PRODUCTIVITY SHOCKS AND THE GREAT DEPRESSION

During the Great Contraction from 1929 to 1933, the U.S. economy exhibited an extremely poor record in output growth and factor utilization. Total nonfarm GDP declined by 34 percent and total hours worked by 31 percent. The decline in manufacturing was even more severe, with declines of 37 and 40 percent for output and working hours respectively.Footnote ¹¹ During this period, movements in productivity were procyclical. A detrended time series of Solow residual TFP for the U.S. economy reveals a decline of circa 18 percent between 1929 and 1933. In a paper published in 1991, Ben Bernanke and Martin Parkinson have explained the procyclical relationship between movements in output and productivity by pointing at the effects of labor hoarding and “true” increasing returns.Footnote ¹² In contrast with this view and in support of RBC theory, Cole and Ohanian have interpreted the fall in Solow residual TFP not as a result of increasing returns but as a major exogenous technology shock. In a range of papers, they have tried to show how this shock led to decreasing marginal returns to capital and labor, and hence to a decline in employment and in the use of other inputs. According to this view, American workers substituted leisure for labor, due to a lower marginal product of labor, resulting in a decline of output.Footnote ¹³ For the period after 1933, the authors did not find a clear procyclical pattern between productivity and output. Solow residual TFP levels in the U.S. economy recovered quickly, but the growth of inputs remained very weak. The authors suggest that from 1934 onwards, the U.S. economy seemed to settle on a lower growth path than its original—pre-1929—steady state growth path. According to their analysis, supply-side constraints related to the New Deal policies increased relative prices and real wages in cartelized sectors, changes that must have weakened the recovery and prolonged the high level of unemployment.Footnote ¹⁴ Note, that from a growth accounting perspective, the RBC approach would attribute the contraction between 1929 and 1933 to a combination of a deteriorated production function and a withdrawal of inputs, not just the latter. Indeed, the former would cause the latter.

Is there strong empirical proof for the RBC—supply-side—interpretation of the causes of the U.S. Depression? In a paper published in 2001, Ohanian applied a broad definition of a productivity shock to determine statistically what factors may possibly have affected measured productivity. He referred to changes in capacity utilization, in the quality of factor inputs, in the composition of production, and changes in labor hoarding and increasing returns in particular. But he found that all of these factors combined explain only about 5 percentage points of the 18 percent decrease in Solow residual TFP between 1929 and 1933. He therefore concluded that his definition of a productivity shock would need revision.Footnote ¹⁵ Recently, Ohanian has tried to find the source of negative Solow residual TFP shocks in ill-advised government programs or initiatives related to the labor market before 1933. He emphasized that wage rate stabilization and work-sharing agreements resulting from President Hoover's industrial labor program contributed to monetary non-neutrality.Footnote ¹⁶

The RBC approach to the Depression has mainly been criticized for its method of analyzing short-run fluctuations with a general equilibrium model and its interpretation of causality running from technology shocks to a drop in output.Footnote ¹⁷ Opponents of the RBC view maintain that business cycles were not exogenously caused by Solow residual TFP fluctuations but by aggregate demand fluctuations. Thus, shocks in Solow residual TFP are seen as the consequence instead of the cause of business cycles and of the Great Depression in particular.Footnote ¹⁸ An alternative explanation of the procyclical relation between productivity and output is put forward by Alexander Field. In a recent paper in this Journal, he has shown that Solow residual TFP in the United States was strongly procyclical between 1890 and 2004.Footnote ¹⁹ But, in contrast to the RBC view, he suggests that procyclicality resulted principally from demand shocks, interacting with capital, which is relatively invariant over the cycle. This point of view proposes a different role for technology in the story of the Depression. Field has pointed to a high level of innovative activity in the American economy that explains both the high peak-to-peak productivity growth and the high real wage levels of industrial workers between 1929 and 1941. In the first phase of the Depression of the 1930s, innovations were endogenously prevented from being taken up into the economy because of the fall in output and employment. But across the Depression years, there were many technological and organizational innovations, leading to rising returns to both labor and capital.Footnote ²⁰ These product and process innovations can be regarded as shocks to technology, but in this case they have the opposite effect of what RBC theorists propose.Footnote ²¹ Clearly a formal framework is needed to establish empirically the precise relationship between technology and the business cycle in this period.

A FRAMEWORK FOR THE ESTIMATION OF HISTORICAL PRODUCTION FUNCTIONS

The theoretical framework closely follows that of Basu, Fernald, and Kimball.Footnote ²² In this model, returns to scale are given by the regression coefficient γ in the following equation

(1)

The dependent variable in this model dy, is the growth of industry output in industry i at time t. In this equation and those that follow, d followed by a lowercase letter is used to indicate the growth rate (change in log value) of that variable. The explanatory variable is the weighted average growth of inputs, dx. When estimating equation 1, one concern can be that the average rate of technological change differs systematically across industries. We therefore include industry dummies (denoted b_i) in every regression. Finally, ε_it is the residual of the regression. Technology change, dz, is defined as dz_it = dy_it −γ dx_it = b_i + ε_it. Growth of inputs is defined as a cost-share weighted average of the growth of individual inputs

(2)

We distinguish four inputs, namely total hours paid to wage laborers (LW), total hours paid to salaried workers (LS), total horsepower installed (HP), and intermediate inputs (M). Cost shares are denoted by c and the upper bar indicates a two-period average. As discussed in more detail in the next section, our data consists of a panel of biennial observations on output and inputs in 19 branches of manufacturing industries from 1919 to 1939, so i runs from 1 to 19 and t from 1 to 10.

A concern in estimating equation 1 is simultaneity bias: faced with a technology shock, an optimizing firm will in general not only change the amount of output produced but also the amount of inputs used, leading to contemporaneous correlation.Footnote ²³ The standard solution in the literature is to estimate the production functions with instrumental variables for the inputs that reflect aspects of industry demand but are not correlated with industry productivity shocks.Footnote ²⁴ This requires that changes in the instrument are not causing or are not being caused by industry productivity shocks. The change in the oil price is frequently used in the postwar period and we use it here for the interwar period as well. In addition, we use the instruments of Bernanke and Parkinson, namely government expenditure (current and lagged), the currency-deposit ratio and real deposits at failed banks. As for the validity of these instruments, it seems implausible that a productivity shock in any one industry will lead to bank failures or large-scale withdrawals of deposits by the public. Likewise, each industry is likely to be too small to influence total government expenditure or the oil price. In return, each of these variables may have some effect on technology, but it is unlikely that this effect occurs in the short run. In our analysis, we find that the estimates using instrumental variables are robust to using any subset of these variables. So even if one might object to one or more instruments, the results can be relied upon as long as not all instruments are objectionable.

Our approach differs from that of Bernanke and Parkinson insofar that they estimated the output elasticity of labor in a value added framework and concluded that there was evidence of short-run increasing returns to labor in the interwar period. However, as Basu and Fernald argued, estimating value added production functions may well lead to biased results since the implicit assumption is made that the output elasticities of intermediate inputs are equal to their cost shares.Footnote ²⁵ We therefore estimate gross output production functions and focus on the broader returns to scale concept rather than short-run increasing returns to labor.

Testing Real Business Cycle Theory

As discussed above, the key prediction from RBC theory is that technology changes lead to changes in inputs. Note that the standard RBC model does not distinguish between individual industries but only makes aggregate predictions. Hence, Basu, Fernald, and Kimball focus their tests on a technology series for the nonfarm private economy, calculated from industry technology residuals based on equation 1. In our analysis, this is not a feasible approach since our data cover manufacturing industries rather than the non-farm private economy. Instead, we use industry technology change directly, comparing the response of output and inputs to Solow residual TFP changes and technology changes.

Formally, we estimate the effect that changes in Solow residual TFP or technology have on inputs

(3)

(4)

where da_it is the change in Solow residual TFP, dz_it is technology change, β ^A is the effect of Solow residual TFP changes on inputs, β ^Z is the effect of technology change on inputs, and η_it is the residual in the two regressions. The change in Solow residual TFP is defined as da_it = dy_it − dx_it, which is the growth of output minus the growth of inputs. This assumes constant returns to scale. Technology change is defined as dz_it = dy_it −γ dx_it, so the growth of output minus returns to scale times the growth of input. These two measures will be different if we find evidence of nonconstant returns to scale.

In equation 3, we test the effect of a change in Solow residual TFP growth on inputs (or total hours worked), while in equation 4 we test the effect of technology change on inputs. RBC theory would be confirmed if we find that both β ^A and β ^Z are significantly positive, since this would imply that both Solow residual TFP and our technology measure have the positive impact on inputs that is predicted by RBC theory. If, on the other hand, only β ^A is significantly positive, it would be an indication that Solow residual TFP change is a poor measure of technology change, because it wrongly assumes constant returns to scale. This would cast doubt on the hypothesis that technology shocks drive the business cycle and contributed to the depth of the Great Depression.Footnote ²⁶

Increasing Returns: Market Power versus Hoarding

In addition to testing whether the RBC predictions are confirmed in the data, we can go a step further and consider the sources of any increasing returns we find. This should allow us to identify why Solow residual TFP change is mismeasured, rather than only concluding that increasing returns lead it to be mismeasured. We consider two hypotheses that are frequently mentioned in the literature, namely market power and labor and capital hoarding. While these explanations are not mutually exclusive, we argue that both hypotheses have different implications for the coefficients estimated from the following regression

(5)

Instead of the weighted average input growth from equation 1, we now include all four inputs separately, alongside the industry fixed effects b_i and residuals ε_it. Coefficient ϕ ^x is the output elasticity of input x. In the basic neoclassical production model with constant returns to scale, these output elasticities will be equal to the cost shares of each input, c^x, and sum to one.Footnote ²⁷ In general, the sum of output elasticities reflects the returns to scale: . When γ is greater than one, there are increasing returns to scale, γ equal to one constant returns, and γ less than one decreasing returns.

If the sum of output elasticities is greater than one, this can be due to market power of firms. But estimating individual output elasticities allows us to test whether this is indeed the case. As we argue in more detail in the online appendix, the market power hypothesis implies that all output elasticities are greater than their cost shares by the same factor γ. In other words, we would find that ϕ ^x =γ c^x for all inputs x. Intuitively, market power induces a firm to restrict its output below the competitive level, but this does not affect the input mix the firm chooses, reducing all inputs proportionally.

The other hypothesis is labor and capital hoarding. Firms may hoard labor and capital because changing the size of the workforce or the capital stock will typically involve adjustment costs: fixed costs associated with hiring and firing, for instance, or retooling of the production line. Therefore, a firm will not immediately change these inputs after a change in demand, but instead it will vary the degree to which it utilizes them. So, after a drop in demand, like in the early 1930s, firms tend to hoard labor and capital temporarily.Footnote ²⁸ As Basu, Fernald, and Kimball argue, hoarding will show up in the output elasticity of the flexible inputs.Footnote ²⁹ If a firm decides to increase its unmeasured inputs, such as the workweek of capital or the effort of workers, it will also increase measured inputs. If the firm wants to work its machines for more hours, the machines require more energy and material inputs.Footnote ³⁰ This implies that the effect on output of changes in the flexible inputs will also in part reflect changes in the unmeasured inputs. Basu, Fernald, and Kimball use changes in average hours worked as their “flexible input,” but in our data we do not know the number of hours worked, only the number of hours paid. Instead, we focus on intermediate inputs as the flexible input, following other studies in this literature.Footnote ³¹

The two hypotheses, hoarding and market power, are not mutually exclusive. So if we find evidence of increasing returns to scale based on equation 1, we might find one of the following four patterns when estimating equation 5. The first pattern states that none of the estimated output elasticities differs significantly from its cost share, so ϕ∘ ^x = c^x, where a hat over a variable denotes an econometric estimate. The elasticity estimates are then too noisy to allow us any conclusions regarding hoarding or market power. A second pattern would reveal that the intermediate input elasticity is larger than its cost share, so >c^M while the other input elasticities do not differ significantly from their cost share. This would be consistent with the hoarding hypothesis, but not with the market power hypothesis. Third, we might find that the intermediate input elasticity is larger than its cost share, but one or more of the other input elasticities is larger as well. This is consistent with the market power hypothesis, but the hoarding hypothesis also cannot be rejected. A fourth finding would be one where the intermediate input elasticity does not differ significantly from its cost share, but one or more of the other input elasticities are significantly larger than their cost shares. This is consistent with the market power hypothesis, but not with the hoarding hypothesis, since intermediate inputs are assumed to be flexible enough to be adjusted without facing costs.

It is important to note that this approach to distinguishing between market power, or “true increasing returns” and hoarding differs from that of Bernanke and Parkinson. They argue that including demand indicators such as the instruments discussed below in the estimation of equation 1 will allow for a distinction between the hypotheses. They hold that if they find increasing returns without such demand indicators but constant returns if those indicators are included, this is evidence of hoarding.³² However, this argument crucially depends on the ability of these demand indicators to proxy for hoarding. To put it differently, if there are still significantly increasing returns to scale when the demand indicators are included in the regression, this could be because market power is driving these increasing returns or because the demand indicators are poor. The advantage of our identification strategy is that there are two possible patterns of output elasticities for which we can confidently rule out one of the hypotheses.

REWORKING THE DATA ON INPUTS AND OUTPUT FOR U.S. MANUFACTURING

This article presents a new data set to analyze the developments in output, inputs and productivity in the interwar period. We will explain here the sources that we have used. More details, however, are given in Appendix 1. The main data source for this article is the Biennial Census of Manufactures of the United States Department of Commerce held between 1919 and 1939.Footnote ³³ We use data on gross output, value added, the cost of materials, installed horsepower of machinery, the number of wage earners and total wages paid, and the number of salary earners and total salaries paid for all industries reported in the census. Because all the information in the census was gathered through the processing of questionnaires at the firm level, there is internal consistency between input and output data. We classified the industry data in 19 manufacturing branches (see Appendix 1, Appendix Table 1), which sum up to total manufacturing.

To calculate the number of annual hours worked in an industry and to measure labor input on an hourly basis, the total wage sum from the census data was divided by an hourly wage rate calculated from the Monthly Labor Review, from W. Woytinski and Associates, and from Wages in the United States, published by the National Industrial Conference Board.Footnote ³⁴ Wage rates are available on a monthly basis for some 100 selected industries, which we matched with the industries in the census. The representativeness of these data for total manufacturing is high. The number of wage earners in the selected industries in the Monthly Labor Review covers about 75 percent of the total manufacturing sector. Next, the industry hourly wages were aggregated to the same 19 industries and weighted with the number of wage earners, to arrive at an average hourly wage rate for each industry.

In addition to data on horsepower of installed machinery, we also estimated data on capital stocks in manufacturing. We used capital-output ratios from Daniel Creamer, Sergei Dobrovolsky, and Israel Borenstein and the annual investment series by J. Frederic Dewhurst et al.Footnote ³⁵ We interpolated linearly between the three benchmark capital stock estimates (1919, 1929, and 1937) and estimated capital stocks for 1939 by applying the average growth over the entire period. In the online appendix, we show that estimations based on this alternative capital measure give results very similar to the results we report in the next section.

Gross outputs of the industries in the census have been converted into constant prices using the price indexes of John Kendrick.Footnote ³⁶ While he applied these prices directly to value added, they are actually (gross) output prices, so we use them accordingly. In addition, we construct intermediate input prices based on industry output prices and input-output weights, a method in line with current statistical practice

(6)

Equation 6 states that the intermediate input price change of industry i is calculated as the weighted average output price change over all N industries, including manufacturing and nonmanufacturing industries. Ideally, the weights w would change over time, but we only have the 1939 input-output table of Wassily Leontief (1953), so we use the same weights in every period.Footnote ³⁷ The output and intermediate input price changes are used to deflate the nominal series from the census.

For the sensitivity analysis reported in the online appendix, we also consider alternative measures of output and intermediate inputs. Following Bernanke and Parkinson, we consider value added instead of gross output. Value added at constant prices can be computed using gross output prices, resulting in single-deflated value added, or double-deflated value added prices. Double-deflated value added prices are based on the intermediate input prices computed according to equation 6 and industry output prices, solving for value added price changes dp^V from the following equation

(7)

where v_it is the share of intermediate inputs in gross output, and a bar over the variable denotes a two-period average share. The calculation method in equation 7 is a Törnqvist index, but other index number formulas can also be used, such as a Fisher or a chained Laspeyres index.Footnote ³⁸

From equation 7, it is easy to see that single-deflated value added, using the output price change for the price change of value added, implicitly assumes that intermediate input price changes are also equal to output price changes: dp^V = dp^Y = dp^M. In the robustness analysis reported in the online appendix, we show that our estimates of returns to scale are not sensitive to using output-price deflated intermediate inputs instead of input-price deflated intermediate inputs. Likewise, estimates of returns to scale based on double-deflated and single-deflated value added are consistent with gross-output based returns to scale. However, the source of these increasing returns cannot be correctly identified in a value added context, because the flexible intermediate inputs are “netted out.”

For most of our instruments, we followed Bernanke and Parkinson for both the selection and data source.Footnote ³⁹ Hence, data on government expenditure is taken from John M. Firestone; the currency-deposit ratio is from Milton Friedman and Anna J. Schwartz and the variable “deposits of failed banks” is from the Federal Reserve Bulletin.Footnote ⁴⁰ To deflate government expenditure and deposits of failed banks, we applied the consumer price index from the Bureau of Labor Statistics. In addition, we have taken the oil price from the NBER Macrohistory Database,Footnote ⁴¹ measured as the “U.S. Wholesale Price of Crude Petroleum, At Wells.”Footnote ⁴² All instruments were included as log differences in the regressions.

RESULTS FROM THE ESTIMATED PRODUCTION FUNCTIONS

We first estimate returns to scale in equation 1, where we explain the biennial change in output by the biennial weighted average input change as an explanatory variable. Weighted average input growth, in turn, is defined in equation 2 and is based on the growth of salaried worker hours, wage worker hours, horsepower installed, and intermediate inputs, each weighted by its cost share. To account for industry-specific technology trends, we include industry-specific constant terms (fixed effects). Although we have alternative measures for each of our output and input measures, we present results using our preferred measures in this section. The online appendix shows that the results using alternative measures are very similar.

We use gross output as the output measure since it is the most comprehensive. As labor inputs, we use total hours paid by salary workers and by wage workers for the same reason.Footnote ⁴³ We use horsepower installed since this is available from the Biennial Census and therefore consistent with the other input and output data; and we use input-price deflated intermediate inputs since this measure is the conceptually more appealing than output-price deflated intermediate inputs.

TABLE 1

RETURNS TO SCALE IN U.S. MANUFACTURING, 1919–1939

* p < 0.1.

** p < 0.05.

*** p < 0.01.

Notes:

Robust standard errors, clustered by industry, are in parentheses. The null hypothesis is that the parameter is equal to 1. The dependent variable is biennial growth of gross output in each of 19 manufacturing industries between 1919 and 1939. Weighted average input growth is calculated using total hours worked, horsepower installed, and input-deflated intermediate inputs, with two-period average cost shares used as weights. All regressions include industry fixed effects (not shown, see the online Appendix Table 4). The results in column 2 are estimated using two-stage least squares with the change in the oil price, real government expenditure, lagged real government expenditure, the currency-deposit ratio, and real deposits of failed banks as instruments. Since the IV-regression is not a linear projection of the independent variables on the dependent variable, no R-squared can be calculated. See the main text for discussion of the overidentification and weak instrument tests.

Sources:

See the text.

Table 1 shows the results from estimating equation 1, using ordinary least squares (OLS) in column 1 and using two-stage least squares based on instrumental variables (IV) in column 2.Footnote ⁴⁴ Column 1 shows significant increasing returns to scale of 1.181, implying that a one percent change in inputs is accompanied by a 1.181 percent change in output. Note that the asterisks denote the statistical significance of the coefficients compared to the null hypothesis of constant returns to scale, i.e., a coefficient of one. Industry fixed effects are included but not shown in Table 1. Instead, the online appendix shows the fixed effects, which measure the period average technology change of each industry, alongside average Solow residual TFP growth, which assumes returns to scale are constant.⁴⁵

Column 2 of Table 1 presents the results where we have used the change in oil price, real government expenditure, lagged real government expenditure, the currency-deposit ratio, and real deposits of failed banks as instruments that reflect industry demand but are not correlated with possible technology shocks. The estimates of returns to scale are very similar to the OLS estimates in column 1. A Hausman test can be used to determine whether there is a statistically significant difference between the ordinary least squares (OLS) and the instrumental variable (IV) regressions and this test shows no statistically significant difference (p = 0.883). So, the Hausman test confirms OLS as the best efficient estimator of the model.Footnote ⁴⁶

For establishing the robustness of our returns to scale estimates, we considered alternative data choices, such as different input and output measures. We also tested whether there is heterogeneity in returns to scale across different groups of industries, such as between capital-intensive or durable-goods producing industries and noncapital intensive or nondurable industries. The results, shown in the online appendix, display little or no sensitivity to alternative input and output measures and no statistically significant differences across industry groups.

Testing the Real Business Cycle Hypothesis

The key test of the RBC model and of a possible technology shock setting off the Great Depression is whether exogenous technology changes have had a positive and significant relationship with overall inputs and total hours worked. Table 2 reports the main results of this test. In the first column, labeled “Technology,” the technology residuals from the IV regression from column 2 of Table 1 have been used as the explanatory variable. This is the residual defined in equation 1 and any increasing returns to scale, due to labor hoarding, for example, are excluded from this technology measure. The measure in the second column, labeled “Solow residual TFP,” assumes constant returns to scale, so includes both technology change and increasing returns to scale. We have used the IV residuals rather than the OLS residuals since the OLS residuals are by construction (contemporaneously) uncorrelated with the explanatory variables.Footnote ⁴⁷ Each row in the table indicates a different dependent variable, so each element in the table represents a separate regression.

TABLE 2

THE EFFECT OF TECHNOLOGY CHANGE AND SOLOW RESIDUAL TFP CHANGE ON INPUTS IN U.S. MANUFACTURING, 1919–1939

* p < 0.1.

** p < 0.05.

*** p < 0.01.

Notes:

Robust standard errors, clustered by industry, are in parentheses. Each cell in the table represents a separate regression with one dependent variable and one explanatory variable. Dependent variables are either total inputs (weighted average growth of inputs) or growth of total hours. Explanatory variables are either technology change, the residual from the IV regression in column 2 of Table 1; or Solow residual TFP change, which is the growth of output minus weighted average growth of inputs.

Sources:

See the text.

The rows labeled “Total inputs” and “Total hours” of Table 2 cast serious doubt on the RBC hypothesis for the interwar period. Changes in Solow residual TFP are associated with large and statistically significant procyclical changes in inputs while a change in technology has no statistically significant effect on inputs. RBC theory predicts a positive relationship between each measure of technological change and inputs, so the absence of a statistically significant effect contradicts RBC theory. Compared to the findings of Basu, Fernald, and Kimball, we do not find a significantly negative relationship between technology and inputs, but this may well be due to the biennial nature of our data. Basu, Fernald, and Kimball find a significant negative effect in year one and a significant positive effect of similar magnitude in year two. Summed over the first two years of their regressions, the effect of technology change on inputs is therefore about zero, as in our results.⁴⁸ We also verified whether these results are robust to adding lagged technology change and Solow residual TFP growth as Basu et al. did and those results were consistent with the findings from Table 2.Footnote ⁴⁹

Much of the analysis of Cole and Ohanian focuses specifically on the depth of the Depression, 1929–1933. To rule out that statistical patterns for the full 1919–1939 period in Tables 1 and 2 are misleading for the Great Contraction years, we split our sample into pre-Contraction (1919–1927), Contraction (1929–1933), and post-Contraction (1935–1939) years. The estimated returns to scale and the effects of technology shocks on inputs are shown in Table 3.Footnote ⁵⁰ The results reveal a clear difference between the pre-Contraction period, where the point estimates suggest decreasing returns to scale, the Contraction period with a statistically insignificant estimate of increasing returns to scale, and the post-Contraction period with strongly increasing returns.⁵¹ As a result, the effect of technology shocks in the 1920s seems more in line with RBC theory, with significantly positive effects on inputs. However, the results for the periods 1929–1933 and 1935–1939 are inconsistent with the RBC view. Indeed, the results for the 1929–1933 period are most closely in line with those for the full period from Table 2.

TABLE 3

RETURNS TO SCALE AND THE EFFECT OF TECHNOLOGY CHANGE BY PERIOD IN U.S. MANUFACTURING, 1919–1939

* p < 0.1.

** p < 0.05.

*** p < 0.01.

Notes:

Robust standard errors, clustered by industry, are in parentheses. In Panel A, the dependent variable is output growth; the explanatory variable is weighted average input growth. “Returns to scale” is the coefficient of weighted average input growth and asterisks denote whether this coefficient is significantly different from 1. Returns to scale are estimated using two-stage least squares with the change in the oil price, real government expenditure, lagged real government expenditure, the currency-deposit ratio, and real deposits of failed banks as instruments (compare column 2 of Table 1). In Panel B, the residuals from Panel A are used to explain (growth of) total inputs and total hours (compare Table 2). All regressions include industry fixed effects (not shown).

Sources:

See the text.

The main conclusion from the first part of the analysis is therefore that negative technology shocks in U.S. manufacturing played little role in causing the Great Depression. The measured short-run standard Solow residual does not reflect changes in technology in the Depression era, which is inconsistent with a key prediction of RBC theorists. However, this provides no clear-cut evidence for what is driving these increasing returns. It could be that utilization effects are important since those would be most relevant during the 1930s. This would support the argument of Field that labor productivity and Solow residual TFP are both procyclical because of involuntary hoarding of capital. Businesses, and especially capital-intensive industries, were unable to get rid of capital in a downturn.⁵² However, it could also signal that surviving firms enjoyed greater market power following New Deal measures that dampened competition. This brings us to the other main question, namely what is driving the increasing returns: market power and/or hoarding?

Increasing Returns: Market Power or Hoarding?

The output elasticities of individual inputs contain valuable information that can help us determine whether the increasing returns that we found were caused by market power or by labor and capital hoarding. Table 4 provides the results from estimating equation 5. Column 1 replicates the estimate from column 1 of Table 1, showing significant increasing returns to scale. Columns 2 and 3 replace weighted average input growth by the growth of the four inputs separately. In column 2, the coefficients of the input-deflated intermediate inputs (our preferred indicator) are displayed, while in column 3 output-deflated intermediate inputs are shown. Column 4 lists the cost shares of each input, averaged across branches and years. The bottom row shows returns to scale. For column 1, this is simply the coefficient on weighted average input growth. For columns 2 and 3, it is the sum of the output elasticities.

The returns to scale estimates are similar across the three specifications, implying increasing returns of about 20 percent. But new are the output elasticities and how they compare to the respective cost shares. For all these estimates we tested whether the output elasticity is equal to the actual cost share shown in column 4. For example, while the estimate of 0.181 in column 3 for the coefficient of growth of hours worked by wage earners is significantly larger than zero, it is not statistically significantly different from the actual cost share of wage earners, which is 0.169. Indeed, for none of the capital (horsepower installed) and labor (wage earners and salary earners) coefficients can we reject equality of output elasticity and cost share. However, the output elasticity of intermediate inputs (0.792 and 0.735) is statistically significantly larger than the cost share of 0.552. Should we focus only on the point estimates, it would imply that the output elasticity of intermediate inputs can account for all increasing returns. In terms of the patterns/hypotheses mentioned in Section 3, it means that we can reject the market power hypothesis, since that hypothesis predicts that all output elasticities would be larger than their cost share by the same factor. The results confirm the hoarding hypothesis since the coefficient of the intermediate inputs shows an output elasticity statistically significantly larger than its cost share, while the other input elasticities do not differ significantly from their cost share.Footnote ⁵³ These results illustrate the importance of using a gross output framework. In a value added framework, intermediate inputs are assumed to have an impact on output that is in line with their cost shares. We show in Table 4 that this is not the case. Indeed, estimating production functions in a value added framework would lead to biased and misleading results.Footnote ⁵⁴

TABLE 4

RETURNS TO SCALE, OUTPUT ELASTICITIES, AND INPUT COST SHARES IN U.S. MANUFACTURING, 1919–1939

* p < 0.1.

** p < 0.05.

*** p < 0.01.

Notes:

Robust standard errors, clustered by industry, are in parentheses. The null hypothesis for weighted average input growth and returns to scale is that the parameter is equal to 1. In columns 2 and 3, returns to scale is the sum of the input coefficients. For other variables, the null hypothesis is that the parameter is equal to its cost share in column 4. Dependent variable in columns 1–3 is biennial growth of gross output in each of the 19 manufacturing industries between 1919 and 1939. Independent variable in column 1 is weighted average input growth based on total hours worked, horsepower installed, and input-deflated intermediate inputs. Column 2 includes input-price deflated growth of intermediate inputs and column 3 includes output-price deflated intermediate inputs. All regressions include industry fixed effects (not shown). Column 4 shows the average cost shares across industries and years of each input in total output. By assumption, the cost shares sum to one.

Sources:

See the text.

In the literature, many examples can be found of actual labor hoarding during the early 1930s. Bernanke explained the drop of the American workweek and the introduction of work-sharing as an efficient way for firms to react to falling demand. Firms cut production but at the same time the work force was left intact by spread-work schedules.Footnote ⁵⁵ Robert Margo has argued that the legislation connected to the National Industry Recovery Act (1933–1935) promoted work-sharing provisions leading to the reduction in the length of the workweek.Footnote ⁵⁶ A theoretical explanation is that especially skilled work might be viewed as a fixed factor in the short run. A certain part of the labor force acts as a buffer stock. Some labor that is normally used in production can be diverted into maintenance and repair operations during a recession.Footnote ⁵⁷ Recently, Field has mentioned the important role of capital hoarding in explaining the procyclicality of Solow residual TFP. Holding existing capital is unavoidable and capital must be held by someone. Field's argument regarding capital hoarding implies that Solow residual TFP really did go down between 1929 and 1933 and it was not just a matter of mismeasurement. Capital service flows, in particular, were amortized over a much-reduced flow of output, so output per unit of input really did fall according to this interpretation.Footnote ⁵⁸

To see how large the impact of hoarding has been in manufacturing, we can illustrate the different time pattern of technology and hoarding in Figure 1.

FIGURE 1

SOLOW RESIDUAL TFP VERSUS TECHNOLOGY INDEX, WEIGHTED AVERAGE FOR TOTAL U.S. MANUFACTURING, 1919–1939

Notes: The series “Solow residual TFP” is an index with 1919 = 1 and growth rates based on industry Solow residual TFP change. Industry Solow residual TFP change is calculated as the growth of industry gross output minus the cost-share-weighted growth of inputs: intermediate inputs (input-price deflated), growth of hours worked by wage and salary earners, and growth of horsepower installed. Industry Solow residual TFP changes are weighted using industry value added shares. The series “Technology” is an index with 1919 = 1 and growth rates based on industry technology change. Industry technology change is calculated as the growth of industry gross output minus returns to scale times cost-share-weighted growth of inputs. Returns to scale are estimated as equal to 1.181 in Table 1. Industry technology change is weighted using industry value added shares.Sources: See the text.

The Solow residual estimate of TFP growth for each industry is calculated as the growth of output minus the weighted growth of intermediate inputs, labor, and capital assuming constant returns to scale. Technological change is calculated as the growth of output minus 1.181 times inputs, where 1.181 is the returns to scale factor estimated in Table 1. We used value added shares to get a weighted average growth for overall manufacturing and turned this into an index with 1919 = 1.

Both series show the same overall pattern. Over the total period, the estimates suggest a rise in TFP of 28 to 31 percent between 1919 and 1939. But there are large differences in the variation of the series in individual periods, notably in 1920/21, the Great Contraction between 1929 and 1933, and the 1937 contraction. In the 1920/21 slump, Solow residual TFP grew at a slower rate than technology, while in the last two periods Solow residual TFP showed larger drops than technology. Our analysis has shown that this difference can be explained by hoarding effects. Between 1933 and 1937, however, Solow residual TFP is growing much faster than technology, because of massive expansion in the utilization of capital and labor.

Focusing on the period 1929–1933, technology dropped by only 1.5 percent, compared with an 8.9 percent fall in Solow residual TFP. Each decline is too small to explain the deep fall of output in the Depression, but each still shows declines. In part, this may reflect that “true” returns to scale will vary by industry and period, compared to our common scale factor, but it may also reflect firm dynamics. While we label our series “technology,” in line with e.g., Basu, Fernald, and Kimball, manufacturing industry consists of many firms and the technology series for each industry will be affected by within-industry firm dynamics. Recently, Amil T. Petrin, Kirk White, and Jerome P. Reiter analyzed firm dynamics in U.S. manufacturing for the 1977– 1996 period.Footnote ⁵⁹ They show how aggregate technological change can be decomposed into contributions from firm technological change in the form of pushing out the production frontier and reallocation of resources between firms with different productivity levels. They find that the reallocation effects are negative during recessions in their sample period, while they are positive in other years. By comparison, technological change shows a more varied pattern that is also most often positive. Still, the findings suggest that changes in market shares of firms with different productivity levels may depress industry or manufacturing technology even in periods when underlying firm technology is improving.

Evidence for the interwar period on distinguishing firm dynamics and technological change is more scattered. There are many documented examples of disembodied technological change through the improvement of plants.Footnote ⁶⁰ Although these developments varied considerably across industries, they also continued during the Depression. It is more challenging to establish the role of firm dynamics, the productivity levels of firms, and how their size varied throughout this period.⁶¹ Timothy Bresnahan and Daniel Raff perform such an analysis for the motor vehicle industry, using the Biennial Census of Manufactures data between 1929 and 1935.Footnote ⁶² They establish that there are two forces at work. First, firms remaining in business experienced large declines in output and relatively smaller declines in employment. This led to a decline in measured labor productivity and the difference in the rates of decline suggest labor hoarding. The second force is the entry of more productive new firms and the exit of less productive old firms. A third force that might have operated but was not important in the motor vehicle industry was shifts in market share between firms that remained in business. The net result of these forces in the motor vehicle industry was an increase in output per man-hour. We do not know the effects on industry technological change due to missing capital data in the Bresnahan and Raff study. However, this net result may well have come out differently in other industries. Indeed, widespread bank failures during the Depression may have cut off credit to low and high productivity firms alike, distorting the market mechanism that would normally have favored highly productive firms.Footnote ⁶³ This remains a potentially fruitful area for further research.