View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.


Mark Bils and James A. Kahn

Federal Reserve Bank of New York
Research Paper No. 9817
July 1998

This paper is being circulated for purposes of discussion and comment.
The views expressed are those of the author and do not necessarily reflect those
of the Federal Reserve Bank ofNew York of the Federal Reserve System.
Single copies are available on request to:
Public Information Department
Federal Reserve Bank of New York
New York, NY 10045

What Inventory Behavior Tells Us about Business Cycles

Mark Bils
University of Rochester and NBER
James A. Kahn
Federal Reserve Bank of New York

May 1998*

We argue that the behavior of manufacturing inventories provides
evidence against models of business cycle fluctuations based on
productivity shocks, increasing returns to scale, or favorable externalities,
whereas it is consistent with models with short-run diminishing returns.
Finished goods inventories move proportionally much less than sales or
production over the business cycle, which we show implies procyclical
marginal cost and countercyclical price markups. Obvious measures for
marginal cost do not show high marginal cost near peaks, as required to
rationalize the inventory behavior, because measured factor productivity
rises during the peak phase of the cycle. We can better explain the
cyclical behavior of inventory holdings by allowing for procyclical factor
utilization, the cost of which is internalized by firms but is not
contemporaneously reflected in measured wage rates.

* Support from

the National Science Foundation while both authors were at the
University of Rochester is gratefully acknowledged. We also thank Anil Kashyap, Peter
Kienow, Valerie Ramey, Julio Rotemberg, Ken West, Michael Woodford, two referees,
and participants at a number of seminars for helpful comments. The views expressed are
those of the authors and do not necessarily reflect those of the Federal Reserve Bank of
New York or of the Federal Reserve System.



There are two distinct views on the nature of business cycle fluctuations. In one
view business cycle peaks represent times of increased productivity and lower production
costs. This includes models based on increasing returns such as Farmer and Guo (1994),
as well as real business cycle models (e.g., Kydland and Prescott, 1982) driven by
fluctuations in technology. According to the second view, at cyclical peaks capacity
constraints and diminishing returns kick in, driving up the costs of production relative to
input prices and relative to other periods. Many researchers have viewed the procyclical
behavior of inventory investment as evidence for the first view because it suggests that
firms bunch production more than is necessary to match the fluctuations in sales. If
short-run marginal cost curves were fixed and upward sloping ( the argument goes), firms
would smooth production relative to sales, making inventory investment countercyclical. 1
Countercyclical marginal cost in turn is viewed as evidence for procyclical technology
shocks, increasing returns, or positive externalities. 2
We argue that this reasoning is false: Inventory investment should be procyclical
even with increasing marginal cost. The argument outlined above overlooks changes in
the shadow value of inventories--which we argue increases with the level of production
and expected sales. 3 We propose a model in which finished inventories facilitate sales,

1 See

West (1985), Blinder (1986), and Fair (1989) for evidence on production volatility

and the cyclical behavior of inventory investment.
2 West

(1991) explicitly uses inventory behavior to decompose the sources of cyclical
fluctuations into cost and demand shocks. Eichenbaum (1989) introduces unobserved cost
shocks that generate simultaneous expansions in production and inventory investment. Ramey

(1991) estimates a downward sloping short-run marginal cost function, which of course reverses
the production-smoothing prediction. See also Hall (1991). Cooper and Haltiwanger (1992)
adopt a nonconvex technology on the basis of observations about inventory behavior. Others
( e.g., Gertler and Gilchrist, 1993, Kashyap, Lamont, and Stein, 1994) argue that credit market
imperfections--essentially countercyclical inventory holding costs for some firms--are responsible
for what is termed "excess volatility" in inventory investment.


with the marginal value of inventories proportional to the level of sales. This implies
that (holding price and marginal cost fixed) inventories should rise proportionately with
anticipated increases in sales.
Procyclical inventory investment implies that inventory stocks are also
procyclical, but does not imply that stocks rise as much as sales. In fact, inventory-sales
ratios are extremely countercyclical. Figure 1 plots the monthly ratios of finished goods
inventory to sales (shipments) in aggregate manufacturing for 1959 through 1997 along
with output, where output is detrended according to a Hodrick-Prescott (H-P) filter.
The inventory-sales ratio increases dramatically in each recession, typically by 5 to 10
percent. Note that these increases do not simply reflect a transitory response to an
unexpected fall in sales, but are highly persistent for the duration of each recession.
Replacing sales with forecasted sales generates a very similar picture. The correlation
between the two series in the figure is 0.675. In the empirical work below we examine
data for six two-digit manufacturing industries that produce primarily to stock. These
data reinforce the picture from aggregate data in Figure 1--inventories fail to keep up
with sales over the business cycle. 4
We find the puzzle then to be why inventory investment is not more procyclical.
Inventories sell with predictably higher probability at peaks, suggesting that firms should
add more inventories in booms so as to equate the ratios (and hence the "returns") over

Pindyck (1994) makes a related point regarding what he calls the "convenience yield"'
of inventories. A number of papers in the inventory literature do include a target inventorysales ratio as part of a more general cost function to similarly generate a procyclical inventory

demand. Many of these papers, for example Blanchard (1983), West (1986), Krane and Braun
(1991), Kashyap and Wilcox (1993), and Durlauf and Maccini (1995), estimate upward-sloping
marginal cost in the presence of procyclical inventory investment. This appears consistent with

our evidence that marginal cost is procyclical. West (1991) demonstrates that the estimated
importance of cost versus demand shocks in output fluctuations is very dependent on the size of
the target inventory-sales ratio.

We find similar results for finished goods inventories and works-in-process for new
housing construction and for finished goods tnventories in wholesale and retail trade.


time. Our model shows that this striking fact implies that in booms either 1) marginal
cost must be high relative to discounted future marginal cost, or 2) the markup of price
over marginal cost must be low.
We initially examine the case of a constant markup. This allows us to measure
expected movements in marginal cost by expected movements in price. For sales to
increase relative to inventories then requires that the rate of price increase be less than
the interest rate. This is sharply rejected for the six industries we study--in fact the
opposite is true. We turn then to allowing for both cyclical movements in marginal cost
and price-cost markup. We ask what behavior of marginal cost is consistent with
marginal cost being temporarily high and/ or price being low relative to marginal cost in
booms, as required to justify the cyclical behavior of inventories.
When we measure marginal cost based on inputs and factor prices, however, we
do not find high marginal cost in booms, or countercyclical markups, because input
prices are less procyclical than productivity. But we can explain the cyclicality of
inventory holdings by allowing for procyclical factor utilization that is not reflected
contemporaneously in wage rates.
We find the joint behavior of inventories, prices, and productivity consistent with
the following view of business cycles: In a boom the capital stock lags behind labor and
output. This raises marginal cost and is associated with cuts in price markups. In turn,
this induces firms to squeeze inventory-sales ratios. Short-run fixity of factors also leads
to higher factor utilization, generating a transitory rise in Solow residuals, which hides
the true short-run increase in costs. Inventory behavior thus points to the second view of
business cycles that stresses short-run diminishing returns.


II. The Demand for Inventories

A. A Firm's Problem
We examine the production to inventory decision for a representative producer,
relying on little more than the following simple elements: Profit maximization, a
production function, and an inventory technology that is specified to reflect the fact that
inventory-sales ratios appear to be stationary and independent of scale. To achieve the
latter, we assume that finished inventories are productive in generating greater sales at a
given price (see Kahn, 1987, 1992). Related approaches in the literature include Kydland
and Prescott (1982), Christiano (1988), and Ramey (1989), who introduce inventories as
a factor of production. Inventory models that incorporate a target inventory-sales ratio,
or that recognize stockouts, create a demand for inventories in addition to any value for
production smoothing.
A producer maximizes expected present-discounted profits according to

subject to:


at = it+ Yt = at-1 - st-1 + Yt,
st = dt(Ptlat ¢ ,

(0 n "l vk l-o-v) 'l']
Yt = min [...'.!L
"t ' t t t t

In the objective function, st and Pt denote sales and price in period t, "t is a vector of
material input requirements, 0t a technology shock, and zt is a vector of input prices.
Ct(Yt) is the cost of producing output Yt during t. ~t,t+i denotes the nominal rate of
discount at time t for i periods ahead. For example ~t,t+l' which for convenience we
write ~t+l' equals l+~+i where Rt+l is the nominal interest rate between t and t+l. 5
Constraint (i) is just a standard stock-flow identity, taking the stock of goods available


for sale during period t, at, as consisting of the inventory it of unsold goods carried
forward from the previous period plus the Yt goods produced in t.
Constraint (ii) depicts the dependence of sales on finished inventories. For a
given price, a producer views its sales as increasing with an elasticity of ¢, with respect to
its available stock. This approach is consistent, for example, with a competitive market
that allows for the possibility of stockouts (e.g., Kahn, 1987, Thurlow, 1995).
Alternatively, one can view the stock as an aggregate of similar goods of different sizes,
colors, locations, and the like. A larger stock in turn facilitates matching with potential
purchasers, who arrive with preferences for a specific type of good. Empirically it is
important that a producer's demand increases at least somewhat with its available
inventory; otherwise it becomes difficult to rationalize even systematically positive
finished goods inventory holdings, much less the one to three months' worth of sales that
we typically observe. We also allow the demand for the producer to move
proportionately with a stochastic function dt(Ptl• Again, this is consistent with a
perfectly competitive market in which charging a price below the market price yields
sales equal to at and charging a price above market clearing implies zero sales. The
function dt(Pt) will more generally depend on total market demand and available supply.
All we require is that the impact of the firm's stock at be captured by the separate
multiplicative term at¢,
From constraint (iii), output is produced using both a vector of material inputs,
qt, and value added produced by a Cobb-Douglas function of production labor, nt,
nonproduction labor, It, and capital, kt. Material inputs are proportional to output as

5 Jn

the empirical work we incorporate a storage cost for inventories. We let the cost of
storing a unit from period t to t+l equals 6 times the cost of production in t. (This follows, for
instance, if storing goods requires the use of capital and labor in proportions similar to
producing goods.) The storage cost then effectively lowers .Bl+l as it now reflects both a rate of
storage cost, 6, as well as an interest rate Rt+l' .Bt+1= (l + R!+l> •


dictated by a vector of per unit material requirements,

-"t ·

(We do not treat elements of

At as choice variables, but At can vary over time.) The value-added production function
has returns to scale ,, potentially greater than one.

B. The First-Order Condition

If yt is positive (which we assume), then the impact on expected discounted
profits of producing one more unit during t must equal zero. This condition is

The expectations operator conditions on variables known when choosing period t 's
output. The producer incurs marginal cost ct= Ct'(Ytl• By increasing the available
stock, sales are increased by ,t,dt(Pt)a/- . These sales are at price Pt· To the extent the
increase in stock available does not increase sales, it does increase the inventory carried
forward to t+l. This inventory can displace a comparable amount of production in t+l,
saving its marginal cost ct+i·
Note that the marginal impact on sales, ,t,dt(Pt)a/-1, is proportional to the ratio
of sales to stock available, equalling ~t . Making this substitution and rearranging gives


Et { [ ~tt mt + 1]v t+ 1 }



lit+l ct+l
and mt


Pt - lit+lct+l
lit+l ct+l

vt+l equals the discounted gross rate of growth in marginal cost. In a pure production
smoothing model, with ,t, equal to zero, its expectation is always one. mt is the percent
markup of price above the present value of marginal cost in t+ 1. We denote this by mt


for markup because i't+lct+l is the opportunity cost of selling a unit during t.
Consider a scenario in which the growth in discounted costs, vt+l' and the pricecost markup are both constant through time. This implies that Eti st l is constant, i.e.

all predictable movements in sales are matched by proportional movements in the stock
available. 6 To generate persistent procyclical movements in the ratio of sales to
inventory such as we see in the data requires either a countercyclical markup or that
marginal cost is transitory high, relative to the expected discounted value of next periods
marginal cost. Thus the behavior of inventories actually points against increasing returns
or countercyclical costs.

It also points against a role for credit market imperfections in

accounting for the cyclical behavior of inventories. To account for the data, credit
constraints would need to bind in expansions, thereby driving up current marginal cost
relative to discounted future marginal cost. This is opposite the scenario emphasized by
Gertler and Gilchrist (1993), Kashyap, Lamont, and Stein (1994), and others. 7
Inventory quantities are often stated in terms of an inventory-sales ratio. The
model produces a desired stock available relative to sales, and therefore a desired
inventory-sales ratio, because sales (conditional on price) are a power function of the
available stock. We can examine the behavior of


to see whether this functional form

assumption is reasonable, as it implies that the steady-state sales to inventory ratio
should be independent of the size of the industry or firm.
Some evidence can be gleaned from observing how the ratio


changes over time

in industries with substantial growth. Below we examine in detail the six manufacturing
industries tobacco, apparel, lumber, chemicals, petroleum, and rubber. For all but


In a steady state with a constant rate of growth in marginal cost the ratio



6 ) ; r here is a real interest rate equalling R minus the inflation rate in marginal cost and

8 is'tne rate of storage cost.

Credit crunches during downturns could still account for the differences in behavior
between firms labelled constrained and unconstrained by these authors.


tobacco, sales increased by 50 percent or more from 1959 to 1997. Figure 2 presents the
behavior of


for each industry for that period. None of the six industries display large

long-run movements in the ratio, even when the level of st changes considerably. The
largest trend movements are for apparel, where the ratio declines by about 25 percent,
and in rubber, where it rises by about 20 percent.
The model's implication that stock available is proportional to expected sales is
also supported by cross-sectional evidence. Kahn (1992) reports average inventory-sales
ratios and sales across divisions of U.S. automobile firms. These data show no tendency
for the ratio to be related to the size of the division, either within or across firms.
Gertler and Gilchrist (1993) present inventory-sales ratios for manufacturing by firm size,
with size defined by firm assets. Their data similarly show little relation between size
and inventory-sales ratio. If anything, larger firms hold a higher inventory-sales ratio.
We conclude that scale effects do not appear a promising explanation for the fall in
inventory-sales ratios in booms. 8

C. Relation to the Linear-Quadratic Model
Much of the inventory literature estimates linear-quadratic cost-function
parameters (e.g. West, 1986, Eichenbaum, 1989, or Ramey, 1991). A typical
specification of the single-period cost function is 9


In a previous version (available as Rochester Center for Economic Research Working

Paper #428, ieptember 1996) we allow for the more general functional form st equal to
dt(Ptll"t- a] , implying st increases with 3t only after the available stock reaches a threshold
value a. This generates a scale effect in inventory holdings, providing another possible
explanation for the failure of inventories to keep pace with sales over the business cycle. Our
estimates for the threshold term a are typically less that 20 percent of the average size of at;
and its introduction did not significantly affect other estimated results.

number of papers include a cost term in the change in output. Its exclusion here is
simply for convenience. Measures for cost shocks, such as wage changes, are also sometimes

included (e.g., Ramey, 1991, or Durlauf and Maccini, 1995).

where, as before, Yt, at, and st are output, stock available, and sales during t. The slope
of marginal cost is governed by the parameter ,/;. Note that a > 0 allows for a target
inventory-sales ratio. Many researchers (e.g., Blinder, 1985, Fair, 1989) have focused on
the relative volatility of production and sales or, relatedly, on explaining why inventory
investment is procyclical. But if a > 0, having 1/; > 0 does not imply that the variance of
sales exceeds the variance of production or that inventory investment is countercyclical
(West, 1986).

On the other hand, under this linear-quadratic model, it can only be

optimal for a firm to systematically have a low

-Jratio when sales are high if its

marginal cost is relatively high in those periods. Otherwise costs could be reduced by
bunching production in high-sales periods, thereby generating a procyclical ratio. 10
Given inventories are so countercyclical relative to sales, we therefore believe the
question should be: Why is inventory investment not more procyclical?
Our approach differs substantially from the linear-quadratic literature in at least
two ways. First, rather than estimate parameters of a quadratic cost function, we exploit
the production function to measure marginal cost directly in terms of observables and
parameters of the underlying production technology. This measure allows not only for
variation in wages, the cost of capital, and other inputs, but also potentially for shocks to
productivity. Second, our model explicitly considers the firm's revenue side. This allows
us to account for variations in inventory holdings caused by price variations. In our
1 °For

example, in the absence of cyclical cost shocks, one can prove by a variance
bounds argument similar to that of West (1986) that if ai/s 1 is countercyclical then 1/; must be
positive. So how do researchers (in particular, Ramey, 1991) who include an inventory-sales
target find downward-sloping marginal cost with data exhibiting countercyclical stock-sales
ratios? One possibility is that the linear-quadratic specification poorly approximates the true
model, as suggested by results in West (1986) and Pindyck's (1994). Also, the findings of
downward sloping marginal cost may be sensitive to how parameters are normalized ( see Krane
and Braun's, 1991, discussion), choice of instruments, and whether cost shocks are allowed.

Furthermore, our reading of the literature is that most authors do estimate marginal cost to be
upward sloping (e.g., Blanchard, 1983, West, 1986, Krane and Braun, 1991, Kashyap and
Wilcox, 1993, and Durlauf and Maccini, 1995)'.


model the return on finished inventory is proportional to the price markup; so sales
relative to stock available should move inversely with the markup.
The tobacco industry provides an excellent experiment. The price of tobacco
products rose very dramatically from 1984 to 1993. Figure 3 shows the behavior of the
producer price for tobacco relative to the general PPI as well as the ratio of sales to stock
available. The relative price doubled. Although material costs in tobacco rose during
this period, the relative price change largely reflected a rise in price markup (Howell et
al., 1994). Consistent with the model, the ratio


fell by about 15 percent. More

striking is what occured in 1993. During one month, August 1993, the price of tobacco
products fell by 25 percent, apparently reflecting a breakdown in collusion (see Figure 3).
Within 3 months the ratio ;


rose dramatically, as predicted by the model, by at least

25 percent. Whereas the linear-quadratic model is silent on these large movements in
inventory-sales ratios, the model in this paper contains a ready explanation.

III. Empirical Implementation

A. The Case of a Constant Markup
Inventory investment is closely related to variations in marginal cost. A
transitory decrease in marginal cost motivates firms to produce now, accumulating
inventory. A higher markup of price over marginal cost also motivates firms to
accumulate inventory. For this reason, much of the empirical work is directed at the
behavior of marginal cost. But first we consider the case of a constant markup. This not
only eliminates markup changes as a factor, but also implies that intertemporal cost
variations can be measured simply by variations in price. This clearly holds regardless of


how we specify the production function or costs of production in equation (1 ).
Under production to stock, the expected opportunity cost of selling a unit of
inventory is equal to E\[l't+l ct+il-

f\ denotes the expectations operator conditioned on

information available at the time of sales during t. In addition to variables incorporated
in Et, we assume it also reflects st and Pt·

Assuming a constant markup m therefore

implies that Pt equals (l+m)Ei[i\+i ct+il• Substituting Pt appropriately for discounted
future cost in the firms first-order condition (2), taking expections, and rearranging yields



{ l'tPt [1 + ,/>mst] }

(3) predicts strong procyclical movements in the ratio
cyclical movements in f3ptPt .



!t only if there are opposite

f3ptPt will be countercyclical if interest rates are

procyclical relative to the expected inflation in the firm's price. We demonstrate below


exhibits no such cyclical behavior. Consequently, we drop the assumption of

a constant markup and proceed to measure movements in marginal cost and markups.


Measuring Marginal Cost of Production

From the firm's problem (1), marginal cost ct equals (>.twt

+ cYJ.

of materials, with >.twt being the cost of materials per unit of output.

wt is the price

er is the marginal

cost of labor and capital required to produce a unit of output from those materials.
Let wt denote the wage for marginally increasing production labor. Given that
production labor enters as a power function in technology in (1 ), the marginal cost of
value added is (,\,)wf:t, which is proportional to the wage divided by production
workers' labor productivity. (See Bils, 1987). This result allows for technology shocks,
the impact of which appear through output. A value for -yo equal to labor's share
roughly corresponds to perfect competition. Higher values for -yo reduce marginal cost.


With data on output, materials cost, production hours, and the production labor
wage, marginal cost can be calculated given a value for the parameter combination 'Y"·

Part 1 of the appendix describes how we construct monthly indices of materials cost,
-X 1w1,

for our six industries. Part 2 of the appendix shows how the parameter

combination 'Y" can be related to observables, such as labor's share, and to the returns to
scale parameter

1. 1,

in turn, is estimated in Section IV. Here we focus attention on the

key question of measuring the effective price of labor, wt.


Measuring the Marginal Price of Labor Input

It is standard practice to measure the price of production labor by average hourly
earnings for production workers. We also consider a competing measure that allows for
the possibility that average hourly earnings do not reflect true variations in the price of
labor, but rather are smoothed relative to labor's effective price for convenience or to
smooth workers' incomes. (See Hall, 1980.) Specifically, we allow for procyclical factor
utilization that drives a cyclical wedge between the effective or true cost of labor and
average hourly earnings. This may be because in booms workers transitorily boost efforts
without contemporaneous increases in wages or because capital is transitorily worked
longer hours (more shifts) with workers being payed shift premia that do not fully
compensate them for the disutility of late work (Shapiro, 1995).
Total factor productivity is markedly procyclical for most manufacturing
industries. One interpretation for this finding is that factors are utilized more intensively
in booms, with these movements in utilization not captured in the measured cyclicality
of inputs (e.g., Solow, 1973). Let xt denote the effort or exertion per hour of labor for


both production and nonproduction workers, and let ut denote a utilization rate for
capital. The production function then becomes

We assume firms choose Xt and ut subject to the constraint that working labor
harder requires higher wages as a compensating differential, and working capital longer
requires working labor at later, odder hours thereby also requiring higher wages.
(Shapiro's estimates suggest that the effective premia for night work represents the
primary cost of working capital longer hours.) Therefore the effective hourly production
worker wage is a function of xt and st, wt(xt, ut), and similarly for the wages of
nonproduction workers. Cost minimization requires that firms choose value for xt and ut
such that the elasticities of these wage functions equal one with respect to xt and equal
1 " v with respect to u .11
If data on wages capture t.he contemporaneous impact of xt and ut on required

wages then the measure for marginal cost in equation (4) remains correct. Higher factor
utilization increases labor productivity but at the same times increases the price of labor,
wt(xt, ut)· Our concern is that hourly wages may reflect a typical level of effort and
capital utilization, say wi("x, u), with employers bearing the cost of their choices for xt
and ut only gradually over time. Shapiro, for instance, estimates that the effective shift
premia is on the order of 25 percent, but the observed premium paid in response to
shifting a worker to a late shift is often 5 percent or less. Thus the cost of working
capital longer hours may appear as a higher wage rate on day shifts in the future, rather
than the contemporaneous payment of the effective shift premium.
If data on hourly earnings reflect average levels of utilization, x and u, then
11 Implicit

here is that the wage functions for production and nonproduction workers
exhibit the same elasticities with respect to xt and ut at particular values for xt and ut.


movements in the effective cost of labor can be approximately related to the observed
movements in hourly earnings and unobserved movements in xt and ut according to

where the tilde over a variable denotes the deviation of the natural log of that variable
from its longer-run path (defined below by an H-P filter). Here we use the result that
the elasticities of wage movements with respect to xt and st must be respectively
approximately one and 1 -~-v . But note that from growth accounting

If we assume that high-frequency fluctuations in 0 are negligible, then combining these
two equations yields our alternative measure of movements in the effective wages

Thus our measure of the wage augmented to account for varying factor utilization
1 ) to average hourly
essentially adds high-frequency movements in TFP (scaled by -+
a V
earnings. It interprets those movements as variations in utilization for which labor is
compensated, though the compensation does not show up contemporaneously in average
hourly earnings. The constructed wage movements in (5), and the implied movements in
marginal cost, depend on the returns to scale ;. From the cyclical behavior of
inventories we can estimate ; , and thereby judge the extent to which the procyclical
behavior of factor productivity reflects increasing returns or procyclical factor utilization.


IV. Results


The Behavior of Inventories
We begin by examining the behavior of the ratio of sales to stock available for


!t,t for the six manufacturing industries:

Tobacco, apparel, lumber, chemicals,

petroleum, and rubber. These are roughly the six industries commonly identified as
production for stock industries (Belsley, 1969). 12 We obtained monthly data on sales
and finished inventories, both in constant dollars and seasonally adjusted, from the
Department of Commerce. The series are available back to 1959. We construct monthly
production from the identity for inventory accumulation, with production equal to sales
plus inventory investment. 13
Figure 2 presents the ratio

!tt for each of the six industries along with industry

sales. The period is for 1959.1 to 1997.9. For every industry the ratio of sales to stock
available is highly procyclical. An industry boom is associated with a much larger
percentage increase in sales than the available stock in each of the six industries. Table
1, Column 1 presents industry correlations between the ratio

!tt and output with both

series H-P filtered. The correlations are all large and positive, ranging from .46 to .84.
To show that these correlations do not merely reflect mistakes, e.g. sales forecast errors,
12 In

comparison to Helsley, we have deleted food and added lumber. We are concerned
that some large food industries, such as meat and dairy, hold relatively little inventories. Thus
any compositional shift during cycles could generate sharp shifts in inventory ratios. On the
other hand, our understanding of the lumber industry is that it is for all practical purposes
production to stock, though there are very small orders numbers collected. This view was
reinforced by discussions with Census.
13 West

(1983) discusses that the relative size of inventories is somewhat understated
relative to sales because inventories are valued on the basis of unit costs whereas sales are
valued at price. We recalculated output adjusting upward the relative size of inventory
investment to reflect the ratio of costs to revenue in each of our 6 industries as given in West.
This had very little effect. The correlation in detrended log of output with and without this
adjustment is greater than 0.99 for each of the industries. It also has very little impact on the
estimates of the Euler equation for inventory investment presented below. Therefore we focus
here solely on results from simply adding the series for inventory investment to sales.


Column 2 of Table 1 presents correlations between a conditional expectation of !t and

output. The expectation is conditioned on a set of variables rt and rt-l> where rt
. 1u d es 1n (at,
) 1n (-a-,
st-1 ) 1n (Yt,
) 1n ( -P-,
Pt-1 ) Rt, 1n (-w-wt ) , 1n ( ,\ >-twt ), ln(-y-),
nt ln(-y-),
t-1 wt-1
ln(TFP tl, and ln(TFP t-il• Price, Pt, is measured by the industry's monthly Producer
Price Index, and Rt refers to the nominal interest rate measured by the 90-day bankers'
acceptance rate. Replacing sales with forecasted sales yields even larger correlations,
ranging from .52 to .88. 14
We want to stress that the strong tendency for !t to be procyclical is not peculiar

to these six industries. Figure 1 depicted a similar finding for aggregate manufacturing.
We also observe this pattern in home construction, the automobile industry, and in
wholesale and retail trade. Furthermore, for most of these six industries production is
more volatile than sales, as it is for aggregate manufacturing.


The Behavior of Marginal Cost and Markups
Our model suggests that the procyclicality of !t requires that marginal cost is

temporarily high in booms or that the price markup be countercyclical. We next ask
whether costs and markups in fact behave in that manner. We start with the case of a
constant markup, so that expected discounted cost can be measured by expected price.
We then drop the assumption of a constant markup, and see how well we can explain
inventory behavior under our two competing measures of the cost of labor.
With a constant markup the first-order condition for inventory investment
reduces to equation (3). If we assume the two variables in this equation are conditionally
14 Data

sources for hours, wages, and TFP are described in part 3 of the appendix. All
variables are H-P filtered, also as detailed in the appendix. We also first differenced the series,
looking at the correlation of the changes in the ratios+ with the rate of growth in output.
The correlations are very positive, ranging across indusfries from 0.18 to 0.70, and averaging
0.47. (Using forecasted growth in :~ yields even higher correlations, ranging from 0.57 to



distributed jointly lognormal, then it can be written 15

/3 1 reflects the nominal interest rate from t-1 tot as well as a rate of storage cost. The
constant term " reflects covariances between the random variables as well as m. (3 1)
implies we should see a strong negative relation between expectations of the two
variables !t and In( f3ptPt ).
We first report, by industry, the correlation of

E\_ 1 [ln(

~:~; )] with output.

E\_ 1

is based on the set of variables rt-l and rt_ 2, where rt is as defined above, plus the
variables In( ~-l) and In( Ppt-l ). All variables are H-P filtered. Results are in the first


column of Table 2. The correlation is significantly positive for every one of the six
industries. This is precisely the opposite of what is necessary to explain the
procyclicality of the ratio !!- The correlation of Et_ 1[In( ~:~; )] with Et_ 1[ !!J appears
in Table 2, Column 2. Again the correlation is positive, significant, and large for every
industry, ranging from .34 to .72. For equation (3') to hold these variables need to be
negatively correlated. Also, estimating (3 1) by GMM yields a statistically significant,
negative coefficient estimate for ¢ for every one of the six industries.
We interpret the evidence in Table 2 as strongly rejecting the constant-markup
assumption. Indeed it leaves us with even more to explain: Absent changes in markups,·
we would expect !t to be not merely acyclical, but actually countercyclical. This

requires a bigger role for the markup (together with intertemporal marginal cost) in
accounting for inventory behavior.

Therefore we proceed by allowing the markup to

vary, as in first-order condition (2). Again assuming variables in the first-order condition


<;fsproximation is arbitrarily gooi for small values for the real interest rate r


for the ratio ma 5 • In steady-state the ratio ma 5 equals r plus the monthly storage rate. So we
would argue this is a small fraction on the order of 0.02.


are conditionally distributed jointly lognormal, the equation can be written

Where " reflects covariances between the random variables.
Before estimating (2 1) we report correlations of discounted growth in marginal
], and the markup, mt, with
• detrended output and with
. Ei[a;--],
cost, Et [f1t+lct+l

Approximating (2 1) around average values of mt and




Thus the procyclicality of Et[ !tJ requires countercyclical movements in the expectations
of t+l~t+l and/or mt. To obtain conditional expectations of the variables we again

project onto the set of variables rt and rt-l described above. For this exercise we
assume constant returns to scale in calibrating the size of markups and the parameter "'·
(See part 2 of the appendix.)
The results, by industry and for each of the two measures of the price of labor,
appear in Tables 3 and 4. Considering first the average hourly earnings measure (the
first two columns of each table), note that for every industry the growth in marginal cost
is very significantly positively correlated with both output and Et[ ';; ]. The correlations

with output range from .45 to .82. The correlations with Et[ ';; ] range from .30 to .72.

Markups do not display a consistent pattern across industries. They are procyclical, and
vary positively with Et[';;], in apparel, lumber, and chemicals, whereas they are

countercyclical, and vary negatively with Et[';;], in tobacco, petroleum, and rubber.

Taken together, these correlations do not bode well for the average hourly earnings-based
measure of marginal cost: Et[

¾] fails to be consistently negatively related to expected


growth in marginal cost or markups, as required by (2 11 ).


The remaining correlations use the wage augmented to reflect uncompensated
variations in factor utilization. These correlations appear in the last set of columns in
Tables 3 and 4. In Table 3 we see that the cyclical behavior of marginal cost changes
completely, with expected growth in marginal cost negatively correlated with output
except in the petroleum industry. (Value added is very small in petroleum. So
adjustments to the cost of value added have very little impact.) But in Table 4 we see
that, even though both Et[

i]t and expected growth in marginal cost are strongly

procyclical, the two are not systematically correlated with each other. Expected growth
in marginal cost is actually positively correlated with Et[

i]t in five of the six industries,

though significantly so only for petroleum. For tobacco the two variables are
significantly negatively related. Using the augmented wage rate does dramatically
decrease the magnitude of the correlation between expected growth in marginal cost and

i t ], except in petroleum.
The expected markups based on our alternate wage and cost measure are much

more consistently and dramatically countercyclical. Looking at the far right columns of
Tables 3 and 4, the markup is highly countercyclical in all but the lumber industry.
Excluding lumber, the correlations of expected markup with output vary from -.43 to
- .90. For lumber the correlation is slightly positive. The correlations of expected
markup with Et[

i]t varies from -.49 to -.79, again excluding lumber where it is

significantly positive.


Estimation of the First-Order Condition
The statistics presented thus far suggest that the wage measure augmented to

reflect procyclical factor utilization is qualitatively more consistent with inventory
behavior. We now evaluate the alternative cost measures more formally by estimating


first-order condition (2 1) by GMM. Bea.ring in mind that the two measures reflect polar
assumptions regarding the interpretation of short-run productivity movements, we do not
necessarily expect either measure to rationalize inventory behavior completely;
nonetheless we will evaluate which one does so more successfully.
Looking at (2 1), the equation contains explicitly the parameter rf, and implicitly
the returns to scale parameter -y through both ct and mt. We first estimate (2




GMM to obtain separate estimates of -y and rf,. Note, however, that given values for the
real interest rate, storage costs, and returns to scale -y, equation (2 1) requires a particular
value of rf, in order for the implied steady-state value of ;


to be consistent with the

average observed value of sl for each industry. (See the appendix, part 2.) We

therefore secondly estimate equation (2 1) imposing this constraint on rf, as a function of~We estimate equation (2 1) separately for each of the two cost measures. Table 5
contains results using the average hourly earnings-based wage, while Table 6 contains
results based on our alternative wage. The results in Table 5 using average hourly
earnings are nonsensical, overwhelmingly indicating misspecification. Returns to scale
are estimated at a very large positive or very large negative number (greater than 16 in
absolute value) for all industries but petroleum. To interpret this, note that marginal
cost of value added reflects a weight of


So by estimating an absurdly high absolute

value for -y, the estimating is essentially negating the marginal cost of value added.
The results in Table 6 using the augmented wage are much more reasonable. The
constraint that rf, take the value implied by the steady-state level of ;


is rejected only

for the lumber and rubber industries. Turning first to the constrained estimates, the
estimate for returns to scale is implausibly large for tobacco (about 2.9), but varies
between 1.09 and 1.42 for the other five industries.

For the unconstrained estimates, rf,

is not always estimated very precisely. The estimate of rf, is positive for four of the


industries, but significantly so for only three: apparel, chemicals, .and petroleum. The
estimates of returns to scale are more robust: They are very similar for the constrained
and unconstrained estimates, with the exception of petroleum, which shows mildly
decreasing returns to scale ( ~ =0.82, though not significantly different from the 1.09
constrained estimate) when </, is estimated separately .16
The estimates in Table 6 suggest that augmenting marginal cost for
uncompensated fluctuations in factor utilization goes quite far in explaining the behavior
of inventory investment. Nevertheless, we would not argue that Table 6 reflects an exact
or "true" measure of marginal cost. The estimate of </, comes primarily from the
relationship between mft and discounted growth of marginal cost. To the extent we

have an imperfect measure of marginal cost, the signal-to-noise ratio in the growth rate
of marginal cost might be rather low (especially if ct is close to a random walk). This
may suggest focusing on the constrained estimates of


The fact that we presumably

have an imperfect measure of marginal cost could also be reflected in the tendency to
reject the overidentifying restrictions of the model according to the J-statistic. (The
restrictions are rejected in four of the six industries). On the other hand, the model is
fairly successful in accounting for most of the persistence of ~t without resorting to ad

hoc adjustment costs. With the exception of the lumber industry, the Durbin-Watson

statistics do not suggest the presence of a large amount of unexplained serial correlation.
Our approach of adding back short-run TFP movements to construct an effective
wage succeeds in explaining the very procyclical behavior of



by generating a

procyclical time-series for marginal cost and a countercyclical one for markups. Table 4
reported correlations of Et[

~t ]


with the expected growth in ( discounted) marginal cost

16 These results are for data with low frequency movements in the variables removed by
an H-P filter. Parameter estimates based on unfiltered data are very similar to those in Table
6. The primary difference is that the test statistics for overidentifying restrictions and for the
constraint on </, more typically reject.


and with the expected markup assuming constant returns to scale. Those correlations
suggest that much of the impact of augmenting marginal cost for procyclical factor
utilization acts through making the markup very countercyclical. This remains true
allowing for the modest increasing returns we estimate in Table 6. Using the estimates
of , from Table 6, Figure 4 presents the implied markup together with the ratio ~t for

each industry. Not only are the markups highly countercyclical, with the exception of
lumber, but their movements are quantitatively important. Figure 3 showed that the
large shifts in price markups in tobacco in the 1980's and 1990's were accompanied by
opposite movements in the ratio ~t as predicted by the model. Figure 4 shows that,

more generally, most of the striking shifts in ~t that occured in these six industries

reflect large opposite movements iri the markup. 17
Our alternate measure for marginal cost movements is much more successful in
explaining inventory investment. But it may be excessive, at least for certain industries.
In the case of rubber, for instanc.e, augmenting the wage for utilization makes the
markup sufficiently countercyclical that Et[ m;;



] is very countercyclical, despite Ei[ ~t ]

being very procyclical. (This is true, though to a lesser extent, for every industry except
lumber.) At the same time, it causes the expected growth in marginal cost,


Et[ t+lc t+l ], to become countercyclical. (See the last row of Table 3.) Thus both

variables in the equation become countercyclical, resulting in a negative (though
insignificant) estimate of ¢. Presumably a somewhat smaller adjustment would yield a
positive estimate for ¢.

17 Several

empirical papers have examined the cyclicality of markups. (Rotemberg and
Woodford, 1995, survey some of these.) Our definition of the markup is slightly different, as it
compares price to discounted next period's marginal cost. The markup of price relative to
contemporaneous marginal cost, however, behaves extremely similarly to the markups pictured

in Figure 4.




Evidence from cross-sectional and low frequency data indicates that firms'
demands for finished goods inventories are proportional to their expected sales. Yet
during business cycles these inventories are highly countercyclical relative to sales. We
can explain this behavior if firms exhibit procyclical marginal cost and countercyclical
price markups. Obvious measures for marginal cost do not show high marginal cost in
booms because factor productivity rises during expansions.

We show that the cyclical

patterns of irtventory holdings can be rationalized by interpreting fluctuations in labor
productivity as arising primarily from mismeasured cyclical factor utilization, the cost of
which is internalized by firms but not contemporaneously reflected in measured wage
Our results challenge the empirical basis for models that generate large
fluctuations from procyclical productivity due to technology shocks, increasing returns, or
favorable externalities. Any such model should have to explain why inventory-holding
firms fail to increase production more during booms when their inventory stocks are more
productive, and less during recessions when the return on these stocks is down.


view that procyclical factor utilization accounts for this puzzle is consistent with other
evidence that factors are worked more intensively in booms (for example, Bernanke and
Parkinson, 1991, Shapiro, 1993, Bils and Cho, 1994, Burnside, Eichenbaum, and Rebelo,
1995, and Gali, 1997). The results further suggest that countercyclical markups (either
purposeful or reflecting price rigidities) may contribute to business cycles by muting the
role of diminishing returns in partially stabilizing fluctuations.


Basu, Susantu and John G. Fernald, "Returns to Scale in U.S. Production: Estimates
and Implications," Journal of Political Economy 105 (1997): 249-283.
Belsley, D.A., Industry Production Behavior: The Order-Stock Distinction.
Amsterdam : North-Holland, 1969.
Bernanke, Ben S., and Martin L. Parkinson, "Procyclical Labor Productivi ty and
Competing Theories of the Business Cycle: Some Evidence from Interwar U.S.
Manufacturing," Journal of Political Economy 99 (June 1991), 439-59.
Bils, Mark, "The Cyclical Behavior of Marginal Cost and Price," American Economic
Review (1987).
Bils, Mark and Jang-Ok Cho, "Cyclical Factor Utilization," Journal of Monetary
Economics 33 (March 1994).
Blanchard, Olivier J ., "The Production and Inventory Behavior of the American
Automobile Industry," Journal of Political Economy 91 (1983), 365-400.
Blinder, Alan, "Can the Production Smoothing Model of Inventory Behavior be Saved?"
Quarterly Journal of Economics 101 (1986), 421-54.
Burnside, Craig, Eichenbau m, Martin, and Sergio Rebelo, "Capital Utilization and
Returns to Scale," in B.S. Bernanke and J.J. Rotemberg, eds., Macroeconomics
Annual. Cambridge, MA: MIT Press, 1995.
Christiano, Lawrence, "Why Does Inventory Investmen t Fluctuate So Much?" Journal
of Monetary Economics (1988).
Cooper, R. and J. Haltiwanger, "Macroeconomic Implications of Production Bunching:
Factor Demand Linkages," Journal of Monetary Economics 30 (1992), 107-128.
Durlauf, Steven N. and Louis J. Maccini, "Measuring Noise in Inventory Models,"
Journal of Monetary Economics 36 (August 1995), 65-89.
Eichenbau m, Martin, "Some Empirical Evidence on the Production Level and
Production Cost Smoothing Models of Inventory Investmen t." American
Economic Review 79 (Sept. 1989), 853-64.
Fair, Ray C., "The Production-Smoothing Model is Alive and Well," Journal of
Monetary Economics 24 (Nov. 1989), 353-70.
Farmer, Roger, and Jang Ting Guo, "Real Business Cycles and the Animal Spirits

Hypothesis," Journal of Economic Theory (1994).
Gali, Jordi, "Technology, Employment, and the Business Cycle: Do Technology Shocks
Explain Aggregate Fluctuations," manuscript, New York, University, 1997.
Gertler, Mark, and Simon Gilchrist, "Monetary Policy, Business Cycles, and the
Behavior of Small Manufacturing Firms," Quarterly Journal of
Economics 109 ( 1994).
Hall, Robert E., "Employment Fluctuations and Wage Rigidity," Brookings Papers on
Economic Activity (1980), 93-123.
Hall, Robert, E., "Labor Demand, Labor Supply, and Employment Volatility," NEER
Macroannual (1991): 17-54.
Howell, C., F. Congelio, and R. Yatsko, "Pricing Practices for Tobacco Products, 19801994," Monthly Labor Review (December 1994), 3-16.
Kahn, James A., "Inventories and the Volatility of Production." American Economic
Review 77 (1987), 667- 79.
Kahn, James A., "Why is Production more Volatile than Sales? Theory and Evidence
on the Stockout-Avoidance Motive for Inventory Holding." Quarterly Journal of
Economics 107 ( 1992).
Kashyap, Anil, Owen Lamont, and Jeremy Stein, "Credit Conditions and the Cyclical
Behavior of Inventories: A Case Study of the 1981-82 Recession," NBER Working
Paper 4211, 1992.
Kashyap, Anil, and David W. Wilcox, "Production and Inventory Control at the General
Motors Corporation in the 1920's and 1930's," American Economic Review 83 (June
1993), 383-401.
Krane, Spencer D. and Steven N Braun, "Production Smoothing Evidence from Physical
Product Data," Journal of Political Economy 99 (1991), 558-581.
Kydland, Fynn E. and Edward C. Prescott, "Time to Build and Aggregate
Fluctuations," Econometrica 50 (1982), 1345-1370.
Pindyck, Robert S., "Inventories and the Short-Run Dynamics of Commodity Prices,"
The Rand Journal of Economics 25 (1994), 141-159.

Ramey, Valerie, "Inventories as Factors of Production and Economic Fluctuations,"
American Economic Review 79 (1989), 338-354.


Ramey, Valerie, "Non-Convex Costs and the Behavior of Inventories." Journal of
Political Economy 99 (1991 ).

Rotemberg, Julio J. and Michael Woodford, "Dynamic General Equilibrium Models with
Imperfectly Competitive Markets," in Frontiers of Business Cycle Research, edited
by T. Cooley. Princeton: Princeton University Press, 1995.
Shapiro, Matthew D., "Cyclical Productivity and the Workweek of Capital," American
Economic Review: Papers and Proceedings 83 (May 1993): 229-233.
Shapiro, Matthew D., "Capital Utilization and the Marginal Premium for Work at
Night," manuscript, University of Michigan, 1995.
Solow, Robert M., "Some Evidence on the Short-Run Productivity Puzzle," in
Development and Planning, edited by J. Baghwati and R.S. Eckaus. New York:
St. Martin's, 1968.
Thurlow, Peter H., Essays on the Macroeconomic Implications of Inventory Behavior.
Ph. D. thesis, University of Toronto, 1993.
West, Kenneth, "A Note on the Econometric Use of Constant Dollar Inventory Series,"
Economics Letters 13 (1983), 337-341.

West, Kenneth, "A Variance Bounds Test of the Linear Quadratic Inventory Model."
Journal of Political Economy 94 (1986), 374-401.

West, Kenneth, "The Sources of Fluctuations in Aggregate Inventories and GNP,"
Quarterly Journal of Economics 105 (1991), 939-972.



The Cost of Materials


We know of no monthly data on material price deflators. We construct our own
monthly price of materials index, wt, for each industry as follows. Based on the 1977
input output matrix, we note every 4-digit industry whose input constituted at least 2
percent of gross output for one of our six industries. This adds up to 13 industries. We
then construct a monthly index for each industry weighting the price movements for
those 13 goods by their relative importance. For most of the industries one or two inputs
constitute a large fraction of material input; for example, crude petroleum for petroleum
refining or leaf tobacco for tobacco manufacture. For the residual material share we use
the general producer price index. This contrasts with Durlauf and Maccini (1995), who
scale up the shares for those inputs they consider so that they sum to one, which results
in more volatile input price indices than ours.
Although we assume that materials are a fixed input per unit of output, we do not
impose that this input be constant through time. We allow low frequency movements in
the input At by imposing that our series Atwt exhibit the same H-P filter as does the
industry's material input measured by the annual survey of manufacturing (from the
NBER Productivity Database).


Production Function Parameters
From equation (4) the relative contributions to marginal cost of materials versus

factors in value added depends on the parameter combination 'I"- 'I" differs from labor's
share not only due to markups, but also because production is to stock. Evaluated at
steady-state, the first-order condition equating the wage to the present value of marginal
revenue product yields




+ ml PY l 1 -


+ m) AP

l .

The term ,B equals 11 - 6 , reflecting discounting for a real rate of interest r and the
storage cost 6.
Conditional on the size of economic profits, the size of the markup is closely
related to the degree of increasing returns to scale. Define " as the rate of profit per
unit cost of value added. The steady-state relation between the markup, returns to scale,


and the profit rate is



+m =

(,+ir)[l - (1--¾-),6]
,6[: + (,-l+ir)[l - (1-: ),6]]

Under production to stock the markup is positive even under constant returns (, equal
one) and zero profits. A small markup is needed to cover costs of holding inventories.
Substituting the markup from (A2) into (Al) yields




This expresses




1 - (1-

! ),6


in terms of the parameter combination ( ,+,,. ), which we estimate, and

observables. We measure the term

1 -


s - by its sample average, where ,6 reflects


a monthly storage cost of one percent and thl real interest rate implied by the interest
rate as measured by the 90-day bankers' acceptance rate. We measure




respectively by H-P filters fit to series for production labor and material shares of gross
output. Therefore


varies at low frequencies as well.

In the text we refer to estimating returns to scale , . From ( A3) we see that the
model actually identifies , plus the profit rate


A number of studies have suggested

that profit rates in manufacturing are fairly close to zero. For example, Basu and
Fernald (1997) experiment with several different industry cost of capital series and
always find very low profit rates, on the order of three percent, for manufacturing
industries. With this rationale, we implicitly treat the profit rate as equalling zero for
convenience in the text discussion. More generally, our estimates of ,-1 in Tables 5 and
6 can be interpreted approximately as estimates of (,-l+ir), that is, returns to scale plus
the profit rate. 18
Finally, the first-order condition in the steady state implies a relationship between
<f,, , ,

,6, and the long-run value of

!tt .

This relationship is

where mis taken from (A2) above as a function of, (or more generally ,+ir). This is
the constraint imposed for the second set of estimation results in Tables 5 and 6.
18 Technically,

the augmented wage in equation ( 4) has I entering separately from ,r.
But in practice this makes no difference: One can still interpret the estimates of ,-1 in Table
6 more generally as estimates of ,-l+ir, even if profit rates are as high as 10 percent.


3. Data sources for Hours, Wages, and TFP
Monthly data for hours and wages for production workers are from the the Bureau
of Labor Statistics (BLS) Establishment Survey. We employ TFP as an instrument and
in adjusting the wage according to equation (4). Output in TFP is measured by sales
plus inventory accumulation, as described in the text. In addition to output and
production labor, TFP reflects movements in nonproduction labor and capital.
Employment for nonproduction workers is based on the BLS Establishment Survey.
There are no monthly data on workweeks for nonproduction workers. We assume
workweeks for nonproduction workers vary according to variations in workweeks for
production workers. We have annual measures of industry capital stocks from the
Commerce Department for 1959 to 1996, which we interpolate to get monthly stocks.
4. Detrending Procedures

Although the first-order condition (2 1) suggests that quantities such as 1:t st and
In( l>t+Jct+l) ought to be stationary (or at least cointegrated), this may not nec~ssarily

hold over the nearly 40-year period covered by the sample. Changes in product
composition or inventory technology, for example, could produce low frequency
movements in these variables that are really outside the scope of this paper. We
therefore remove low frequency shifts in these variables with a Hodrick-Prescott filter,
using a parameter of 86,400. (The conventional choice of 14,400 for monthly data is only
appropriate for series with significant trends--for the above variables it would take out
too much high frequency variation.) Moreover, because these variables depend on an
, estimated parameter (-y), it is necessary to detrend subcomponents that do not involve,.
We use the same H-P filter on the instruments.
We also use the same filter on log(TFP) in constructing the augmented wage,
though here the purpose is different. Our assumption is that low-frequency movements
in log(TFP), the part removed by the filter, reflect technical change, so we remove that
component before using the residual (which we assume reflects varying utilization) to
augment average hourly earnings.


Table 1--Corre lations Between ln Yt and !tt t


~t and ln Yt

Et( !! ) and ln Yt













Petroleu m






t The sample is 1959.1 to 1997.9. All correlations have p-values < 0.01.
y tis output; !t is the ratio of sales to the stock available for sale.

Table 2- -Constant Markup Case: Correlations of Et_ 1 [ln(

!:~; )]

with ln Yt and with Et_ 1 [ !:Jt

with ln Yt

with Et-l ( at )



















t The sample is 1959.1 to 1997.9. All correlations have p-values < 0.01.
f3ptPt is the discounted growth in output price from t-1 tot; Ytis output; !t is

the ratio of sales to the stock available for sale.

Using the

Average Hourly Earnings

Augmented Wage Measure

E c8t+lct+l]


E c8t+l Ct+l]

































The sample is 1959.1 to 1997.9.
Yt is output; l't+{t+l is the discounted growth in marginal cost from t to t+l; mt is

the net markup of price over discounted next period marginal cost.
* All p-values < 0.05, except for this correlation.


Using the

Average Hourly Earnings

Augmented Wage Measure































t The sample is 1959.1 to 1997.9.
s is the ratio of sales to the stock available for sale; l't+lct+l
. the discounted


growth in marginal cost from t to t+ 1; mt is the net markup of price over discounted
next period's marginal cost.

* All p-values < 0.05, except for these correlations.

Table 5--GM M Estimate s of Inventory Demand Using Average Hourly Earnings!





Petroleu m


D-W statistic



J-statisti c

( .042)
















( .025)





(14. 72)











( .061)

( .778)




( .028)



( .016)





(104. 7)



----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ---

1The sample is 1959.1 to 1997.9. Standard errors are in parentheses. The 0.05 critical value
for the J-statisti c is 28. 87.
*Constrained based on estimate s of 'Y, according to steady state. The constrain t on ¢ and
'Y is rejected at a 0.05 critical value for all industrie s except apparel and lumber.

Table 6- -GMM Estimates of Inventory Demand Using the Wage Augmented
for Variations in Factor Utilization t










( .043)
















( .027)

( .051)







( .029)





( .043)





. 21.1



( .021)











D- W statistic

---------------------------------------------------tThe sample is 1959.1 to 1997.9. Standard errors are in parentheses.
value for the J-statistic is 28.87.
*Constrained based on estimates of 1 , according to steady state.
**Constraint on ¢ and -y is rejected with a 0.05 critical value.

The 0.05 critical

Figure 1: The Cyclical Behavior of the Sales-Stock Ratio
in Aggregate Manufacturing

. - - - - - - - - - - - - - - - - - - - - - - - - - , . . . . 0.1















log(s/a) ------ log(y) detrended

Note: Shaded areas indicate recessions. log(y) detrended with H-P filter.
y=output, s=sales, a=i+y, i=beginning finished goods inventory stock.


Figure 2: Cycles and Trends in s/a and s









































































log(s) (left scale)
---- log(s/a)

Shaded areas indicate recessions
s=sales, a=i+y, i=beginning finished goods inventory stock.



Figure 3: Price ands/a in the Tobac co Industry













s/a ------ log(price)*



*Tobacco products price deflated by the general Producer Price Index


Figure 4
Markups ands/a Ratio with Estimated Returns to Scale









0.04 ;-,..,...,..,..,..,.,.....,...,..,.,.....,...,..,..,......,..,.....,..,.,......,..,...,...,..,.,..,..,...,..,.,......,..J


















































0.06 +.,-rn.,.....,...,..,...,...,.....,...,..,.,......,..,...,...,..,.,...,..,..,..,...,....,..,......,..,.,...,..r1



Markup •••• s/a

s=sales, a=i+y, i=beginning finished goods inventory stock.
The markup is price in t relative to discounted marginal cost in t+ 1, minus 1