock on productivity is negative but is long-run response of the nominal interest not statistically different from zero. rate to a permanent technology shock Koustas and Serletis (1999) use the equal to zero. King and Watson (1997) methodology of Rapach uses unit-root diagnostic tests searching across alternative identification to conclude that the variables are reasonably schemes to study the Fisher relation between described as I(1) for these countries, and nominal interest rates and inflation rates. runs the trivariate VAR in an effort to esti- They employ data from the postwar period mate, primarily, the long-run responses of for 11 industrialized countries: Belgium, the level of real output to a permanent Canada, Denmark, France, Germany, Greece, inflation shock, and of the real interest rate Ireland, Japan, the Netherlands, the United to a permanent inflation shock (the differ- Kingdom, and the United States. According ence between two estimated long-run to the authors’ unit root diagnostic tests, all responses in this system). For all countries, of these countries except two (Denmark the point estimates indicate that real interest and Japan) can reasonably be interpreted as rates fall in response to a permanent infla- possessing the nonstationarity in interest tion shock. Moreover, these effects are rates and inflation rates required to use the generally statistically significant (or very King and Watson techniques. The basic close) at conventional significance levels. finding is that the long-run Fisher relation The point estimates also indicate that the can be rejected across countries for a wide response of the level of real output to a range of plausible identification assumptions. permanent inflation shock is positive for The authors also argue that taking tax effects 11 of 14 countries, and four of these are into account accentuates this finding. statistically significant, or nearly so, at 16 The countries are Australia, The Koustas and Serletis results are more conventional significance levels. These Austria, Belgium, Canada, consistent across countries on this question latter results are generally consistent with Denmark, France, Ireland, Italy, than those of Weber (1994), who found the findings of Bullard and Keating for low Japan, the Netherlands, New more mixed results for a similar set inflation countries in a bivariate VAR Zealand, Sweden, the United of countries. framework. The results on real interest Kingdom, and the United States.

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rates are more strikingly in favor of These effects are large and statistically sig- nonsuperneutrality than the findings of nificant. The Fisher effect does not hold, Weber for G7 economies in bivariate as Ahmed and Rogers infer that real interest systems. Weber searched over identification rates decline in the face of permanent, schemes while Rapach commits to a partic- positive inflation shocks according to ular scheme, but Rapach studies interactions these estimates. between three variables instead of two and Ahmed and Rogers then turn to estima- analyzes more countries. tion of a VECM using the cointegrating relationships implied by their theoretical model, in an effort to find out what happens Related Methodology to the levels of the real variables following Using U.S. Data a permanent inflation shock. For two dif- Ahmed and Rogers (1996, 1998) work ferent specifications, the estimates indicate on empirical issues related to the long-run that a permanent shock to inflation increases impact of permanent inflation shocks on the level of output, consumption, and real variables, but with methods somewhat investment. Ahmed and Rogers also con- different from those discussed earlier. In sider variance decompositions and note particular, Ahmed and Rogers construct a that the inflation shock only accounts for a theoretical model economy and use this small fraction of the forecast error variance economy to motivate restrictions imposed in consumption, investment, and output.17 in their empirical work. The model They interpret these results as follows: consists of an infinitely-lived representative Permanent inflation shocks do not occur agent who might hold money either because very often, but when they do, they have it enters the utility function or because of a a significant impact on the economy. cash-in-advance constraint. The technology Accordingly, when looking at the data for production of private sector real output historically, one might reasonably abstract is Cobb-Douglas, multiplied by a technology from inflation in building a model, but shift variable and also by a function of when contemplating significant changes government size. Special cases of this in inflation rates, one should not assume framework (restrictions on theoretical the effects will be negligible.18 parameters) deliver the standard results Bernanke and Mihov (1998a) test from the theoretical literature on monetary long-run monetary neutrality, and, like superneutrality surveyed by Orphanides Ahmed and Rogers (1998), they depart and Solow (1990). from the methodology described in the Ahmed and Rogers (1998) use annual main portion of this survey. In particular, U.S. data from 1889 to 1995 covering Bernanke and Mihov use their own, larger inflation, real output, real consumption VAR model of short-run monetary policy expenditures, real investment, and the which is described in more detail in another ratio of government spending to output. paper (Bernanke and Mihov, 1998b) as a 17 Rapach (1999a) also com- Much of the data is from Kendrick (1961). starting point. This model uses monthly putes variance decompositions and concludes that inflation Based on diagnostic testing, Ahmed and data for the United States during the postwar shocks do not explain a signifi- Rogers conclude that a reasonable descrip- era, and has the following variables: total cant fraction of output forecast tion of the data is that these series are I(1), bank reserves and nonborrowed reserves, error variance. with the exception of the size of govern- both measured as deviations from a trend ment, which they sometimes treat as I(0). and the federal funds rate (collectively the 18 Ahmed and Rogers (1998) The authors then estimate cointegrating policy variables); interpolated monthly real also consider subsamples. They find that the effects of relationships for two specifications of the GDP and interpolated monthly GDP deflator inflation on real variables move model. Based on these estimates, a perma- inflation, an index of spot commodity in the same direction, but are nent, positive shock to inflation is asso- prices and real balances (with money mea- much weaker, during the post- ciated with a permanent drop in the sured as M2). They use a semi-structural war period as opposed to the consumption-output ratio and a permanent approach to derive identification restrictions pre-WWI or the interwar period. increase in the investment-output ratio. based on relationships between the policy

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72 N OVEMBER/DECEMBER 1999 and nonpolicy variables, and among the (Geweke’s 1986 title notwithstanding!), policy variables, and they estimate the once one takes proper account of the time VAR. They do not examine the temporary- series properties of the data. While Fisher permanent dichotomy of the shocks to the and Seater (1993) found evidence against variables in their system; the focus instead long-run neutrality with respect to real is on isolating an action that can reasonably output for the United States during the last be termed “a shock to monetary policy.” century, Boschen and Otrok (1994) pointed Bernanke and Mihov’s evidence in favor of out that such a result did not hold once the long-run neutrality is based on the impulse- Great Depression years were excluded from response functions of their estimated VAR: the sample. In another comment on this These functions show that the long-run question, Haug and Lucas (1997) could not (120-month) response of output to the reject long-run neutrality in a century of policy shock is not significantly different Canadian data. Olekalns (1996) did find from zero, although positive. At the same some evidence against long-run neutrality time, they find short-term impacts of the in a near-century of Australian data using policy shock, such as a liquidity effect, that a broad money measure, but the neutrality are in accord with conventional wisdom. hypothesis could not be rejected using a Bernanke and Mihov (1998a) then narrower money measure. Coe and Nason turn to an analysis of the robustness of (1999) find that long-run neutrality cannot their results, by considering alternative be rejected for a century of U.S. data when identification schemes in a manner analo- the monetary base is the monetary variable, gous to the King and Watson (1997) nor could they reject long-run neutrality methodology. They find that the evidence for a century of U.K. data.19 on long-run neutrality is in a sense stronger Long-run neutrality received support when one is willing to accept an identifica- from the studies focused exclusively on the tion that produces a smaller liquidity effect. postwar U.S. data. King and Watson (1997) They also find that imposing long-run neu- searched over a wide range of identification trality as an identifying restriction does not schemes and found little evidence against imply that one can reject their specification. long-run neutrality. Boschen and Mills Bernanke and Mihov conclude that these (1995), studying a larger system of vari- findings inspire confidence in their VAR ables with cointegration techniques, but model of monetary policy, since it is con- without the extensive robustness checking, sistent with both a liquidity effect and also found little reason to doubt long-run long-run monetary neutrality. neutrality. Bernanke and Mihov (1998a) argue that their model is consistent with long-run neutrality using the postwar U.S. CONCLUSIONS data; like King and Watson (1997), they This survey has covered a fair amount explore the robustness of their findings to of territory. To avoid confusion about what an extensive range of alternative identifica- the results actually say, this section includes tion schemes. a summary of the main findings organized The studies that used data from more by the nature of the proposition. than one country also found general support for the long-run monetary neutrality pro- Long-Run Monetary Neutrality. In this position. For instance, Weber (1994), survey, we did not find much evidence using techniques similar to those of King against the long-run neutrality of money. and Watson (1997), generally supports Fisher and Seater (1993) usefully reinter- long-run neutrality for the G7 economies preted some of the major time series studies during the postwar period across a wide 19 Coe and Nason also raise on neutrality published in the 1970s and variety of identification schemes, especially important questions concerning 1980s as consistent with long-run monetary when money is measured using broader the statistical properties of the neutrality, and uninformative regarding monetary aggregates. Weber’s results also Fisher and Seater long-horizon long-run monetary superneutrality confirm the findings of King and Watson regression test.

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(1997) and Boschen and Mills (1995) for low inflation countries (such as the G7), the postwar U.S. data. Serletis and Krause point estimates tend to be positive and are (1996) use the Backus and Kehoe (1992) sometimes statistically significant. Serletis data set for 10 industrialized countries, and Koustas (1998) reject long-run mone- including the United States and Australia, tary superneutrality for Italy over the last covering more than a century. They found century, in a bivariate system with money general support for long-run monetary and real output, over a range of identifying neutrality, even in the United States and restrictions. Crosby and Otto (1998) gen- Australia, where Fisher and Seater (1993) erally find that permanent inflation shocks —for the United States—and Olekalns have little or no permanent effect on the (1996)—for Australia—had cast doubt. level of the capital stock in a large sample In a more extensive study, Serletis and of countries during the postwar period. Koustas (1998), use the same data set When they do find statistically significant and apply the King and Watson (1997) effects, permanently higher inflation is technology of searching over plausible associated with a permanently higher cap- identification schemes. Here, wide support ital stock. In Rapach’s (1999a) study of a for long-run monetary neutrality is found trivariate VAR using postwar data from across industrialized countries and plausible 14 OECD countries, permanent inflation identification schemes, even though the data shocks generally were associated with per- set is a very long-time series of the type that manently higher levels of real output and, sometimes displayed evidence against long- more strikingly, with permanently lower run monetary neutrality in previous studies. real interest rates. Ahmed and Rogers (1998), using methodology that departs Long-Run Monetary Superneutrality. This somewhat from the other studies in the survey has also shown that the evidence in survey, consider a century of U.S. data and favor of long-run monetary superneutrality conclude that permanent inflation shocks is far more mixed. This is perhaps not too have permanent, positive effects on impor- surprising since, as was stressed in the tant real variables, including output, introduction, it is a relatively simple matter consumption, and investment. They also to write down neoclassical, market clearing, stress that these shocks do not explain rational expectations theories in which a large portion of the forecast error superneutrality does not hold. In addition, variance in the data. since inflation is generally regarded as a While the overall evidence on these distortionary force in macroeconomic questions is mixed, considering only lower systems, we might reasonably expect real inflation countries leads to the conclusion variables to be altered in the face of perma- that permanently higher money growth or nent shocks to money growth and inflation. inflation is associated with permanently Analyzing postwar U.S. data, King and higher output and permanently lower real Watson (1997) find that rejection of long- interest rates. As Ahmed and Rogers (1998) run monetary superneutrality with respect stress, this result is inconsistent with many to real output is possible for a range of —almost all?—current quantitative busi- identification schemes they consider ness cycle models, which generally predict reasonable. Weber (1994) confirms this that permanently higher inflation perma- result using similar methodology across nently lowers consumption and output. the G7 economies during the postwar There is little support for such a prediction period. Bullard and Keating (1995) analyze in the studies surveyed here. This is an data from a number of countries worldwide important empirical puzzle that stands as during the postwar period. They consider a challenge for future research. permanent inflation shocks and the subse- quent reaction of the level of real output. Related Propositions. We have also seen The results generally support superneutrality, in this survey a smattering of evidence on but Bullard and Keating note that in the other, related neutrality propositions.

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King and Watson (1994, 1997) analyze the One problem is in the nature of the slope of a long-run Phillips curve in the unit-root diagnostic tests. Since time series postwar U.S. data, and find that a vertical characterized by a unit root have such dif- curve is a reasonable approximation. ferent properties from stationary time series, Weber (1994) reports generally similar the researcher is forced into a declaration findings for the G7 economies. of a unit root or not. Once this declaration King and Watson (1997) also study is made, the researcher can proceed with Fisher relations between interest rates further analysis. This brings to mind a and inflation, and conclude that nominal possible role for fractional integration in interest rates do not adjust one-for-one testing neutrality propositions. In fact, this with permanent inflation shocks under possibility has been explored recently in a a wide range of plausible identification study by Bae and Jensen (1998). More work schemes. Weber (1994) finds more mixed in this area may be fruitful in the future. results for the G7 economies, but evidence Canova (1994) also comments that presented by Rapach (1999a) and Koustas Weber’s (1994) results are based on bivariate and Serletis (1999) is squarely on the side VAR systems, as are many others reported of less than one-for-one adjustment across here. He worries that the results may not industrialized nations. be the same when larger systems are Bullard and Keating (1995) comment on explored. Some papers surveyed here have the effect of permanent inflation shocks on taken steps in that direction, including long-run economic growth. Because growth Boschen and Mills (1995), Ahmed and rates are generally stationary according to Rogers (1998), Rapach (1999a), and diagnostic tests, and inflation rates often Bernanke and Mihov (1998a). These are not, the methodology of Fisher and studies generally have supported results Seater (1993) and King and Watson (1997) from the bivariate VARs. However, much suggests that permanent inflation shocks more could be done in multivariate systems have no permanent effect on economic than has been completed to date. growth. Ahmed and Rogers (1998) include Even without turning to multivariate a comment in a similar vein.20 systems, one notes that much of the work surveyed has focused on real output, and Areas for Further Research. Canova (1994), that less work has been done on the long- commenting on Weber (1994), stressed that run bivariate relationship between money or the nature of the methodology of Fisher and inflation and other important real variables. Seater (1993) and King and Watson (1997) One exception is Crosby and Otto (1999), —however correct it may be from a logical who take a step in this direction, using the point of view—places heavy reliance on capital stock instead of real output as their the existence of (and on the number of) primary real variable.21 A good deal more unit roots in the time series being studied. could be done by simply investigating the Canova comments that these tests of neu- long-run bivariate relationships more system- trality propositions depend in an important atically for variables other than real output. way on getting the inference on the unit All of the analyses surveyed consider root correct, and yet, tests for unit roots one country at a time when testing neutrality are known to have low power. Most authors, propositions. One would like to know if a including Weber (1994), are well aware of panel approach, implemented for a group this issue, and many use a battery of tests of similar countries like the G7, would for a unit root in a series or other measures produce results similar to the ones reported in an effort to be conservative about their in the studies surveyed here, or if important conclusions in this regard. But Canova interactions between the countries are being (1994, p. 121) notes, nevertheless, that left out. A simpler line would be to study 20 This idea is also related to work this procedure “... conditions the results multivariate systems for a single country by Jones (1995). of economic hypotheses on shaky that attempt to account for cross-border 21 For another exception see statistical ground. ...” effects by including an international Rapach (1999b).

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variable.This would seem to be particularly Boschen, John F., and Leonard O. Mills. “Tests of Long-Run Neutrality important for some smaller, open economies Using Permanent Monetary and Real Shocks,” Journal of Monetary sometimes included in these studies.22 Economics (February 1995), pp. 25-44. While problems certainly remain, it ______, and Christopher M. Otrok. “Long-Run Neutrality and seems that the 1990s have been quite fruit- Superneutrality in an ARIMA Framework: Comment,” American ful in this area of empirical macroeco- Economic Review (December 1994), pp. 1470-73. nomics. Tests of neutrality propositions not Bullard, James, and John W. Keating. “The Long-Run Relationship subject to the critique of Lucas (1972) and Between Inflation and Output in Postwar Economies,” Journal of Sargent (1971)—tests that have eluded Monetary Economics (December 1995), pp. 477-96. economists during much of the postwar era—have been devised and executed for a Canova, F. “Testing Long-Run Neutrality: Empirical Evidence For G7 Countries With Special Emphasis on Germany,” Carnegie-Rochester variety of times and places. This body of Conference Series on Public Policy (1994), pp. 119-25. work gives us economists what is perhaps our first glimpse at the evidence on long-run Coe, Patrick J., and James M. Nason. “Long-Run Monetary Neutrality in monetary neutrality and superneutrality, and Three Samples: The United Kingdom, the United States, and the allows assessment of the merits of these pro- Small,” manuscript, University of Calgary and University of British Columbia (May 1999). positions separate from the logical force of theoretical arguments. Crosby, Mark, and Glen Otto. “Inflation and the Capital Stock,” Journal of Money, Credit, and Banking, forthcoming (1999). Fischer, Stanley. “Why are Central Banks Pursuing Long-Run Price REFERENCES Stability?” in Achieving Price Stability, Federal Reserve Bank of Kansas City Symposium, 1996. Ahmed, Shaghil, and John H. Rogers. “Long-Term Evidence on the Tobin and Fisher Effects: A New Approach,” International Finance Discussion Fisher, Mark E. “The Time Series Implications of the Long-Run Neutrality Paper #566, Board of Governors of the Federal Reserve System and Superneutrality of Money,” Ph.D. Dissertation, University of (September 1996). Chicago (1988). ______, and ______. “Inflation and the Great ______, and John J. Seater. “Neutralities of Money,” Ratios: Long-Term Evidence From the U.S.,” International Finance manuscript, Board of Governors of the Federal Reserve System Discussion Paper #628, Board of Governors of the Federal Reserve and North Carolina State University (1989). System (October 1998). ______, and ______. “Long-Run Neutrality and Andersen, Leonall, and Denis Karnovsky. “The Appropriate Time Frame Superneutrality in an ARIMA Framework,” American Economic Review For Controlling Monetary Aggregates: The St. Louis Evidence,” in (June 1993), pp. 402-15. Controlling Monetary Aggregates II: The Implementation, Federal Friedman, Milton, and Anna Schwartz. A Monetary History of the United Reserve Bank of Boston, 1972. States, 1867-1960, Princeton University Press, 1963. Backus, David K., and Patrick J. Kehoe. “International Evidence on the ______, and ______. Monetary Trends in the United Historical Properties of Business Cycles,” American Economic Review States and the United Kingdom, University of Chicago Press, 1982. (September 1992), pp. 864-88. Geweke, John F. “The Superneutrality of Money in the United States: Bae, Sangkun, and Mark J. Jensen. “Long-Run Neutrality in a Long- An Interpretation of the Evidence,” Econometrica (January 1986), Memory Model,” working paper, University of Missouri at Columbia pp. 1-21. (December 1998). Haug, Alfred A., and Robert F. Lucas. “Long-Run Neutrality and Barro, Robert J. “Inflation and Growth,” this Review (May/June 1996), Superneutrality in an ARIMA Framework: Comment,” American pp. 153-69. Economic Review (September 1997), pp. 756-59.

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