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o r K in g
r a p e r
s e r ie s
Production and Inventory Control at the
General Motors Corporation During the
1920s and 1930s
A n il K. K a s h y a p a n d D a vid W . W ilc o x
3
W o rk in g P a p e rs S e rie s
Is s u e s in M a c ro e c o n o m ic s
R e s e a rc h D e p a rtm e n t
F e d e ra l R e s e rv e B a n k o f C h ic a g o
M a y 1 9 9 2 (W P -9 2 -1 0 )
FED ER AL R £SER VE B A N K
O F C H IC A G O
Production and Inventory Control at the General Motors Corporation
During the 1920s and 1930s
*
Anil K Kashyap and David W. Wilcox
May 1989
revised: April 1992
This paper develops a rich body of anecdotal evidence on the design
and implementation of a production control system at the General Motors
Corporation during the 1920s and 1930s. We evaluate that evidence by first
modifying the conventional linear-quadratic model of production behavior to
take account of annual shutdown, and then testing it using newly available
data covering the period 1924 to 1940. On the whole, the model appears to
fit the data adequately. GM appears to have been aiming to maintain a
targeted level of inventory relative to expected sales, and, secondarily, to
smooth production. The production control program was more successful
before 1932 than after.
I . In tro d u ctio n
This paper studies the development and implementation of production
control methods at the General Motors Corporation (GM) during the 1920s and
1930s.1
Especially during the early portion of this period, GM faced large
seasonal fluctuations in the demand for its automobiles (much larger, in
fact, than it faces today) that seemingly should have provided an ideal
opportunity for production smoothing.
A rich body of anecdotal evidence
shows that GM's senior management thoroughly understood the costs and
benefits of production smoothing, and that they implemented a program of
production control that was well conceived, in principle, for the purpose of
smoothing production relative to sales.
We evaluate the success of the
program using newly available data on units of production, inventories, and
sales.
The next section of the paper reviews the design of the inventory
and production procedures in place at GM during the 1920s and 1930s.
Much
of our information about the development of production control at GM comes
from a retrospective study conducted in 1946 by F. Leslie Hayford— a GM
economist who had played a leading role in the design of the system and who
was later called out of retirement by GM's senior management to describe its
main features and evaluate its success.
We use Hayford's report together
with contemporary public statements of other GM executives to document the
essential objectives and operating characteristics of the GM system, and to
describe the economic environment in which the company perceived itself to
be operating.
Section III turns from the anecdotal record to an analytical model
of inventory and production behavior.
The discussion in this section
-2focuses on the predictions of the model for the long-run comovements of
production, sales, and inventories, and the implications of those
comovements for the conduct of hypothesis testing.
In Section IV, we modify
the basic model by introducing a crude form of annual shutdown.
In
particular, we explore the implications of specifying that the firm can
produce new cars only in selected months of the year, even though it can
sell them in all months of the year.
The model delivers some useful
guidelines as to how we should carry out the empirical work in production
data where annual shutdown is important.
Section V uses new data covering the period from 1924 to 1940 to
assess empirically the new production control procedures.
Much of the
analysis rests on a series of charts that demonstrate five important
features of the data:
First, that the seasonality in sales was much greater
during the 1920s and 1930s than it is today, and that GM consequently faced
an ideal laboratory for the practice of production smoothing.
Second, that
as the model predicts, inventories, sales, and production moved together
over the longer run.
Third, that lumping together operating and shutdown
periods can in some respects be quite misleading.
Fourth, that despite the
rhetoric surrounding the control policy, production seemed to be geared
mainly toward maintaining a tight correspondence between inventories and
near-term expected sales; production smoothing considerations appear to have
influenced the behavior of production only at the margin.
Finally, that the
behavior of production was different after 1932 than it had been before
1932.
We also report a variety of Euler equation estimates from the model.
On the whole, the model estimates corroborate the graphical evidence; we
-3interpret the exceptions to this pattern as reflecting mainly on the smallsample properties of the econometric estimates rather than on the economic
content of the model.
The last section of the paper presents conclusions.
II. Production Control and Planning in General Motors: 1921-1946
General Motors entered the 1920s on a tide of optimism.
2
Believing
that the post-war surge in demand would be sustained, the corporation
accumulated large stocks of raw materials and made unusually large
commitments to buy more (Hayford, p.2).
The economy slowed sharply,
however, leaving the corporation in a precarious position and leading some
of its officers to push for a new program to control production more
closely:
At the beginning of [1921] material commitments were abnormal,
inventories greatly over-expanded, and some $80 million had been
borrowed from banks. Financial control and coordination of the
Corporation's activities were imperative. (Donaldson Brown, Vice
President in Charge of Finances, as quoted in Hayford, p.4)
The first step was to begin collecting better data.
Early in 1921,
Brown appealed to Alfred Sloan (then Operating Vice President and later
President of the corporation) for help in obtaining data on stocks in the
hands of dealers and distributors (Hayford, p.8-9).
Later in the same year,
Brown raised the possibility of also collecting data on deliveries by
dealers to retail customers.
Although Brown's efforts initially were
resisted by others within the corporation, eventually he prevailed, and by
October 1921 the divisions were reporting "production and factory sales by
ten-day periods; and, as of the end of each month, orders on hand and stocks
at divisions and in dealers' hands" (Hayford, p.13).
Hayford further
reported that "although dealers did not begin reporting their deliveries to
consumers until 1925, the Central Office and the divisions were making use
-4of 'calculated7 deliveries to consumers figures long before that time"
(Hayford, p.15).
Indeed, GM began publishing monthly data on retail sales
in July, 1924.
During late 1923 and early 1924, inventories once again piled up
because the divisions had been overly optimistic about sales prospects.
Whereas the 1920-21 downturn had spurred the corporation to revise its
policy on purchases of materials, this second crisis caused them to act on
controlling inventories of finished cars, and by mid-1924 the new control
system was in place (Hayford, p.28).
In the opinion of the creators of the
new control program, its distinguishing characteristic was that it tied
production schedules over the forecast period (current month plus three
months following) to anticipated deliveries to consumers for the model year
as a whole (Hayford p.2).
Fluctuations in the business cycle were taken
into account only insofar as they were expected to influence current-modelyear sales; model changeover effectively limited the planning horizon to one
year.
Under the new production control program, the divisions were
required to file with the Central Office a monthly "Analysis of Production
Requirements."
The function of the Analysis was to record each of the
elements of the inventory accumulation identity: stocks on hand at the
beginning of the forecast period, projected retail deliveries during the
forecast period, desired stocks at end of forecast period, and— as a
residual— the "indicated maximum production required."
The divisions were
encouraged to give close and frequent scrutiny to their sales projections.
In the words of the 1924 Procedure (the corporate handbook that detailed the
mechanics of the control program), these projections "should be subject to
-5constant consideration on the part of the division and subject to change
whenever warranted by conditions of any kind" (Hayford p.43).
A key element of these monthly production statements from the
divisions was the target level for stocks at the end of the forecast period.
In the 1924 Procedure/ this target level was defined as being "calculated to
provide a sufficient number of cars or trucks to meet the requirements of
Deliveries to Consumers with the plants operating on the so-called 'level
production' basis."
In turn, "level production" was to be calculated by
assuming "'that 8.7 percent of the year's production for domestic
requirements will be produced in each month of the year except December/ for
which month 4.3 percent is assumed/ to allow for inventory taking.'"
(Hayford, p.39, quoting from the Procedure of August 1924.)
Alfred Sloan summarized the objectives of the new system in the
Annual Report to the stockholders for 1924:
During 1924 the Corporation adopted a production policy as
affecting stocks of finished cars which its dealers and
distributors will be expected to carry. This policy is
predicated upon the sale of cars to consumers as a fundamental
index. Such sales are subject to seasonal fluctuations/ and the
merchandising policy of the Corporation requires that dealers
and distributors shall accumulate stocks during seasons of
relatively low retail deliveries in order to facilitate prompt
deliveries in seasonal periods of heavy retail demand as well as
to maintain manufacturing and distributing economies afforded by
a reasonably level rate of production. The amount of such
stocks varies with the seasons of the year and is based upon a
careful analysis of the trend of retail demand... It is
believed that the Corporation in the future will be free from
the evils resulting from excess accumulation of stocks involving
unnecessary storage, interest and carrying charges as well as
drastic curtailment of production schedules such as have
occurred at times in the past, (p.9)
In 1926/ Albert Bradley— then assistant treasurer of the corporation and
later chairman of the board— described the potential benefits of the
control program in an address before the American Management Association:
-6 -
If this problem [the marked seasonality in demand] is solved by
adjusting production to correspond closely with sales two major
objections arise. Productive capacity required to take care of
April's sales, for example, would be twice that needed if
production were evenly distributed throughout the year, thus
increasing capital investment, depreciation, taxes, and similar
items and making necessary much larger earnings in order to
provide an equivalent return on the investment. Labor offers a
second objection to this course, for not only are workmen
entitled to steady employment which might be impossible with
such wide fluctuations in output, but it is unlikely that the
necessary amount of labor would be available when needed for
peak production and it is certain that a factory operating under
such conditions would be hard pressed to keep its skilled
workers, so that the quality of the product might suffer
(Bradley as quoted in Automotive Industries, March 18, 1926
p.489) .
Such statements notwithstanding, GM executives recognized that any move
toward production smoothing would entail certain costs.
Indeed, Bradley
himself went on to say:
Flattening out the rate of production and building up stocks of
cars against future heavy demand also has its drawbacks.
Such
storage requires additional capital with its interest charge,
greater insurance expense and similar items. If sales do not
come up to expectation the cost of carrying stocks may be unduly
increased through prolonging the storage period and further
losses may result from the necessity of forced selling of the
excess stock. (Automotive Industries, p.489)
We find these statements significant because they highlight several elements
of cost that often feature prominently in modern-day formulations of the
production scheduling problem.
The procedure as described above was kept in place with only minor
changes throughout the remainder of the 1920s.
However, the auto industry
was particularly hard hit during the Great Depression.
New car
registrations fell more than 2.7 million units (over 70 percent) between
1929 and 1932 (Survey of Current Business, Annual Supplements, 1932 and
1938), compared with a 28 percent decline in real GNP over the period.
GM
fared little better than the rest of the industry, suffering a 66 percent
-7 reduction in retail deliveries of autos.
These developments caused GM to
reconsider the design of the control program:
In view of the instability of economic conditions in the early
1930s and the resultant greater difficulty in appraising
consumer demand, it was recognized that sudden and considerable
changes in forecast might become necessary. (Hayford, p.87)
In May, 1932, a new Procedure was issued.
In tone, the new Procedure was similar to previous ones, the
operating divisions being instructed to set production "giving consideration
to the best estimate of deliveries to consumers for the complete model sales
year and having regard to the extreme desirability of running at as level a
rate of production as practicable" (Hayford, p.85).
In practice, however,
the revised program differed importantly from the ones that had been in
force during the 1920s.
Under the revised program, the Central Office no
longer transmitted to the divisions a "Preliminary Analysis of Production
Requirements" which, under the earlier program, had been a starting point
for the divisional decisionmaking process.
And, in recognition of the
greater uncertainty about market conditions, the new Procedure specified
that the divisions were required to notify the Central Office only "whenever
a change in the outlook necessitates a change of ten percent or more in the
total Production Schedule for the entire Forecast period" (Hayford, p.87).
Another factor that may have limited the apparent effectiveness of
the production control program during the 1930s was a reduction in the
amplitude of the seasonal swings in sales.
In part, this reduction
undoubtedly reflected the increasing mechanical reliability of newly
manufactured cars, the gradual disappearance of open cars, and the increased
extent of paved roads.
In addition, the reduction in seasonal amplitude
probably reflected the coordinated shift of the shutdown period from the
-8turn of the year to the late summer.
The Automobile Manufacturers
Association proposed in 1933 "that the industry as a whole shift its new
model announcement dates to the fall of the year for the purpose of
attaining a greater regularity of production and employment"
(Hayford, p.59) .
The Roosevelt Adminstration supported the plan, and
between 1934 and 1935 the introduction dates were moved forward by several
months (see Cooper and Haltiwanger (1991)).
Finally, labor relations became more difficult during the late
1930s.
The problems reached the boiling point in 1937, when a sitdown
strike by GM workers effectively closed most GM plants in late January and
early February.
Aside from these labor disputes, however, we found no
mention (either in Hayford's report or elsewhere) of transitory fluctuations
in costs.
III. The Basic Model
Our baseline model is similar to one proposed by Holt et al.
(1960)
3
and subsequently studied by many others.
We assume that the firm
. . .
4
minimizes expected cost as given by:
(1)
min E
t-l
£
+
al IOt+j>
+ a2 IHt+3 - “3St+j+l)2)
*-t - “f j ' Ht+j-l + «t+J - St+j
Hfc_^ given
where P is a discount factor, H
cars, Q
is the end-of-period stock of finished
is production, and Sfc is sales.
We assume that the firm makes its
production decision before current-period sales are known.
The three
components of the cost function all are standard from the inventory
literature, and are consistent with the anecdotal evidence provided above.
-9 -
The first-order condition necessary for cost minimization is given
by:
(2i
+
+ "
i
W
w
"
- °-
In this baseline model, a similar equation holds for all periods "t".^
A. Identification
The parameters {0Cq ,
identified.
a2 ) in equation (2) are not separately
We achieve identification by requiring that the strong form of
the Legendre-Clebsch condition be satisfied.
The Legendre-Clebsch condition
is an additional condition that is necessary for optimality; it states that
the second derivative of the objective function with respect to the choice
variable must be strictly positive (Stengel (1986) page 213).
In our model,
the Legendre-Clebsch condition is given by:
<x0 (l+4p+p2) + o^d+p) + a2 > 0.
g
We guarantee that this condition will be satisfied by imposing:
(3)
aQ (l+4p+p2) + a^l+p) + a2 = 1.
We also impose a priori the value of the discount factor P, in line
with the suggestion made by Gregory, Pagan and Smith (1989), who discuss the
difficulty in identifying P in this class of models, and following a long
tradition in this literature.
B. Multicointegration and the importance of allowing
to be non-zero
Equation (2) can be rewritten as follows:
(2'|
Et_l(a0 (p2aC!t+2-2|iAQttl+A<!t) - a ^ A H ^ + A S ^ )
a^l-p)
+ a1AHfc - a2a3Ast+i + a2 [Ht ” (a3
This form of the equation highlights that H
must be cointegrated.7
)St J} = 0.
and S
(and hence Q
and S )
Hence, our analytical model predicts that H, Q, and
-1 0 -
S should exhibit the type of long-run interrelationships labelled
"multicointegration" by Granger and Lee (1988a, 1988b).
Equation (2') also highlights the importance of allowing
differ from zero.
to
As West (1986) noted, some authors have argued that
should be set equal to zero.
Equation (2') makes clear, however, that the
cointegrating parameter would, be negative if
were set equal to zero
and a ^ are positive), in which case a permanent increase in
(provided
g
sales would induce a permanent decrease in inventories.
In fact, a common
feature of actual data is that inventories and sales covary positively in
the long run as well as in the short run.
C. Inference
Most inference in our model can be carried out using standard
asymptotic distributions even if the stochastic process for sales contains a
unit root.
9
The argument revolves around showing that the variables
attached to the remaining parameters (after the identifying assumption has
been imposed) are cointegrated.
To verify that this condition obtains in
our model, we drop the expectations operator from equation (2), and
eliminate
0C2
using equation (3)
(similar arguments hold for other
identifying assumptions):
(2” )
a0 (|J24Qtt2-2|J4Qt+1+4(!t) ♦ Oj <-PQt+1+Qt>
+ [I-o^
cl m
P+p V
ojU+MJ
<Ht-a3st+1) = st
Then we calculate the derivative of the expectational error,
with respect to each of the parameters remaining in the model:
V
- 5 ^ - <!>2«2tt2-2|iAQt+1« Q t) - U+4P+P2) (Ht-03St+1)
-11-
” it - 5 ^ * -P°t+i+Qt - ^ l 5' ' W t + i 1
[i-“o (1+4^
It is easy to verify that v
\
■v
2)-“i <1+P,Ist+i
is stationary, where
l+4g±g_
1 1+p 1''it
1--------- 1Z2--------- 1’’3t) '
1-a (l+4|S+r>-a(1+p)
Thus, TlQt/ ’
Hit' anc* ^bt are c°inte9ratec*-
Given this fact, results from
Sims, Stock, and Watson (1990) and West (1988) can be applied to show that
the estimated a's will be asymptotically normal, and that Hansen's (1982)
J-statistic will be asymptotically chi-square.
This analysis shows that if the stochastic process followed by sales
is the only source of nonstationarity, then there is no need to include time
trends in the specification of the model, regardless of whether sales are
trend- or difference-stationary.
However, if there is some other source of
a deterministic trend in the data— say, a deterministic trend in costs
unrelated to production— then deterministic trends should be included in the
specification of the Euler equation.
Even in that case, asymptotic
arguments similar to the one given above will be valid (again, see Sims,
Stock, and Watson (1990) and West (1988)).
Therefore, previous results
derived from equations that included deterministic trends should be valid
asymptotically, even if the only source of nonstationarity in fact was a
stochastic trend in the sales process.1^
We carry out our estimation and
hypothesis testing under the assumption that deterministic trends need not
be included in the equation.
-1 2 The expectational error that results from dropping the expectations
operator from equation (2) is MA(1).
We estimate the coefficients and their
standard errors using GMM with a Newey-West (1987) covariance matrix.11
Our
RATS code and a complete dataset are available from the authors upon
request.
IV. The Model With Annual Shutdown
Thus far, we have followed earlier authors in assuming that the
manufacturer is producing every period.
We view this assumption as
particularly unsatisfactory for the automobile industry:
After all, even
during the 1920s and 1930s GM closed its assembly plants each year for
inventory-taking and retooling.
We take a small step toward reality in our
theoretical model by assuming that the manufacturing plant shuts down once a
year.
We treat this shutdown period as exogenous to the model, as if it
were, say, constitutionally imposed upon the company as a condition of
incorporation.
12
We maintain the assumption that sales are made throughout
the year, including during the shutdown period.
We further assume that the
manufacturer pays a fixed cost to open or shut a plant, and does not, in
opening one up or shutting one down, bear the cost usually associated with
changing production.
In most months, equation (2) remains the relevant first-order
condition despite the explicit introduction of annual shutdown into the
problem.
When shutdown is just past or is imminent, however, a modified
first-order condition is relevant.
For example, in the first period
following a shutdown, the relevant first-order condition is given by:
(4|
V l ' V ^ W ^ t + l 1 + Oj (-PQt+1+Ot ) + «2 <Ht- V t+1)) ■ °'
-13where the absence of the term in AQ^ reflects our assumption about the cost
of re-opening a plant.
In the last period of operation before a one-month shutdown period,
the following first-order condition obtains:
(5)
Et_1 ia0 i|i3i<;t+3-2|iiQt+1) + «i H > 2W « t >
+ a2 [(Ht”a3St+l) + P (Ht+l"a3St+2)]J = 0;
while in the penultimate month of production before shutdown the following
first-order condition is relevant (regardless of how long the shutdown is
expected to last) :
(61
Et.l(a 0 (-2p4Qt+1+iQt) ♦ V ' P W V
+ V W t + l 11 * °'
Modifications of equation (5) relevant for two- and three-month shutdowns
are easily derived.
Of course, we recover the condition Qt=0 for months in
which the plant is not operating.
Thus, the augmented model predicts that the specification of the
first-order condition for any given month will depend on the orientation of
that month with respect to shutdown periods, both preceding and following.
Many strategies for dealing this with situation are possible; we pursue two
of them here.
The first involves simply dropping the shutdown-contaminated
observations from our sample, and estimating the cost parameters using the
remaining observations.
The second involves retaining all non-shutdown
observations in the sample, and applying to each observation the appropriate
form of the Euler equation, enforcing that (Xq , a^,
in all specifications.
13
anc* a3 are the same
The advantage of the second approach is that it
attempts to exploit the information in the observations coming just after
and just before shutdown periods, and therefore holds out the possibility of
a gain in statistical efficiency.
The risk in this approach, however, is
-14-
that we will not be able to incorporate that additional information into our
model in a valid fashion, and that in expanding the sample we may primarily
be increasing the specification error in the equation rather than augmenting
its statistical efficiency.
One troubling indicator in this regard is that
we never observe production to be zero in any month in our sample, contrary
to the key assumption in our shutdown-augmented model.
On balance,
therefore, we favor the first approach, but we implement both of them in the
next section.
V. Empirical Results
We begin with five charts that highlight the main features of the
data.15
First, monthly sales during the 1920s and 1930s were much more
variable than they are today.
Especially during the 1920s and early 1930s,
the bulk of this variation was accounted for by regular seasonal
fluctuations. Chart 1 demonstrates these points by showing monthly domestic
unit sales by all GM divisions as a percent of a twelve-month centered
moving average for the periods 1924-1940 (top panel) and 1971-1987 (bottom
panel).
In the 1920s, the pace of sales during the busiest month of the
year (generally March or April) frequently was more than three times as
great as the sales pace during the slowest month (generally November or
December).
In the mid and late 1930s, the amplitude of the variation in
sales declined somewhat, and the seasonal pattern became less regular.
Even
in that later period, however, the amplitude of the variation in sales was
enormous compared with more recent experience:
Since 1971, sales in the
busiest months have rarely been even twice as great as sales in the slowest
months (bottom panel).
Second, the long-run comovements between inventories, sales, and
production conform to the predictions of the model.
Chart 2 abstracts from
-15short-run (especially seasonal) fluctuations by plotting twelve-month
centered moving averages.
The top panel shows sales and production, and
leaves no doubt that those two variables are cointegrated and that the
cointegrating parameter equals 1.
The bottom panel shows sales against a
linear transformation of inventories (where the linear transformation was
chosen in line with one of our preferred sets of estimates reported below),
and shows that inventories and sales also appear to have moved together over
the long term.
The relationship between these two variables was not as
tight as the one between production and sales.
However, our confidence in
the validity of the underlying relationship is bolstered by the fact that
all of the important deviations from the equilibrium relationship between
inventories and sales have obvious economic interpretations:
On the upside,
inventories were unusually high during 1924 (the very episode that caused GM
to institute the new program of production control), the first three years
of the Great Depression, and the recession of 1938.
On the downside,
inventories were unusually low during 1928— at the peak of the expansion—
and in the winter of 1936-1937, when labor strife culminated in the sitdown
strike of 1937.
Third, the behavior of production during months we identify as
"operating" months differed markedly from the behavior of production during
the year as a whole.
Chart 3 compares the variance of production with the
variance of sales for each model year on two different bases: first using
data from all months of each model year (the dashed line), and second using
data from only the operating months of each model year (the solid line).^
In more than half the years between 1925 and 1940, the variance ratio
calculated over operating months was at least 30 percent lower than the
variance ratio calculated over all months.
Only once— in 1938— was the
-16-
variance ratio for operating months higher than the variance ratio for all
months .^
Fourth, contrary to the anecdotal evidence presented above, GM
appears to have arranged its production chiefly to maintain a reasonable
short-run correspondence between the level of inventories and expected
sales.
At the margin, production appears to have been a bit smoother than
it would have been if GM had aimed to hold the inventory-sales ratio fixed
to the exclusion of all other factors.
Chart 4 provides evidence in support
of the first part of this proposition.
It plots the unfiltered levels of
production and sales in the top panel and inventories and sales in the
bottom panel.
The bottom panel shows that inventories tracked sales not
only at business-cycle frequencies, as was evident in Chart 2, but also at
seasonal frequencies, suggesting that one of GM's objectives was to tie the
level of inventories to the volume of sales within each model year as well
as between model years.
Chart 5, which shows the inventory-sales ratio
(Hfc/St+1) as the solid line and production as the dotted line, supports the
second part of the proposition.
In every year between 1925 and 1931, the
inventory-sales ratio hit its seasonal low when production was at or near
its high, consistent with the conclusion that production was smoother than
it would have been if GM had been aiming to hold the inventory-sales ratio
constant at some fixed level year-round.
Finally, the behavior of production was different after 1932 than it
had been before 1932.
This difference is evident in Chart 5:
In some years
after 1932, the correlation between the inventory-sales ratio and production
appears to have been about zero; in other years (such as 1939 and 1940), it
appears to have been strongly positive.
Overall, it is much more difficult
to make the case that production after 1932 was smoother than it would have
-17been under a policy of fixing the inventory-sales ratio.
Chart 3 provides
another perspective on the change in the behavior of production in 1932:
In
the eight years after 1932, the variance ratio measured over operating
months exceeded 1 four times; by contrast, in the eight years up to and
including 1932, the variance ratio exceeded 1 only once, in 1932.
We view
both these pieces of evidence as suggesting that some factor or factors
inhibited the apparent effectiveness of the production control program after
1932.
Such factors could have been either internal or external to the firm.
Two obvious candidates in this regard are the 1932 modification in the
production control program and the increased difficulty of labor relations.
We now report the results of estimating the parameters appearing in
the first-order conditions for cost minimization.
Our goal here is to
develop additional evidence either corroborating or contradicting the
graphical evidence already presented.
Table 1 summarizes nine sets of
results, reflecting three different methods of handling the influence of
annual shutdown and three different sample periods.
With regard to the
treatment of shutdown periods, the first method involves simply ignoring any
special considerations related to the handling of the shutdown periods and
applying the basic first-order condition (equation (2)) to all observations
in the sample.
The second method is our preferred one; it involves dropping
all shutdown-contaminated observations from the sample and applying equation
(2) to the remaining observations.
In line with the results from our
theoretical model, we treat an observation as "shutdown-contaminated” if it
was either (a) a shutdown month;
(b) a month that immediately followed a
shutdown period; or (c) a month that preceded a shutdown period by either
one or two months.
The third method involves dropping only the shutdown
months themselves, and selecting for each of the remaining observations in
-1 8 -
the sample the appropriate specification of the first-order condition from
among equations (5)-(7) above, and the modification of (6) for multi-period
shutdowns.
As for sample periods, we implement each of these three methods
over: the full sample period, 1925:1-1940:12; the period before any major
changes were made in the original program, 1925:1-1932:5; and the remainder
of the sample period, 1932:6-1940:12.
All nine sets of results shown in
Table 1 were derived using equation (3) as the identifying assumption.
18
Several features of the results in Table 1 are worth highlighting
First, the direct cost of producing, as reflected in oc^, is
briefly.
estimated to be negative in every specification, and significantly so in
several.
19
Nonetheless, the estimated slope of the marginal cost curve,
given by oCgU+pKa^, is positive in all specifications, reflecting the
positive estimated cost of changing the rate of production.
Second, the
cost of deviating from the target level of production also is positive in
every case, but significantly so only over the early sample period.
Third,
the target inventory-sales ratio is positive and significant in the early
sample period, but insignificantly different from zero in the late sample.
(In fact, when we use either the second or third method of handling the
shutdown periods, the point estimate of
is negative.)
Overall, the model
seems to do an adequate job of describing the data, as evidenced by the fact
that the residuals from these specifications look to be well-behaved.
As an
example, we plot the residuals from line lb in the top panel of Chart 6.
(The negative autocorrelation at the first lag evident in the residuals
shown in the top panel does not contradict the assumption that they follow
an M A (1) process.)
Table 2 provides additional results based on alternative assumptions
about various features of the model.
The first three sets of estimates
-19reported there were derived using our preferred method of handling the
shutdown periods.
Lines 1 and 2 examine the ability of the data to
distinguish between costs of changing production and direct costs of
producing as sources of production smoothing.
Like Blanchard (1983), we
find that the model is about equally happy with either alternative:
In both
cases, the estimated slope of the marginal cost curve remains positive and
highly significant.
Line 3 shows the results of fixing P at 0.99 rather
than 0.995; not surprisingly, this perturbation makes hardly any difference.
The last three lines in Table 2 report the results of using <*2=1 as
the identifying assumption rather than equation (3), and handling shutdown
20
periods by the first method (that is, ignoring their presence).
Recall
that, asymptotically, the specification of the identifying assumption should
have no effect on either the nature of the decision rule implied by the
parameter estimates, or the overall statistical adequacy of the model.
In
our sample, however, the choice of the identifying assumption turns out to
matter a great deal.
As shown on line 4b of Table 2, aQ is estimated to be
negative in the early sample period under the alternative identifying
assumption, and the estimated slope of the marginal cost curve is negative
in all three samples.
Clearly, the economic implications of the alternative
estimates differ dramatically from those of the baseline estimates.
In our view, however, the alternative estimates should be discounted
for three reasons:
First, the estimated residuals associated with those
estimates are so highly autocorrelated as to suggest that the variables in
the model are not cointegrated.
To show this, we plot the residuals from
line 4b in the bottom panel of Chart 6; the contrast with the residuals from
the baseline specification is stark.
The Durbin-Watson statistic for these
residuals is 0.22— well below the level that would be required to reject the
-2 0 null of nonstationarity.
A second reason for taking a skeptical view of the
alternative estimates is that they fly in the face of the graphical evidence
presented earlier, which pointed toward production smoothing, at least
before 1932.
By contrast, the baseline results reported in Table 1 were
fully consistent with this evidence.
Finally, we note that Krane and Braun
(1991) also experimented with the a2=l normalization, and found that it
delivered peculiar results.
For example, they report that the Legendre-
Clebsch condition was violated in about a third of the industries they
studied when they used a2=l as their identifying assumption; by contrast,
they found no such violations whey they achieved identification by setting
aQ (l+P)+a1=l.
On balance, we view the alternative results as more of a
puzzle with regard to their econometric implications— that the asymptotic
approximations of the statistical distributions are very poor— than with
regard to their economic implications.
As a result, we focus the remainder
of our discussion on the baseline econometric estimates, which we view as
being both more statistically defensible, and consistent with the graphical
evidence.
In particular, we now briefly revisit the questions posed earlier
with respect to shutdown, the possible break in the data in 1932, and the
propensity to smooth production.
First, with regard to possible differences
in the behavior of production during normal operating months versus shutdown
periods, we find the Euler equation evidence frankly surprising.
Although
the relative variability of production and sales differed substantially
depending on the treatment of the shutdown periods, the Euler equation
estimates appear to be affected only a little.
The most that can be said,
in our view, is that the over-identifying restrictions are rejected less
vigorously under the more cautious method of treating shutdown (lines 2a,
-2 1 2b, and 2c of Table 1) than they are when shutdown is ignored.
Given the
substantial difference in the available number of observations under these
two methods, though, we would hesitate to read too much into even this
finding.
Overall, while we continue to believe that the handling of
shutdown can be important for some questions, it does not appear to be
universally important.
On the question of whether there was a break in the data around
1932, the message from the various pieces of evidence is much more
consistent.
First, the autocorrelation structure of the disturbances
appears to have changed between the early and late subsamples.
For the
residuals underlying line 2b (estimated from the pre-1932 sample), the
correlogram is as follows:
lag:
correlation:
1
-.36
2
.08
3
.13
4
-.04
5
.04
6
-.03
For the residuals underlying line 2c (estimated from the post-1932 sample),
the correlogram is:
lag:
correlation:
1
-.43
2
.17
3
.18
4
.04
5
.02
In both cases the asymptotic standard error is 0.13.
6
-.19
Over the early sample
period there is no evidence that would reject the view that the disturbance
follow the hypothesized MA(1) process.
However, the post-1932 disturbances
betray greater evidence of correlation at longer lags, consistent with the
view that cost shocks may have become more important after 1932 (see
Eichenbaum (1989), among others, on the implications of cost shocks for
models of the type we study).
Second, the estimates of a3 derived from the later subsample are
less plausible than the ones derived from the early subsample (especially
the negative estimates reported on lines 2c and 3c).
Third, and perhaps
-2 2 most importantly from an economic perspective, the decision rules implied by
the early- and late-sample parameter estimates are considerably different.
Below we report some simple simulations that display these differences
clearly.
Finally, we return to the keystone question of whether GM was a
production smoother or a production buncher.
The implications of the
parameter estimates for GM's propensity to smooth production are difficult
to discern given the complexity of the model (especially with regard to its
predictions for the dynamic response of production to a shock in sales).
To
illuminate the extent to which GM may have been acting as a production
smoother, we conduct a simulation exercise:
We transport GM to a simplified
world (where there is no annual shutdown and where sales follow a random
walk), solve for the decision rule in that simplified world, and then
simulate GM's response to a one-unit shock to sales given a particular set
of parameter values.
21
Needless to say, we are exploiting to the maximum
degree the structural interpretation of our cost parameters.
The top panel of Chart 7 shows the outcome of this exercise when we
use our preferred coefficients from the early period (line 2b of Table 1).
The solid line represents the hypothetical sales trajectory.
Sales are
assumed to have been constant at 100 units per period until period 0, at
which time they are assumed to have jumped permanently to 101 units.
The
dashed line represents the production trajectory given the parameter
estimates from line 2b.
Prior to period 0, production and inventories are
assumed to have been at their equilibrium levels.
In period 0, production
remains at 100 units because the increase in sales was unanticipated; as a
result, inventories decline by one unit in that period.
Starting in period
1, however, production begins to follow a hump-shaped path.
During much of
-23the adjustment period, production exceeds 101 units per period, and, in this
sense, production is more variable than sales.
Over the entire adjustment
period (including period 0), the cumulative excess of production over
101 units is sufficient not only to offset the initial inventory drawdown of
1 unit but also to build up inventories to their new higher equilibrium
level.
The dotted line shows what the manufacturer's response would have
been if there had been no incentive to smooth production.
(We compute this
A
A
path by setting 0Cq and
equal to zero.)
In this no-smoothing world, the
entire production adjustment occurs in period 1, and the manufacturer builds
enough cars all at once to boost inventories to their long-run level.
Clearly, production in the no-smoothing world is more variable than it is
when cXq and
are at their estimated values.
We conclude that, in this
sense, over the early portion of our sample period, GM was a production
smoother.
The bottom panel repeats the exercise using the coefficients we
estimated from the late sample, shown on line 2c of Table 1.
These
parameters imply hardly any smoothing relative to the path that the producer
would have chosen if
and
had been equal to zero.
The simulation
exercises show that seemingly slight differences in parameter values can
imply important differences in economic behavior.
On balance, we read the bulk of the evidence as suggesting that GM
was engaged in some production smoothing between 1925 and 1932.
of the data after 1932, however, is less clear:
The message
Production appears to have
been no smoother than it would have been under a rule tying inventories to
near-term expected sales.
On the other hand, the corporation did succeed in
-2 4 navigating through extremely turbulent times while avoiding a repetition of
the nearly-disastrous inventory accumulation of 1923-24.
V I . Conclusion
In 1924, General Motors implemented a new production control
procedure that was intended to "regularize" production and employment.
In a
report to the Executive and Operations Committees of the corporation,
Donaldson Brown described the program as "permitting] an accumulation of
stock during the period of the year when sales to consumers are below the
average rate, and requir[ing] a liquidation of stock during the period of
the year when sales to consumers are above the average rate" (Hayford,
p.42).
A simple plot of monthly inventories and sales suggests that,
measured against Brown's yardstick, the program was a failure:
During the
period we study, GM usually accumulated inventory in the spring, when sales
were on their seasonal upswing, and decumulated inventory in the late summer
and fall, when sales were tailing off.
Further examination of the data, however, reveals considerable
success in smoothing production relative to a different yardstick.
A plot
of production and the inventory-sales ratio shows that, during the early
years of the production control program, GM drove its inventory-sales ratio
down during the time of the year when production was at its highest, and
allowed its inventory-sales ratio to spike up when production was at its
lowest.
Moreover (and to our surprise), the data contain some hints of
smoothing of this type even at business-cycle frequencies:
Inventories were
taken down to unusually low levels relative to sales at the peak of
expansion at the end of the 1920s, and were allowed to accumulate to
unusually high levels, relative to sales, during the Great Depression.
Formal statistical evidence, based on a modified linear-quadratic model of
-25production behavior, largely corroborates the graphical evidence.
We
conclude that GM did succeed, during the 1920s and early 1930s, in making
production smoother than it would have been if the corporation had only
sought to stabilize the inventory-sales ratio.
In 1932, however, the corporation revised the structure of the
program.
We also adduce indirect evidence that cost shocks became more
important.
In the second half of our sample, there is little or no evidence
of production smoothing, even by our more expansive definition.
We close with three summary points:
First, the fact that production
tracked sales does not cast doubt on the standard linear-quadratic model.
Indeed, as we noted above, the model itself predicts that production and
sales will be cointegrated.
22
Second, the fact that production tracked
sales does not, by itself, imply that GM faced a flat or declining marginal
cost curve.
Indeed, our preferred parameter estimates imply that GM faced
an upward-sloping marginal cost curve and yet still chose to make production
mimic sales closely.
Overall, our interpretation of the evidence relies
heavily on the importance of the inventory-sales target as a determinant of
GM's behavior, and reinforces the importance of research such as Kahn's
(1992)
that seeks to provide a firmer microfoundation for the observed
inventory-sales targeting.
Third, annual shutdown influenced GM's
production behavior importantly.
As Cooper and Haltiwanger (1990) note, the
type of machine replacement that often motivates annual shutdown is common
to many industries.
We see promising possibilities in further study of the
influence of machine replacement on the dynamics of production.
-26-
References
Blanchard, Olivier J. (1983) "The Production and Inventory Behavior
of the American Automobile Industry,” Journal of Political Economy 91(3)
365-400.
Blinder, Alan S. (1986) "Can the Production Smoothing Model of
Inventory Behavior be Saved?" Quarterly Journal of Economics 101 431-454.
Cooper, Russell and John Haltiwanger (1990) "The Macroeconomic
Implications of Machine Replacement: Theory and Evidence", unpublished
mimeo, University of Maryland.
______________________ (1991) "Autos and the National Industrial
Recovery Act: Evidence on Industry Complementarities," unpublished mimeo,
University of Maryland.
Eichenbaum, Martin (1989) "Some Empirical Evidence on the Production
Level and Production Cost Smoothing Models of Inventory Investment,"
American Economic Review, 79(4) 853-864.
Fair, Ray C. (1989) "The Production Smoothing Model is Alive and
Well," Journal of Monetary Economics 24 353-370.
Forbes (1977) "1917, 1929, 1945, 1966, 1977: Sixty Years of
Corporate Ups, Downs, and Outs," September, 127-60.
Granger, Clive W. J., and Tae-Hwy Lee (1988a) "Multicointegration",
unpublished manuscript, University of California, San Diego.
_____________________ (1988b) "Investigation of Production, Sales
and Inventory Relationships Using Multicointegration and Nonsymmetric Error
Correction Models", unpublished manuscript, University of California, San
Diego.
Gregory, Allan W., Adrian R. Pagan and Gregor W. Smith (1989)
"Estimating Euler Equations from Linear Quadratic Models", unpublished
manuscript, Rochester University.
Hayford, F. Leslie (1946) "Production Control and Planning in
General Motors: 1921-1946," unpublished manuscript, General Motors
Corporation, Detroit.
-2 7 Hansen, Lars P. (1982) "Large Sample Properties of Generalized
Method of Moments Estimators," Econometrica 50(4) 1029-1054.
Holt, Charles F., Franco Modigliani, John F. Muth, and Herbert A.
Simon (1960) Planning, Production, Inventories and the Work Force, Englewood
Cliffs: Prentice-Hall.
Kahn, James A. (1992) "Why is Production More Volatile than Sales?
Theory and Evidence on the Stockout-Avoidance Motive for Inventory Holding,"
forthcoming, Quarterly Journal of Economics.
Krane, Spencer D. (1991) "Induced Seasonality and Production
Smoothing Models of Inventory Behavior," forthcoming, Journal of
Econometrics.
, and Steven N. Braun (1990) "Production Smoothing
Evidence From Physical-Product Data," Journal of Political Economy 99(3)
558-581.
Modigliani, Franco, and Franz E. Hohn (1955) "Production Planning
Over Time and the Nature of the Expectation and Planning Horizon,"
Econometrica 23(5) 46-66.
___________________ and Owen H. Sauerlander (1955) "Economic
Expectations and Plans of Firms in Relation to Short-Term Forecasting," in
Short-Term Economic Forecasting, Studies in Income and Wealth, Vol. 17,
National Bureau of Economic Research. Princeton, New Jersey: Princeton
University Press.
Newey, Whitney K., and Kenneth D. West (1987) "A Simple, Positive
Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance
Matrix," Econometrica 55(3) 703-708.
Ramey, Valerie A. (1991) "Non-Convex Costs and the Behavior of
Inventories," Journal of Political Economy 99(2) 306-334.
Sims, Christopher A., James H. Stock, and Mark W. Watson (1990)
"Inference in Linear Time Series Models with Some Unit Roots," Econometrica
58, 113-144.
Stengel, Robert F. (1986) Stochastic Optimal Control: Theory and
Application, New York, Wiley.
-2 8 West, Kenneth D. (1986) "A Variance Bounds Test of the Linear
Quadratic Inventory Model," Journal of Political Economy 91(2) 374-401.
________________ (1988) "Asymptotic Normality when Regressors Have a
Unit Root," Econametrica 56, 1397-1418.
-2 9 Table 1
Estimated Cost Parameters: The Baseline Estimates
Sample
1. All months
a. 1925:1 - 1940:12
ao
“l
a2
a3
J-statistic
.213
(.013)
-.149
(.041)
.027
(.025)
1.13
(.91)
32.4
[-02]
b. 1925:1 - 1932:5
.187
(.012)
-.083
(.033)
.052
(.029)
.715
(.34)
26.0
[.10]
c. 1932:6 - 1940:12
.252
(.014)
-.294
(.049)
.082
(.030)
.500
(.27)
25.3
[.12]
-.106
(.054)
.029
(.021)
1.47
(.97)
23.3
[.14]
2. Non-Shutdown-Contaminated Months
.198
a. 1925:1 - 1940:12
(.018)
b. 1925:1 - 1932:5
.176
(.014)
-.054
(.041)
.056
(.027)
.752
(.27)
19.7
[.19]
c. 1932:6 - 1940:12
.212
(.027)
-.150
(.088)
.033
(.023)
-.127
(.99)
16.9
[-39]
.215
(.019)
-.143
(.059)
.003
(.021)
-6.03
(47.7)
15.3
[.43]
b. 1925:1 - 1932:5
.200
(.014)
-.109
(.041)
.025
(.014)
1.56
(.85)
22.6
[.09]
c. 1932:6 - 1940:12
.194
(.027)
-.091
(.088)
.022
(.028)
-2.27
(3.76)
20.7
[.15]
3. All Operating Months
a. 1925:1 - 1940:12
Notes:
1. Estimates of constant terms are not reported. In all regressions
reported here, P was fixed at 0.995.
2. We assumed that the shutdown months were as follows: 12/25, 12/26,
11/27, 12/27, 11/28, 12/28, 11/29, 12/29, 10/30, 11/30, 10/31, 11/31, 10/32,
11/32, 11/33, 12/33, 10/34, 11/34, 12/34, 9/35, 9/36, 9/37, 8/38, 9/38,
7/39, 8/39, 9/39, 8/40, and 9/40.
3. Standard errors are in parentheses; p-values are in square brackets.
-3 0 Table 2
Estimated Cost Parameters: Alternative Estimates
Sample
ao
al
a2
a3
J-statistic
1. Non-Shutdown-Contaminated Months; a =0
1925:1 - 1932:5
0
.455
(.022)
.093
(.043)
.266
(.24)
18.1
[.32]
2. Non-Shutdown-Contaminated Months; a =0
1925:1 - 1932:5
.159
1 0
(.004)
.050
(.025)
.688
(.27)
19.9
[-22]
3. Non-Shutdown-Contaminated Months; P=.99
1925:1 - 1932:5
.177
-.055
(.014)
(.041)
.057
(.027)
.751
(.27)
19.7
[.19]
4. All months; a«=l
a. 1925:1 - 1950:12
.174
(.060)
-.747
(.122)
1.0
.440
(.07)
25.8
[.10]
b. 1925:1 - 1932:5
-.053
(.054)
-.232
(.105)
1.0
.384
(.06)
20.8
[.29]
c. 1932:6 - 1940:12
.337
(.069)
-1.08
(.136)
1.0
.518
(.09)
20.2
[.32]
Notes: See Table 1.
-31*University of Chicago and NBER, and Federal Reserve Board, respectively.
We have benefitted from many helpful comments and suggestions, especially
those from Spencer Krane, Adrian Pagan, and Mark Watson, and two anonymous
referees.
We also thank Maura Doyle for excellent research assistance.
The
views expressed are those of the authors, and not necessarily those of the
Board of Governors nor of the other members of its staff.
Any errors are
our own.
1. As measured by total assets in 1929, General Motors was the third
largest industrial firm in the United States, exceeded only by US Steel and
Standard Oil of New Jersey (Forbes 1977).
According to registrations data,
GM had slightly less than a third of the domestic new car market in 1929.
2. This section takes its title from the report written by F. Leslie
Hayford in 1946.
3. Elements of this model can be found in earlier work by Modigliani and
Sauerlander (1955) and Modigliani and Hohn (1955).
More recent work using
this framework includes Blanchard (1983), Blinder (1986), West (1986),
Eichenbaum (1989), Ramey (1991), and Krane and Braun (1991).
4. For expositional convenience, we suppress here linear terms in the cost
function.
In the empirical work, we allow for such terms by including an
intercept in the Euler equation.
5. Equation (2) is derived by using the accumulation identity to substitute
out all occurrences of Q
. in the objective function, differentiating with
respect to Efc 1Ht, and then simplifying again using the accumulation
identity.
6. Ramey (1991) provides the cite to Stengel (1986) .
She imposes a2=l as
-32-
an identifying assumption, and then tests whether the Legendre-Clebsch
condition is satisfied.
The fact that we set the Legendre-Clebsch linear combination of the a's
equal to 1 rather than any other non-zero scalar is irrelevant for the
implied decision rule even in small samples.
The specification of the
linear combination of the parameters is relevant for the implied decision
rule in small samples, but not asymptotically.
Previous investigators have
reported, however, that their empirical results were sensitive to the choice
of an identifying assumption (see, among others, Krane and Braun (1991),
pages 574-575, and Ramey (1991), page 322).
7. If Ht and Sfc are cointegrated and St is 1(1), then Hfc must be 1(1).
if
is ^(1)/ then AH^=Q^-S^ must be 1(0).
combination of
and
But
Thus, there exists a linear
(namely the difference between them) that is
stationary; therefore, Q^_ and S^_ must be cointegrated.
8. In the new steady state after a positive innovation in permanent sales,
the firm will choose to incur a higher marginal stockout cost because it
wi H be experiencing a higher marginal production cost (associated with a^)
Unless the target level of inventories is a positive function of sales, the
higher marginal stockout cost will entail a lower level of inventories.
9. We are grateful to one of the anonymous referees for supplying the
outline of the following argument.
10. It is an open question as to how the finite sample properties of the
estimates are affected by the use of the time trends.
11. In the first step, we estimate the a's using nonlinear two-stage least
squares.
Then we form the cross products of the residuals from the first
-33stage with the instruments, using the lags=l options in RATS to alert the
program to the MA(1) error structure, and the damp=l option to ensure the
positive semi-definiteness of this matrix.
Then we reestimate the a's using
the inverse of the cross-products matrix as a weighting matrix, again
invoking the lags=l and damp=l options.
12. A more complete treatment of the problem would include an explanation
for the choice of a technology that requires shutdown to occur (see Cooper
and Haltiwanger (1990) for a serious consideration of the machine
replacement problem).
13. When we are estimating under this approach, we make room for other
differences across the periods by allowing the intercept to take on a
different value depending on whether the observation in question is (1) a
normal operating month,
(2) a month immediately following a shutdown period,
(3) a month immediately preceding a shutdown period, or (4) a month
preceding a shutdown period by two months.
14. We suspect that our failure to observe zero production mainly reflects
that GM did not perfectly align its shutdown periods either across divisions
or with the calendar months, and so was always operating at least one of its
plants during at least part of a "shutdown" month.
Since our model views
each period as a point in time, it is silent on the issue of how production
should behave during a month when GM was operating only part of its capacity
part of the time.
15. The data were kindly provided to us by a member of GM staff.
are monthly, and cover the corporation as a whole.
level are not available.
Data at the divisional
The data for 1925 include Chevrolet trucks; data
for the other years do not include Chevrolet trucks.
In 1925, Chevy trucks
accounted for about 5 percent of total sales and production of the
The data
-3 4 corporation as a whole.
We made a simple adjustment to the level of sales
and production in 1925, which preserved the inventory accounting identity
between 1924 and 1926.
Details of this adjustment will be provided along
with the data upon request.
The GM staff member cautioned that the
from the early years may be less reliable than those from the later
data
years.
16. We were unable to develop conclusive information on the exact timing of
the annual shutdowns at the individual plant level.
We inferred approximate
shutdown dates from Hayford and various issues of Automotive Industries, a
contemporary trade journal.
Whenever we had substantial doubt about whether
GM was fully operational during a given month, we erred on the side of
caution and flagged that month as a shutdown month.
The list of months we
identified as shutdown months is given in the notes to Table 1.
17. The spike in 1938 appears to reflect a colossal forecasting error.
GM
opened the 1938 model year with two months of extremely aggressive
production, even as the economy was turning into a sharp nosedive.
They
then spent the rest of the model year slashing production not only in line
with the weakness in sales, but also to decumulate the inventories that had
piled up in the first few months of the model year.
18. The estimates in Tables 1 and 2 were obtained using an instrument set
that included the following 10 variables: the contemporaneous value and the
first two lags of the change in production; the first two lags each of the
change in sales, the change in the log of industrial production, and the
change in the log of the composite Standard and Poor's stock index; and the
first lag of the difference between production and sales.
In addition, the
instrument set included as many seasonal dummy variables as possible (a
dummy variable for December could not be included, for example, if no
December observations were included in the particular sample being
-35-
estimated).
This instrument set reflects our assumption that GM did not
know current-period sales when it chose production.
We included the
contemporaneous value of production in the instrument set because it was the
choice variable of the firm.
19. The statistical significance of a q , a^, and
is difficult to interpret
because in fact, of course, we are estimating the ratio of those parameters
to the linear combination of them given in equation (3); it is difficult to
know when we should be able to estimate such a ratio precisely and when we
should not.
Therefore, rather than relying heavily on statistical
significance per se, we look for other clues as to the economic importance
of any given parameter.
20. We obtain similar results using the second method of handling the
shutdown periods.
21. This approach of simulating decision rules to assess the importance of
production smoothing is similar to the approach pursued in Fair (1989).
22. In his study of the seasonal comovement of sales and production, Krane
(1991) makes a similar observation in explaining the close correspondence of
sales and production in some of the industries he examines.
Chart1
Monthly Sales
as a percent of a centered twelve—month moving average
1924-1940
1971 -1 9 8 7
Percent
16
J_____l
1971
1973
1975
1977
1979
1981
1983
1985
1987
Chart2
The Long-Run Relationships Between Production, Inventories, and Sales
(centered twelve-month moving averages)
Chart3
Ratio of Within-year Variance of Production to Within—Year Variance of Sales
3.5
3
2.5
2
1.5
1
0.5
0
Chart4
Production, Sales, and the Level of Inventories
Thousands of Units
Thousands of Units
Chart5
The Inventory-Sales Ratio and Production
Thousands of Units
Months
6
5
4
3
2
1
0
Thousands of Units
Months
Chart6
R esiduals from th e B asic E uler E quation E stim ated O v e r All M onths
Alternative Identifying Assumption: a2*1
60
40
20
+
0
20
40
60
80
Chart7
Im pulse R e s p o n s e Functions
Early Sample Period
104
Sales
----------- Production as Implied by the coefficients on line 2b of Table 1
- - - - - - Production In the no-smoothing world
103
102
101
100
I
99
t=0
Late Sample Period
104
Sales
----------- Production as Implied by the coefficients on line 2c of Table 1
------- -- - Production In the no-smoothing world
—
103
102
#*
■' '•
/■
N.
101
/ /
V
......................................................................
t-0
100
99
@FedFRASER