# Income uncertainty and the onset of the Great Depression.

INCOME UNCERTAINTY AND THE ONSET OF THE GREAT DEPRESSION

Income uncertainty contributes substantially to explaining the fall in consumption

that marks the onset of the Great Depression. Consistent estimates of the variance of

income measure income uncertainty from 1921-30 and are produced using a linear

moment model. This series provides a statistical link between the large erratic swings

in income uncertainty after September 1929 and the Great Crash in the stock market.

Comparison of the behavior of income uncertainty in the 1920s to the pre-World War

I and post-World War II eras suggests that the experience after the Great Crash was

historically unique.

I. INTRODUCTION

The Great Depression of 1929-41 can be broken down into several phases: (i) the initial recessionary phase from October 1929 to October 1930, (ii) the first two waves of bank failures between November 1930 and December 1931, (iii) the incipient recovery of late 1932 and the impending collapse in March 1933, (iv) the recovery of the financial system and the economy from the cyclical trough, and (v) the recession of 1937-38, among others. Many researchers have presented well-articulated theories and extensive empirical analyses for each phase of the Depression. Friedman and Schwartz [1963], Hamilton [1987], Gordon and Wilcox [1981], and Burbidge and Harrison [1985] have examined the role of money and monetary policy during the Depression. Brown [1956] examined the stance of fiscal policy during this period. Bernanke [1983b] provided an explanation of the role of the financial crisis in the propagation of the Great Depression. Most of this research has focused on the events that turned a recession in 1929-30 that was not historically unprecedented (that is, it is comparable to the recession of 1920-22) into the deepest slide in the history of the American business cycle.

Explanations of the Depression's initial phase, from late 1929 to October 1930, however, are much less satisfactory. Meltzer [1976] and Mishkin [1978] examined this period and concluded that the fall in output can be attributed largely to the stance of monetary policy and the stock market's impact on the household balance sheet, respectively. The remainder of the existing literature centers around a debate between Temin [1976; 1981] and Schwartz [1981] that has produced no consensus about the role of monetary and nonmonetary factors in providing the impetus for the Great Depression. Hence, the period sometimes called "the mysterious first year"(1) is the least understood of all the phases of the Depression.

We think that recent advances in our understanding of the influence of income uncertainty on consumption expenditures may help explain the onset of the Great Depression. The theoretical work of Leland [1968], Sandmo [1970], Dreze and Modigliani [1972], and others has shown that an increase in uncertainty about future income (measured as the variance of income) results in a reduction in current consumption expenditures under standard assumptions regarding risk preferences. Recently, Flacco and Parker [1990] included an estimate of the standard deviation of income in a conventional specification of the consumption function from Blinder and Deaton [1985] and found that this measure of income uncertainty is indeed negatively related to consumption. This result, estimated using post-World War II data, holds up to a number of statistical significance and specification tests.

Romer [1990] examined the relationship between consumer expenditure (proxied by various disaggregate spending series) and stock market volatility during the first year and a half of the Great Depression. Expanding on Bernanke's [1983a] analysis of investment under uncertainty, Romer estimates a model of consumer spending on durable goods in the face of temporary uncertainty. Empirical evidence reveals that inclusion of the volatility of the stock market as a proxy for income uncertainty dramatically reduces forecast errors for consumption of durable goods in 1929 and 1930.

This paper uses the linear moment model developed by Antle [1983] to generate a time series of consistent estimates of the variance of income from January 1921 to October 1930. These estimates of the variance of income are then employed in a historical decomposition of the behavior of consumption over the same period. We find that income uncertainty not only goes up around October 1929, but in fact reverses from a downward trend that began in 1921. This upward trend continues until the end of the sample in late 1930. Since changes in an index of stock prices over the sample period are used (as an independent variable) to generate the estimates of the variance of income, these results provide empirical evidence of a connection between the Great Crash in the stock market and the resulting uncertainty about income that ultimately contributed to the onset of the Great Depression.

Our empirical results show that the inclusion of the variance of income contributes substantially toward explaining the initial fall in consumption that marks the beginning of the Great Depression in October 1929. Further, inclusion of the variance of income as the measure of income uncertainty reduces the root-mean-square error of the base projection by an average of 33 percent. To test the sensitivity of this result to the uncertainty measure employed, we also use Romer's [1990] measure of stock market volatility as a proxy for income uncertainty. We find a 25 percent average reduction in the root-mean-square error of the base projection when Romer's measure of income uncertainty is employed.

The paper is organized as follows. Section II briefly outlines the theoretical model of consumption behavior under income uncertainty. Section III discusses the linear moment model, the data, and the procedure used to derive the second-moment function. Section IV presents the main empirical results and describes the historical decomposition technique. Section V examines the behavior of income uncertainty in the pre-World War I and post-World War II eras, thereby providing a comparison with the pre-Depression era. Section VI contains our conclusions.

II. THEORY

In this section we briefly delineate the theoretical model of consumption under uncertainty found in Leland [1968], Sandmo [1970], and Dreze and Modigliani [1972]. The model is most easily developed for two periods. Let [Y.sub.1], [C.sub.1], and [S.sub.1] be income, consumption, and saving in the first period which satisfy the budget constraint [Y.sub.1] = [C.sub.1] + [S.sub.1]. Let [C.sub.2] and [Y.sub.2] be consumption and income in the second period and let r be the real interest rate, with future consumption given by [C.sub.2] = [Y.sub.2] + [S.sub.1] (1+r). Second period income is stochastic with density f([Y.sub.2]) and mean and variance E([Y.sub.2]) = [Mu] and V([Y.sub.2]) = [[Sigma].sup.2], Assume that the consumer is risk averse and displays decreasing temporal risk aversion as defined by Sandmo [1970, 354-55]. The consumer seeks to maximize the expected utility of consumption in the two periods, E[U([C.sub.1], [C.sub.2])], given by (1) [Mathematical Expression Omitted] where U is a von Neumann-Morganstern utility. Necessary and sufficient conditions for an optimum [Mathematical Expression Omitted] are (2) [Mathematical Expression Omitted] where subscripts on U([C.sub.1], [C.sub.2]) indicate partial derivatives.

Now define a linear shift in the distribution of future income as [Mathematical Expression Omitted] and change the variance of income, [Mathematical Expression Omitted], (by changing b) while holding the mean constant, i.e., dE(a + b[Y.sub.2]) = 0 implies that da/db = -[Mu]. Substituting [Mathematical Expression Omitted] for [Y.sub.2] in the first- and second-order conditions above and differentiating with respect to b, Sandmo [1970, 356, 359-60] shows that [Mathematical Expression Omitted] so that an increase in the variance of future income (by a scale factor b) will reduce current consumption, [Mathematical Expression Omitted]. That is, theory predicts that an increase in the level of uncertainty about future income leads consumers to defer consumption, to be more prudent, while a reduction in uncertainty about future income results in increased current consumption. This standard theoretical model of consumer behavior under uncertainty provides the background for our investigation of the influence of increased income uncertainty on consumption at the start of the Great Depression.

Three important issues relevant to the analysis of consumption behavior under uncertainty are worth discussing. First, when analyzing the behavior of consumers over a number of periods, the question arises whether the uncertainty in income is perceived as permanent or temporary. Notice that the standard model presented above does not address this question explicitly. Rather, income is simply specified as a random variable with known mean [Mu] and variance [[Sigma].sup.2]. If one were to consider a two-moment world, so that uncertainty is completely represented by variance, then in the two-period model outlined above an increase in [[Sigma].sup.2] must constitute a permanent increase in uncertainty in the future period. However, this limitation is not restricted to two-period models because models which consider an arbitrary number of periods t = 1, 2, ..., T do not permit the variance of income to be different in different periods, but rather assume that the variance [[Sigma].sup.2] is constant over the entire time horizon (see, Blanchard and Mankiw [1988] for a summary of such models). Uncertainty must therefore be viewed as permanent in these models as well. Hence, interpreting the theory strictly, consumers are viewed as responding to permanent increases or decreases in uncertainty in their intertemporal consumption choices in these models. The ability to model changes in uncertainty that may persist for perhaps one or two periods (such as during an election campaign), and then stabilize for a time at some other level, will apparently have to await the development of more sophisticated theoretical models of optimal intertemporal consumption choices.

Second, our analysis of the effects of income uncertainty on consumer spending, like that of Romer [1990], depends upon the assumption that consumers in the pre-Depression era did not know the true model of the economy. This is the case because a rational consumer, knowing that greater uncertainty would depress consumption and thus lower output, would have been pessimistic, and not just uncertain, after a positive shock in uncertainly such as that which occurred after the Great Crash.

Lastly, we consider the effects of income uncertainty on an electric consumer spending series using department store sales as our proxy for consumption. The series on department store sales contains durable goods (furniture, floor coverings, and china), semi-durable goods (clothing, shoes, and linens), and nondurable goods (cosmetics and drugs). In the theoretical model outlined above, no distinction is made between the types of goods that are consumed. However, there are other models of consumer behavior under uncertainty that do draw these distinctions. Romer [1988; 1990] argues that the influence of income uncertainty on consumption should be more dramatic for goods that have longer life spans and poor resale markets. These conditions make purchases of goods more irreversible and thus increase the incentive to delay their purchase. Therefore, consumption of durable goods should decrease more than consumption of semi-durable goods when uncertainty increases. Romer [1990] argues that a corollary to this is the proposition that purchases of nondurables may actually rise. While our model does not draw these distinctions, we recognize that the literature contains models that do. The important papers by Romer [1988; 1990] include theoretical and empirical results that address these concerns.

III. ESTIMATING THE VARIANCE OF INCOME

Linear Moment Model

In this section we describe how a time series of consistent estimates of the second moment of income, the variance of income, is generated. Real income, [Y.sub.t], is assumed to be a random variable whose density is characterized by a sequence of moments. Thus, in each period [Y.sub.t] will have a mean, a variance, and other higher moments. Income is modelled as a function, that is linear in its parameters, of its own lagged values and other important macroeconomic variables. That is, (4) [Mathematical Expression Omitted] where [X.sub.j] are explanatory variables thought to influence [Y.sub.t], t is a time trend, n is the longest lag considered for income, [Tau] is the lag for the other (k) explanatory variables and may be different for different variables, b = ([a.sub.o],[a.sub.j],[b.sub.o],[b.sub.i]) is a vector of parameters, and [Xi.sub.t] is the disturbance term. Using Antle's [1983] linear moment model, the moments of [Y.sub.t] are modelled as linear functions of (Mathematical Expression Omitted]), so that the rth moment function is (5) [Mathematical Expression Omitted] where [Mathematical Expression Omitted] is the vector of parameters in the rth moment function, E([v.sub.tr]) = 0, and [Mathematical Expression Omitted]

For the purposes of this paper, we are interested in the second moment, i.e., where r=2. The second moment can be represented as [Mathematical Expression Omitted] so that the estimated series of the variance of income is (6) [Mathematical Expression Omitted]

The intuition behind this technique for estimating the variance of a dependent variable has its foundation in Slutsky's theorem that the probability limit of a nonlinear function is the nonlinear function of the probability limit, i.e., plim g([Theta] [Caret]) = g (plim [Theta] [Caret]). This applies to the regression model in the following way. The probability limits of the successive powers of the residuals from (4), after being estimated as specified in (5), are the true moments of the disturbance term in (4). Taking the expectation of (5) produces the moments of the disturbance term, and because the independent variables on the right-hand side of (4) are nonstochastic, these are also the moments of the dependent variable [Y.sub.t] for r [is greater than or equal to] 2. This is seen most simply for the case in which r = 2. The squared residuals obtained from the estimation of (4) are regressed on the same right-hand-side variables by estimating (5), and equation (6) thereby generates consistent estimates of the second moment (the variance) of income. Perhaps the most common application of the Antle technique is encountered when a researcher postulates an additive structure for heteroskedasticity. Estimates of the variance of the disturbance term, used to correct the heteroskedasticity, are computed by regressing the squares of the errors from the model on the independent variable(s) thought to be responsible for the heteroskedasticity. These estimates of the variance of the disturbance term are simultaneously estimates of the variance of the dependent variable, because V ([Alpha] + [Beta] X + u) = V(u) = V(Y) where Y = [Alpha] + [Beta] X + u.

Data and the Specification of the Income Equation

Before estimating equations (4) and (6), we will describe the procedures used to arrive at an appropriate specification for [Y.sub.t]. We employed a seasonally adjusted monthly index of industrial production as a proxy for [Y.sub.t] over the period January 1921 to October 1930. Data on personal disposable income over this period are not available, and industrial production is as reasonable a substitute as any that exist in spite of its limitations. The major shortcoming is that these data do not contain information from the agricultural and service sectors. However, this may not be serious since the percentage changes in annual industrial production and annual real personal disposable income have a correlation coefficient of 0.85.

In choosing the empirical specification for [Y.sub.t], we included variables of macroeconomic importance that have received attention in the literature on the Depression era business cycle. The M1 money supply was included given the discussions in Friedman and Schwartz [1963], Hamilton [1987] and Fackler and Parker [1990a] of the importance of money and monetary policy for the Depression and pre-Depression era business cycle. Bernanke [1983b], Rush [1985] and Fackler and Parker [1990a] demonstrate the importance of including a proxy for the real costs of credit intermediation and the level of financial intermediation. For these reasons, the differential yield between long-term U.S. government bonds and Baa corporate bonds (RDIFF) was included in the specification. The wholesale price index (WPI) was added to control for price effects. Lastly, we included the changes in the level of stock prices (CSP) to account for both wealth and uncertainty effects that movements in stock prices may have had over this period. Further, if consumers used the stock market in the pre-Depression era as an explanatory variable with which predictions of the real economy were formulated, as argued by Romer [1990], then including the changes in the level of stock prices is appropriate in the specification of [Y.sub.t].

The above theoretical considerations in combination with parsimony of the model lead us to a specification, for the purposes of estimating equations (4) and (6), that regresses [Y.sub.t] on a constant, a trend, one of its own lagged values and one lag each of M1, the wholesale price index, the interest rate differential and the change in the level of stock prices. The model is estimated over the January 1921-December 1928 period to represent the behavior of the economy in the 1920s.

IV. ESTIMATES OF INCOME UNCERTAINTY: THE PRE-DEPRESSION ERA

Estimation of the specification for equation (4) yielded the following results for the first-moment function: (7) [Mathematical Expression Omitted] where t-values are given in parentheses and Q is the Ljung-Box Q-statistic with degrees of freedom in parentheses.(2)

The coefficient estimates reveal that [Y.sub.t-1] has a statistically significant positive persistence effect on [Y.sub.t], and that lagged changes in stock prices are positive and statistically significant. This suggests the potential benefit of using the stock market as a predictor of the real economy over this period. The coefficient on the interest rate differential is negative and statistically significant, indicating that increases in the real cost of financial intermediation lower [Y.sub.t]. The coefficients on the trend, lagged M1 ([M1.sub.t-1]) and lagged wholesale prices ([WPI.sub.t-1]) are negative and not statistically significant but are retained due to their theoretical relevance.

The linear moment model postulates that there is information that can be extracted from the assumed relationship between ([Mathematical Expression Omitted]) and [[Xi].sub.t]. Therefore, one can perform a test for unconditional heteroskedasticity in equation (7) as a pretest for the validity and estimation of a linear moment model. Calculation of a Breusch-Pagan statistic for equation (7) yielded a value of 5.58, which rejects the null hypothesis of homoskedasticity at the marginal significance level of 6 percent. Hence, there is apparently some information available in the disturbance term of equation (7) that can be used to estimate the variance of [Y.sub.t]. Since the [R.sup.2] = .99 for equation (7) and the Breusch-Pagan statistic is significant at the 6 percent level, we would not be surprised if the second-moment function did not exhibit powerful statistical significance. Nevertheless, the linear moment model provides a technique to estimate the desired variance of [Y.sub.t] over the pre-Depression era.

The second-moment function, used to estimate a consistent time series of the variance of income, is produced by estimating equation (6). This is accomplished by obtaining the squared errors from equation (7) and regressing them on the same set of right-hand-side variables (see Antle [1983, 196-99]) as in equation (7). The results are presented in equation (8). (8) [Mathematical Expression Omitted]

The results in equation (8) are used to characterize the behavior of income uncertainty, [Mathematical Expression Omitted], over the 1920s. Note again that the equation which provides estimates of the first moment of income, [Y.sub.t] [Caret] in (7), fits the data fairly well (with [R.sup.2] = 0.99). This does not leave much variation in the disturbance term of (7) to extract estimates of the second moment of income in equation (8). However, the linear moment model provides more structure for the analysis because its maintained hypothesis is that all of the moments of the dependent variable [Y.sub.t], not just the first, depend on the same set of independent variables (as specified in (7)). Hence, due to the theoretical relevance and statistical significance of the independent variables in the equation for expected income in (7), and the additional structure placed on the model by the linear moment specification in (5), it is worthwhile to examine the predicted values of the variance from equation (8). Although the parameters in equation (8) have been estimated somewhat imprecisely, before rejecting the potential usefulness of these estimates we employed them in empirical exercises to determine their ability to explain movements in macroeconomic variables. While it may eventually become possible to develop more precise and robust estimators of the moments of a dependent variable in a regression model (other than the linear moment estimators, ARCH estimators, or the use of some proxy variables for relevant moments), it will be seen in the succeeding analysis that the linear moment model performs quite well.

We therefore use the predicted values from equation (8) to characterize the behavior of income uncertainty over the 1920s. These results, estimated from January 1921-December 1928, were then used to statically forecast [Mathematical Expresssion Omitted] over the January 1929-October 1930 period (so that the upheaval of 1929 and 1930 could not influence the parameter estimates used in constructing [Mathematical Expression Omitted]).(3) Figure 1 shows the estimated standard deviations of income generated.

When we consider the overall secular trends in Figure 1, a rather striking feature is revealed. That is, although the month-to-month movements are not universally negative, there is a negative secular trend from January 1921 to August 1929. Then, beginning in September 1929, [[Sigma].sub.t] [Caret] rises from its historical trough in the 1920s, reversing a negative secular trend extending from 1921 to a positive secular trend that jumps sharply in October 1929 through December 1929 and reaches the highest levels of uncertainty experienced in the decade; thereafter [[Sigma].sub.t] [Caret] remains high until the end of the sample.

Considering equation (8), from which the estimates of [[Sigma] [caret].sub.t] were computed, the reason for the climb in [[Sigma] [caret].sub.t] from September 1929 until late 1930 becomes apparent. If the stock market was thought to be an imperfect predictor of the real economy by consumers in the pre-Depression economy, then "larger than usual movements in stock prices will be associated with greater uncertainty about one's prediction of future income" (Romer [1990, 604]). Equation (8) indicates that positive changes in stock prices lower uncertainty, while negative changes increase uncertainty. The historically unprecedented negative shocks to the stock market that took place beginning in October 1929 are the dominant component accounting for the erratic behavior and burst of uncertainty that began in late 1929.

It is important to note that the statistical evidence linking the stock market crash with the behavior of [[Sigma] [caret].sub.t] is corroborated by qualitative evidence from the forecasts of contemporary business analysts during the 1920s. Romer [1990] reports many contemporary accounts of business forecasters who became much less confident of their forecasts and the future course of business activity after the Great Crash. Further, the forecasters who were less confident pointed to the fall in the stock market as the reason for their increased uncertainty. Thus, for both statistical and qualitative reasons, we believe the erratic behavior of income uncertainty after October 1929 can be attributed to the Great Crash and subsequent gyrations in the stock market.

While the comparative statics in the theory and the evidence in Figure 1 are compelling, casual glances at the data are not sufficiently convincing. A statistical link between [[Sigma] [caret].sub.t] and the behavior of consumption still remains to be shown.

The problems inherent in obtaining a monthly measure of consumption are similar to those of income discussed earlier. Following Romer [1990], an index of department store sales (seasonally adjusted) is used as a proxy for consumption expenditures. Shortcomings in using this series may be present to some limited extent since the correlation coefficient between the percentage changes in annual department store sales and annual consumption expenditures equals 0.75.

Additional evidence is provided by computing a historical decomposition of department store sales over the January 1929-October 1930 period.(4) The historical decomposition is a vector autoregressive (VAR) technique that attributes differences between a base projection and the actual series among the innovations of the variables in a VAR system. More formally, for any j = 1,2,..,t+j such that t+j is less than or equal to the last period in the sample, [Y.sub.t+j] can be written in its moving average representation as (10) [Mathematical Expression Omitted] where [C.sub.s] is a matix of parameters and the [Epsilon]'s are vectors of innovations. Note that [Y.sub.t+j] is written as the sum of two components. The second part is the base projection of [Y.sub.t+j] and is computed based completely on information available in time t and before. The first part represents movements in [Y.sub.t+j] that have occurred since t, and this can be partitioned further to assign responsibility for these movements among the variables in the VAR. One may set t to whatever starting point is of particular interest.

Before a historical decomposition is computed, a VAR must be estimated. We decided to include (along with department store sales) income, wealth, wholesale prices, and the standard deviation of income in the VAR system. As discussed above, consumption is proxied by department store sales and real income is proxied by industrial production. Wealth is represented as the sum of time and mutual savings deposits. This use of liquid assets as a proxy for wealth is an identical procedure to that used by Bolch and Pilgrim [1973] for their study of the interwar period. Wholesale prices are included to control for price effects on consumption that may have been present over this period.

Explanatory variables were lagged one period since forecasting exercises over the sample period showed the one-lag specification was by far the best. We estimated the system with all variables except [[Sigma] [caret].sub.t] in logs, and January 1929 was chosen as the starting point for the historical decomposition. Each equation included constant and trend terms.

When computing a historical decomposition, the variables must be ordered in a particular way. The ordering we used (to perform a Choleski decomposition) places income uncertainty first, followed by income, wealth, prices, and department store sales. The limitations of this technique are well known, and the reader is referred to Cooley and LeRoy [1985] for a further discussion. However, for the period of interest, this ordering can be strongly justified. That is, there is reason to believe that the stock market crash in October 1929 was an exogenous event, which therefore would place income uncertainty first in the ordering. If the crash resulted from the bursting of a speculative bubble, then it is associated with arbitrary events and not fundamental causal changes in the real economy. There are many contemporary accounts that reveal the crash was thought to be the bursting of a speculative bubble (see Romer [1988] for a more indepth analysis). Changes in income uncertainty then lead to changes in income, wealth, and prices, which ultimately generate changes in consumption. Further, the results are virtually unchanged when [[Sigma] [caret].sub.t] is placed last in the ordering after income, wealth, prices, and consumption. This is the least favorable ordering for the uncertainty hypothesis, and these results are also presented.

Figure 2 presents the results over the January 1929-October 1930 period. The actual series (SALES), the base projection (BPSALES), and the base projection plus the contribution of income uncertainty (BPUNCERT) are shown. The historical decomposition reveals that the peak in department store sales in September 1929 is also reflected in BPUNCERT although the magnitude is not captured. Thereafter, the inclusion of income uncertainty pulls the base projection closer to the actual series from October 1929 to December 1929, although it overshoots a bit in October. In fact, since the definition of the historical decomposition indicates that the sum of the base projection and the contribution of all of the system's variables add up to the actual series, there is little additional responsibility to be assigned among any of the remaining system variables for explaining consumption in November and December 1929 once the contribution of income uncertainty has been accounted for. This result differs somewhat when [[Sigma] [caret].sub.t] is ordered last; here, the base projection plus the contribution of income uncertainty (BPUNCERT) completely accounts for the behavior of consumption in November but does not add to the base projection in December.

All of the turning points in the actual series of department store sales for December 1929-March 1930 are also reflected in BPUNCERT, although from January 1930 to May 1930 the base projection tracks consumption better than does BPUNCERT. However, from June 1930 until the end of the sample, the contribution of income uncertainty pulls the base projection much closer to the actual series, although it does not close the gap as completely as it does in November 1929. Romer [1990] reports that contemporary business analysts displayed a (perhaps superficial) calm in the spring of 1930 that was replaced in the summer of 1930 by a return to a loss of confidence and greater uncertainty. This is shown in the statistical evidence in both Figures 1 and 2. The continued gyrations of the stock market, the overly optimistic evaluations of business activity promulgated by the Hoover administration, and the enactment of the Hawley-Smoot tariffs are all good reasons why uncertainty remained high and contributed substantially to explaining consumption in the end of the sample. In order to bring additional evidence to bear, the root-mean-square error was computed over January 1929-October 1930 for the base projection and the base projection plus the contribution of income uncertainty. The results reveal that the inclusion of income uncertainty reduces the root-mean-square error of the base projection by an average of 33 percent whether [[Sigma] [caret].sub.t] is ordered first or last. Additionally, inclusion of income uncertainty pulls the base projection closer to the actual series in fourteen of the twenty-two months (64 percent).

For purposes of comparison, we repeated the empirical exercises by first replacing our estimates of [[Sigma] [caret].sub.t] with estimates we computed using the ARCH technique developed by Engle [1983].(5) The results revealed little resemblance to the results contained in Figure 2, and the contribution of [[Sigma] [caret].sub.t] actually raised the root-mean-square error of the base projection by 12 percent. We also repeated the empirical exercises by replacing our estimates of [[Sigma] [caret].sub.t] with the stock market volatility measure used as a proxy for income uncertainty by Romer [1990]. The results here are remarkably similar to those contained in Figure 2 as the base projection plus the contribution of income uncertainty tracked actual consumption very well in October-December 1929 and May-October 1930. Further, the contribution of the stock market volatility measure reduced the root-mean-square error by 25 percent. Thus, the stock market volatility measure seems to be a good proxy for income uncertainty during the 1920s and serves as a check on the reliability of our results.

Figure 3 presents the results of the historical decomposition for the remaining variables in the VAR system. These results indicate that wealth appears to pull the base projection much closer to the actual series from June 1930 to the end of the sample, and the contribution of income comes very close to the actual series during the peak in September 1929. However, after considering these examples (both in terms of mimicking the behavior of department store sales and pulling the base projection closer to the actual series) the variables income, wealth, prices, and lagged sales performed poorly for the period after the Great Crash.

V. INCOME UNCERTAINTY: PRE-WORLD WAR I AND POST-WORLD WAR II

While the behavior of income uncertainty in 1929-30 displayed a clear break from its behavior during the rest of the 1920s, it would still be useful to know whether the behavior of [[Sigma] [caret].sub.t] during 1929-30 was truly unique or whether it could be observed in all serious recessions.(6) Furthermore, are the results in Figure 1 representative of time variation in uncertainty, or do they result from the fact that the linear models used in the specification of [Y.sub.t] are often bad predictors of cyclical turning points?

To address these questions, we estimated [[Sigma] [caret].sub.t] over the pre-World War I and the post-World War II periods. Figure 4 presents the results of estimating income uncertainty over the January 1890-December 1913 period. We generated these estimates using a specification similar to that of equation (7) except that the interest rate differential was replaced with the commercial paper rate.(7) The results indicate that income uncertainty spikes sharply in both the 1893 and 1907 recessions. However, these observed spikes and the erratic behavior of income uncertainty are not unique to severe recessions. Gyrations of comparable magnitude also occurred during the expansionary periods of 1901 and 1904-06. Therefore, between January 1890 and December 1913 the movements of income uncertainty during expansions are comparable to the movements in income uncertainty during recessions. This was not the case for the Great Crash in relation to the behavior of income uncertainty during the 1920s. That is, the behavior of income uncertainty after the Great Crash was unlike anything else experienced during the 1920s.

Figure 5 presents the results of estimating [Mathematical Expression Omitted] over the January 1954--February 1988 period using a quarterly measure of labor income and postulating [Y.sub.t] as a random walk with drift.(8) The standard deviation of income falls during the 1974 recession and remains constant during the 1981-82 recession, rather than rising as one would expect if these results were generated solely from the poor ability of linear models to predict cyclical turning points. Further, unlike the Great Crash, there are no episodes between 1954 and 1988 in which the movements in [Mathematical Expression Omitted] are clearly aberrant relative to the entire post-World War II period.

Taken as a whole, Figures 1, 4 and 5 demonstrate that increased uncertainty is not always associated with severe recessions. More important, the most striking feature of the behavior of income uncertainty over all three periods is its unique surge in 1929 after almost a decade of steady decline and relative calm. The characteristics of this reversal in income uncertainty are not exhibited in any other period of comparable length over the entire period for which income uncertainty could be estimated.

VI. CONCLUSIONS

We use a linear moment model to produce estimates of income uncertainty during the 1920s and the first year of the Great Depression. The estimates show that there was a dramatic change in income uncertainty at the time of the Great Crash in the stock market. Income uncertainty not only went up, but reversed from a negative secular trend to a positive secular trend that saw uncertainty about future income reach the highest levels attained during the 1920s. Thereafter, income uncertainty remained high the entire first year of the Depression. From the estimates obtained in the paper and the qualitative evidence provided by business analysts at the time, it seems clear that the aberrant behavior of income uncertainty after September 1929 can largely be attributed to the Great Crash. These results provide statistical evidence that the dramatic increase in income uncertainty at the onset of the Depression was generated by the Great Crash in the stock market.

Further, the influence of income uncertainty alone provides a virtually complete explanation for the initial decline in consumption that marks the onset of the Great Depression. If it is believed that exogenous forces (such as the bursting of a speculative bubble) brought about the Great Crash, then there is a causal link between the behavior of income uncertainty and the recession of October 1929-October 1930 that ultimately turned into the Great Depression. Future research may focus on the role of income uncertainty over subsequent periods of the Great Depression(9) in addition to the period marking its onset.

DATA APPENDIX

The series on the M1 money supply and the sum of time and mutual savings deposits are from Friedman and Schwartz [1963], Table A1.

The series used to construct the interest rate differential variable are from Banking and Monetary Statistics, Board of Governors of the Federal Reserve System.

The series on industrial production, wholesale prices and department store sales are from the Federal Reserve Bulletin, Board of Governors of the Federal Reserve System.

The stock market index is from Cowles [1939].

The annual data used to compute the correlations reported in the text are from Temin [1976] and the U.S. Department of Commerce, Long Term Economic Growth 1860--1970.

The pre-World War I data for industrial production are from Miron and Romer [1989].

The pre-World War I data for the commercial paper rate and wholesale prices are from Macaulay [1938].

The pre-World War I data for high-powered money are from Friedman and Schwartz [1963] and NBER series 14,135 constructed by Jeffrey Miron. Details on this series are available on request.

Descriptions of the post--World War II data are contained in Flacco and Parker [1990].

(1)This expression for the period October 1929-October 1930 is taken from Romer [1988, 5]. (2)This specification was compared to several alternatives. Out-of-sample forecasting exercises for the January 1929-October 1930 period were conducted for this model as well as other common-lag models with lags two-eight (seven models). The results indicated that the one-lag model was superior. Given that we are interested in reproducing the behavior of the economy in our specification as closely as we can so as not to bias our results, we chose the one-lag specification. (3)Note that this procedure is similar to the one employed by Romer [1988]. She used the January 1919-December 1928 period to statically forecast consumption behavior until 1930. We apply the same procedure in constructing the variance of income for use as the measure of income uncertainty. (4)We restrict attention to the January 1929-October 1930 period since we are only concerned with the initial phase of the Depression. Furthermore, the first wave of bank failures that occurred in November/December of 1930 cause a "change in the character of the contraction," in the words of Friedman and Schwartz [1963, 11]. We regard these months as the start of the second phase of the Depression and thus stop our sample prior to this. (5)Tests indicated the presence of significant ARCH effects at lag eight. (6)Romer [1990] presents qualitative evidence on forecaster uncertainty for the earlier contractions of 1920-21 and 1923-24 and concludes that there was no systematic loss of confidence surrounding these episodes, unlike after the Great Crash. (7)The equation we estimated for [Y.sub.t] over this period has an [R.sup.2] = .94 but contains serial correlation and no amount of respecification could remove it. Therefore, we offer the results in Figure 4 with this caveat. (8)These results are contained in Flacco and Parker [1990]. (9)See Fackler and Parker [1990b] for additional results on the role of income uncertainty and other macroeconomic variables in the propagation of the Depression over the October 1929-December 1933 period.

REFERENCES

Antle, John M. "Testing the Stochastic Structure of Production: A Flexible Moment-Based Approach." Journal of Business and Economic Statistics, July 1983, 192-201. Bernanke, Ben S. "Irreversibility, Uncentainty, and Cyclical Investment." Quarterly Journal of Economics, February 1983a, 85-106. ____. "Nonmonetary Effects of the Financial Crisis in the Propagation of the Great Depression." American Economic Review, May 1988, 173-77. Blinder, Alan S., and Angus Deaton. "The Time Series Consumption Function Revisited." Brookings Papers on Economic Activity 2, 1985, 465-521. Board of Governors of the Federal Reserve System. Banking and Monetary Statistic, 1943. Board of Governors of the Federal Reserve System. Federal Reserve Bulletin, various issues, 1940-44. Bolch, Ben, and John Pilgrim. "A Reappraisal of Some Factors Associated with Fluctuations in the United States in the Interwar Period." Southern Economic Journal, January 1973, 327-44. Brown, E. Cary. "Fiscal Policy in the Thirties: A Reappraisal." American Economic Review, December 1956, 857-79. Burbidge, John, and Alan Harrison. "A Historical Decomposition of the Great Depression to Determine the Role of Money." Journal of Monetary Economics, July 1985, 45-54. Cooley, Thomas F., and Stephen F. LeRoy. "Atheoretical Macroeconomics: A Critique." Journal of Monetary Economics, November 1985, 283-308. Cowles, Alfred, and Associates. Common-Stock Indexes. Bloomington, Indiana: Principia Press, 1939. Dreze, Jacques H., and Franco Modigliani. "Consumption Decisions under Uncertainty." Journal of Economic Theory, December 1972, 30p-35. Engle, Robert F. "Estimates of the Variance of U.S. Inflation Based upon the ARCH Model." Journal of Money, Credit, and Banking, August 1983, 286-301. Fackler, James S., and Randall Parker. "Anticipated Money, Unanticipated Money, and Output: 1873-1930." Economic Inquiry, October 1990a, 774-87. ___. "Accounting for the Great Depression: A Historical Decomposition." Mimeo, East Carolina University, 1990b. Flacco, Paul R., and Randall Parker. "Some Evidence on the Influence of Income Uncertainty on Aggregate Consumption." Journal of Macroeconomics, Fall 1990, 653-62. Friedman, Milton, and Anna J. Schwartz. A Monetary History of the United States. 1867-1960. Princeton: Princeton University Press, 1963. Gordon, Robert J., and James A. Wilcox. "Monetarist Interpretations of the Great Depression: An Evaluation and Critique," in The Great Depression Revisited, edited by K. Brunner. Boston: Martinus Nijhoff, 1981, 49-107. Hamilton, James D. "Monetary Factors in the Great Depression." Journal of Monetary Economics, March 1987, 145-69. Leland, Hayne E. "Saving and Uncertainty: The Precautionary Demand for Saving." Quarterly Journal of Economics, August 1968, 465-73. Macaulay, Fredrick R. The Movement of Interest Rates, Bond Yields and Stock Prices in the United States Since 1856. New York: National Bureau of Economic Research, 1938. Meltzer, Allan H. "Monetary and Other Explanations of the Start of the Great Depression." Journal of Monetary Economics, November 1976, 455-71. Miron, Jeffrey A., and Christia D. Romer. "A New Monthly Index of Industrial Production, 1884-1940." National Bureau of Economic Research Working Paper No. 3172, November 1989. Mishkin, Frederic S. "The Household Balance Sheet and the Great Depression." Journal of Economic History, December 1978, 918-37. Romer, Christina D. "The Great Crash and the Onset of the Great Depression." National Bureau of Economic Research Working Paper No. 2639, June 1988. ___. "The Great Crash and the Onset of the Great Depression." Quarterly Journal of Economics, August 1990, 597-624. Rush, Mark. "Unexpected Monetary Disturbances During the Gold Standard Era." Journal of Monetary Economics, May 1985, 309-21. Sandmo, Agnar. "The Effect of Uncertainty on Savings Decisions." Review of Economic Studies, July 1970, 353-60. Schwartz, Anna J. "Understanding 1929-1933," in The Great Depression Revisited, edited by K. Brunner. Boston: Martinus Nijhoff, 1981, 5-48. Temin, Peter. Did Monetary Forces Cause the Great Depression? New York: W. W. Norton, 1976. ___. "Notes on the Causes of the Great Depression," in The Great Depression Revisited, edited by K. Brunner. Boston: Martinus Nijhoff, 1981, 108-24. U.S. Departmnet of Commerce, Bureau of Economic Analysis. Long-Term Economic Growth, 1860-1970, Washington, D.C., Government Printing Office, 1973. [Figures 1 to 5 Omitted]

PAUL R. FLACCO and RANDALL E. PARKER, Associate Professor and Assistant Professor respectively, Department of Economics, East Carolina University, Greenville, NC, 27858. Thanks are due W. Douglas McMillin, James Fackler, A. Steven Holland, G. S. Laumas, Richard J. Sweeney, Cacki Chambers, and Sherri Moore for help and comments. The careful and insightful comments of two anonymous referees were also extremely helpful. The authors are responsible for any errors that may remain.

Income uncertainty contributes substantially to explaining the fall in consumption

that marks the onset of the Great Depression. Consistent estimates of the variance of

income measure income uncertainty from 1921-30 and are produced using a linear

moment model. This series provides a statistical link between the large erratic swings

in income uncertainty after September 1929 and the Great Crash in the stock market.

Comparison of the behavior of income uncertainty in the 1920s to the pre-World War

I and post-World War II eras suggests that the experience after the Great Crash was

historically unique.

I. INTRODUCTION

The Great Depression of 1929-41 can be broken down into several phases: (i) the initial recessionary phase from October 1929 to October 1930, (ii) the first two waves of bank failures between November 1930 and December 1931, (iii) the incipient recovery of late 1932 and the impending collapse in March 1933, (iv) the recovery of the financial system and the economy from the cyclical trough, and (v) the recession of 1937-38, among others. Many researchers have presented well-articulated theories and extensive empirical analyses for each phase of the Depression. Friedman and Schwartz [1963], Hamilton [1987], Gordon and Wilcox [1981], and Burbidge and Harrison [1985] have examined the role of money and monetary policy during the Depression. Brown [1956] examined the stance of fiscal policy during this period. Bernanke [1983b] provided an explanation of the role of the financial crisis in the propagation of the Great Depression. Most of this research has focused on the events that turned a recession in 1929-30 that was not historically unprecedented (that is, it is comparable to the recession of 1920-22) into the deepest slide in the history of the American business cycle.

Explanations of the Depression's initial phase, from late 1929 to October 1930, however, are much less satisfactory. Meltzer [1976] and Mishkin [1978] examined this period and concluded that the fall in output can be attributed largely to the stance of monetary policy and the stock market's impact on the household balance sheet, respectively. The remainder of the existing literature centers around a debate between Temin [1976; 1981] and Schwartz [1981] that has produced no consensus about the role of monetary and nonmonetary factors in providing the impetus for the Great Depression. Hence, the period sometimes called "the mysterious first year"(1) is the least understood of all the phases of the Depression.

We think that recent advances in our understanding of the influence of income uncertainty on consumption expenditures may help explain the onset of the Great Depression. The theoretical work of Leland [1968], Sandmo [1970], Dreze and Modigliani [1972], and others has shown that an increase in uncertainty about future income (measured as the variance of income) results in a reduction in current consumption expenditures under standard assumptions regarding risk preferences. Recently, Flacco and Parker [1990] included an estimate of the standard deviation of income in a conventional specification of the consumption function from Blinder and Deaton [1985] and found that this measure of income uncertainty is indeed negatively related to consumption. This result, estimated using post-World War II data, holds up to a number of statistical significance and specification tests.

Romer [1990] examined the relationship between consumer expenditure (proxied by various disaggregate spending series) and stock market volatility during the first year and a half of the Great Depression. Expanding on Bernanke's [1983a] analysis of investment under uncertainty, Romer estimates a model of consumer spending on durable goods in the face of temporary uncertainty. Empirical evidence reveals that inclusion of the volatility of the stock market as a proxy for income uncertainty dramatically reduces forecast errors for consumption of durable goods in 1929 and 1930.

This paper uses the linear moment model developed by Antle [1983] to generate a time series of consistent estimates of the variance of income from January 1921 to October 1930. These estimates of the variance of income are then employed in a historical decomposition of the behavior of consumption over the same period. We find that income uncertainty not only goes up around October 1929, but in fact reverses from a downward trend that began in 1921. This upward trend continues until the end of the sample in late 1930. Since changes in an index of stock prices over the sample period are used (as an independent variable) to generate the estimates of the variance of income, these results provide empirical evidence of a connection between the Great Crash in the stock market and the resulting uncertainty about income that ultimately contributed to the onset of the Great Depression.

Our empirical results show that the inclusion of the variance of income contributes substantially toward explaining the initial fall in consumption that marks the beginning of the Great Depression in October 1929. Further, inclusion of the variance of income as the measure of income uncertainty reduces the root-mean-square error of the base projection by an average of 33 percent. To test the sensitivity of this result to the uncertainty measure employed, we also use Romer's [1990] measure of stock market volatility as a proxy for income uncertainty. We find a 25 percent average reduction in the root-mean-square error of the base projection when Romer's measure of income uncertainty is employed.

The paper is organized as follows. Section II briefly outlines the theoretical model of consumption behavior under income uncertainty. Section III discusses the linear moment model, the data, and the procedure used to derive the second-moment function. Section IV presents the main empirical results and describes the historical decomposition technique. Section V examines the behavior of income uncertainty in the pre-World War I and post-World War II eras, thereby providing a comparison with the pre-Depression era. Section VI contains our conclusions.

II. THEORY

In this section we briefly delineate the theoretical model of consumption under uncertainty found in Leland [1968], Sandmo [1970], and Dreze and Modigliani [1972]. The model is most easily developed for two periods. Let [Y.sub.1], [C.sub.1], and [S.sub.1] be income, consumption, and saving in the first period which satisfy the budget constraint [Y.sub.1] = [C.sub.1] + [S.sub.1]. Let [C.sub.2] and [Y.sub.2] be consumption and income in the second period and let r be the real interest rate, with future consumption given by [C.sub.2] = [Y.sub.2] + [S.sub.1] (1+r). Second period income is stochastic with density f([Y.sub.2]) and mean and variance E([Y.sub.2]) = [Mu] and V([Y.sub.2]) = [[Sigma].sup.2], Assume that the consumer is risk averse and displays decreasing temporal risk aversion as defined by Sandmo [1970, 354-55]. The consumer seeks to maximize the expected utility of consumption in the two periods, E[U([C.sub.1], [C.sub.2])], given by (1) [Mathematical Expression Omitted] where U is a von Neumann-Morganstern utility. Necessary and sufficient conditions for an optimum [Mathematical Expression Omitted] are (2) [Mathematical Expression Omitted] where subscripts on U([C.sub.1], [C.sub.2]) indicate partial derivatives.

Now define a linear shift in the distribution of future income as [Mathematical Expression Omitted] and change the variance of income, [Mathematical Expression Omitted], (by changing b) while holding the mean constant, i.e., dE(a + b[Y.sub.2]) = 0 implies that da/db = -[Mu]. Substituting [Mathematical Expression Omitted] for [Y.sub.2] in the first- and second-order conditions above and differentiating with respect to b, Sandmo [1970, 356, 359-60] shows that [Mathematical Expression Omitted] so that an increase in the variance of future income (by a scale factor b) will reduce current consumption, [Mathematical Expression Omitted]. That is, theory predicts that an increase in the level of uncertainty about future income leads consumers to defer consumption, to be more prudent, while a reduction in uncertainty about future income results in increased current consumption. This standard theoretical model of consumer behavior under uncertainty provides the background for our investigation of the influence of increased income uncertainty on consumption at the start of the Great Depression.

Three important issues relevant to the analysis of consumption behavior under uncertainty are worth discussing. First, when analyzing the behavior of consumers over a number of periods, the question arises whether the uncertainty in income is perceived as permanent or temporary. Notice that the standard model presented above does not address this question explicitly. Rather, income is simply specified as a random variable with known mean [Mu] and variance [[Sigma].sup.2]. If one were to consider a two-moment world, so that uncertainty is completely represented by variance, then in the two-period model outlined above an increase in [[Sigma].sup.2] must constitute a permanent increase in uncertainty in the future period. However, this limitation is not restricted to two-period models because models which consider an arbitrary number of periods t = 1, 2, ..., T do not permit the variance of income to be different in different periods, but rather assume that the variance [[Sigma].sup.2] is constant over the entire time horizon (see, Blanchard and Mankiw [1988] for a summary of such models). Uncertainty must therefore be viewed as permanent in these models as well. Hence, interpreting the theory strictly, consumers are viewed as responding to permanent increases or decreases in uncertainty in their intertemporal consumption choices in these models. The ability to model changes in uncertainty that may persist for perhaps one or two periods (such as during an election campaign), and then stabilize for a time at some other level, will apparently have to await the development of more sophisticated theoretical models of optimal intertemporal consumption choices.

Second, our analysis of the effects of income uncertainty on consumer spending, like that of Romer [1990], depends upon the assumption that consumers in the pre-Depression era did not know the true model of the economy. This is the case because a rational consumer, knowing that greater uncertainty would depress consumption and thus lower output, would have been pessimistic, and not just uncertain, after a positive shock in uncertainly such as that which occurred after the Great Crash.

Lastly, we consider the effects of income uncertainty on an electric consumer spending series using department store sales as our proxy for consumption. The series on department store sales contains durable goods (furniture, floor coverings, and china), semi-durable goods (clothing, shoes, and linens), and nondurable goods (cosmetics and drugs). In the theoretical model outlined above, no distinction is made between the types of goods that are consumed. However, there are other models of consumer behavior under uncertainty that do draw these distinctions. Romer [1988; 1990] argues that the influence of income uncertainty on consumption should be more dramatic for goods that have longer life spans and poor resale markets. These conditions make purchases of goods more irreversible and thus increase the incentive to delay their purchase. Therefore, consumption of durable goods should decrease more than consumption of semi-durable goods when uncertainty increases. Romer [1990] argues that a corollary to this is the proposition that purchases of nondurables may actually rise. While our model does not draw these distinctions, we recognize that the literature contains models that do. The important papers by Romer [1988; 1990] include theoretical and empirical results that address these concerns.

III. ESTIMATING THE VARIANCE OF INCOME

Linear Moment Model

In this section we describe how a time series of consistent estimates of the second moment of income, the variance of income, is generated. Real income, [Y.sub.t], is assumed to be a random variable whose density is characterized by a sequence of moments. Thus, in each period [Y.sub.t] will have a mean, a variance, and other higher moments. Income is modelled as a function, that is linear in its parameters, of its own lagged values and other important macroeconomic variables. That is, (4) [Mathematical Expression Omitted] where [X.sub.j] are explanatory variables thought to influence [Y.sub.t], t is a time trend, n is the longest lag considered for income, [Tau] is the lag for the other (k) explanatory variables and may be different for different variables, b = ([a.sub.o],[a.sub.j],[b.sub.o],[b.sub.i]) is a vector of parameters, and [Xi.sub.t] is the disturbance term. Using Antle's [1983] linear moment model, the moments of [Y.sub.t] are modelled as linear functions of (Mathematical Expression Omitted]), so that the rth moment function is (5) [Mathematical Expression Omitted] where [Mathematical Expression Omitted] is the vector of parameters in the rth moment function, E([v.sub.tr]) = 0, and [Mathematical Expression Omitted]

For the purposes of this paper, we are interested in the second moment, i.e., where r=2. The second moment can be represented as [Mathematical Expression Omitted] so that the estimated series of the variance of income is (6) [Mathematical Expression Omitted]

The intuition behind this technique for estimating the variance of a dependent variable has its foundation in Slutsky's theorem that the probability limit of a nonlinear function is the nonlinear function of the probability limit, i.e., plim g([Theta] [Caret]) = g (plim [Theta] [Caret]). This applies to the regression model in the following way. The probability limits of the successive powers of the residuals from (4), after being estimated as specified in (5), are the true moments of the disturbance term in (4). Taking the expectation of (5) produces the moments of the disturbance term, and because the independent variables on the right-hand side of (4) are nonstochastic, these are also the moments of the dependent variable [Y.sub.t] for r [is greater than or equal to] 2. This is seen most simply for the case in which r = 2. The squared residuals obtained from the estimation of (4) are regressed on the same right-hand-side variables by estimating (5), and equation (6) thereby generates consistent estimates of the second moment (the variance) of income. Perhaps the most common application of the Antle technique is encountered when a researcher postulates an additive structure for heteroskedasticity. Estimates of the variance of the disturbance term, used to correct the heteroskedasticity, are computed by regressing the squares of the errors from the model on the independent variable(s) thought to be responsible for the heteroskedasticity. These estimates of the variance of the disturbance term are simultaneously estimates of the variance of the dependent variable, because V ([Alpha] + [Beta] X + u) = V(u) = V(Y) where Y = [Alpha] + [Beta] X + u.

Data and the Specification of the Income Equation

Before estimating equations (4) and (6), we will describe the procedures used to arrive at an appropriate specification for [Y.sub.t]. We employed a seasonally adjusted monthly index of industrial production as a proxy for [Y.sub.t] over the period January 1921 to October 1930. Data on personal disposable income over this period are not available, and industrial production is as reasonable a substitute as any that exist in spite of its limitations. The major shortcoming is that these data do not contain information from the agricultural and service sectors. However, this may not be serious since the percentage changes in annual industrial production and annual real personal disposable income have a correlation coefficient of 0.85.

In choosing the empirical specification for [Y.sub.t], we included variables of macroeconomic importance that have received attention in the literature on the Depression era business cycle. The M1 money supply was included given the discussions in Friedman and Schwartz [1963], Hamilton [1987] and Fackler and Parker [1990a] of the importance of money and monetary policy for the Depression and pre-Depression era business cycle. Bernanke [1983b], Rush [1985] and Fackler and Parker [1990a] demonstrate the importance of including a proxy for the real costs of credit intermediation and the level of financial intermediation. For these reasons, the differential yield between long-term U.S. government bonds and Baa corporate bonds (RDIFF) was included in the specification. The wholesale price index (WPI) was added to control for price effects. Lastly, we included the changes in the level of stock prices (CSP) to account for both wealth and uncertainty effects that movements in stock prices may have had over this period. Further, if consumers used the stock market in the pre-Depression era as an explanatory variable with which predictions of the real economy were formulated, as argued by Romer [1990], then including the changes in the level of stock prices is appropriate in the specification of [Y.sub.t].

The above theoretical considerations in combination with parsimony of the model lead us to a specification, for the purposes of estimating equations (4) and (6), that regresses [Y.sub.t] on a constant, a trend, one of its own lagged values and one lag each of M1, the wholesale price index, the interest rate differential and the change in the level of stock prices. The model is estimated over the January 1921-December 1928 period to represent the behavior of the economy in the 1920s.

IV. ESTIMATES OF INCOME UNCERTAINTY: THE PRE-DEPRESSION ERA

Estimation of the specification for equation (4) yielded the following results for the first-moment function: (7) [Mathematical Expression Omitted] where t-values are given in parentheses and Q is the Ljung-Box Q-statistic with degrees of freedom in parentheses.(2)

The coefficient estimates reveal that [Y.sub.t-1] has a statistically significant positive persistence effect on [Y.sub.t], and that lagged changes in stock prices are positive and statistically significant. This suggests the potential benefit of using the stock market as a predictor of the real economy over this period. The coefficient on the interest rate differential is negative and statistically significant, indicating that increases in the real cost of financial intermediation lower [Y.sub.t]. The coefficients on the trend, lagged M1 ([M1.sub.t-1]) and lagged wholesale prices ([WPI.sub.t-1]) are negative and not statistically significant but are retained due to their theoretical relevance.

The linear moment model postulates that there is information that can be extracted from the assumed relationship between ([Mathematical Expression Omitted]) and [[Xi].sub.t]. Therefore, one can perform a test for unconditional heteroskedasticity in equation (7) as a pretest for the validity and estimation of a linear moment model. Calculation of a Breusch-Pagan statistic for equation (7) yielded a value of 5.58, which rejects the null hypothesis of homoskedasticity at the marginal significance level of 6 percent. Hence, there is apparently some information available in the disturbance term of equation (7) that can be used to estimate the variance of [Y.sub.t]. Since the [R.sup.2] = .99 for equation (7) and the Breusch-Pagan statistic is significant at the 6 percent level, we would not be surprised if the second-moment function did not exhibit powerful statistical significance. Nevertheless, the linear moment model provides a technique to estimate the desired variance of [Y.sub.t] over the pre-Depression era.

The second-moment function, used to estimate a consistent time series of the variance of income, is produced by estimating equation (6). This is accomplished by obtaining the squared errors from equation (7) and regressing them on the same set of right-hand-side variables (see Antle [1983, 196-99]) as in equation (7). The results are presented in equation (8). (8) [Mathematical Expression Omitted]

The results in equation (8) are used to characterize the behavior of income uncertainty, [Mathematical Expression Omitted], over the 1920s. Note again that the equation which provides estimates of the first moment of income, [Y.sub.t] [Caret] in (7), fits the data fairly well (with [R.sup.2] = 0.99). This does not leave much variation in the disturbance term of (7) to extract estimates of the second moment of income in equation (8). However, the linear moment model provides more structure for the analysis because its maintained hypothesis is that all of the moments of the dependent variable [Y.sub.t], not just the first, depend on the same set of independent variables (as specified in (7)). Hence, due to the theoretical relevance and statistical significance of the independent variables in the equation for expected income in (7), and the additional structure placed on the model by the linear moment specification in (5), it is worthwhile to examine the predicted values of the variance from equation (8). Although the parameters in equation (8) have been estimated somewhat imprecisely, before rejecting the potential usefulness of these estimates we employed them in empirical exercises to determine their ability to explain movements in macroeconomic variables. While it may eventually become possible to develop more precise and robust estimators of the moments of a dependent variable in a regression model (other than the linear moment estimators, ARCH estimators, or the use of some proxy variables for relevant moments), it will be seen in the succeeding analysis that the linear moment model performs quite well.

We therefore use the predicted values from equation (8) to characterize the behavior of income uncertainty over the 1920s. These results, estimated from January 1921-December 1928, were then used to statically forecast [Mathematical Expresssion Omitted] over the January 1929-October 1930 period (so that the upheaval of 1929 and 1930 could not influence the parameter estimates used in constructing [Mathematical Expression Omitted]).(3) Figure 1 shows the estimated standard deviations of income generated.

When we consider the overall secular trends in Figure 1, a rather striking feature is revealed. That is, although the month-to-month movements are not universally negative, there is a negative secular trend from January 1921 to August 1929. Then, beginning in September 1929, [[Sigma].sub.t] [Caret] rises from its historical trough in the 1920s, reversing a negative secular trend extending from 1921 to a positive secular trend that jumps sharply in October 1929 through December 1929 and reaches the highest levels of uncertainty experienced in the decade; thereafter [[Sigma].sub.t] [Caret] remains high until the end of the sample.

Considering equation (8), from which the estimates of [[Sigma] [caret].sub.t] were computed, the reason for the climb in [[Sigma] [caret].sub.t] from September 1929 until late 1930 becomes apparent. If the stock market was thought to be an imperfect predictor of the real economy by consumers in the pre-Depression economy, then "larger than usual movements in stock prices will be associated with greater uncertainty about one's prediction of future income" (Romer [1990, 604]). Equation (8) indicates that positive changes in stock prices lower uncertainty, while negative changes increase uncertainty. The historically unprecedented negative shocks to the stock market that took place beginning in October 1929 are the dominant component accounting for the erratic behavior and burst of uncertainty that began in late 1929.

It is important to note that the statistical evidence linking the stock market crash with the behavior of [[Sigma] [caret].sub.t] is corroborated by qualitative evidence from the forecasts of contemporary business analysts during the 1920s. Romer [1990] reports many contemporary accounts of business forecasters who became much less confident of their forecasts and the future course of business activity after the Great Crash. Further, the forecasters who were less confident pointed to the fall in the stock market as the reason for their increased uncertainty. Thus, for both statistical and qualitative reasons, we believe the erratic behavior of income uncertainty after October 1929 can be attributed to the Great Crash and subsequent gyrations in the stock market.

While the comparative statics in the theory and the evidence in Figure 1 are compelling, casual glances at the data are not sufficiently convincing. A statistical link between [[Sigma] [caret].sub.t] and the behavior of consumption still remains to be shown.

The problems inherent in obtaining a monthly measure of consumption are similar to those of income discussed earlier. Following Romer [1990], an index of department store sales (seasonally adjusted) is used as a proxy for consumption expenditures. Shortcomings in using this series may be present to some limited extent since the correlation coefficient between the percentage changes in annual department store sales and annual consumption expenditures equals 0.75.

Additional evidence is provided by computing a historical decomposition of department store sales over the January 1929-October 1930 period.(4) The historical decomposition is a vector autoregressive (VAR) technique that attributes differences between a base projection and the actual series among the innovations of the variables in a VAR system. More formally, for any j = 1,2,..,t+j such that t+j is less than or equal to the last period in the sample, [Y.sub.t+j] can be written in its moving average representation as (10) [Mathematical Expression Omitted] where [C.sub.s] is a matix of parameters and the [Epsilon]'s are vectors of innovations. Note that [Y.sub.t+j] is written as the sum of two components. The second part is the base projection of [Y.sub.t+j] and is computed based completely on information available in time t and before. The first part represents movements in [Y.sub.t+j] that have occurred since t, and this can be partitioned further to assign responsibility for these movements among the variables in the VAR. One may set t to whatever starting point is of particular interest.

Before a historical decomposition is computed, a VAR must be estimated. We decided to include (along with department store sales) income, wealth, wholesale prices, and the standard deviation of income in the VAR system. As discussed above, consumption is proxied by department store sales and real income is proxied by industrial production. Wealth is represented as the sum of time and mutual savings deposits. This use of liquid assets as a proxy for wealth is an identical procedure to that used by Bolch and Pilgrim [1973] for their study of the interwar period. Wholesale prices are included to control for price effects on consumption that may have been present over this period.

Explanatory variables were lagged one period since forecasting exercises over the sample period showed the one-lag specification was by far the best. We estimated the system with all variables except [[Sigma] [caret].sub.t] in logs, and January 1929 was chosen as the starting point for the historical decomposition. Each equation included constant and trend terms.

When computing a historical decomposition, the variables must be ordered in a particular way. The ordering we used (to perform a Choleski decomposition) places income uncertainty first, followed by income, wealth, prices, and department store sales. The limitations of this technique are well known, and the reader is referred to Cooley and LeRoy [1985] for a further discussion. However, for the period of interest, this ordering can be strongly justified. That is, there is reason to believe that the stock market crash in October 1929 was an exogenous event, which therefore would place income uncertainty first in the ordering. If the crash resulted from the bursting of a speculative bubble, then it is associated with arbitrary events and not fundamental causal changes in the real economy. There are many contemporary accounts that reveal the crash was thought to be the bursting of a speculative bubble (see Romer [1988] for a more indepth analysis). Changes in income uncertainty then lead to changes in income, wealth, and prices, which ultimately generate changes in consumption. Further, the results are virtually unchanged when [[Sigma] [caret].sub.t] is placed last in the ordering after income, wealth, prices, and consumption. This is the least favorable ordering for the uncertainty hypothesis, and these results are also presented.

Figure 2 presents the results over the January 1929-October 1930 period. The actual series (SALES), the base projection (BPSALES), and the base projection plus the contribution of income uncertainty (BPUNCERT) are shown. The historical decomposition reveals that the peak in department store sales in September 1929 is also reflected in BPUNCERT although the magnitude is not captured. Thereafter, the inclusion of income uncertainty pulls the base projection closer to the actual series from October 1929 to December 1929, although it overshoots a bit in October. In fact, since the definition of the historical decomposition indicates that the sum of the base projection and the contribution of all of the system's variables add up to the actual series, there is little additional responsibility to be assigned among any of the remaining system variables for explaining consumption in November and December 1929 once the contribution of income uncertainty has been accounted for. This result differs somewhat when [[Sigma] [caret].sub.t] is ordered last; here, the base projection plus the contribution of income uncertainty (BPUNCERT) completely accounts for the behavior of consumption in November but does not add to the base projection in December.

All of the turning points in the actual series of department store sales for December 1929-March 1930 are also reflected in BPUNCERT, although from January 1930 to May 1930 the base projection tracks consumption better than does BPUNCERT. However, from June 1930 until the end of the sample, the contribution of income uncertainty pulls the base projection much closer to the actual series, although it does not close the gap as completely as it does in November 1929. Romer [1990] reports that contemporary business analysts displayed a (perhaps superficial) calm in the spring of 1930 that was replaced in the summer of 1930 by a return to a loss of confidence and greater uncertainty. This is shown in the statistical evidence in both Figures 1 and 2. The continued gyrations of the stock market, the overly optimistic evaluations of business activity promulgated by the Hoover administration, and the enactment of the Hawley-Smoot tariffs are all good reasons why uncertainty remained high and contributed substantially to explaining consumption in the end of the sample. In order to bring additional evidence to bear, the root-mean-square error was computed over January 1929-October 1930 for the base projection and the base projection plus the contribution of income uncertainty. The results reveal that the inclusion of income uncertainty reduces the root-mean-square error of the base projection by an average of 33 percent whether [[Sigma] [caret].sub.t] is ordered first or last. Additionally, inclusion of income uncertainty pulls the base projection closer to the actual series in fourteen of the twenty-two months (64 percent).

For purposes of comparison, we repeated the empirical exercises by first replacing our estimates of [[Sigma] [caret].sub.t] with estimates we computed using the ARCH technique developed by Engle [1983].(5) The results revealed little resemblance to the results contained in Figure 2, and the contribution of [[Sigma] [caret].sub.t] actually raised the root-mean-square error of the base projection by 12 percent. We also repeated the empirical exercises by replacing our estimates of [[Sigma] [caret].sub.t] with the stock market volatility measure used as a proxy for income uncertainty by Romer [1990]. The results here are remarkably similar to those contained in Figure 2 as the base projection plus the contribution of income uncertainty tracked actual consumption very well in October-December 1929 and May-October 1930. Further, the contribution of the stock market volatility measure reduced the root-mean-square error by 25 percent. Thus, the stock market volatility measure seems to be a good proxy for income uncertainty during the 1920s and serves as a check on the reliability of our results.

Figure 3 presents the results of the historical decomposition for the remaining variables in the VAR system. These results indicate that wealth appears to pull the base projection much closer to the actual series from June 1930 to the end of the sample, and the contribution of income comes very close to the actual series during the peak in September 1929. However, after considering these examples (both in terms of mimicking the behavior of department store sales and pulling the base projection closer to the actual series) the variables income, wealth, prices, and lagged sales performed poorly for the period after the Great Crash.

V. INCOME UNCERTAINTY: PRE-WORLD WAR I AND POST-WORLD WAR II

While the behavior of income uncertainty in 1929-30 displayed a clear break from its behavior during the rest of the 1920s, it would still be useful to know whether the behavior of [[Sigma] [caret].sub.t] during 1929-30 was truly unique or whether it could be observed in all serious recessions.(6) Furthermore, are the results in Figure 1 representative of time variation in uncertainty, or do they result from the fact that the linear models used in the specification of [Y.sub.t] are often bad predictors of cyclical turning points?

To address these questions, we estimated [[Sigma] [caret].sub.t] over the pre-World War I and the post-World War II periods. Figure 4 presents the results of estimating income uncertainty over the January 1890-December 1913 period. We generated these estimates using a specification similar to that of equation (7) except that the interest rate differential was replaced with the commercial paper rate.(7) The results indicate that income uncertainty spikes sharply in both the 1893 and 1907 recessions. However, these observed spikes and the erratic behavior of income uncertainty are not unique to severe recessions. Gyrations of comparable magnitude also occurred during the expansionary periods of 1901 and 1904-06. Therefore, between January 1890 and December 1913 the movements of income uncertainty during expansions are comparable to the movements in income uncertainty during recessions. This was not the case for the Great Crash in relation to the behavior of income uncertainty during the 1920s. That is, the behavior of income uncertainty after the Great Crash was unlike anything else experienced during the 1920s.

Figure 5 presents the results of estimating [Mathematical Expression Omitted] over the January 1954--February 1988 period using a quarterly measure of labor income and postulating [Y.sub.t] as a random walk with drift.(8) The standard deviation of income falls during the 1974 recession and remains constant during the 1981-82 recession, rather than rising as one would expect if these results were generated solely from the poor ability of linear models to predict cyclical turning points. Further, unlike the Great Crash, there are no episodes between 1954 and 1988 in which the movements in [Mathematical Expression Omitted] are clearly aberrant relative to the entire post-World War II period.

Taken as a whole, Figures 1, 4 and 5 demonstrate that increased uncertainty is not always associated with severe recessions. More important, the most striking feature of the behavior of income uncertainty over all three periods is its unique surge in 1929 after almost a decade of steady decline and relative calm. The characteristics of this reversal in income uncertainty are not exhibited in any other period of comparable length over the entire period for which income uncertainty could be estimated.

VI. CONCLUSIONS

We use a linear moment model to produce estimates of income uncertainty during the 1920s and the first year of the Great Depression. The estimates show that there was a dramatic change in income uncertainty at the time of the Great Crash in the stock market. Income uncertainty not only went up, but reversed from a negative secular trend to a positive secular trend that saw uncertainty about future income reach the highest levels attained during the 1920s. Thereafter, income uncertainty remained high the entire first year of the Depression. From the estimates obtained in the paper and the qualitative evidence provided by business analysts at the time, it seems clear that the aberrant behavior of income uncertainty after September 1929 can largely be attributed to the Great Crash. These results provide statistical evidence that the dramatic increase in income uncertainty at the onset of the Depression was generated by the Great Crash in the stock market.

Further, the influence of income uncertainty alone provides a virtually complete explanation for the initial decline in consumption that marks the onset of the Great Depression. If it is believed that exogenous forces (such as the bursting of a speculative bubble) brought about the Great Crash, then there is a causal link between the behavior of income uncertainty and the recession of October 1929-October 1930 that ultimately turned into the Great Depression. Future research may focus on the role of income uncertainty over subsequent periods of the Great Depression(9) in addition to the period marking its onset.

DATA APPENDIX

The series on the M1 money supply and the sum of time and mutual savings deposits are from Friedman and Schwartz [1963], Table A1.

The series used to construct the interest rate differential variable are from Banking and Monetary Statistics, Board of Governors of the Federal Reserve System.

The series on industrial production, wholesale prices and department store sales are from the Federal Reserve Bulletin, Board of Governors of the Federal Reserve System.

The stock market index is from Cowles [1939].

The annual data used to compute the correlations reported in the text are from Temin [1976] and the U.S. Department of Commerce, Long Term Economic Growth 1860--1970.

The pre-World War I data for industrial production are from Miron and Romer [1989].

The pre-World War I data for the commercial paper rate and wholesale prices are from Macaulay [1938].

The pre-World War I data for high-powered money are from Friedman and Schwartz [1963] and NBER series 14,135 constructed by Jeffrey Miron. Details on this series are available on request.

Descriptions of the post--World War II data are contained in Flacco and Parker [1990].

(1)This expression for the period October 1929-October 1930 is taken from Romer [1988, 5]. (2)This specification was compared to several alternatives. Out-of-sample forecasting exercises for the January 1929-October 1930 period were conducted for this model as well as other common-lag models with lags two-eight (seven models). The results indicated that the one-lag model was superior. Given that we are interested in reproducing the behavior of the economy in our specification as closely as we can so as not to bias our results, we chose the one-lag specification. (3)Note that this procedure is similar to the one employed by Romer [1988]. She used the January 1919-December 1928 period to statically forecast consumption behavior until 1930. We apply the same procedure in constructing the variance of income for use as the measure of income uncertainty. (4)We restrict attention to the January 1929-October 1930 period since we are only concerned with the initial phase of the Depression. Furthermore, the first wave of bank failures that occurred in November/December of 1930 cause a "change in the character of the contraction," in the words of Friedman and Schwartz [1963, 11]. We regard these months as the start of the second phase of the Depression and thus stop our sample prior to this. (5)Tests indicated the presence of significant ARCH effects at lag eight. (6)Romer [1990] presents qualitative evidence on forecaster uncertainty for the earlier contractions of 1920-21 and 1923-24 and concludes that there was no systematic loss of confidence surrounding these episodes, unlike after the Great Crash. (7)The equation we estimated for [Y.sub.t] over this period has an [R.sup.2] = .94 but contains serial correlation and no amount of respecification could remove it. Therefore, we offer the results in Figure 4 with this caveat. (8)These results are contained in Flacco and Parker [1990]. (9)See Fackler and Parker [1990b] for additional results on the role of income uncertainty and other macroeconomic variables in the propagation of the Depression over the October 1929-December 1933 period.

REFERENCES

Antle, John M. "Testing the Stochastic Structure of Production: A Flexible Moment-Based Approach." Journal of Business and Economic Statistics, July 1983, 192-201. Bernanke, Ben S. "Irreversibility, Uncentainty, and Cyclical Investment." Quarterly Journal of Economics, February 1983a, 85-106. ____. "Nonmonetary Effects of the Financial Crisis in the Propagation of the Great Depression." American Economic Review, May 1988, 173-77. Blinder, Alan S., and Angus Deaton. "The Time Series Consumption Function Revisited." Brookings Papers on Economic Activity 2, 1985, 465-521. Board of Governors of the Federal Reserve System. Banking and Monetary Statistic, 1943. Board of Governors of the Federal Reserve System. Federal Reserve Bulletin, various issues, 1940-44. Bolch, Ben, and John Pilgrim. "A Reappraisal of Some Factors Associated with Fluctuations in the United States in the Interwar Period." Southern Economic Journal, January 1973, 327-44. Brown, E. Cary. "Fiscal Policy in the Thirties: A Reappraisal." American Economic Review, December 1956, 857-79. Burbidge, John, and Alan Harrison. "A Historical Decomposition of the Great Depression to Determine the Role of Money." Journal of Monetary Economics, July 1985, 45-54. Cooley, Thomas F., and Stephen F. LeRoy. "Atheoretical Macroeconomics: A Critique." Journal of Monetary Economics, November 1985, 283-308. Cowles, Alfred, and Associates. Common-Stock Indexes. Bloomington, Indiana: Principia Press, 1939. Dreze, Jacques H., and Franco Modigliani. "Consumption Decisions under Uncertainty." Journal of Economic Theory, December 1972, 30p-35. Engle, Robert F. "Estimates of the Variance of U.S. Inflation Based upon the ARCH Model." Journal of Money, Credit, and Banking, August 1983, 286-301. Fackler, James S., and Randall Parker. "Anticipated Money, Unanticipated Money, and Output: 1873-1930." Economic Inquiry, October 1990a, 774-87. ___. "Accounting for the Great Depression: A Historical Decomposition." Mimeo, East Carolina University, 1990b. Flacco, Paul R., and Randall Parker. "Some Evidence on the Influence of Income Uncertainty on Aggregate Consumption." Journal of Macroeconomics, Fall 1990, 653-62. Friedman, Milton, and Anna J. Schwartz. A Monetary History of the United States. 1867-1960. Princeton: Princeton University Press, 1963. Gordon, Robert J., and James A. Wilcox. "Monetarist Interpretations of the Great Depression: An Evaluation and Critique," in The Great Depression Revisited, edited by K. Brunner. Boston: Martinus Nijhoff, 1981, 49-107. Hamilton, James D. "Monetary Factors in the Great Depression." Journal of Monetary Economics, March 1987, 145-69. Leland, Hayne E. "Saving and Uncertainty: The Precautionary Demand for Saving." Quarterly Journal of Economics, August 1968, 465-73. Macaulay, Fredrick R. The Movement of Interest Rates, Bond Yields and Stock Prices in the United States Since 1856. New York: National Bureau of Economic Research, 1938. Meltzer, Allan H. "Monetary and Other Explanations of the Start of the Great Depression." Journal of Monetary Economics, November 1976, 455-71. Miron, Jeffrey A., and Christia D. Romer. "A New Monthly Index of Industrial Production, 1884-1940." National Bureau of Economic Research Working Paper No. 3172, November 1989. Mishkin, Frederic S. "The Household Balance Sheet and the Great Depression." Journal of Economic History, December 1978, 918-37. Romer, Christina D. "The Great Crash and the Onset of the Great Depression." National Bureau of Economic Research Working Paper No. 2639, June 1988. ___. "The Great Crash and the Onset of the Great Depression." Quarterly Journal of Economics, August 1990, 597-624. Rush, Mark. "Unexpected Monetary Disturbances During the Gold Standard Era." Journal of Monetary Economics, May 1985, 309-21. Sandmo, Agnar. "The Effect of Uncertainty on Savings Decisions." Review of Economic Studies, July 1970, 353-60. Schwartz, Anna J. "Understanding 1929-1933," in The Great Depression Revisited, edited by K. Brunner. Boston: Martinus Nijhoff, 1981, 5-48. Temin, Peter. Did Monetary Forces Cause the Great Depression? New York: W. W. Norton, 1976. ___. "Notes on the Causes of the Great Depression," in The Great Depression Revisited, edited by K. Brunner. Boston: Martinus Nijhoff, 1981, 108-24. U.S. Departmnet of Commerce, Bureau of Economic Analysis. Long-Term Economic Growth, 1860-1970, Washington, D.C., Government Printing Office, 1973. [Figures 1 to 5 Omitted]

PAUL R. FLACCO and RANDALL E. PARKER, Associate Professor and Assistant Professor respectively, Department of Economics, East Carolina University, Greenville, NC, 27858. Thanks are due W. Douglas McMillin, James Fackler, A. Steven Holland, G. S. Laumas, Richard J. Sweeney, Cacki Chambers, and Sherri Moore for help and comments. The careful and insightful comments of two anonymous referees were also extremely helpful. The authors are responsible for any errors that may remain.

Printer friendly Cite/link Email Feedback | |

Author: | Flacco, Paul R.; Parker, Randall E. |
---|---|

Publication: | Economic Inquiry |

Date: | Jan 1, 1992 |

Words: | 7243 |

Previous Article: | Liquidity constraints and aggregate consumption behavior. |

Next Article: | Taxation aggregate activity and economic growth; further cross-country evidence on some supply-side hypotheses. |

Topics: |