# Anticipated money, unanticipated money, and output: 1873-1930.

ANTICIPATED MONEY, UNANTICIPATED MONEY, AND OUTPUT: 1873-1930

I. INTRODUCTION

This paper examines the roles of anticipated and unanticipated money in the period between the Civil War and the Depression.(1) Such an examination is warranted for at least two reasons. First, estimation of the impact of anticipated and unanticipated money on output for historical periods can enhance our understanding of the responses of economic activity to these key variables.(2) Second, recent work has shown that traditional historical estimates of output may be faulty; see Romer [1986a; 1986b; 1986c; 1988]. Not only do most studies investigating the economic roles played by anticipated and unanticipated money concentrate on the post-World War II era, those that discuss the period before World War II, such as Rush [1985; 1986], use traditional data. Indeed, despite the interesting analyses by Rush, if the validity of the conventional data on output and unemployment for the era under consideration is rejected, then virtually no results on the importance of monetary and real factors for economic activity are available for this important period. Thus, further discussion of this topic is needed to answer two important questions: What do the revised data show us about the historical economy? Do these revisions change the inferences drawn about monetary influences on economic activity?

The analysis presented here is comprehensive in that a wide range of output measures are employed, both in terms of the types of output and in terms of the manner in which the output measures are constructed. Given this variety in the output measures, consistent results on the effects of anticipated and unanticipated money across output measures indicate that conclusions drawn from the analysis are robust. In particular, the empirical results presented below support the following hypotheses: (i) that anticipated M2 and monetary base growth have no effect on output, regardless of the output measure used; (ii) that unanticipated M2 and monetary base growth do effect output, regardless of the output measure used; and (iii) that changes in financial intermediation may be important for the evolution of output over time. Support for hypotheses (i) and (ii) is consistent with the "monetary" explanation of business cycles. Support for hypotheses (iii) may be consistent with "real" explanations of business cycles if exogenous shocks to the monetary production technology subsequently affect output.(3) Taken together, the joint support for hypotheses (i) - (iii) suggests that, at a minimum, neither the real nor the monetary explanations for historical U.S. business cycles can be discounted without additional work.

The remainder of the paper is organized as follows. Section II presents a brief overview of the historical period under consideration, along with a discussion of prior work on the effects of anticipated and unanticipated money on output determination during this time period. Section III discusses the data and the methodology. The empirical results are presented in section IV and the conclusions in section V.

II. OVERVIEW

The Historical Period

The period under investigation, 1873-1930, is one of substantial economic change. Banking panics, the return to the gold standard, the founding of the Federal Reserve System, and World War I are some of the more important events occuring during this period. We consider the role played by expected and unexpected money in output determination for several major subperiods. While data availability largely determined the selection of these subperiods, they generally correspond to major economic events.

Despite the structural and institutional changes over the period, we also examine the roles of anticipated and unticipated money growth in the determination of output over the entire time period. To be valid, tests of the impact of money growth on output require a reasonable degree of homogeneity in the economic environment. There are at least three arguments supporting this assumption. First, the U.S. was effectively on some form of the gold standard until 1933.(4) Second, while the establishment of the Fed brought the possibility of more active government involvement in monetary affairs, it was not until the Banking Act of 1935 that the Fed gained control over reserve requirements and established centralized control over open market operations. In fact, we argue that the M2 growth equation, used to distinguish between expected and unexpected money growth, did not shift over this time period.(5) Third, although he distinguishes the gold standard era of 1880-1915 from the "transitional" period of 1916-55, Klein [1975, 472] nonetheless argues that while "... the 1916-1955 period was `transitional' in terms of actual price change behavior, it does not appear to be transitional period in terms of a change in the public's adjustment of price expectations to past price behavior."

As it seems unlikely that the structure of the real side of the economy would change without a discernable shift in either price expectations or M2 growth, to treat the entire period as at least roughly homogeneous does not seem to be greatly at odds with the available evidence.(6) This paper's basic conclusion does not hinge on the economic homogeneity of the overall period, however. In particular, unanticipated money does (and anticipated money does not) influence output for the various sub-periods as well as for the overall period.

Earlier Literature

There are two important precedents to the analysis undertaken here. The first, a paper by Rush [1985] covering the 1880-1913 period, investigates the roles of the growth rates of the anticipated and unanticipated domestic components of the monetary base explaining output fluctuations. He also investigates the effect of changes in the money multiplier. His results show no significant effects on output of either anticipated or unanticipated monetary base movements. He does find, however, that growth in the money multiplier is significant in explaining output. If changes in the multiplier represent exogenous changes in the production function for monetary services (and hence real factors) in the economy, then the significance of the growth of the multiplier suggests that real factors are important in determining output. In combination with the general insignificance of both anticipated and unanticipated monetary base movements, the multiplier results raise questions about the monetary explanation of business cycle movements. Thus, Rush's results lend at least some support to the real business cycle interpretation of output fluctuations.

The second paper, also by Rush [1986], investigates the rate of unemployment for 1920-83. While the time period considered is largely outside that under scrutiny here, the results are nonetheless of interest. In contrast to his earlier results, Rush finds that the growth rate of the money multiplier does not contain significant explanatory power for unemployment movements during "normal" times. Also in contrast to his earlier results, he finds that surprises to the growth rate of the monetary base are significant in explaining unemployment. Rush speculates that the change in the significance of monetary base surprises may be due to the different monetary standards in place before and after World War I.

The issues raised by Rush deserve additional attention for at least two reasons. First, the conventional measures of real activity used in his study are challenged in a recent series of papers by Romer [1986a; 1986b; 1986c; 1988], who argues that the data construction techniques employed to assemble the historical measures of real activity (including those used by Rush) are inconsistent with modern techniques. Thus, the Rush results may not hold up if the newly-available estimates of output are used. Second, Rush does not report on the robustness of his results across the time period including the founding of the Federal Reserve System or across alternative measures of output. The results below provide evidence on each of these issues.

III. DATA AND METHODOLOGY

Data

The econometric results of this paper are based on a wide variety or measures of output. This sub-section briefly describes the data used below. Since the charateristics of these data are available elsewhere, little detail is provided here on issues sorrounding construction and limitations of the data.

The various measures of output used, along with the dates for which each series is available and the source, are: net national product, 1869-1930, Friedman and Schwartz [1982]; gross national product, 1869-1930, Romer [1986c]; Kuznets/Shaw commodity output, 1869-1930, Kuznets [1961]; Frickey's index of industrial production, 1866-1914, Romer [1986b]; Lebergott's [1964] unemployment rate, 1890-1930, Romer [1986a]; and Romer's unemployment rate, 1890-1930, Romer [1986a]. As noted in the introduction, these output series vary in both basic coverage and statistical characteristics. For example, the Romer data reflects her argument that conventional historical representations of output are "excessively volatile" relative to post World War II data.

Data used to estimate the money growth equations employed to produce anticipated and unanticipated money growth are: M2, the monetary base, the commercial paper rate, a corporate bond rate, and the deflator for net national product; all these data are obtained from Friedman and Schwartz [1982]. As discussed in more detail below, we estimate a wide variety of money growth equations for each time period in order to insure that the "best" money growth equation was selected. It should be noted, though, that both growth in M2 and in the monetary base are used as the dependent variables in the money growth equations. This paper employs the latter variable in view of the potential endogeneity of M2.(7)

Estimation of Money Growth Equations

To construct anticipated and unanticipated money growth, we assume that economic agents know both the functional form and the parameter values of the process generating money growth. Accordingly, an attempt is made to identify the "true" money and base growth equations used by agents in forming money growth expectations.

Procedures used by researchers to identify money growth equations have generally been a theoretical: from a list of regressors, money growth equations are fit for the time period of interest to subsets of the regressor list. The researcher then uses some statistical criterion to determine which regressors should be retained, thus specifying the "true" model. If one interprets this process as the researcher merely discovering, using the entire data set, what agents already knew at the beginning of the period, then any particular fitted value along the regression line represents the projection of money growth based on information available in the previous years. Such procedures are used by Barro [1977], Hoffman and Schlagenhauf [1982], and Mishkin [1982a], for example.

The procedure used here also applies a statistical criterion to determine the number of lags of each regressor to include in the money growth equation. Speciffically, the money and monetary base equations were determined by final prediction error (FPE) criterion. This criterion adjust the standard error of the equation for the number of degrees of freedom, a potentially important adjustment given the relatively small number of data points. Alternatively, one can view the FPE as balancing the "fit" of the equation against the efficiency of estimation as degrees of freedom decline.

In the FPE procedure, determined first are the optimal number of "own" lags. These are found by regressing each money measure on one through five own lags. The FPE for each equation is:

FPE = [(T + m + 1)/(T - m - 1)](SSR/T)

where T is the sample size, m is the number of own lags used, and SSR is the sum of squared residuals. Once the optimal own lags are determined, bivariate regressions are run to determine which (if any) of the other variables lowers the FPE further. These FPEs are computed according to [(T+m'+n+1)/(T-m'-n-1)](SSR/T), with n the number of lags of the second variable and m' the optimal number of own lags determined in the first step. If at least one of the bivariate regressions produces an FPE lower than the univariate regression, then trivariate regressions are next investigated. By proceeding in this way, the optimal equations for money and base growth are determined.(8) The fitted values and residuals from the FPE-minimizing equations then represent, respectively, anticipated and unanticipated money.

Testing for the Presence of Anticipated and Unanticipated Money

An early test of the hypothesis that unanticipated money growth affects output, but that anticipated money growth does not, was a two-step procedure proposed by Barro [1977]. In the first step, a money growth equation is estimated, with the fitted values and residuals representing, respectively, anticipated and unanticipated money growth. In the second step, the fitted values and residuals from this equation are used as regressors in an output (or unemployment) equation. It was subsequently recognized that while this two-step procedure yields consistent parameter estimates, the conventional F-statistic used to test hypotheses on the group of coefficients on either the anticipated or unanticipated money growth variables is biased. Specifically, this F-statistic tends to reject too frequently the null hypothesis of zero coefficients. As a result, Barro and Rush [1980], Mishkin [1982a; 1982b], and Leiderman [1980] proposed joint estimation of the money growth and output equations in order to obtain correct inferences. Finally, Hoffman, Low, and Schlagenhauf [1984], drawing on Pagan [1984], presented a valid F-statistic for the two-step Barro procedure and conducted Monte Carlo experiments for the original Barro, Mishkin and modified Barro procedures.(9)

With rationality as a maintained assumption, we test the roles of anticipated and unanticipated money growth in the context of the following regression:

[Mathematical Expression Omitted]

where yt is a measure of economic activity and where [DMR.sub.t] and [DME.sub.t] represent respectively, the residual and fitted values from the money growth equation. Since the standard F-statistics on the [Beta] or [Delta] coefficients are biased, we instead report valid F-statistics as implied by Pagan and analogous to those discussed by Hoffman, Low and Schlagenhauf.(10)

IV. EMPIRICAL RESULTS

Table I presents the results of the two-step test for the importance of anticipated and unanticipated M2 and base measures of money.(11) Before a detailed discussion of these results, several general comments are in order. First, the reported equations use differences of the unemployment rate and log differences of the various measures of production (the Frickey industrial production index, Romer's GNP, the Friedman-Schwartz NNP, and the Kuznets/Shaw commodity output series). The use of difference, rather than trend, stationary data over this period is consistent with Kormendi and Meguire [1987], who demonstrate using the Romer GNP data that output over this time period evolved according to a stochastic trend process. Second, the F-statistics in Table I for M2 growth are for output equations that include, in addition to the constant, the current and four lagged values of both anticipated and unanticipated M2. Those for monetary base growth are for equations that include not only four lags of expected and unexpected base growth, but also current growth in the M2/monetary base multiplier. There is no propensity for the importance of expected money (however measured) to increase as additional lags are added to the output equations. Four-lag results are reported since Mishkin [1983] and Hoffman, Low and Schlagenhauf [1984] suggest that researchers should err on the side of including superfluous lags; shorter lags risk biased parameter estimates while longer lags risk inefficient estimates.

The results in Table I support the hypothesis that anticipated money does not influence output. Anticipated M2 is significant at less than the 10 percent level only in one of the sixteen reported equations, and is never significant at the 5 percent level. Unanticipated M2 growth is often significant and always has lower marginal significance levels (higher F-statistics) than anticipated money growth. Anticipated monetary base growth is significant at less that the 10 percent level in four of sixteen cases (and significant at less that the 10 percent level in one additional equation); it is significant once at the 5 percent level. Unanticipated monetary base growth is frequently significant (though not as consistently as M2), and generally has lower marginal significance levels than anticipated base growth. In the equations using the monetary base, the current growth rate of the M2/monetary base multiplier (not reported in Table I) is always significant, generally with coefficients in the range between .60 and 1.0 with t-statistics in excess of 4.0. Further, the money multiplier is often significant along with unanticipated monetary base growth, so that unlike Rush's results, both monetary and real factors contain important explanatory power for output fluctuations.

Table : TABLE I Marginal Significance Levels of F-statistics

(*) Output equations include as regressors a constant, contemporaneous and lagged values of unanticipated money growth, and contemporaneous and lagged values of anticipated money growth. In addition, equations with the monetary base include contemporaneous growth of the money multiplier.

(**) Definitions of output variables: GNP = log of Romer's measure of GNP (extended from 1919-1930 with Kuznets' measure); NNP = log of Friedman and Schwartz's measure of NNP; PRODUCTION = log of Frickey's measure of industrial production; COMMODITY OUTPUT = log of Kuznets/Shaw commodity output series; ROMER UNEMP. = Romer's estimate of the unemployment rate; LEBERGOTT UNEMP. = Lebergott's measure of the unemployment rate.

The differences between our results and those of Rush lie in the relative importance of unanticipated monetary base growth for output, results consistent with traditional monetary interpretations of the business cycle. The source of these differences is the set of explanatory variables used in the monetary base growth regressions rather than the fact that the traditional measure of the base was used rather than its domestic component.[12] While the domestic component of the monetary base is less likely to be endogenous, the traditional base measure is used nonetheless. Since data on the domestic component apparently extends back only until 1875, while the traditional base extends back until 1867, use of the domestic component severely limits the available degrees of freedom. As detailed below, Monte Carlo results suggest that endogeneity of the money measure does not affect the F-statistics employed in the hypothesis tests. Thus, use of the domestic component does not appear to be worth the cost of the reduction in degress of freedom.

Although Rush did not report results for M2 due to worries about endogeneity, M2 results are presented here in view of the Monte Carlo evidence of Hoffman, Low and Schlagenhauf [1984] in which the errors in the money growth equation and the output equation are correlated. They state [1984, 353] that their tests" ... are essentially unaffected by contemporaneous correlation of disturbances and increasing the correlation in errors does not exacerbate the problem." Their Monte Carlo results are only suggestive, however, in light of the differences in functional form as between their tests and our models; see note 7.

Finally, both the insignificance of anticipated money and the significance of unanticipated money appear to hold regardless of whether the view is adopted that the historical data on the business cycle is "excessively volatile." When money growth surprises, however measured, are significant for Romer's data, they also tend to be significant for the traditional data. Thus, whatever the outcome of the debate regarding the proper way to characterize the historical business cycle, it seems safe to say that unanticipated money does, and anticipated money does not, affect output in the period between the Civil War and the Depression.

In order to check the robustness of the above results, an additional test was performed that bears at least indirectly on the assumption underlying the basic results: the period is sufficiently stable that the results presented in Table I are not overturned when explicit account is taken of the financial upheavals which occurred during the period.

The time periods selected for the results in Table I potentially contain years of substantial economic shocks. If financial panics are unexpected events, then inclusion of panic years could bias the results in favor of a finding that unanticipated money dominates anticipated money in the determination of output. Do such outliers dominate the results presented above? In an effort to determine whether years of substantial financial upheaval dominate the results, we omitted from the basic equations the years 1893 and 1907, years of major financial panics. This omission from the sample, however, resulted in no change in our conclusions. Anticipated money (both M2 and the monetary base) was still insignificant while money shocks were generally significant. Further, in the monetary base equations, the M2/base multiplier retains its significance, so that "normal" changes in financial intermediation (as measured by the money multiplier) have an important effect on output, even when the disruptive effects on the financial system of banking panics are removed. Details are available from the authors.

V. CONCLUSIONS

This paper presents results regarding the roles of anticipated and unanticipated money for the determination of output growth over the time period between the Civil War and the Depression. The results for M2 money growth suggest that anticipated money had no effect on output over the 1873-1930 period and selected sub-periods. In contrast, unanticipated M2 growth is frequently significant in explaining output fluctuations and almost always has higher F-statistics than anticipated M2 growth. The results for monetary base growth, as a whole, are quite similar. In addition, for the monetary base equations the M2/base multiplier is always significant. Thus, the evidence is consistent with the view that both monetary and real factors were important for output determination over the time period studied. Further, the results summarized here hold regardless of whether one uses traditional output data (characterized by some as "excessively volatile") or new measures of output.

These results are interesting since the six decades under investigation encompass enormous changes in the structure of the U.S. economy, financial panics, World War I, and the establishment of the Federal Reserve System. Although not formally tested, the results of this paper are consistent with the hypothesis that changes in financial institutions (e.g., the founding of the Federal Reserve System) do not alter the roles of anticipated and unanticipated money, nor the importance of financial intermediation, in determining output. In light of the observational equivalence problems that occur when investigating the roles of expected and unexpected money in a period with a given institutional framework, finding results that are largely invariant across financial structures is broadly consistent with the characterization of the historical economy as "classical" in nature rather than "Keynesian;" see, Neftci and Sargent [1978]. (1.) Empirical tests of the roles of anticipated and unanticipated money follow from the Lucas [1973] Sargent-Wallace [1975] hypothesis that unanticipated money growth influences output, but anticipated money growth does not. To date, empirical tests of this hypothesis have been presented by Barro [1977; 1978] for alternative measures of output, by Rush [1985; 1986] for different time periods, and by Hoffman and Schlagenhauf [1982], Mishkin [1983], Pagan [1984], and Hoffman, Low and Schlagenhauf [1984] using increasingly sophisticated econometric methodologies.

(2.) The usefulness of analyses such as those undertaken here follows in part from discussion in Sargent [1976]. In considering the issue of observational equivalence, Sargent [1976, 637] notes that "reduced forms estimated for a given sampling interval ... over a given estimation period cannot settle the policy rules controversy. That does not mean that there is no way that empirical evidence can be brought to bear on the question." He continues by noting that light can be shed on the controversy "by estimating reduced forms for various subperiods ... across which policy rules differed systematically ... ." Among other things, we estimate such relationships across the founding of the Federal Reserve System.

(3.) We stress the phase "may be consistent" in this statement. Shocks to the monetary production technology and/or changes in the level of financial intermediation could be endogenous responses to changes in output. Since we have no definitive evidence on the direction of causality, the interpretation of the evidence supporting real business cycles is viewed as being suggestive.

(4.) By the mid-1920s most of the rest of the world was no longer linked to gold and the Federal Reserve had learned how to sterilize gold flows. Thus, it could be argued that the gold standard in the second half of our period was quite different than in the first half. While we don't want to discount the potential importance of such a shift, the behavior of the money supply process is an empirical issue.

(5.) There is, however, a shift in the base growth equation in the middle of the period. Reported below are results on the stability of the M2 and monetary base growth processes; also referenced below is a Monte Carlo study suggesting that, even if the money supply process is subject to certain kinds of instability, the tests on the importance of anticipated and unanticipated money are still valid.

(6.) As indicated above, the monetary base growth equation does show some instability, in contrast to the M2 growth equation. It should be noted that neither the M2 growth equation nor the monetary base growth equation exhibits evidence of heteroskedasticity. This conclusion is based on results from the Breusch-Pagan [1979] test. Thus, the computed F-statistics for the stability of the M2 and monetary base growth equations appear valid. Accordingly, the evidence on the homogeneity of the entire period can be viewed as mixed. However, Monte Carlo evidence is cited below that such instability does not appear to reduce the validity of the major findings of this paper on the relative roles of anticipated and unanticipated money growth.

(7.) Rush [1985] notes not only the potential endogeneity of the money supply but also that the monetary base, as used here, also may be endogenous. He advocates the domestic component of the base as the appropriate measure of money. However, the Monte Carlo results in Hoffman, Low, and Schlagenhauf [1984] show that such endogeneity does not appear to lower the power of the hypothesis tests, at least in their framework. As noted below, the model used in the Monte Carlo experiments performed by Hoffman, Low and Schlagenhauf is different from the basic model estimated here. Their models are of the trend stationary variety; the models presented here use differences of the output variables.

(8.) It should be noted that a more complete search to determine the minimum FPE could be conducted. For example, all possible regressions using own lags and lags of the other variables could be estimated, with the FPE for each computed. It is possible that an FPE smaller than those identified by our more limited approach could be found. The additional expense of this grid search did not appear to be worthwhile, however.

(9.) Hoffman, Low and Schlagenhauf [1984, 360] report that their Monte Carlo experiments appeared to possess "considerable power in detecting failure of neutrality." In fact, they argue that their approach, which they refer to as the "corrected two-step test," is as good in large samples as alternative full information techniques such as the one advocated by Mishkin. It should also be noted that the Mishkin approach has the concenptual advantage of being able to distinguish between failures of rationality and failures of neutrality. It is reported in Hoffman, Low, and Schlagenhauf that this technique, in practice, has a tendency to confuse violations of rationality and neutrality. This result lessens the attractiveness of the Mishkin approach relative to the two-step approach used here.

(10.) The F-statistic computed here differs from that presented by Hoffman, Low and Schlagenhauf in that our model does not include a deterministic trend term. Rather, our model is of the "different stationary" type in that the dependent variable in our regressions is the rate of growth of output.

(11.) With the difference stationary specification of the output equations, no serial correlation is evident.

(12.) This conclusion was reached by undertaking a variety of comparisons between our specifications and Rush's. The comparisons were of the following nature. First, we replicated Rush's results for both his monetary base growth equation and his output equations. Second, we used our measure of the monetary base (rather than Rush's domestic component of the base) along with Rush's explanatory variables for base growth to generate anticipated and unanticipated base growth. These were then used in Rush's specification of the output equation. The conclusions reached by Rush were not overturned, implying that the source of our difference with Rush is not the measure of the monetary base. Similar comparisons for the different functional forms as between our output equation and Rush's also failed to turn up the source of differences. The differences between our results and Rush's appeared when we undertook comparisons of the regressors of the explanatory variables in the money growth equation. Finally, using the FPE criterion, the explanatory variables included in Rush's monetary base growth equation would have been excluded from our final equation for base growth. Thus, the monetary base growth equations used in the text appear to provide a preferred decomposition of monetary base growth into its anticipated and unanticipated parts. Full details of these results are contained in an appendix available from the authors.

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(*) Associated Professor, University of Kentucky, and Assistant Professor, East Carolina University. We wish to thank Mukhtar Ali, Dan Black, G. S. Laumas, W. Douglas McMillin, Mark Tom and two anonymous referees of this journal for suggestions and comments that substantially improved the quality of the paper. The present paper also benefited from seminar presentations at the Federal Reserve Bank of Kansas City, Louisiana State University, East Carolina University, the University of Toledo, and the University of Kentucky.

I. INTRODUCTION

This paper examines the roles of anticipated and unanticipated money in the period between the Civil War and the Depression.(1) Such an examination is warranted for at least two reasons. First, estimation of the impact of anticipated and unanticipated money on output for historical periods can enhance our understanding of the responses of economic activity to these key variables.(2) Second, recent work has shown that traditional historical estimates of output may be faulty; see Romer [1986a; 1986b; 1986c; 1988]. Not only do most studies investigating the economic roles played by anticipated and unanticipated money concentrate on the post-World War II era, those that discuss the period before World War II, such as Rush [1985; 1986], use traditional data. Indeed, despite the interesting analyses by Rush, if the validity of the conventional data on output and unemployment for the era under consideration is rejected, then virtually no results on the importance of monetary and real factors for economic activity are available for this important period. Thus, further discussion of this topic is needed to answer two important questions: What do the revised data show us about the historical economy? Do these revisions change the inferences drawn about monetary influences on economic activity?

The analysis presented here is comprehensive in that a wide range of output measures are employed, both in terms of the types of output and in terms of the manner in which the output measures are constructed. Given this variety in the output measures, consistent results on the effects of anticipated and unanticipated money across output measures indicate that conclusions drawn from the analysis are robust. In particular, the empirical results presented below support the following hypotheses: (i) that anticipated M2 and monetary base growth have no effect on output, regardless of the output measure used; (ii) that unanticipated M2 and monetary base growth do effect output, regardless of the output measure used; and (iii) that changes in financial intermediation may be important for the evolution of output over time. Support for hypotheses (i) and (ii) is consistent with the "monetary" explanation of business cycles. Support for hypotheses (iii) may be consistent with "real" explanations of business cycles if exogenous shocks to the monetary production technology subsequently affect output.(3) Taken together, the joint support for hypotheses (i) - (iii) suggests that, at a minimum, neither the real nor the monetary explanations for historical U.S. business cycles can be discounted without additional work.

The remainder of the paper is organized as follows. Section II presents a brief overview of the historical period under consideration, along with a discussion of prior work on the effects of anticipated and unanticipated money on output determination during this time period. Section III discusses the data and the methodology. The empirical results are presented in section IV and the conclusions in section V.

II. OVERVIEW

The Historical Period

The period under investigation, 1873-1930, is one of substantial economic change. Banking panics, the return to the gold standard, the founding of the Federal Reserve System, and World War I are some of the more important events occuring during this period. We consider the role played by expected and unexpected money in output determination for several major subperiods. While data availability largely determined the selection of these subperiods, they generally correspond to major economic events.

Despite the structural and institutional changes over the period, we also examine the roles of anticipated and unticipated money growth in the determination of output over the entire time period. To be valid, tests of the impact of money growth on output require a reasonable degree of homogeneity in the economic environment. There are at least three arguments supporting this assumption. First, the U.S. was effectively on some form of the gold standard until 1933.(4) Second, while the establishment of the Fed brought the possibility of more active government involvement in monetary affairs, it was not until the Banking Act of 1935 that the Fed gained control over reserve requirements and established centralized control over open market operations. In fact, we argue that the M2 growth equation, used to distinguish between expected and unexpected money growth, did not shift over this time period.(5) Third, although he distinguishes the gold standard era of 1880-1915 from the "transitional" period of 1916-55, Klein [1975, 472] nonetheless argues that while "... the 1916-1955 period was `transitional' in terms of actual price change behavior, it does not appear to be transitional period in terms of a change in the public's adjustment of price expectations to past price behavior."

As it seems unlikely that the structure of the real side of the economy would change without a discernable shift in either price expectations or M2 growth, to treat the entire period as at least roughly homogeneous does not seem to be greatly at odds with the available evidence.(6) This paper's basic conclusion does not hinge on the economic homogeneity of the overall period, however. In particular, unanticipated money does (and anticipated money does not) influence output for the various sub-periods as well as for the overall period.

Earlier Literature

There are two important precedents to the analysis undertaken here. The first, a paper by Rush [1985] covering the 1880-1913 period, investigates the roles of the growth rates of the anticipated and unanticipated domestic components of the monetary base explaining output fluctuations. He also investigates the effect of changes in the money multiplier. His results show no significant effects on output of either anticipated or unanticipated monetary base movements. He does find, however, that growth in the money multiplier is significant in explaining output. If changes in the multiplier represent exogenous changes in the production function for monetary services (and hence real factors) in the economy, then the significance of the growth of the multiplier suggests that real factors are important in determining output. In combination with the general insignificance of both anticipated and unanticipated monetary base movements, the multiplier results raise questions about the monetary explanation of business cycle movements. Thus, Rush's results lend at least some support to the real business cycle interpretation of output fluctuations.

The second paper, also by Rush [1986], investigates the rate of unemployment for 1920-83. While the time period considered is largely outside that under scrutiny here, the results are nonetheless of interest. In contrast to his earlier results, Rush finds that the growth rate of the money multiplier does not contain significant explanatory power for unemployment movements during "normal" times. Also in contrast to his earlier results, he finds that surprises to the growth rate of the monetary base are significant in explaining unemployment. Rush speculates that the change in the significance of monetary base surprises may be due to the different monetary standards in place before and after World War I.

The issues raised by Rush deserve additional attention for at least two reasons. First, the conventional measures of real activity used in his study are challenged in a recent series of papers by Romer [1986a; 1986b; 1986c; 1988], who argues that the data construction techniques employed to assemble the historical measures of real activity (including those used by Rush) are inconsistent with modern techniques. Thus, the Rush results may not hold up if the newly-available estimates of output are used. Second, Rush does not report on the robustness of his results across the time period including the founding of the Federal Reserve System or across alternative measures of output. The results below provide evidence on each of these issues.

III. DATA AND METHODOLOGY

Data

The econometric results of this paper are based on a wide variety or measures of output. This sub-section briefly describes the data used below. Since the charateristics of these data are available elsewhere, little detail is provided here on issues sorrounding construction and limitations of the data.

The various measures of output used, along with the dates for which each series is available and the source, are: net national product, 1869-1930, Friedman and Schwartz [1982]; gross national product, 1869-1930, Romer [1986c]; Kuznets/Shaw commodity output, 1869-1930, Kuznets [1961]; Frickey's index of industrial production, 1866-1914, Romer [1986b]; Lebergott's [1964] unemployment rate, 1890-1930, Romer [1986a]; and Romer's unemployment rate, 1890-1930, Romer [1986a]. As noted in the introduction, these output series vary in both basic coverage and statistical characteristics. For example, the Romer data reflects her argument that conventional historical representations of output are "excessively volatile" relative to post World War II data.

Data used to estimate the money growth equations employed to produce anticipated and unanticipated money growth are: M2, the monetary base, the commercial paper rate, a corporate bond rate, and the deflator for net national product; all these data are obtained from Friedman and Schwartz [1982]. As discussed in more detail below, we estimate a wide variety of money growth equations for each time period in order to insure that the "best" money growth equation was selected. It should be noted, though, that both growth in M2 and in the monetary base are used as the dependent variables in the money growth equations. This paper employs the latter variable in view of the potential endogeneity of M2.(7)

Estimation of Money Growth Equations

To construct anticipated and unanticipated money growth, we assume that economic agents know both the functional form and the parameter values of the process generating money growth. Accordingly, an attempt is made to identify the "true" money and base growth equations used by agents in forming money growth expectations.

Procedures used by researchers to identify money growth equations have generally been a theoretical: from a list of regressors, money growth equations are fit for the time period of interest to subsets of the regressor list. The researcher then uses some statistical criterion to determine which regressors should be retained, thus specifying the "true" model. If one interprets this process as the researcher merely discovering, using the entire data set, what agents already knew at the beginning of the period, then any particular fitted value along the regression line represents the projection of money growth based on information available in the previous years. Such procedures are used by Barro [1977], Hoffman and Schlagenhauf [1982], and Mishkin [1982a], for example.

The procedure used here also applies a statistical criterion to determine the number of lags of each regressor to include in the money growth equation. Speciffically, the money and monetary base equations were determined by final prediction error (FPE) criterion. This criterion adjust the standard error of the equation for the number of degrees of freedom, a potentially important adjustment given the relatively small number of data points. Alternatively, one can view the FPE as balancing the "fit" of the equation against the efficiency of estimation as degrees of freedom decline.

In the FPE procedure, determined first are the optimal number of "own" lags. These are found by regressing each money measure on one through five own lags. The FPE for each equation is:

FPE = [(T + m + 1)/(T - m - 1)](SSR/T)

where T is the sample size, m is the number of own lags used, and SSR is the sum of squared residuals. Once the optimal own lags are determined, bivariate regressions are run to determine which (if any) of the other variables lowers the FPE further. These FPEs are computed according to [(T+m'+n+1)/(T-m'-n-1)](SSR/T), with n the number of lags of the second variable and m' the optimal number of own lags determined in the first step. If at least one of the bivariate regressions produces an FPE lower than the univariate regression, then trivariate regressions are next investigated. By proceeding in this way, the optimal equations for money and base growth are determined.(8) The fitted values and residuals from the FPE-minimizing equations then represent, respectively, anticipated and unanticipated money.

Testing for the Presence of Anticipated and Unanticipated Money

An early test of the hypothesis that unanticipated money growth affects output, but that anticipated money growth does not, was a two-step procedure proposed by Barro [1977]. In the first step, a money growth equation is estimated, with the fitted values and residuals representing, respectively, anticipated and unanticipated money growth. In the second step, the fitted values and residuals from this equation are used as regressors in an output (or unemployment) equation. It was subsequently recognized that while this two-step procedure yields consistent parameter estimates, the conventional F-statistic used to test hypotheses on the group of coefficients on either the anticipated or unanticipated money growth variables is biased. Specifically, this F-statistic tends to reject too frequently the null hypothesis of zero coefficients. As a result, Barro and Rush [1980], Mishkin [1982a; 1982b], and Leiderman [1980] proposed joint estimation of the money growth and output equations in order to obtain correct inferences. Finally, Hoffman, Low, and Schlagenhauf [1984], drawing on Pagan [1984], presented a valid F-statistic for the two-step Barro procedure and conducted Monte Carlo experiments for the original Barro, Mishkin and modified Barro procedures.(9)

With rationality as a maintained assumption, we test the roles of anticipated and unanticipated money growth in the context of the following regression:

[Mathematical Expression Omitted]

where yt is a measure of economic activity and where [DMR.sub.t] and [DME.sub.t] represent respectively, the residual and fitted values from the money growth equation. Since the standard F-statistics on the [Beta] or [Delta] coefficients are biased, we instead report valid F-statistics as implied by Pagan and analogous to those discussed by Hoffman, Low and Schlagenhauf.(10)

IV. EMPIRICAL RESULTS

Table I presents the results of the two-step test for the importance of anticipated and unanticipated M2 and base measures of money.(11) Before a detailed discussion of these results, several general comments are in order. First, the reported equations use differences of the unemployment rate and log differences of the various measures of production (the Frickey industrial production index, Romer's GNP, the Friedman-Schwartz NNP, and the Kuznets/Shaw commodity output series). The use of difference, rather than trend, stationary data over this period is consistent with Kormendi and Meguire [1987], who demonstrate using the Romer GNP data that output over this time period evolved according to a stochastic trend process. Second, the F-statistics in Table I for M2 growth are for output equations that include, in addition to the constant, the current and four lagged values of both anticipated and unanticipated M2. Those for monetary base growth are for equations that include not only four lags of expected and unexpected base growth, but also current growth in the M2/monetary base multiplier. There is no propensity for the importance of expected money (however measured) to increase as additional lags are added to the output equations. Four-lag results are reported since Mishkin [1983] and Hoffman, Low and Schlagenhauf [1984] suggest that researchers should err on the side of including superfluous lags; shorter lags risk biased parameter estimates while longer lags risk inefficient estimates.

The results in Table I support the hypothesis that anticipated money does not influence output. Anticipated M2 is significant at less than the 10 percent level only in one of the sixteen reported equations, and is never significant at the 5 percent level. Unanticipated M2 growth is often significant and always has lower marginal significance levels (higher F-statistics) than anticipated money growth. Anticipated monetary base growth is significant at less that the 10 percent level in four of sixteen cases (and significant at less that the 10 percent level in one additional equation); it is significant once at the 5 percent level. Unanticipated monetary base growth is frequently significant (though not as consistently as M2), and generally has lower marginal significance levels than anticipated base growth. In the equations using the monetary base, the current growth rate of the M2/monetary base multiplier (not reported in Table I) is always significant, generally with coefficients in the range between .60 and 1.0 with t-statistics in excess of 4.0. Further, the money multiplier is often significant along with unanticipated monetary base growth, so that unlike Rush's results, both monetary and real factors contain important explanatory power for output fluctuations.

Table : TABLE I Marginal Significance Levels of F-statistics

Marginal Marginal Significance Significance Level of Level of Money F-Statistic: F-Statistic: Output Growth Unanticipated Anticipated Variable Variable Money Money a. 1873-1914 GNP M2 .001 .78 NNP M2 .01 .60 PRODUCTION M2 .002 .08 COMMODITY OUTPUT M2 .01 .85 GNP BASE .07 .75 NNP BASE .08 .81 PRODUCTION BASE .61 .58 COMMODITY OUTPUT BASE .11 .73 b. 1890-1914 ROMER UNEMP. M2 .01 .19 LEBERGOTT UNEMP. M2 .01 .57 ROMER UNEMP. BASE .14 .70 LEBERGOTT UNEMP. BASE .21 .84 c. 1873-1918 GNP M2 .02 .65 NNP M2 .02 .59 COMMODITY OUTPUT M2 .02 .64 GNP BASE .05 .63 NNP BASE .13 .88 COMMODITY OUTPUT BASE .06 .56 d. 1890-1918 ROMER UNEMP. M2 .38 .41 LEBERGOTT UNEMP. M2 .21 .33 ROMER UNEMP. BASE .45 .05 LEBERGOTT UNEMP. BASE .59 .07 e. 1873-1930 GNP M2 .0004 .60 NNP M2 .01 .58 COMMODITY OUTPUT M2 .002 .78 GNP BASE .01 .08 NNP BASE .04 .20 COMMODITY OUTPUT BASE .01 .09 f. 1890-1930 ROMER UNEMP. M2 .12 .19 LEBERGOTT UNEMP. M2 .05 .12 ROMER UNEMP. BASE .14 .10 LEBERGOTT UNEMP. BASE .05 .13

(*) Output equations include as regressors a constant, contemporaneous and lagged values of unanticipated money growth, and contemporaneous and lagged values of anticipated money growth. In addition, equations with the monetary base include contemporaneous growth of the money multiplier.

(**) Definitions of output variables: GNP = log of Romer's measure of GNP (extended from 1919-1930 with Kuznets' measure); NNP = log of Friedman and Schwartz's measure of NNP; PRODUCTION = log of Frickey's measure of industrial production; COMMODITY OUTPUT = log of Kuznets/Shaw commodity output series; ROMER UNEMP. = Romer's estimate of the unemployment rate; LEBERGOTT UNEMP. = Lebergott's measure of the unemployment rate.

The differences between our results and those of Rush lie in the relative importance of unanticipated monetary base growth for output, results consistent with traditional monetary interpretations of the business cycle. The source of these differences is the set of explanatory variables used in the monetary base growth regressions rather than the fact that the traditional measure of the base was used rather than its domestic component.[12] While the domestic component of the monetary base is less likely to be endogenous, the traditional base measure is used nonetheless. Since data on the domestic component apparently extends back only until 1875, while the traditional base extends back until 1867, use of the domestic component severely limits the available degrees of freedom. As detailed below, Monte Carlo results suggest that endogeneity of the money measure does not affect the F-statistics employed in the hypothesis tests. Thus, use of the domestic component does not appear to be worth the cost of the reduction in degress of freedom.

Although Rush did not report results for M2 due to worries about endogeneity, M2 results are presented here in view of the Monte Carlo evidence of Hoffman, Low and Schlagenhauf [1984] in which the errors in the money growth equation and the output equation are correlated. They state [1984, 353] that their tests" ... are essentially unaffected by contemporaneous correlation of disturbances and increasing the correlation in errors does not exacerbate the problem." Their Monte Carlo results are only suggestive, however, in light of the differences in functional form as between their tests and our models; see note 7.

Finally, both the insignificance of anticipated money and the significance of unanticipated money appear to hold regardless of whether the view is adopted that the historical data on the business cycle is "excessively volatile." When money growth surprises, however measured, are significant for Romer's data, they also tend to be significant for the traditional data. Thus, whatever the outcome of the debate regarding the proper way to characterize the historical business cycle, it seems safe to say that unanticipated money does, and anticipated money does not, affect output in the period between the Civil War and the Depression.

In order to check the robustness of the above results, an additional test was performed that bears at least indirectly on the assumption underlying the basic results: the period is sufficiently stable that the results presented in Table I are not overturned when explicit account is taken of the financial upheavals which occurred during the period.

The time periods selected for the results in Table I potentially contain years of substantial economic shocks. If financial panics are unexpected events, then inclusion of panic years could bias the results in favor of a finding that unanticipated money dominates anticipated money in the determination of output. Do such outliers dominate the results presented above? In an effort to determine whether years of substantial financial upheaval dominate the results, we omitted from the basic equations the years 1893 and 1907, years of major financial panics. This omission from the sample, however, resulted in no change in our conclusions. Anticipated money (both M2 and the monetary base) was still insignificant while money shocks were generally significant. Further, in the monetary base equations, the M2/base multiplier retains its significance, so that "normal" changes in financial intermediation (as measured by the money multiplier) have an important effect on output, even when the disruptive effects on the financial system of banking panics are removed. Details are available from the authors.

V. CONCLUSIONS

This paper presents results regarding the roles of anticipated and unanticipated money for the determination of output growth over the time period between the Civil War and the Depression. The results for M2 money growth suggest that anticipated money had no effect on output over the 1873-1930 period and selected sub-periods. In contrast, unanticipated M2 growth is frequently significant in explaining output fluctuations and almost always has higher F-statistics than anticipated M2 growth. The results for monetary base growth, as a whole, are quite similar. In addition, for the monetary base equations the M2/base multiplier is always significant. Thus, the evidence is consistent with the view that both monetary and real factors were important for output determination over the time period studied. Further, the results summarized here hold regardless of whether one uses traditional output data (characterized by some as "excessively volatile") or new measures of output.

These results are interesting since the six decades under investigation encompass enormous changes in the structure of the U.S. economy, financial panics, World War I, and the establishment of the Federal Reserve System. Although not formally tested, the results of this paper are consistent with the hypothesis that changes in financial institutions (e.g., the founding of the Federal Reserve System) do not alter the roles of anticipated and unanticipated money, nor the importance of financial intermediation, in determining output. In light of the observational equivalence problems that occur when investigating the roles of expected and unexpected money in a period with a given institutional framework, finding results that are largely invariant across financial structures is broadly consistent with the characterization of the historical economy as "classical" in nature rather than "Keynesian;" see, Neftci and Sargent [1978]. (1.) Empirical tests of the roles of anticipated and unanticipated money follow from the Lucas [1973] Sargent-Wallace [1975] hypothesis that unanticipated money growth influences output, but anticipated money growth does not. To date, empirical tests of this hypothesis have been presented by Barro [1977; 1978] for alternative measures of output, by Rush [1985; 1986] for different time periods, and by Hoffman and Schlagenhauf [1982], Mishkin [1983], Pagan [1984], and Hoffman, Low and Schlagenhauf [1984] using increasingly sophisticated econometric methodologies.

(2.) The usefulness of analyses such as those undertaken here follows in part from discussion in Sargent [1976]. In considering the issue of observational equivalence, Sargent [1976, 637] notes that "reduced forms estimated for a given sampling interval ... over a given estimation period cannot settle the policy rules controversy. That does not mean that there is no way that empirical evidence can be brought to bear on the question." He continues by noting that light can be shed on the controversy "by estimating reduced forms for various subperiods ... across which policy rules differed systematically ... ." Among other things, we estimate such relationships across the founding of the Federal Reserve System.

(3.) We stress the phase "may be consistent" in this statement. Shocks to the monetary production technology and/or changes in the level of financial intermediation could be endogenous responses to changes in output. Since we have no definitive evidence on the direction of causality, the interpretation of the evidence supporting real business cycles is viewed as being suggestive.

(4.) By the mid-1920s most of the rest of the world was no longer linked to gold and the Federal Reserve had learned how to sterilize gold flows. Thus, it could be argued that the gold standard in the second half of our period was quite different than in the first half. While we don't want to discount the potential importance of such a shift, the behavior of the money supply process is an empirical issue.

(5.) There is, however, a shift in the base growth equation in the middle of the period. Reported below are results on the stability of the M2 and monetary base growth processes; also referenced below is a Monte Carlo study suggesting that, even if the money supply process is subject to certain kinds of instability, the tests on the importance of anticipated and unanticipated money are still valid.

(6.) As indicated above, the monetary base growth equation does show some instability, in contrast to the M2 growth equation. It should be noted that neither the M2 growth equation nor the monetary base growth equation exhibits evidence of heteroskedasticity. This conclusion is based on results from the Breusch-Pagan [1979] test. Thus, the computed F-statistics for the stability of the M2 and monetary base growth equations appear valid. Accordingly, the evidence on the homogeneity of the entire period can be viewed as mixed. However, Monte Carlo evidence is cited below that such instability does not appear to reduce the validity of the major findings of this paper on the relative roles of anticipated and unanticipated money growth.

(7.) Rush [1985] notes not only the potential endogeneity of the money supply but also that the monetary base, as used here, also may be endogenous. He advocates the domestic component of the base as the appropriate measure of money. However, the Monte Carlo results in Hoffman, Low, and Schlagenhauf [1984] show that such endogeneity does not appear to lower the power of the hypothesis tests, at least in their framework. As noted below, the model used in the Monte Carlo experiments performed by Hoffman, Low and Schlagenhauf is different from the basic model estimated here. Their models are of the trend stationary variety; the models presented here use differences of the output variables.

(8.) It should be noted that a more complete search to determine the minimum FPE could be conducted. For example, all possible regressions using own lags and lags of the other variables could be estimated, with the FPE for each computed. It is possible that an FPE smaller than those identified by our more limited approach could be found. The additional expense of this grid search did not appear to be worthwhile, however.

(9.) Hoffman, Low and Schlagenhauf [1984, 360] report that their Monte Carlo experiments appeared to possess "considerable power in detecting failure of neutrality." In fact, they argue that their approach, which they refer to as the "corrected two-step test," is as good in large samples as alternative full information techniques such as the one advocated by Mishkin. It should also be noted that the Mishkin approach has the concenptual advantage of being able to distinguish between failures of rationality and failures of neutrality. It is reported in Hoffman, Low, and Schlagenhauf that this technique, in practice, has a tendency to confuse violations of rationality and neutrality. This result lessens the attractiveness of the Mishkin approach relative to the two-step approach used here.

(10.) The F-statistic computed here differs from that presented by Hoffman, Low and Schlagenhauf in that our model does not include a deterministic trend term. Rather, our model is of the "different stationary" type in that the dependent variable in our regressions is the rate of growth of output.

(11.) With the difference stationary specification of the output equations, no serial correlation is evident.

(12.) This conclusion was reached by undertaking a variety of comparisons between our specifications and Rush's. The comparisons were of the following nature. First, we replicated Rush's results for both his monetary base growth equation and his output equations. Second, we used our measure of the monetary base (rather than Rush's domestic component of the base) along with Rush's explanatory variables for base growth to generate anticipated and unanticipated base growth. These were then used in Rush's specification of the output equation. The conclusions reached by Rush were not overturned, implying that the source of our difference with Rush is not the measure of the monetary base. Similar comparisons for the different functional forms as between our output equation and Rush's also failed to turn up the source of differences. The differences between our results and Rush's appeared when we undertook comparisons of the regressors of the explanatory variables in the money growth equation. Finally, using the FPE criterion, the explanatory variables included in Rush's monetary base growth equation would have been excluded from our final equation for base growth. Thus, the monetary base growth equations used in the text appear to provide a preferred decomposition of monetary base growth into its anticipated and unanticipated parts. Full details of these results are contained in an appendix available from the authors.

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(*) Associated Professor, University of Kentucky, and Assistant Professor, East Carolina University. We wish to thank Mukhtar Ali, Dan Black, G. S. Laumas, W. Douglas McMillin, Mark Tom and two anonymous referees of this journal for suggestions and comments that substantially improved the quality of the paper. The present paper also benefited from seminar presentations at the Federal Reserve Bank of Kansas City, Louisiana State University, East Carolina University, the University of Toledo, and the University of Kentucky.

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Author: | Fackler, James S.; Parker, Randall E. |
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Publication: | Economic Inquiry |

Date: | Oct 1, 1990 |

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