Robert Inklaar, Herman de Jong, and Reitze Gouma
Groningen Growth and Development Centre
University of Groningen
Paper prepared for the 8th conference of the European Historical Economics Society
4-5 September 2009 Geneva
Please do not quote without permission of the authors
For correspondence:
[email protected]
Abstract: Technology shocks have been advanced as a factor contributing to the
Great Depression in the US based on real-business cycle theory (Cole and Ohanian,
1999). In this paper we construct an improved measure of technology for interwar US
manufacturing, based on robust estimates of short-run increasing returns to scale. Using
a methodology pioneered by Basu, Fernald and Kimball (2006) for postwar US growth,
we find that technology shocks do not lead to a change in hours worked or other
inputs. This invalidates a key prediction of real business cycle theory and shows that
negative technology shocks did not drive the Great Depression.
1
In a recently published volume Great Depressions of the Twentieth Century Timothy
Kehoe and Edward Prescott collected 16 studies that apply dynamic general
equilibrium models and growth accounting to analyze past economic depressions in 14
countries. Together these studies present a research agenda to study short run income
fluctuations applying the real business cycle (RBC) theory. One of the key contributions
in this book is the chapter by Harold Cole and Lee Ohanian on the Great Depression in
the United States (Cole and Ohanian, 2007). Taking the efficiency of production as
exogenous, they try to explain why hours worked in the U.S. fell so sharply between 1929
and 1933 and stayed at a low level during the rest of the 1930s. Central in their
approach is the idea that short-run fluctuations or shifts in the production function can
be substantial, due to large and sudden changes in technology. Between 1929 and
1933 total factor productivity (TFP) in the United States declined. Cole and Ohanian
advance this as a central explanation for the Great Depression in the United States,
implying that the period 1929-1933 was a technologically regressive period in U.S.
economic history. This technology shock would have set in motion a contraction in
inputs, such as total hours worked, because workers substituted leisure for labor due to
falling productivity and wages (Cole and Ohanian 1999, 2007).
The approach of RBC theory into the study of the Great Depression has been criticized
on the ground that technological shocks to industry production functions would have
resulted in diminishing returns to labor, which cannot be observed in the data. The real
shocks that took place impacted on aggregate demand (Bernanke and Parkinson
1991, p. 448-449). Advocates of the role of technological progress prefer to broaden
the time horizon and state that the 1930s actually saw many technological innovations
that even may help to explain the high peak to peak productivity and high real wages
of industrial workers (Field 2003, p. 1410).
In this paper, we more directly test the central prediction of RBC theory that technology
shocks and inputs are positively correlated using data for the U.S. manufacturing sector
in the interwar years. We question the usefulness of taking the ‘crude’ Solow residual as
an indicator to measure technological capabilities over short time horizons as is
commonly done in the RBC approach. Using a similar methodology as has been
applied to post-war U.S. economic growth by Basu, Fernald and Kimball (2006), we
estimate a measure of technological change that does not rely on some of the
restrictive assumptions used in constructing TFP measures.
For this analysis, we use a newly constructed dataset covering all U.S. manufacturing
industries for the period 1919-1939 based on data from the Biennial Census of
Manufactures. We classify the industries in 19 branches, covering total manufacturing.
We calculate input and output price data for every branch, to deflate gross output
and intermediate inputs. New estimates of labor (employment and average hours
2
worked) and capital (amount of horsepower installed, capital stocks) complete the
statistics for inputs.
We estimate a wide range of industry production functions, based on 1) gross output,
single-deflated and double-deflated value added; 2) capital, labor and (if applicable)
intermediate inputs separately or as an aggregated measure of total inputs; 3)
alternative measures for employment; and 4) alternative capital measures. We also run
our analysis for different sub-samples of industries, such as capital-intensive versus noncapital-intensive industries and different time periods, such as the 1920s versus the
1930s. Nearly all these estimates confirm the main finding of (significant) short-run
increasing returns to scale. This is similar to the findings of Bernanke and Parkinson (1991)
based on different data sources and a much less comprehensive set of manufacturing
industries.
We then use the estimates of returns to scale to calculate, what Basu et al. call a
‘purified’ measure of technological change, equal to the residual from the estimated
production functions (Basu et al. 2006, p. 1418). Unlike standard TFP measures, this
measure of technological change would not be affected by factors such as labor
hoarding or imperfect competition. We test the RBC hypothesis that inputs follow
technology shocks procyclically, using both the standard TFP measure and our
‘purified’ technological change measure. In line with the RBC literature we find that an
increase in TFP is associated with an increase in total hours worked and total inputs.
However, we find that an increase in purified technological change has no significant
effect on any input. This is consistent with the findings of Basu et al. for the U.S. post-war
period (taking the bi-annual nature of our data into account). It leads us to conclude
that in contrast to RBC theory, the Great Depression in the U.S. was not caused by
negative technology shocks.
!
The Depression in the United States got its adjective ‘Great’ for its extremely bad record
of output and the persistingly low utilization of inputs between 1929 and 1933. During this
period output in manufacturing declined by more than 40 percent, and hourly
employment by almost 50 percent (Kendrick 1961). In the following years recovery was
slow and levels of unemployment remained high. The depth and duration of this
downturn makes this a fascinating period for studying business cycle theories, such as
real business cycle theory (RBC). Within the RBC view, the explanation of the procyclical
behavior of TFP growth lies in technological shocks, i.e. random fluctuations in a
detrended TFP series (Prescott 1986). Examples of such shocks are innovations,
government policies or price changes of important commodities e.g. petroleum. These
shocks may result in cyclical fluctuations because they directly influence productivity
3
(the efficiency of transforming inputs into output) and thus affect the decisions of
workers and firms. A negative shock to technology decreases the marginal product
and hence compensation of inputs, such as labor. As a result, employment and use of
other inputs will decrease also.
Bernanke and Parkinson (1991) provide some circumstantial evidence against RBC
theory. They first find that labor productivity in 10 US manufacturing industries is broadly
procyclical, both in the interwar and the postwar period.1 Next, they argue that this
finding could be explained by technology shocks as a driving business cycle force as in
RBC theory, true increasing returns (for example due to imperfect competition) or labor
hoarding. They argue that the RBC explanation is implausible and instead suggest that
in different industries either increasing returns or labor hoarding are more likely.
In line with RBC theory, Cole and Ohanian (1995) find that TFP declined during the
period 1929-1933. However, they find no conclusive evidence for technological regress
or more in general, a negative supply shock. On the other hand they observe that real
wages in manufacturing rose above trend during the 1929-33 decline; in 1939 wages
were about 16 percent above trend, even though manufacturing hours were
substantially below trend (Cole and Ohanian, 1999, p. 11). This finding contradicts the
neoclassical view that recovery from the Depression should have been accompanied
by lower real wages. Cole and Ohanian conclude that recovery from the Great
Depression was weak despite rapid productivity growth after 1933. In their view the New
Deal legislation, limiting competition and raising real wages, had the effect of
needlessly prolonging the high level of unemployment.2
A recent investigation into historical economic fluctuations by Neville Francis and
Valerie Ramey decomposes productivity, hours worked, and output into technology
and non-technology shocks. Using macro data on the U.S. economy and several
models they conclude that the Great Depression was characterized by shocks of both
types. Our impression from the diverse specifications in the paper is that there were
many positive technology shocks during the Great Depression strengthened by
historically very large positive shocks from 1934 to 1936. Francis and Ramey also point at
the exceptionally high productivity growth between 1933 and 1941. For the total U.S.
economy they measure an annual growth rate of labor productivity of 4.55 percent per
year (Francis and Ramey, 2006, p. 21). Although these results strengthen the case for
The finding of procyclical labor productivity has been challenged by Bordo and Evans (1995)
and Goldin (2000), who find evidence of counter-cyclicality.
1
2
See also Cole and Ohanian (2001). This argument in fact is in line with the points made by
Temin (1989). Temin, however, has expressed serious doubts about the validity and usefulness of
the RBC approach in general. In his eyes the RBC view of the Great Depression overlooks existing
explanations for why the initial contraction of the economy turned into a large depression, such
as the role of the gold standard and the policy of the Federal Reserve (Temin, 2008).
4
procyclicality of technology during the Great Depression, it raises fundamental
questions about RBC-theory’s predictions and the idea that technology shocks are the
cause and not the consequence of business cycles.
For the postwar U.S. period, Basu, Fernald and Kimball (Basu et al. 2006) follow a
different approach than Cole and Ohanian or Francis and Ramey. Cole and Ohanian
rely on the standard measure of TFP as their technology shock measure, but as we will
discuss in more detail in the next section, this assumes there is perfect competition and
fully flexible inputs. If there is imperfect competition or labor hoarding, technology and
TFP may be quite different. Francis and Ramey (2006) identify technology shocks as
those shocks that have a permanent effect on labor productivity. However, as they
acknowledge, factors besides shifts in the production function can have a permanent
effect on labor productivity. Instead, Basu et al. estimate production functions that can
take imperfect competition and labor hoarding into account. Using the resulting
‘purified’ technology measure they find no positive correlation between technology
shocks and input use. So far more than Francis and Ramey (2006), the findings of Basu
et al. for the postwar period (1948-1996) directly contradict the main prediction from
RBC theory.
Finally, Alexander Field puts forward the most ‘historical’ or long-term point of view.
Using macro-data on U.S. total economy TFP and the unemployment rate (to capture
output gap fluctuations) Field finds that TFP growth was strongly procyclical throughout
the period 1890-2004: “ Procyclical TFP…reflects short run economies of scale resulting
from amortizing relatively fixed and unavoidable capital costs over a larger flow volume
of output as one comes out of a recession.” (Field, 2008, p. 29) The Great Depression is a
very specific example in case, because TFP growth rates were exceptionally high by
any standard and were associated with very little input growth. Field stresses the secular
character of this advance, brought on by (disembodied) technological change and
organizational progress. Even in the 1930s the performance “…was not disastrous from
the standpoint of long-term economic growth. The reverse was true...” (Field, 2003, p.
1411). Field acknowledges that selective retention could have had its effects on
productivity growth in the 1930s. But he proposes, contrary to Bernanke and Parkinson,
that investment in infrastructure and the emergence and implementation of new
technologies during the 1930s had a much greater impact. Bernanke and Parkinson see
no room for supply shocks to the production functions of individual manufacturing
industries (Bernanke and Parkinson, 1991, p. 441). Field, however, argues that there were
powerful supply shocks and organizational innovations (Field, 2003, p. 1410-1411). He
also notes that during the depression R&D investments were higher than in the 1920s
(Field, 2006, p. 214-215). This can be explained by the fact that real wages were
relatively high during the depression, as a result of which firms were substituting labor for
capital. These innovations can also be regarded as technological shocks, but in this
case having the opposite effect of what RBC-theorists propose.
5
"
"
Real business cycle theory makes the key prediction that technology shocks lead to
adjustments of inputs such as hours worked and the capital stock in the same direction;
see e.g. Kydland and Prescott (1982). The basis of the prediction is the observed positive
correlation between total factor productivity (TFP) growth and growth in inputs. As a
result, RBC theory considers a technology shock as the exogenous factor that is the
prime driver of recessions. However, it is well known that TFP growth is only a good
measure of technology shocks under highly restrictive assumptions, in particular perfect
competition in output markets, constant returns to scale and full input utilization.
In this section we develop a measure of what Basu et al. label as ‘purified’
technological change, a measure that does not rely on these assumptions, because it
is controlled for nonconstant returns, imperfect competition etc. For this we follow also
their methodology (Basu et al., 2006). They start from the following production function
for industry i:
(
=
(1)
).
Gross output Y is produced using capital K, the number of employees N who work an
average number of hours H, and intermediate inputs M. The level of technology is given
by Z. It is assumed that capital and the number of employees are costly to adjust, but
the intensity with which these inputs are used can be changed: C is the capital
utilization rate and E is the effort per worker.
If firms in each industry minimize costs and are price takers in input markets, we can still
use the standard growth accounting methodology to aggregate across inputs since
under those assumptions the output elasticity of each input is equal to the cost share.3
In that case we can write the growth of total inputs
as:
=
(2)
Where , for example,
example,
(
+
is the logarithmic growth rate of
+
+
:
(
−1
)
and, for
is the average share of labor cost in gross output. Similarly, we can write
the change in (unobserved) input utilization
(3)
)+
=
as:
+
See Hall (1990) and Basu and Fernald (2001). As we will discuss later, our results do not rely on
making these assumptions.
3
6
Note that the standard method of calculating TFP growth,
, involves subtracting the
growth of inputs from equation (2) from the growth of output:
(4)
=
+
.
Here, we estimate the technological change based on:
(5)
=γ (
)+
+
,
Where γ is the returns to scale parameter. As Basu et al. argue and show, if firms can
costlessly adjust the average number of hours worked H, this variable can be used as a
proxy for the unmeasured utilization terms in equation (3). In that case, equation (5) can
be rewritten solely in terms of observable variables:
(6)
=γ
+β
+
" #
As discussed in more detail in the next section, our data consists of a panel of bi-annual
observations on output and inputs in 19 manufacturing industries from 1919 to 1939.
When estimating equation (6) as an industry-time panel, one concern can be that the
average rate of technological change over the period is different across industries. In
all our estimates we therefore include an industry-specific constant:
(7)
=
+γ
+β
=
So that technological change is given by
+ε ,
+ ε . Another concern in estimating
equation (7) is simultaneity bias: faced with a productivity 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 (see e.g. Griliches and Mairesse;
1998).
The standard solution in the literature since Hall (1990), and also used by Bernanke and
Parkinson (1991), has been to reestimate the production functions with instrumental
variables that reflect (part of) industry employment and output but are not correlated
with industry productivity shocks. Oil prices are frequently used in the postwar period
and we use them here as well. In addition, we will explore some of the instruments of
Bernanke and Parkinson, namely government expenditure, the currency/deposit ratio
and real deposits at failed banks. However, as we will discuss in more detail below,
even though the oil price is a very relevant instrument, the results using instrumental
variables are not statistically different from results using ordinary least squares.
7
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 (SRIRL). However, as Basu and
Fernald (1997) argued, estimating value added production functions may well lead to
biased results since the implicit assumption is made that the output elasticity of
intermediate inputs is equal to its cost share. We therefore estimate gross output
production functions and focus on the broader returns to scale concept rather than
SRIRL.
""$
%
As discussed above, the key prediction from RBC theory is that technology shocks are
positively correlated with inputs. Note that the standard RBC model does not distinguish
individual industries, making only aggregate predictions. Hence, Basu et al. focus their
tests on an aggregate technology series calculated from industry technology residuals
based on equation (7). This is not a feasible approach in our analysis since our data only
cover manufacturing industries rather than the total economy. Instead, we use the
industry technology residuals, comparing the response of output and inputs to a TFP
shock and a technology shock.
Formally, we estimate the effect that changes in TFP or technology have on output and
inputs:
(8)
dxit = α iA + β A dait + ηitA
(9)
dxit = α iZ + β Z dzit + ηitZ
So in equation (8), we test the effect of a change in TFP growth on inputs (or total hours
worked, or the number of employees), while in equation (9) we test the effect of a
change in the technology residual on inputs. RBC theory would be confirmed if we find
that both β A and β Z are significantly positive. If on the other hand only β A is
significantly positive, it would be an indication that standard TFP growth is mismeasured
because of non-technological effects that are included in the residual. As a
consequence, the hypothesis that technology shocks drive the business cycle and
contributed to the depth of the Great Depression would be untenable.4
Like Basu et al. (2006) we also looked at the effect of adding lagged values of TFP and
technology growth to equations (8) and (9). The contemporaneous effect that we test in (8) and
(9) was never statistically different and the lagged results were in line with those of Basu et al.
4
8
&
This paper presents a new dataset to analyze the developments in labor productivity in
the interwar period. We will shortly explain here the sources that we used. More details
are given in the appendix.
The main data source used in this paper is the Biennial Census of Manufactures of the
United States Department of Commerce held between 1919 and 1939. We used data
on gross output, value added, the cost of materials, installed horsepower of machinery,
the number of wage earners and total wages paid for all industries reported in the
census. Because all the information was gathered through the processing of
questionnaires at firm level internal consistency between input and output data is
guaranteed. We classified the industry data in 19 manufacturing branches (see
Appendix), summing up to total manufacturing.
To calculate the number of annual hours worked in a branch, the total wage sum from
the census data were divided by an hourly wage rate calculated from the Monthly
Labor Review, Woytinski et al. (1953) and Wages in the United States, published by the
National Industrial Conference Board. Wage rates are available on a monthly basis for
some 100 selected industries, which have been matched by us with census industries.
The number of wage earners in the selected industries in the Monthly Labor Review
covers about 75% of the total manufacturing sector. The industry hourly wages are
aggregated to the above mentioned branch level, weighted with the number of
employees, to arrive at an average hourly wage rate for each branch.
In addition to data on horsepower installed, we also estimated data on capital stocks.
We used capital/output ratios from Creamer et al. (1960) and the annual investment
series by Dewhurst et al. (1955). 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 appendix we discuss some
alternative estimations. It can be noted in advance that the overall regression results
were not affected by the choice of the capital stock estimates. In all cases increasing
returns to scale were found.
Gross output and value added of the industries and branches in the census have been
converted into constant prices. We combined data on output at constant prices from
John Kendrick (1961) with the current value added from the census to calculate
deflators. Since the census produced data on a detailed industry level, it was possible
to concord the current data to the industries for which Kendrick reported data in
constant prices. He applied a single-deflation procedure, using output prices to deflate
value added, implicitly assuming that the price of intermediate inputs (energy,
materials, etc.) move in line with output prices. More in general, we can decompose
output prices as:
9
(10)
dpY = vdp I + (1 − v )dpV ,
where dpY is the change in the output price, dp I is the change in the price of
intermediate inputs, v is the (two-period average) share of intermediate inputs in
output and dpV is the implicit value added deflator. This implicit deflator is also referred
to as a double-deflated value added deflator. The calculation method in equation (10)
is a Törnqvist index, but other index number formulas can also be used, such as a Fisher
or a chained Laspeyres index.5 From equation (10), it can be seen that the value
added deflator will only be equal to the output price if the intermediate input price is
equal to the output price ( dpV = dp I = dpY ).
Of course, implementation of equation (10) requires prices for intermediate inputs.
Again following current statistical practice, we use the 1939 Leontief (1953) input-output
table to estimate intermediate input prices for each industry:
(11)
dpiI =
N
n =1
win dpnY .
We use output prices for each manufacturing industry, adding additional price data on
agriculture, coal, electricity, construction and the overall price level to come with a
price series for each of the N industries. As we only have an input-output table for 1939
we cannot take into account changes in patterns of intermediate input use during this
period.
Because of the experimental nature of this procedure, we will use in our empirical
analysis both the single-deflated value added series (assuming dpV = dp I = dpY ) and the
double-deflated series based on equation (10) and (11). In models where we use
intermediate inputs as a separate input, we will distinguish between output-deflated
and input-deflated series, where output-deflated intermediate inputs assume dp I = dpY
while the input-deflated series use the results from equation (11). As we will show, the
results are qualitatively similar whether we use single-deflated or double-deflated value
added and whether we use output-deflated or input-deflated intermediate input series.
The Törnqvist index is appealing because it is an exact index for a wide range of possible
production functions. The US Bureau of Economic Analysis uses the Fisher index while the
chained Laspeyres index is used by European agencies. In practice, we find that the differences
between these index number formulas are generally small.
5
10
'(
' (
%
As discussed in the section on methodology, our key estimating equation is given by
equation (7), where we explain the bi-annual growth in output using the bi-annual
growth in total inputs and the bi-annual change in hours worked per person. To
account for industry-specific technology trends, we include industry-specific constant
terms (fixed effects). As discussed in the data section, we have a number of different
options for outputs and inputs: we can use gross output or value added as the
dependent variable; we can use total hours worked or the number of workers as the
measure of labor input; we can use horsepower installed or capital stocks as the
measure of capital input; and we can use input-deflated or output-deflated
intermediate inputs.
Furthermore, we can include the weighted average growth in inputs (using equation
(2)) or we can enter each input separately into the regression. When using weighted
average input growth, the coefficient is the returns to scale parameter. When each
input is entered separately, the degree of returns to scale can be inferred by adding up
the output elasticities of each input (the input coefficients). The appealing feature of
using weighted average input growth is that we can use instruments to correct for
simultaneity bias since we have too few instruments to estimate regressions where each
input enters separately. The appeal of entering each input separately is that we then
do not have to rely on the assumption that firms minimize costs and are price takers in
input markets.
Our main findings are robust to the choices we make. We will therefore first report
production function results using our preferred output and input measures and
specification. Afterwards, we will show how these results would change when making
different choices. Our preferred specification uses gross output (and not value added
as in Bernanke and Parkinson 1991) as the output measure since it is the most
comprehensive. As inputs we use total hours worked for the same reason; 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-deflated
intermediate inputs since that is the most conceptually appealing. As the main
estimating equation, we use equation (7), so the weighted average input growth as
explanatory variable.
Table 1 shows the first set of results.6 Column (1) shows highly significant increasing
returns to scale. The estimated coefficient is larger than one, indicating that a one
As noted before, we include industry fixed effects in all specifications. Also including year
effects do not change the results but are omitted since oil prices are not industry-specific so our
instrument would be perfectly collinear with the year effects.
6
11
percent change in weighted inputs is accompanied by a 1.2 percent change in
output. Note that the asterisks denote the significance of the coefficients compared to
the null hypothesis of constant returns to scale, i.e. a coefficient of one. However, the
change in the utilization variable hours worked per person is not significant. When we
omit the utilization variable in column (2) the coefficient shows an almost similar value
as in column (1).
Our finding has two possible implications. It could be that input utilization did not vary
substantially over this period. This could be the case if adjustment costs over two-year
periods are no longer an important concern. Alternatively, changes in hours worked per
worker may not be a good proxy for unmeasured input utilization, for instance if it is
costly to change the number of hour worked. This explanation could be particularly
relevant since we measure the number of hours paid, rather than actual hours worked
due to data limitations. This explanation though does not fit well with the rapid declines
in the workweek between 1929 and 1933 of more than 20 percent. More statistically
oriented explanations would be that if all industries reduce their workweek by a similar
amount but output declines vary considerably across industries, variations in changes in
the workweek do not well explain variations in output declines. Also, the declines in
overall inputs may be much more strongly correlated with output declines than the
declines in the workweek. The lack of a significant utilization effect is not unique to this
dataset. Inklaar (2007) also found low utilization effects for (postwar) European
countries. The lack of significance of the specific utilization effect need not be
problematic though. If instead of change in hours worked per worker, utilization would
be reflected in intermediate inputs or in the number of employees when it comes to
12
capital utilization, the returns to scale parameter ( ) would partly reflect this. Suppose
demand is high, then firms would increase both these measured inputs and input
utilization, leading to a larger than measured increase in overall inputs. In other words,
from now on we will interpret increasing returns to scale as partly reflecting input
utilization (i.e. labor and capital hoarding) and partly other factors, such as imperfect
competition.7
In column (3) of Table 1, we use the change in oil price as an instrument that reflects
industry employment and output but is not correlated with shocks to manufacturing
production functions. Again we see very similar estimates for the returns to scale as in
the previous columns. A Hausman test can be used to determine whether there is a
significant difference between the ordinary least squares (OLS) and the instrumental
variable (IV) regressions and this test shows no significant difference (p=0.49), implying
that there is no statistical need to use instrumental variables.8 Explorations with other
instrumental variables (government expenditure, currency/deposit ratio etc.) will be
needed to fully establish the robustness of this finding. However, in the specifications
that we have been able to compare, the IV regressions were never significantly
different from the OLS estimates.9 Since we cannot use IV to estimate production
functions with all inputs entering separately, we will use the OLS specification from
column (2) as the baseline.
Although we show only one specification where the change in hours worked per person is not
significant, this is a general finding in other specifications too. Those results are available from the
authors on request.
8 More formally, the Hausman test has the null hypothesis that OLS is consistent and this null
hypothesis cannot be rejected.
9 Results are available from the authors on request.
7
13
The main finding from Table 1 is that U.S. manufacturing between 1919 and 1939 was
characterized by (short-run) increasing returns to scale. Table 2 examines the robustness
of this finding to alternative input data. Column (1) replicates column (2) from Table 1,
using total hours worked, horsepower installed and input-deflated intermediate inputs
to calculate overall weighted average input growth. Column (2) replaces inputdeflated by output-deflated intermediate inputs; column (3) replaces total hours
worked by the total number of workers and column (4) replaces horsepower installed
by the capital stock. The returns to scale parameter ( ) is remarkably similar across
specifications and we cannot reject the hypothesis that they are the same.10 We also
note that a different deflation of intermediate inputs (input prices vs. output prices) has
the largest impact on the estimates. In fact, this is not surprising since intermediate
inputs on average make up more than half of total inputs.
As a further robustness analysis, we look at different output concepts. Up to now, we
have used gross output as it is the broadest output measure. However, research on this
period as in Bernanke and Parkinson (1991) and Bordo and Evans (1995) has tended to
use value added. Furthermore, these studies have relied on single-deflated rather than
double-deflated value added, so in Table 3, we compare our baseline results with
results using double-deflated and single-deflated value added as the dependent
variable. Since intermediate inputs are netted out of the output measure, they should
also be netted out of the input measure, so weighted average input growth in columns
(2) and (3) are based on total hours worked and horsepower installed, weighted using
the cost shares in value added rather than in gross output.
We can of course make eight different input combinations, but the results from Table 2 carry
through for those combinations. Results are available on request.
10
14
As the table shows, both alternative output measures show evidence of increasing
returns to scale. The point estimates are much larger though, as expected since
intermediate inputs make up 55 percent of gross output on average in this dataset.
Basu and Fernald (1997) provide a formula to transform the gross-output based returns
to scale estimates to a value added basis:
(12)
1 − vM
γ =γ
,
1 − γ vM
V
where γ V is the value-added based returns to scale parameter and, as above, v M is
the share of intermediate inputs in gross output. Applying equation (12) to the
estimated returns to scale from column (1) gives a value-added based returns to scale
parameter of 1.733, very close to the estimate in column (2). Single-deflated value
added leads to a higher estimate, but it is not significantly different from the doubledeflated estimate. In other words, we get nearly the same estimate of returns to scale
regardless of the output concept or input data used. One final thing to note is that the
single-deflated value added regression in column (3) shows a notably higher R-squared
and a lower standard error of the estimated coefficient. This is not surprising since
double deflation takes into account the price movements in other industries rather than
only the own industry output prices, leading to higher variability.
We next divide up our dataset in different ways. First we compare estimates for the
industries that Bernanke and Parkinson (1991) included in their study to those that they
omitted. Second, we compare estimates for capital-intensive to non-capital intensive
industries since capital-intensive industries might have to rely more on input utilization
adjustments than other industries. Appendix Table A shows which industries where
covered by Bernanke and Parkinson (‘BP-industries’) and which were capital-intensive.
Third, we compare estimates for the 1920s to those for the 1930s, since pre-Depression
firm behavior may be different from Depression era behavior.
Table 4 shows the results of this analysis. Column (1) shows, for reference, the results
based on all industries and years and the subsequent columns show the different
subdivisions. First, returns to scale are most clearly present in the industries covered by
15
BP. While the point estimate for the non-BP industries is similar, the standard error is too
large to draw statistically meaningful conclusions. Likewise, the capital-intensive
industries (which overlap to a substantial degree with the BP-industries) show significant
increasing returns to scale, while the non-capital-intensive industries do not. Finally, the
1920s seem characterized by constant returns to scale (the returns to scale parameter
( ) is close to 1, but not statistically significant), while the 1930s reveal substantial
increasing returns. This provides no clear-cut evidence what is driving these increasing
returns. It could be that utilization effects are important since those would be most
relevant during the 1930s and for capital-intensive industries that cannot easily adjust
their capital stocks. However, it could also mean that capital-intensive industries enjoy
greater market power due to higher barriers to entry, or that during the Depression
surviving firms enjoyed some market power, in particular following New Deal measures
that dampened competition. This also implies that in our RBC test (see further), we
should examine the robustness when using specific estimates for capital-intensive versus
non-capital-intensive industries, since there the point estimates differ most, and when
using specific estimates for the 1920s and 1930s.
Table 5 reports the last of the robustness tests by directly estimating the output
elasticities of individual inputs rather than assuming the output elasticity is equal to the
input’s cost share, as in the standard neo-classical production function. The first column
shows the baseline estimation again, for reference. In column (2) output elasticities are
estimated for labor, capital and input-deflated intermediate inputs. Column (3)
replaces the intermediate inputs variable by the output-deflated version for
comparison. Column (2) shows a highly significant effect from growth of intermediate
inputs, a marginally significant capital elasticity and an insignificant labor elasticity.
Column (3) shows significant elasticity estimates for all inputs. Note though that this is
almost entirely due to the lower standard errors compared to column (2). As noted in
the discussion on Table 3, double-deflated value added and input-deflated
intermediate inputs take into account additional information on prices and hence
contain additional variability. Focusing on the point estimates shows fewer differences
between columns (2) and (3). In the bottom part of the table, returns to scale are
shown, which is the sum of parameter estimates in columns (2) through (5). The point
estimate in column (2) is very close to the baseline estimate in column (1), but it is not
significant. The estimate in column (3) is significant though and nearly similar in size to
column (1).
16
The value added estimates in columns (4) and (5) are included as a comparison with
Bernanke and Parkinson (1991), who use single-deflated value added (measured by
physical output estimators) as their variable and find insignificant capital estimates and
for that reason only include labor as their explanatory variable. Our labor coefficient is
smaller than that found by Bernanke and Parkinson (p. 447), but since we also find
significant capital coefficients, our results are broadly similar to theirs. Again we find that
using the double-deflated series leads to higher standard errors but we find significantly
increasing returns to scale for both specifications, similar in size in column (4) and
somewhat smaller in column (5).
Table 6 compares the output elasticities from Table 5 to the cost shares used in
calculating weighted average input growth. As the Gross output panel makes clear,
labor and capital elasticities are very similar to their cost shares but the elasticity for
intermediate inputs is considerably higher than its cost share. This provides further insight
into the increasing returns vs. utilization effect puzzle. If there are true increasing returns,
due to say imperfect competition, cost shares underestimate output elasticities by the
same degree, ε i = γ ci , where ε i is the output elasticity of input i and ci is its cost share.
Instead, we only find a higher elasticity in the case of the most flexible input,
intermediate inputs. This could mean that changes in intermediate inputs are a proxy
for changes in unmeasured input utilization; so labor and capital hoarding would be the
most plausible explanation.
17
The value added estimates show the bias from netting out intermediate inputs using
their cost share (rather than the output elasticity). It shows capital elasticities broadly in
line with the cost share but much higher labor elasticities. This would suggest that
changes in labor input have an outsize effect on output, for example because of labor
hoarding. Instead, our gross output results suggest that firms may vary the intensity of
capital and labor use (i.e. utilization) together with intermediate inputs. In other words,
we confirm the finding of Basu and Fernald (1997) that estimating value added instead
of gross output production functions is potentially misleading.
' )
%
As discussed in section 3, the key test of the RBC model is whether technology changes
have a positive and significant effect on overall inputs and total hours worked. Table 7
reports the main results of this test. In the left-hand part, labeled ‘Technology’, the
technology residuals from the IV regression from Table 1 are used as the explanatory
variable. This is the residual defined in equation (7) and any increasing returns to scale
or unmeasured input utilization such as labor hoarding are not included in this
technology measure. In the right-hand part, labeled ‘TFP’, traditional TFP growth is used,
i.e. assuming constant returns to scale. In other words, TFP growth includes both
technology change and increasing returns to scale.
We use the IV residuals rather than the OLS residuals since the OLS residuals are by
construction (contemporaneously) uncorrelated with the explanatory variables.11 In
addition to the effect on inputs, we also report for completeness the effect on output,
since by definition a one percent increase in the technology or TFP residual has to lead
to an increase in inputs plus output of one percent.
The first row of Table 7 provides the key evidence against the RBC hypothesis for the
interwar period: changes in TFP are associated with large and significant procyclical
changes in inputs while a change in ‘purified’ technology has no significant effect on
inputs. As discussed earlier, RBC theory predicts a significant positive relationship
11
This follows from the geometry of least squares, see e.g. Johnston and DiNardo (1997, p. 83-84).
18
between technological change and inputs, so the absence of a significant effect
contradicts RBC theory. Compared to Basu et al. (2006), we do not find a significantly
negative effect between technology and inputs, but this may well be due to the biannual nature of our data: summed over the first two years of their regressions, the
effect of technology changes is about zero. We also verified whether these results are
robust to adding lagged technology change and TFP growth as Basu et al. did and
those results confirm the findings from Table 7.12
For the robustness analysis, the key issue is whether technology changes remain
uncorrelated with input growth. Given the similarity between the contemporaneous
and the lagged specification, we will only report the contemporaneous specification. In
the previous section we saw significant differences in the returns to scale estimates only
for the distinctions between capital-intensive vs. non-capital-intensive and between
1920s vs. 1930s, so we focus on these distinctions. Further robustness test are available
on request.
Table 8 shows the results of these robustness checks. First, allowing for different returns to
scale for capital-intensive and non-capital-intensive industries does not affect the main
conclusion that technology change does not lead to increased input use. Second,
allowing for different returns to scale in the 1920s and the 1930s does change the results.
As shown in Table 4, the 1920s taken in isolation seem best described by constant
returns to scale rather than increasing returns to scale. Given that and the results from
Table 7, the positive and significant effect of technology change on inputs is no surprise:
if returns to scale are constant, TFP growth and technological change are the same, so
the results would be the same. However, it does weaken the argument that
mismeasured technology change is to blame for the observed positive correlation
between TFP growth and inputs.
12
Available on request.
19
On the other hand, these results do strongly reject the argument that the Depression
may have been driven by negative technology shocks since during the 1930s,
technology changes are uncorrelated with input changes. Indeed, while the estimates
are not significantly different from zero, the negative point estimates are in line with
Field’s observations on the relation between technology and labour input.
*+
The driving force, or impulse, behind recessions remains a topic a great interest and for
the Great Depression in the US in particular. In this paper we have aimed to determine
whether technology shocks are likely to have played an important role during this
episode. If one believes a strict version of Real Business Cycle (RBC) theory, the answer
would be that technology shocks are the only driving force. This is strict version is not a
commonly held view, but a number of authors claim that technology shocks play a
considerable part. Our findings are that this was not the case.
For this paper, we have constructed an industry productivity dataset covering all of
manufacturing in 19 branches for the period 1919-1939. This dataset includes all the
variables that are commonly used for productivity analysis: output, intermediate inputs,
capital and labor. To test for the role of technology shocks, we estimate industry
production functions, finding robust evidence of increasing returns to scale. These
increasing returns could in turn be driven by imperfect competition or labor hoarding
and incomplete capital utilization. For our purposes, the most important thing is that
these production function estimates allow us to construct a measure of industry
technological change that is not influenced by factors such as labor and capital
hoarding. We use this ‘purified’ technological change measure to test a central
prediction of RBC theory, namely whether technological change is positively correlated
20
with input use such as total hours worked. Our findings for the interwar period closely
resemble those of Basu et al. (2006) for the postwar US period: over a two-year time
horizon, technological change has no significant effect on inputs. This finding is robust to
a wide range of alternative specifications of the production function.
These findings suggest that even the weaker version of RBC theory, namely that
technology shocks play a role alongside other factors (e.g. Francis and Ramey, 2004)
does not hold up. This suggests that what Francis and Ramey (2004) identify as
‘technology shocks’ includes supply shocks unrelated to industry technology such as
shocks from the financial sector or government policy. More broadly, our findings
suggest that the interwar and postwar economic dynamics in the US are not too
different as the response to technology shocks is very similar in both periods and
production function estimates suggest imperfect competition and labor and capital
hoarding are factors that should not be ignored.
21
,
This appendix describes the methods used to construct the dataset. We will explain in
more detail how we arrived at the hourly wage rates, used to calculate the total
number of hours worked for each branch. Additionally, the census data on capital – or
to be more precise – on horsepower of installed machinery did not cover all years for
the period under investigation. Therefore we will also explain the methods applied to
calculate annual capital data. Appendix table A1 shows the 19 separate branches
distinguished in this paper. Together they cover total manufacturing. The division of
branches is based on aggregates for which wage data was available. The
miscellaneous industries branch is an aggregation of all manufacturing industries not
included in the other branches.
The wage data used in this paper come from three sources. For the period 1933-1939
data from the Monthly Labor Review (MLR) was used for some 100 selected industries.
From this monthly data, annual averages were calculated for each industry. These
industries were matched with census industries and the numbers of wage earners
working in these industries were added. Using employment as weights, the circa 100
industries were then classified into the 19 branches presented here.
The MLR did not collect hourly wage rates prior to 1933. However, index numbers are
available for the entire period. Woytinsky et al. (1953) present index numbers on hourly
earnings from 1919 to 1939 for 38 industries. Again we have matched these industries
with census industries and summed over the total number of employees available from
the census. Employment in these industries covers close to 50 percent of the entire
manufacturing sector. The index series of the individual industries were aggregated to
the branch level, using the census’ employment of wage earners as weights. For the
Machinery branch, Woytinski et al. present only index numbers on agricultural
implements and machinery, which constitutes between 3 and 5 percent of the total
branch. Therefore other sources have been employed to increase coverage in this
branch.
The National Industrial Conference Board (NICB) has also collected hourly wages for a
selection of industries. Following the same procedure as with the other two data
sources, these industries were matched to census industries and their hourly wages are
aggregated to branch level using industry wage earner employment as weights. The
NICB data was used to provide additional coverage for the Machinery branch.
To arrive at hourly earnings for each of the 19 branches we employed a combination of
the sources described above. For the years 1933-1939 the data from the Monthly Labor
Review is used. To calculate hourly wages for 1919 to 1931, the growth of the indices
found in Woytinski et al. is used together with the levels of 1933 for each branch. For the
22
Machinery branch the level data of the NICB were taken for the period between 1921
and 1929, due to its superior coverage of industries in the Machinery branch. To
calculate the wages in Machinery for 1929 and 1931 the growth of the index for
Transportation Equipment was used. Average hourly wages for total manufacturing
were calculated from the individual branches, using the total number of wage earners
from the census in each branch as weights to ensure consistency. The MLR does not
provide hourly wages for any industries in the Miscellaneous Industries branch, nor do
any of the other sources used. Therefore, the weighted average hourly wage rate of
total manufacturing is used as a proxy for the wage rate in this branch.
From the total wages paid data in the census and the hourly wages at the branch
level, total hours worked in each branch can be calculated. In Figure 1 we compare
our results for the total manufacturing sector with the estimates of Ethel Jones (1963) to
provide a reference. Jones produced estimates of the average number of hours
worked per week for wage earners in manufacturing, allowing for holidays and sick
leave. To make the figures comparable, we divided our data on total hours by the total
number of wage earners and subsequently divided this number by 52 to arrive at the
total number of hours paid for per person per week. In order to allow for days not spent
on the job we added 5 percent to this average. As can be seen from Figure 1, the
numbers calculated in this paper fluctuate around Jones’s results at the total
manufacturing level. Therefore it can be concluded that there is no systematic over- or
underestimation of the actual number of hours worked.13 However, we use only the
logarithmic growth rates in the regression.
Appendix Figure 1
Actual hours worked per week in total manufacturing
50
Hoursworked per week
48
46
44
Inklaar, De Jong,
Gouma
42
40
Jones
38
36
34
32
30
1919
1921
1923
1925
1927
1929
1931
1933
1935
1937
1939
Year
The sharp fall in average weekly working hours in American manufacturing differs from the
general pattern in Europe; in the U.K. and in Germany the working week stayed well above 45
hours during the Depression. See De Jong & Woltjer (2009)
13
23
+
We constructed an annual capital stock series at the disaggregated level using the
investment series by Dewhurst et al. (1955) and a perpetual inventory method (PIM) to
estimate stocks. We found that annual depreciation rates averaging at 45 percent
were needed to arrive at the benchmark capital stock estimates by Creamer et al.
(1960). This suggests that the benchmark capital estimates and the investment series
are inconsistent. As an alternative method we used PIM estimates from the 1919
benchmark with an arbitrarily established depreciation rate of 15%. However, as was
noted in the main text, the overall conclusions are not sensitive to the capital stock
estimates.
Census horsepower (HP) statistics were available for 1919, 1923 to 1929, and 1939.
Therefore, data for the other census years had to be estimated. We did not simply
interpolate linearly but tried to take cyclical variations into account. This was done in
the following way: Value Added (VA) minus Total Wages paid (TW) was calculated and
deflated with the deflator of the Machinery branch. The result (VA-TW) was taken as a
proxy for gross investment. To calculate the level of horsepower for an industry for a
particular year the difference in the level of horsepower of the surrounding years was
measured. We added to this value a depreciation of horsepower which was calculated
by multiplying horsepower in the year prior to the year(s) lacking data by a flat biannual depreciation rate of 10% times the number of missing observations in between.
This gives a measure of change in horsepower between the years surrounding the
missing data. Than we added the (VA-TW) values of all intervening years plus the end
year for which data is available. Dividing the change in horsepower by this number
gives the amount of horsepower per unit of (VA-TW) for each branch, which will be
referred to as (R). This number is used to calculate the value of horsepower in the
intervening years. Calculating forward from the year prior to the missing data,
horsepower for each intervening year can be calculated by:
Alternatively (HP)t can also be calculated backwards from the year after the missing
data using:
Using both methods produced two estimates for each year. As the last (first) year for
which data is available can also be estimated in this way, we were able to see whether
this estimation led to a bias. Typically, calculating forward yields a downward bias in the
last year and calculating backward yields an upward bias for the first year. To offset
these, a weighted average was calculated, with weights decreasing with the number
of years from the starting year from which is calculated.
24
These results are dependent on the depreciation rate that is chosen. In this case we
based it on an average asset lifetime of 20 years. However, experimenting with other
depreciation rates showed that increasing the depreciation rate works to reduce the
growth in horsepower installed in the early years of the depression and increases it in
the second part of the 1930s for branches experiencing slow to moderate growth in
terms of horsepower installed. For fast growing branches with respect to horsepower
installed, we find the opposite.
Notes:
Capital-intensive: 1 means that the branch has a higher than average amount of capital per unit of labor.
(Source: U.S. Dept. of Commerce, Biennial)
Bernanke/Parkinson: 1 means that this branch includes industries that were also covered by the study of
Bernanke and Parkinson (1991).
25
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