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Working Paper Series

Understanding How Employment
Responds to Productivity Shocks in a
Model with Inventories

WP 06-06

Yongsung Chang
Seoul National University
Andreas Hornstein
Federal Reserve Bank of Richmond
Pierre-Daniel Sarte
Federal Reserve Bank of Richmond

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

Understanding How Employment Responds to
Productivity Shocks in a Model with Inventories∗
Yongsung Chang

Andreas Hornstein

Seoul National University

Federal Reserve Bank of Richmond

Pierre-Daniel Sarte
Federal Reserve Bank of Richmond
Federal Reserve Bank of Richmond Working Paper 2006-06
Abstract
Whether technological progress raises or lowers aggregate employment in the short
run has been the subject of much debate in recent years. Using a simple model of industry employment, we show that cross-industry diﬀerences of inventory holding costs,
demand elasticities, and price rigidities potentially all aﬀect employment decisions in
the face of productivity shocks. In particular, the employment response to a permanent
productivity shock is more likely to be positive the less costly it is to hold inventories, the more elastic industry demand is, and the more flexible prices are. Using data
on 458 4-digit U.S. manufacturing industries over the period 1958-1996, we find statistically significant eﬀects of variations in inventory holdings and demand elasticities
on short-run employment responses, but find less evidence pertaining to the eﬀects of
measured price stickiness.
Keywords: Productivity, Employment, Inventory Investment, Sticky Prices
JEL Classification: E13, E22, E31
∗

This is a substantially revised version of the Federal Reserve Bank of Richmond Working Paper 2004-09,
“Productivity, Employment, and Inventories.” We wish to thank Bennett McCallum, John Fernald, Mark
Watson, as well as seminar participants at the 2004 NBER Economic Fluctuations Group meeting and the
NBER summer workshop for their comments. We further thank Valerie Ramey for calling our attention
to the importance of industry demand elasticities. Her suggestions have led to substantial re-writing of
an earlier draft. We thank Dan Hurley for excellent research assistance. Chang acknowledges financial
support from the Korea Research Foundation grant KRF-2005-0035. Any opinions expressed in this paper
are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the
Federal Reserve System. Our e-mail addresses are: yohg@snu.ac.kr, andreas.hornstein@rich.frb.org,
and pierre.sarte@rich.frb.org.

1. Introduction
In 2004, inventories held throughout the U.S. economy represented approximately 120 percent of final sales of goods and structures.1 Industries that produce goods for inventory, or
for which inventories are a significant component of the sales process, currently account for
half of all private sector employment. Furthermore, during recessions, changes in inventories
account for about 70 percent of the peak-to-trough decline in real GDP.2 In spite of these
facts, modern business cycle analysis has traditionally placed little emphasis on the role of
inventories.3
The nature of business cycles changes considerably when firms carry inventories. Firms
are able to make current production diﬀer from current sales, speculate on future price
movements, and absorb shocks to demand and costs. Using a simple industry model, we
describe how inventories aﬀect firms’ employment response to productivity shocks. In a
cross-section of U.S. manufacturing industries, consistent with the theory we develop, we
find statistically significant eﬀects of variations in inventory holdings and demand elasticities
in the employment response to changes in technology. In particular, industries with larger
inventory holdings and more elastic demand see a more pronounced increase in employment
following a productivity improvement.
Motivated by Gali (1999), a considerable body of work in contemporary macroeconomics
has argued that aggregate employment falls in response to permanent increases in productivity and, moreover, that this fall persists over time. While this notion remains controversial
and the subject of an active research agenda, a negative response of employment to an improvement in productivity is often interpreted as evidence in favor of sticky prices. While
most of this work is confined to the analysis of aggregate data, Chang and Hong (2006)
find substantial variation in the way that employment responds to technology shocks in U.S.
manufacturing industry data. When we shift the analysis to industry data, the number of observations on the employment eﬀects of changes in technology increases significantly. Hence,
one can more deeply explore how the heterogeneity in employment responses is aﬀected by
industry characteristics.
Sticky price models typically imply that employment falls in response to a positive technology shock. When productivity increases, fixed prices imply unchanged real sales so that
less labor is required to meet a given level of nominal demand. Contrary to this conventional
prediction, we show that when firms hold inventories, they can choose to expand output
relative to sales in response to a favorable cost shock despite having sticky prices. They
1

This ratio refers to quarterly final sales and inventories from the NIA Table 5.7.5.B and is taken from
Haver.
2
See Blinder (1981).
3
Notbale exceptions include Blinder (1981), Ramey (1991), and Bils and Kahn (2000).

would do so both to exploit relatively low production costs and to increase inventory stocks
in anticipation of higher future sales.
To study the role of inventories in a model that allows for price rigidities, we introduce
inventories into a standard Taylor (1980)-type framework. Consistent with the inventory
literature, we assume that firms value inventories because they reduce the cost of possible
stock-outs while allowing production smoothing over time (Ramey and West, 1999; Bils
and Kahn, 2000). Within this setting, the flexible price model is nested as the case with
no price staggering. In addition, we explore the role of diﬀerences in demand elasticities
across industries. Specifically, we formalize the notion that when industry demand is sufficiently inelastic, permanent technological improvements lead to decreases in employment
even when prices are fully flexible. Ultimately, we clarify that both the sticky price and flexible price framework are consistent with either decreases or increases in employment following
a productivity improvement. Employment increases associated with such an improvement,
however, always coincide with a build-up in inventories.
Given our model’s predictions, we estimate the employment responses to productivity
shocks in U.S. manufacturing industries using structural vector autoregressions (VARs) in
the spirit of Gali (1999), and more recently Christiano et al. (2004). The VARs consist
of total factor productivity (TFP), hours worked, and inventory holdings derived from the
NBER Manufacturing Productivity Database, where productivity shocks are identified as the
permanent component of TFP. We also estimate demand elasticities for all manufacturing
industries. We then correlate the magnitude of an industry’s short-run employment and
inventory responses to productivity shocks with industry measures of demand elasticity,
inventory-sales ratios, and price stickiness. To measure price stickiness, we use data on the
average duration for which prices remain unchanged provided by Bils and Klenow (2004).
As predicted by our theoretical model, a positive (negative) response of employment
to technological improvements coincides with a build up (decline) of inventories in many
industries. Furthermore, we find that both the employment and inventory responses to a
productivity shift are positively correlated with industry inventory holdings and demand
elasticity in the cross section. We find less evidence, however, in support of price stickiness.
Specifically, in the sample of industries for which the Bils and Klenow data are available, the
eﬀects of price stickiness are not statistically significant. We also find that the price decline
associated with a permanent productivity increase is generally larger in the long run than
in the short run.
Our analysis of inventories and how they aﬀect the employment response to productivity
shocks builds on a suggestion by Bils (1998). Accounting for changes in industry employment,
Bils finds a positive and significant eﬀect of the inventory-sales ratio interacted with changes
in labor productivity. Besides providing an explicit theoretical justification for this argument,
2

we connect the empirical work that emphasizes the use of disaggregated industry data (see
Basu et al. 2004; Shea, 1999; Marchetti and Nucci, 2004; and Chang and Hong, 2006) with
the structural VAR identification of productivity shocks using aggregate data.
This paper is organized as follows. Section 2 presents an industry model with staggered
prices augmented to include inventory investment. In Section 3, we calibrate the model
and study the employment response to productivity shocks across diﬀerent degrees of goods
storability, price stickiness, and demand elasticity. In Section 4, we explore the model implications in disaggregated data from the U.S. manufacturing industry. Section 5 concludes.

2. A Model with Staggered Prices and Inventories
We introduce inventories into a standard Taylor (1980)-type model with staggered prices.
We study a partial-equilibrium industry model where monopolistically competitive firms
may adjust their prices infrequently. Firms value inventories because they reduce the cost
of possible stock-outs while allowing for production smoothing over time (Ramey and West
1999, Bils and Kahn 2000).
In a standard sticky price environment, a favorable productivity shock reduces the marginal cost of production and, consequently, prices. Due to the staggered price setting across
firms, this adjustment is spread out over time so that the price level (output) only gradually
decreases (increases) to its new long-run equilibrium path. Along the transition path, firms
that can adjust their price set lower relative prices and, consequently, increase both their
sales and production. In contrast, firms that cannot adjust their nominal prices see their
relative prices increase and face declining sales. When goods are not storable, these firms
then correspondingly reduce production and employment as in Gali (1999). When goods
are storable, however, firms have an incentive to increase production, both to take advantage of the current relatively low marginal cost of production and to build up inventories in
anticipation of higher future sales; indeed, these firms know that they will be able to lower
their relative price at some future date. Therefore, despite prices being rigid, employment
can increase across all firms in response to a positive productivity shock when the cost of
holding inventories is suﬃciently low. When holding inventories is very costly, because of
high depreciation in storage for instance, work hours decrease in response to a productivity
shock, as in the simple sticky-price model without inventories.
Without any price staggering, firms adjust their price at every date. In that case, a
permanent improvement in productivity can lead to either an increase or decrease in employment depending on the elasticity of industry demand. In particular, if the demand curve
is inelastic, sales do not change much with respect to prices and, therefore, improvements in
productivity allow lower levels of labor input to be used. The reverse is true when demand
3

is elastic so that employment increases after a positive technology shock. In principle, this
mechanism is also operational when prices are sticky but we argue that without inventories,
implausibly large demand elasticities are needed in order that improvements in technology
generate increases in employment. Simply put, by virtue of fixing real demand in the short
run, sticky prices largely mitigate the eﬀects of a very elastic demand.
2.1. Industry Demand
Consider an industry where monopolistically competitive firms produce a continuum of differentiated products, i ∈ [0, 1]. The industry output, qtI , is a CES aggregate of diﬀerentiated
products, {qt (i) : i ∈ [0, 1]}:
qtI

∙Z

(θ−1)/θ

qt (i)

¸θ/(θ−1)
di
,

θ > 1.

(2.1)

Given nominal prices for the diﬀerentiated products, {Pt (i) : i ∈ [0, 1]}, the industry-price
index, that is, the unit cost of industry output, is
PtI

∙Z

1
1−θ

Pt (i)

¸1/(1−θ)

(2.2)

and the demand for product i is
£
¤−θ I
qt (i) = Pt (i) /PtI
qt .

(2.3)

We assume that an industry’s demand depends on economy-wide aggregate demand, qtA , as
well as its relative price, pIt = PtI /PtA , where PtA is the economy-wide aggregate price index,
¡ ¢−φ A
qtI = pIt
qt ,

φ > 0.

(2.4)

Hence, we diﬀerentiate between an industry’s demand elasticity, φ, and an individual firm’s
demand elasticity, θ, (which measures the elasticity of substitution across diﬀerentiated products in the industry). In particular, while profit maximization, in order to be well defined,
requires the firm’s demand to be elastic (θ > 1), industry demand can be inelastic. We assume that economy-wide demand, qtA , is exogenous and that the economy-wide price index
A
grows at a constant rate, Pt+1
/PtA = μ > 1.

2.2. Production
We base our model of production and inventory holdings on the empirical inventory investment literature (see Ramey and West, 1999). Firms choose a production path that
minimizes total cost, or more specifically, production cost and the cost of making sales. In
this subsection, we drop the firm index for ease of exposition.
A firm produces xt units of a commodity using labor, ht , as the single input to a
decreasing-returns-to-scale production function
xt = zt hαt ,

0 < α ≤ 1,

(2.5)

with productivity zt . We can think of production as being constant-returns-to-scale in capital
and labor, with capital being costly to adjust relative to labor in the short run. Since our
focus is on short-run adjustments in production, it is convenient to abstract from capital
adjustment in our model.
We assume that making sales is costly and that only part of current production, denoted
by yt , makes up output that can potentially be sold. This output, along with beginning-ofperiod inventory, nt , add up to total goods available for sales in the current period,
at = nt + yt .

(2.6)

Generating qt units of sales requires κqt (qt /at )η , κ, η ≥ 0, units of the commodity produced. The resource constraint on output that can potentially be sold is given by
µ ¶η
qt
yt = xt − κqt
.
at

(2.7)

Observe that having more goods available for sales, at , reduces the cost of making an actual
sale (say, by reducing the probability of stock-outs). The particular functional form adopted
for the cost of making sales implies an average inventory-sales ratio that is independent of
scale, both with respect to production and sales. Bils and Kahn (2000), as well as Ramey
and West (1999), document and emphasize this feature in a number of industries.
Firms hire labor in a competitive labor market at wage rate Wt . Together with the
production function (2.5), this implies the production-cost function
c(xt ) = wt (xt /zt )1/α ,

(2.8)

where wt = Wt /PtA is the real wage. With α < 1, this cost function is strictly increasing
and strictly convex–that is, the marginal cost of production is strictly increasing. Goods

not sold in a given period can be stored, but depreciate at rate δ,
nt+1 = (1 − δ) (at − qt ) ,

0 ≤ δ ≤ 1.

(2.9)

Alternatively, we could have assumed that firms pay an inventory holding cost proportional
to the inventory stock, but the depreciation in storage framework has the advantage of
nesting the standard sticky price model with non-storable goods as a special case.
2.3. Optimal Production and Price Setting
A firm can only adjust its price every J periods, and in any period a fraction 1/J of firms
can adjust their prices. Prices are fully flexible when J = 1. Each producer is indexed
according to how much time, j, has elapsed as of time t since its previous price change.
We restrict our attention to symmetric outcomes in which producers that adjust their price
at the same time are identical. Thus there are J types of firms, and we index firms by
j ∈ {0, 1, ..., J − 1}. We denote by nj,t the beginning-of-period t inventory holdings of a firm
that, j periods ago, set its price to P0,t−j . The relative price of a type j firm at time t is
denoted by pj,t = Pj,t /PtI . Because of changes in the industry price level, a firm unable to
I
adjust its price sees its relative price change over time, pj+1,t+1 = pj,t PtI /Pt+1
for j = 0, ...,
J − 1.
Firms maximize the discounted present value of current and future real profits. These
profits are discounted at the constant real interest rate 1/β, 0 < β < 1, and nominal profits
are deflated using the aggregate price index PtA . The value of a type j = 0 firm that currently
adjusts its nominal price, V0,t (n0 ), depends on its beginning-of-period inventory holdings and
the aggregate state of the industry.4
V0,t (n0,t ) = maxp0t , q0t ,

ª
© I
pt p0,t q0,t − ct (x0,t ) + βEt V1,t+1 (p1,t+1 , n1,t+1 )
subject to (2.3), and (2.5) to (2.9).

a0t , x0t , n1,t+1

The value of firms that cannot change the price of their products, Vj,t (pj , nj ), j = 1, . . . , J −1,
depends on their current relative prices, pj , their beginning-of-period inventory holdings, nj ,
4

Hereafter, we subsume the dependence on the aggregate state in the time index t.

and the aggregate state:
Vj,t (pj,t , nj,t ) = maxqjt ,

ª
© I
pt pj,t qj,t − ct (xj,t ) + βEt Vj+1,t+1 (pj+1,t+1 , nj+1,t+1 ) ,
subject to (2.3), and (2.5) to (2.9),

ajt , xjt , nj+1,t+1

VJ−1,t (pJ−1,t , nJ−1,t ) = maxqJ−1,t , aJ−1,t , xJ−1,t ,n0,t+1
ª
© I
pt pJ−1,t qJ−1,t − ct (xJ−1,t ) + βEt V0,t+1 (n0,t+1 )
subject to (2.3), and (2.5) to (2.9).
Optimal price setting satisfies the following first-order conditions,
∙
¸
£
¤
∂Vj+1,t+1 PtI
∂Vj,t
I
−θ−1
for j = 0, .., J − 1(2.10)
= pt qj,t − λj,t θpj,t q̃t + βEt
I
∂pj,t
∂pj+1,t+1 Pt+1
∂VJ,t
∂V0,t
=
= 0,
with
∂p0,t
∂pJ,t
where λj,t is the shadow value of additional sales (that is, the Lagrange multiplier on the sales
constraint (2.3)). The shadow value of sales is equal to the real price minus the marginal
cost of an additional unit sold, ψ j,t ,
©
ª
λj,t = pIt pj,t − c0j,t 1 + κ (1 + η) (qj,t /aj,t )η − κη (qj,t /aj,t )1+η .
{z
}
|

(2.11)

ψ j,t

Equation (2.11) combines the first-order conditions for optimal sales and inventory holdings.
The marginal cost of an additional sale reflects three components: the marginal cost of
producing the commodity, c0j,t , the marginal cost of making sales, κ (1 + η) (qj,t /aj,t )η , and the
sales-facilitating eﬀect of inventory holdings, −κη (qj,t /aj,t )1+η . We can repeatedly substitute
expression (2.11) for the shadow value of sales in equation (2.10) to obtain an expression for
the optimal price as

p0,t =

θ
θ−1

hP
i
J−1 j
β
ψ
q
Et
j,t+j j,t+j
j=0
hP
i.
¡
¢
J−1 j
I
I
Et
β
/P
P
q
j,t+j
t
t+j
j=0

(2.12)

Hence, price-adjusting firms set their price as a generalized markup over the marginal cost
of sales. In a steady state with no inflation and no relative price changes, equation (2.12)
reduces to a static markup over marginal cost. Expression (2.12) for the optimal price diﬀers
from the one that emerges in a standard Taylor-type sticky-price model only with respect
to the definition of marginal cost. Thus, our analysis takes into consideration the marginal
cost of sales rather than the marginal cost of production.
In contrast to conventional sticky-price models, inventories aﬀect the marginal cost of
7

additional sales in our framework. Specifically, the production-smoothing role of inventories
can be observed in the optimal choice of aj,t and nj+1,t+1 ,
©
ª
£
¤
c0j,t 1 − κη (qj,t /aj,t )1+η = β (1 − δ) Et c0j+1,t+1 ,

(2.13)

which equates the marginal increase in cost from producing one additional unit today, given
no change in current sales, to the decrease in the discounted present value of marginal cost
from producing one less unit tomorrow. Aside from production smoothing, note also that
today’s marginal cost of holding additional inventories implicitly reflects the sales facilitating
eﬀect of inventories,−κη (qj,t /aj,t )1+η .
2.4. Industry Equilibrium
We close the model by assuming that the real wage in the industry labor market is an
increasing function of industry employment,
wt = w̄h̄γt , γ > 0.

(2.14)

Our industry labor supply specification, therefore, allows a permanent increase in industry
productivity to cause a permanent increase in hours worked. We shall see in section 4.2 that
hours appear to be non-stationary in most manufacturing industries.
The following section explores a recursive industry equilibrium where prices and quantities depend on the state of the industry. The state of the industry is characterized by
the relative prices inherited from the previous period (by the firms that cannot adjust their
nominal prices), {pj,t : j = 1, ..., J − 1}, the beginning-of-period inventory holdings of all
firm types, {nj,t : j = 0, ..., J − 1}, and productivity, zt . We define aggregate industry employment, production, sales, and inventory holdings respectively as
J−1
J−1
J−1
J−1
1X
1X
1X
1X
hjt , ȳt =
yjt , q̄t =
qjt , n̄t =
nj,t .
h̄t =
J j=0
J j=0
J j=0
J j=0

(2.15)

3. The Response of Employment and Inventories to Productivity
Shocks in the Model
We now study the industry’s response to a permanent productivity shock. For this purpose,
we linearize our model around its deterministic steady state. We show that when goods are
storable, firms use inventories to smooth production and employment increases in response
to a permanent productivity shock. This finding applies to various parametrizations of price
rigidity and the sales-cost function. Consistent with conventional sticky-price models, we also
8

show that if commodities depreciate rapidly while in storage, that is, if it is costly for firms
to use inventories, industry employment responds negatively to a permanent productivity
shock. Finally, we provide a description of how the employment response changes with
inventory-sales ratios, the degree of price stickiness, and demand elasticities.
3.1. Calibration
Our benchmark parameter values are selected along the lines of other quantitative studies
on business cycles. A time period represents a quarter. We assume a 4 percent annual
real interest rate, β = 0.99. The labor elasticity of synthetic output, α, equals 2/3 and
a firm’s price elasticity of product demand, θ, is set to 10, which implies an 11 percent
markup of price over marginal cost when prices are flexible. Because firms set their price
as a markup over marginal cost, the labor-income share is lower than the output elasticity
P
P
with respect to labor, w j hj,t / j pj,t yj,t = 0.6. We normalize both economy-wide real
aggregate demand and the industry relative price at one, and assume that the economy-wide
price index increases at a fixed 4 percent annual rate.5 For our baseline model, we assume
that goods do not depreciate in storage, δ = 0, that industry demand is elastic, φ = 1.5,
and that nominal prices remain fixed for 4 quarters, J = 4. Alternative parameterizations
are also considered for robustness, in particular 0 ≤ δ ≤ 0.95, 0.5 ≤ φ ≤ 5, and 1 ≤ J ≤ 6.
Productivity, zt , is assumed to follow a random walk with zero drift.
We use observations on average inventory-sales ratios to determine the scaling parameter
κ in the sales-cost function, conditional on the sales-cost elasticity, η. For the baseline
model, we use η = 1 and set the steady state inventory-sales ratio, n/q, to 0.2 at an annual
frequency. If marginal cost were constant and equal across firms, the first-order conditions
for inventories (2.13) would imply that the steady state sales-inventory ratio, q/a, is the
same for all firm types,
κη (q/a)1+η = 1 − (1 − δ) β.
(3.1)
Given the assumptions on the sales-cost elasticity and the annual inventory-sales ratio, which
implies q/a = 0.55 at a quarterly frequency, this yields κ = 0.0329. In our economy,
firms face increasing marginal costs so that sales-inventory ratios diﬀer across firms, but the
average annual sales-inventory ratio remains close to 0.2 under this parameterization. For
alternative parameterizations of the inventory-sales ratio, we consider values in the range
0.05 ≤ n/q ≤ 0.4, which cover 96 percent of average inventory-sales ratios across 458 4-digit
5

Since real aggregate demand and the aggregate price index are exogenous, monetary policy does not
accommodate productivity disturbances at the industry level. Dotsey (2002), and Galí et al. (2003), have
shown that even with sticky prices, employment can respond positively to a productivity increase if monetary
policy accommodates productivity shocks.

manufacturing industries over the period 1958-1996.6 Finally, we assume that the elasticity
of industry wage with respect to hours (the inverse of the labor-supply elasticity), γ, is 1.
3.2. Dynamic Eﬀects of Productivity Shocks
Figure 1 shows the aggregate and individual-firm responses of sales, output, and employment
to a permanent productivity increase when goods do not depreciate in storage (δ = 0), and
prices remain fixed for 4 periods. Observe first that in response to a productivity shock,
industry employment increases on impact and converges to a higher steady state. Since the
productivity shock lowers firms’ marginal costs, firms that adjust prices at the time of the
shock (type 0 firms) lower their nominal price and see their sales increase in the current as
well as upcoming periods. To meet the immediate increase in demand, as well as to build
inventories so as to lower the cost of making future sales, price-adjusting firms hire more
labor and increase production in the current period (see the upper-left panel of Figure 1B). In
contrast, firms that cannot change their nominal price see their relative prices rise and their
current sales decline. However, type 3 firms (those that adjusted their price three periods
ago), knowing that they will be able to lower their price in the near future, anticipate higher
future sales. Hence, in an eﬀort to build up inventories to meet these sales, they increase
production and employment contemporaneously. Only firms that have adjusted their price
in the last period (type 1 firms) significantly lower their employment on impact following
the productivity shock. At the aggregate industry level, therefore, output, employment, and
inventories all increase following a positive productivity shock when goods are durable.
In contrast, Figure 2 shows that when it is very costly to store goods due to a high
depreciation rate in storage (δ = 0.9), industry employment declines following a permanent
increase in productivity. In this case, even anticipating higher future sales, firms whose prices
are fixed at the time of the shock (types 1, 2, and 3) cannot eﬀectively use inventories to
smooth marginal cost since goods deteriorate rapidly while in storage. As their relative price
increases on impact, sales and production decline and, consequently, they hire less labor. As
depicted in Figure 2, output closely tracks sales under this scenario. Furthermore, output and
employment increase only for firms that can change their price at the time of the productivity
shock. At the industry level, therefore, employment declines. In this sense, our model with
costly storage essentially reproduces the intuition underlying standard sticky-price models
without inventories, including Gali (1999) and others.
6

With regards to the sales-cost elasticity, we study parameterizations in the range η ∈ [0.05, 2.5]. Results
are not sensitive with respect to this parameter.

3.3. Storability, Demand Elasticity, and Price Stickiness
Given the framework we have just laid out, the short-run hours response to a permanent
technology disturbance varies with an industry’s use of inventories, its demand elasticity,
and the degree of nominal price rigidity in that industry. Figure 3 shows the cumulative
one-year response of employment to a one-percent permanent increase in productivity for
model solutions computed using various combinations of the parameters δ, κ, φ, and J.
Panels A.1 and A.2 of Figure 3 contrast two cases with diﬀerent industry demand
elasticities. In particular, employment responses are plotted for diﬀerent price durations
(1 ≤ J ≤ 4), and depreciation in storage (0 ≤ δ ≤ 0.9), according to whether industry
demand is inelastic (panel A.1, φ = 0.75), or elastic (panel A.2, φ = 1.5). For each choice
of depreciation rate, δ, we adjust κ so as to generate an annual inventory-sales ratio of 0.2,
as in our baseline case. When demand is relatively inelastic in Panel A.1, the short-run
response of hours to a productivity increase is always negative irrespective of price duration
and depreciation in storage. As the depreciation rate increases, the hours response becomes
more negative the greater the degree of price stickiness. When demand is relatively elastic
in Panel A.2, the short-run hours response to a productivity increase is always positive when
goods do not depreciate in storage, δ = 0, irrespective of price stickiness. The hours response
is always positive when prices are fully flexible, J = 1. When prices are sticky, J = 4, small
values of the depreciation rate are enough to generate negative employment responses.
To sum up, when prices are fully flexible, permanent improvements in productivity can
either increase or decrease short-run employment depending on the elasticity of industry
demand. When prices are sticky, improvements in productivity can either increase or decrease
short-run employment depending on firms’ ability to carry inventories.
Panels B.1 and B.2 plot employment responses for diﬀerent degrees of price duration,
J = 1, 2, 3, and annual inventory-sales ratios, 0.05 ≤ n/q ≤ 0.4, when industry demand is
elastic and inelastic, respectively. We adjust the sales cost κ in order to generate diﬀerent
annual inventory-sales ratios. When φ = 0.75 in panel B.1, the employment response is
negative whether prices are sticky or flexible. In contrast, when demand is elastic, φ = 1.5
in panel B.2, an industry’s employment response is always positive irrespective of price
stickiness. Observe that in both cases, however, an industry’s short-run employment response
to a productivity improvement always increases with its average inventory-sales ratio.
Panels C.1 and C.2 depict the eﬀects of industry demand elasticity, φ, and price stickiness,
J, on hours worked when goods do not depreciate in storage, δ = 0, and when goods perish
rapidly in storage, δ = 0.9. When δ = 0, irrespective of price stickiness, employment responds
positively to an improvement in productivity as long as industry demand is suﬃciently elastic,
φ > 1. When goods are more perishable, with a price duration of 2 quarters, an industry

demand of elasticity of 2 is required to obtain a positive employment response. When prices
are fixed for a year, J = 4, a larger demand elasticity, φ = 6, is required in order that
employment increase in response to a positive technology shock. Irrespective of depreciation
in storage and price stickiness, note that the employment response always increases with the
magnitude of industry demand elasticity.

4. The Response of Employment and Inventories to Productivity
in U.S. Manufacturing
As we have just argued, an industry’s employment response to a productivity shock depends
in principle not only on the extent of price stickiness in that industry, but also on its ability to
carry inventories and the elasticity of demand for the industry’s product. To investigate these
implications in the data, we now turn our attention to the joint behavior of productivity,
employment, and inventories in U.S. manufacturing industries. For each industry, we estimate
the short-run employment response to a permanent productivity increase. We then relate
that employment response to measures of demand elasticity, price stickiness, and inventory
holdings.
4.1. Data
We obtain data on industry productivity, employment, and inventory holdings from the
NBER Manufacturing Productivity Database (see Bartelsman and Gray, 1996). The Database
includes annual information on 458 4-digit SIC manufacturing industries over the period
1958-1996, and largely reflects information from the Annual Survey of Manufacturing.
To measure industry productivity, some adjustment to the industry TFP growth series
of the Database is necessary. The cost of labor in the Database only includes wages and
salaries but does not include fringe benefits. Therefore, we scale each 4-digit industry’s
payments to labor based on the ratio of employer FICA payments to wages and salaries in
the corresponding 2-digit industry. Given the adjusted wage income share, we recalculate
the industry’s TFP growth series following the procedure described in Bartelsman and Gray
(1996).
Industry employment is the sum of aggregate hours worked by production and nonproduction workers in that industry. Unfortunately, data on the average workweek of nonproduction workers is not available. We follow the Database’s convention and set the workweek of non-production workers to 40 hours. Our measure of real inventory stocks is the
total end-of-period nominal inventory stock deflated by the value of shipments price deflator.
We estimate the price elasticity of industry demand, φ̂, from a regression of industry real

sales growth on the rate of industry price change. To account for the simultaneity problem
intrinsic to such regressions, we instrument for the rate of price change using variables that
reflect supply shocks, namely TFP growth and energy price changes. While energy prices are
most likely exogenous relative to demand shifts, their correlation with output prices is limited
since they make up only a small portion of total cost. In contrast, TFP growth rates are
more strongly correlated with industry output price changes but, due to unobserved factor
utilization, they may not represent strictly exogenous supply shocks. Wages and material
prices are likely to be poor instruments since they are non-trivially aﬀected by industry
demand shifts when the industry has a significant share in factor markets. While our price
elasticity measures vary with the choice of instruments, our cross-industry regressions below
are not significantly aﬀected by the particular choice of demand elasticity estimate. As a
practical matter, the most statistically significant estimates are obtained with our benchmark
instruments, TFP growth rates, and energy price changes.
We obtain statistically significant demand elasticity estimates in 343 out of the 458 industries available. There are only 18 industries (or less than 4 percent of all industries)
whose demand elasticities are estimated with an incorrect sign (i.e., the demand elasticity is
positive). For those industries, we set the price elasticity to 0 in our cross-industry regressions.7 For the 440 industries whose estimated demand elasticities are negative, estimates
range from −7.30 to −0.04, with a mean of −1.52 and a median of −1.26.
We control for the eﬀects of inventory holding costs on the employment response to
changes in technology by using industry average inventory-sales ratios, n/q. While inventorysales ratios are endogenous in the model, without a production smoothing motive, long-run
inventory-sales ratios reflect only inventory technology parameters that are unrelated to
demand (i.e., unrelated to φ and θ), or average price duration, J.8 This feature of the model
limits the potential endogeneity problem associated with using average inventory-sales ratios
as a control variable rather than some more direct measure of inventory holding costs.
Finally, we measure the length of time over which prices are fixed (J) using the average
duration for which product prices remain unchanged as documented by Bils and Klenow
(2004). The Bils-Klenow price data are based on unpublished price quotes collected by
the Bureau of Labor Statistics over the period 1995-1997. At the 4-digit level, we obtain
measures of average price duration for 110 manufacturing goods. Across these goods, price
duration, weighted by industry average output, is on average 4.6 months.
7
8

Our results are not aﬀected by this transformation.
Recall equation (3.1) which holds when firms face constant marginal costs.

4.2. Empirical Specification
For each industry, we estimate a baseline structural VAR in the growth rates of industry
TFP, ∆ zt , hours worked, ∆ht , and end-of-period inventory holdings, ∆nt+1 . We then calculate the response of hours worked to a permanent increase in productivity. Following the
original work of Galí (1999), we identify permanent productivity shocks by assuming that
measured productivity is non-stationary and that productivity shocks are the only source of
movements in long-run productivity. Following Chang and Hong (2006), we use TFP rather
than labor productivity as our measure of productivity. At the industry level, labor productivity is not an appropriate measure of productivity since shocks with permanent eﬀects on
labor productivity confound true productivity shocks with other shocks. Put another way,
permanent changes in industry labor productivity result not only from permanent productivity changes, but also from permanent changes in input ratios stemming from permanent
changes in relative prices.9
We do not require hours worked or inventories to be stationary at the industry level.
While current empirical evidence on the stationarity of aggregate hours worked is mixed,
the assumption that aggregate per capita hours worked are stationary is often motivated
by reference to balanced growth path considerations.10 At the industry level, however, a
permanent change in the productivity of a given industry leads to a permanent change in
relative productivity across industries. Therefore, for aggregate hours to remain unchanged,
industry hours must change permanently to reflect the change in relative productivity. Using
standard Dickey-Fuller unit root tests across all 458 industries, we reject non-stationarity
of hours worked and inventory stocks at the 10 percent significance level in only one out of
twenty industries. Thus, we do not restrict hours or inventories to be stationary and write
our industry VARs in first-diﬀerences of TFP, hours worked, and inventory holdings.
Our estimation procedure can be summarized as follows. Consider the vector MA repre9

The same argument can be made for the aggregate data used by Galí (1999). The identification assumption that only permanent productivity shocks have permanent eﬀects on labor productivity is based
on a balanced growth argument within the neoclassical growth model. Implicitly, one assumes that other
permanent changes to the return on capital, such as permanent changes to the capital income tax rate, have
only a minor impact on the (productivity-normalized) capital-labor ratio. See for instance Uhlig (2004). At
the industry level, however, one expects that permanent changes in relative prices and factor rentals are
large.
10
This was first discussed by Shapiro and Watson (1988). For some recent and opposing views, see
Christiano et al. (2003), and Francis and Ramey (2002).

sentation of our three variable system,
⎤⎡
⎤ ⎡
a11 (L) a12 (L) a13 (L)
∆zt
⎢
⎥⎢
⎥ ⎢
⎣ ∆ht ⎦ = ⎣ a21 (L) a22 (L) a23 (L) ⎦⎣
a31 (L) a32 (L) a33 (L)
∆nt
| {z } |
{z
}|
⎡

A(L)

⎤
εz,t
⎥
eh,t ⎦
en,t
{z }

(4.1)

εt

where εz,t and {eh,t , en,t } denote productivity and non-productivity shocks respectively. The
disturbance terms are assumed to be orthogonal, that is Eεt ε0t = Σ is diagonal, and the
polynomial in the lag operator need not be finite. We do, however, assume that a VAR representation exists, that is A(L) in (4.1) is invertible, B (L) = A(L)−1 . Our main identifying
restriction — that only productivity shocks aﬀect industry TFP in the long run — implies
that a12 (1) = a13 (1) = 0. The responses of hours worked and inventories to a productivity
shock identified in this way will be independent of the other shocks. Thus, there is no need to
disentangle the non-productivity shocks through additional identifying assumptions. As in
Gali (1999), we simply impose a block triangular structure on the inverse matrix of long-run
multipliers in the VAR, B(1), as a way to orthogonalize the reduced form errors {eh,t , en,t }.
The triangular nature of B(1), and the fact that Σ is diagonal, allows us to estimate each
equation in B (L) Yt recursively. All VARs are estimated using a one-year lag and standard
errors are computed by bootstrapping based on 500 draws.
Since industries may have experienced diﬀerent degrees of technological change over time,
we normalize the productivity shocks across industries. In particular, for each industry we
scale the productivity shock such that it increases TFP by one percent in the long run. We
denote industry i’s short-run response of hours worked (i.e. the first-year response) to this
normalized productivity shock by SRh .
We then perform cross-industry regressions that relate the estimated short-run response
of employment, SRh , to industry characteristics, X, such as average inventory-sales ratios,
demand elasticity, and the average duration of output prices,
SRh = α + Xb + u.

(4.2)

Note that the dependent variable in (4.2), SRh , is only an estimate of the true short-run
employment response to a technology shock. Since this uncertainty introduces heteroskedasticity into our cross-industry regressions, we use Huber-White robust standard errors for
inference.11
11

In addition to the use of Huber-White standard errors, we also estimated equation (4.2) with industry
observations weighted by the inverse of the standard error corresponding to that industry’s short-run employment response. In other words, industries with less precise estimates of SRh are given less weight. This

4.3. Employment and Inventories in a Cross-Section of Manufacturing Industries
The results from our estimated structural VARs are best illustrated by comparing the impulse
response functions for two industry aggregates that diﬀer widely in their ability to store their
output and in their estimated demand elasticities: raw foods (meat and dairy products) on
the one hand, and durable goods on the other hand. The raw foods industry has relatively
low inventory holdings and faces a relatively inelastic demand: industry inventories are 3.5
percent of annual sales, and the mean estimated demand elasticity is 0.5.12 For comparison,
in aggregate manufacturing, inventories represent 14 percent of annual sales and the mean
estimated demand elasticity is 1.04. Conversely, the durable goods industry has relatively
high inventory holdings and faces a relatively elastic demand: inventories represent 18 percent
of annual sales, and the mean estimated demand elasticity is 1.64.13
Figure 4 shows the responses of TFP, hours worked, and inventory holdings to a permanent productivity increase in each of our benchmark industries.14 In the raw foods industry
(Figure 4A), hours worked unambiguously fall following a one-standard-deviation productivity shock, while inventories show little movement. Our theory suggests that these responses
for raw foods arise because of their inelastic demand and, to the degree that prices are sticky,
because inventory holding costs are high in that industry. Conversely, in the durable goods
industry (Figure 4B), hours worked increase significantly after a productivity shock and a
significant inventory build-up takes place. Given the theory we have laid out, we naturally
expect these findings in that the relative ease with which durable goods can be carried as
inventories mitigates any negative eﬀects of price stickiness on employment. Moreover, even
if prices were fully flexible, the fact that durable goods have elastic demand helps produce a
positive response of employment to productivity shocks.
According to our industry VARs estimated across 458 4-digit manufacturing industries,
following a productivity shock that raises industry long-run TFP by 1 percent, hours worked
increase in 302 industries. While the estimated hours response vary considerably across
industries, from −2.77 to 3.59 percent, the mean employment increase is 0.32 percent, (see
the first row of Table 1).15 In Table 2, the short-run response in hours, SRh , is highly
additional weighting scheme does not have a substantive eﬀect on our regression results.
12
The estimated demand elasticities range from 0.2 to 1.19 (in absolute value) with a median of 0.41.
13
For the durable goods aggregate, we estimate negative demand elasticities in 253 out of 260 industries.
Estimated demand elasticities range from 0.06 to 7.26 in absolute value with a median of 1.39.
14
When we estimate structural VARs forPthe two industry aggregates, “raw foods” and “durable goods,”
TFP growth, ∆zt , is aggregated as: ∆zt = i μi,t ∆zi,t , where ∆zi,t and μi,t are TFP growth and the output
share of industry i in the industry aggregate. Industry aggregate employment and inventory stocks are the
sum of the component industries employment and inventories.
15
This finding stands in sharp contrast to Kiley (1998) who finds a negative correlation between hours and
the permanent component of labor productivity across 2-digit U.S. manufacturing industries. As pointed out
above, in our structural VARs with industry data, TFP rather than labor productivity is the theoretically

correlated with the short-run response of inventories, SRn , with a correlation coeﬃcient of
0.57 across all industries. The employment response is also positively correlated with both
average inventory-sales ratios (0.13) and industry demand elasticities (0.22), as predicted by
the theory.
Results from cross-industry regressions, shown in Table 3, indicate that both average
inventory-sales ratios and estimated demand elasticities have significant explanatory power
in accounting for diﬀerences in employment responses to technology shocks. Moving from
an industry with an average inventory-sales ratio of 0.16 (the sample mean), to one with
an average inventory-sales ratio of 0.43 (a one-unit log increase), increases the employment
response to an improvement in technology (which ultimately raises industry TFP by one percent) from 0.32 percent to 0.52 percent. Similarly, moving from an industry with a demand
elasticity of 1.04 (the sample mean) to 2.04 (a one-unit increase), raises the employment
response to a normalized technology shock from 0.32 to 0.54 percent. Both these eﬀects are
highly significant, with p values well below 1 percent.
To explore the eﬀects of price stickiness, we are forced to use the smaller sample size for
which the Bils and Klenow (2004) measure of average price duration is available, 111 out of
458 industries. In this smaller sample, a regression of the short-run employment response
to technology shocks against average inventory-sales ratios, demand elasticities, and price
stickiness, shown in Table 3, Column (2), continues to identify average inventory-sales ratios
as a significant explanatory variable, with a coeﬃcient of 0.14 compared to 0.20 in the larger
sample (Table 3, Column 1). The coeﬃcient on demand elasticity, however, is now close to
zero and ceases to be significant. This result reflects the fact that the correlation between
the employment response to technology shocks and industry demand elasticity declines from
0.22 in the large sample to 0.04 in the restricted sample. In excluding more than 3/4 of
our original data sample, therefore, important information is omitted. In this regression,
the average price duration of industry products appears unrelated to the way employment
responds to technology shocks. While this finding somewhat undermines the importance of
price stickiness in determining firms’ employment response to technology shocks, the small
sample size of the Bils and Klenow (2004) data set prevents us from viewing this finding as
conclusive.
In general, we retain from our findings, based on the full sample of 458 observations, that
an industry’s ability to carry inventories and its demand elasticity significantly aﬀect the way
employment and inventories respond to productivity disturbances. In particular, industries
preferred measure of productivity. Chang and Hong (2006) show that this distinction is also empirically
relevant. Indeed, for the same data, they find mostly negative employment responses to identified permanent
productivity changes when labor productivity is used as a measure of technology. They attribute this
predominantly negative response to permanent changes in relative input use.

that are either able to carry large inventories or in which demand elasticity is high tend
to display large positive employment and inventory responses to permanent productivity
increases.

5. Further Considerations
5.1. Alternative VAR Specifications
It should be clear that our model has implications not only for employment but also for such
variables as sales, inventory-sales ratios, and prices that are not included in our baseline
3-variable VAR. Although our data encompasses a large number of industries, the fact that
each industry contains only about forty observations confines us to relatively small scale
VARs. Therefore, to evaluate the robustness of our results, we estimate three alternative
3-variable VARs that continue to include productivity and employment, but we substitute
either sales, inventory-sales ratios, or prices for inventories. Data on industry sales and
prices can be directly obtained from the NBER Database. Real sales is defined as the value
of industry shipments deflated by the value of shipments price deflator, and we use the latter
deflator as our industry price measure.
We find that the short-run employment responses to a permanent productivity increase
in these alternative 3-variable VARs generally mimic those of our baseline specification.
First, the distribution of short-run employment responses across industries is very similar
for the four diﬀerent VAR specifications. Employment tends to increase in most industries,
and the mean employment increase in response to a 1 percent permanent TFP increase is
about 0.3 percent across VAR specifications. Second, the industry short-run employment
responses are highly correlated among the diﬀerent VAR specifications, with correlations
ranging from 0.80 to 0.85. Third, the impact of inventory-sales ratios and estimated demand
elasticities on the cross-industry variation of short-run employment responses is qualitatively
and quantitatively very similar to those shown in Table 2. In Table 4, Columns (1)-(4),
practically all coeﬃcients are significant at the 1 percent level. We see the only exception
to this pattern in the alternative VAR estimates with the price series as the third variable
(Column 4). The employment responses from this price-based VAR tend to be smaller, but
even this VAR yields predominantly positive employment responses.
We find that in response to a permanent productivity increase, sales tend to increase more
than inventories, and inventory-sales ratios tend to fall. This feature replicates the stylized
facts for unconditional correlations of sales and inventory-sales ratios, cf. Ramey and West
(1999) and Bils and Kahn (2000). We also find, however, that the countercyclical behavior
of inventory-sales ratios is not uniform: in 94 out of the 458 industries, inventory-sales ratios

rise following a productivity increase.16
Finally, in most industries, prices fall in response to a permanent increase of TFP. Overall,
prices decrease in both the short run and the long run in 411 out of 458 industries. Furthermore, in 361 out of these 411 industries, the long-run price decline exceeds the decline in
short-run prices. The mean decline in prices following a normalized technology shock is 0.56
percent in the short run, and 0.98 percent in the long run across all industries. Note that
the long-run magnitude of the mean fall in prices is almost equal to the long-run increase
in TFP. These observations are suggestive of an industry supply that is more elastic in the
short run than in the long run.
5.2. Searching for a More Direct Measure of Inventory Holding Costs
We have argued that inventory holdings play a significant role in accounting for crosssectional diﬀerences in firms’ employment response to technology shocks in manufacturing
data. While long-run inventory-sales ratios are independent of demand considerations absent a production-smoothing motive in our model, variations in industry demand elasticity
and the volatility of demand likely aﬀect these ratios in practice. To avoid this potential
endogeneity problem requires that one obtain a more direct exogenous measure of inventory
holding costs.
To address this issue, we examine a data set provided by Bils and Klenow (1998) on the
average service-life of products. This data set is based on information from the Bureau of
Economic Analysis and the interoﬃce memorandum used by major U.S. property casualty
insurance companies. We augment the Bils-Klenow service-life data by assuming that raw
foods and processed foods (e.g., canned and frozen foods) can be stored for 0.2 years and
0.5 years, respectively. Specifically, raw foods include meat products (SIC 2011, 2013, 2015),
dairy products (2021, 2022, 2023, 2024, 2026), and bakery products (2051, 2052). Processed
foods include the rest of food industries under SIC 20. In total, we are able to obtain service
life measures for 98 manufacturing products at the 4-digit level, with a mean weighted by
average industry output of 4.2 years. In the sample of industries for which we have average
service life data, the correlation between service life and inventory-sales ratios is high and
positive at 0.44, which suggests that service life might constitute a useful instrument for
average inventory-sales ratios.
In Table 5, Column (1), we re-estimate the regression of employment responses to technology shocks on inventory-sales ratios and industry demand elasticity but, in doing so,
we instrument for inventory-sales ratios using Bils and Klenow’s service life data. We find
that the coeﬃcient on average inventory-sales ratios increases considerably, from 0.2 to 0.68.
16

Additional tables are available upon request.

However, the coeﬃcient on demand elasticity now becomes statistically insignificant. The
increase in the standard error associated with the demand elasticity coeﬃcient arises from
the fact that, while the service life data is correlated with average inventory-sales ratios, it is
even more strongly correlated with industry demand elasticity (0.59). The second stage regression, therefore, is subject to non-trivial multicollinearity. In a model with durable goods
consumption, goods that are more durable are typically associated with a larger investment
response to a change in their price. The reason is that following a price change, a lower
depreciation rate helps create a larger change in the implicit rental rate of the durable good.
As shown in Table 5, Column (2), the multicollinearity issue we have just described also
applies if we were to use average service life as an instrument for demand elasticity instead
of average inventory-sales ratios. In this case, of course, it is the coeﬃcient on demand
elasticity that increases considerably, from 0.22 to 0.53, but so does the estimated standard
error on the average inventory-sales ratios coeﬃcient. Ultimately, the ideal instrument for
our model should be correlated with inventory-sales ratios but uncorrelated with industry
demand elasticity.

6. Conclusion
Recent studies have interpreted the employment response to productivity shifts as a litmus
test for the existence of frictions in nominal price adjustment. This paper has shown that
whether or not inventories can be used to break the link between production and sales is
crucial for understanding firms’ employment response to productivity shocks. In conventional
sticky price models without inventories, productivity shocks reduce employment. In contrast,
the same shocks cause firms that can carry inventories to expand output relative to sales
and, as a result, to hire more workers. For quantitatively reasonable calibrations, we show
that following a productivity shock, employment increases when the inventory holding costs
are suﬃciently low and industry demand is elastic.
Based on 458 4-digit disaggregated U.S. manufacturing data over the period 1958 to 1996,
we estimate how firms respond to productivity shocks. Consistent with our theory, we find
that an industry’s employment response to shifts in productivity is strongly correlated with
its standard characteristics, such as inventories and demand elasticities, that are entirely
within the domain of flexible price models. On the other hand, using direct evidence on the
degree of price rigidities across industries, we could not find a link between price stickiness
and the short-run employment response to productivity shocks.

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Table 1. Summary Statistics
Mean S.D.
SRh
.32
n
SR
.85
n/q
.16
φ̂
1.04
J
4.3 mo.
−1
δ
4.5 yrs.

Min Max obs.

.77 -2.77
.98 -2.05
.07
.02
.76
0
3.3
.77
5.64
.2

3.59
6.32
.55
4.85
29.9
27.5

458
458
458
458
111
98

Note: SRh and SRn are the short-run responses of hours and inventories
obtained from our baseline industry VAR. n/q is the average inventory-sales
ratio; φ̂ the estimated industry demand elasticity; J: the average duration of
output price (in months) for 111 industries; δ −1 the average service life (in years)
of the output for 98 industries.

Table 2 Cross-Industry Correlations
SRh SRn ln n/q
SRh
SRn
ln n/q
φ̂
ln J
ln δ−1

1.00
0.57
0.13
0.22
0.07
0.21

1.00
0.05
0.14
0.01
0.10

1.00
0.03
0.1
0.44

ln J

ln δ −1

1.00
0.03 1.00
0.59 0.2

1.00

φ̂

Note: The variables are as defined in Table 1. Correlations with the log
average price duration (ln J) are based on 111 industries. Correlations for the
log average service life (ln δ −1 ) are based on 98 industries. Correlation between
ln J and ln δ −1 is based on 72 industry products.

Table 3. The Employment Response to Productivity Shocks:
The Eﬀects of Inventory-Sales Ratio, Demand Elasticity, and Price Stickiness
(1)

(2)

ln(n/q) 0.20∗∗∗
(0.07)

0.14∗
(0.07)

0.22∗∗∗
(0.06)

0.01
(0.07)

φ̂

0.07
(0.09)

ln J

Nobs
R2

458
0.06

111
0.02

Note: The dependent variable is SRh , an industry’s short-run response of
hours to a 1 percent permanent productivity increase estimated from our baseline
3-variable industry VAR. The right-hand side industry variables are as defined
in Table 1. The numbers in parenthesis are standard deviations based on robust
Huber-White sandwich estimators of variance. Asterisks denote p-values of less
than 10% (*), less than 5% (**), and less than 1% (***). All regressions include
a constant term, not displayed in the Table.

Table 4. Alternative VARs: The Response of Employment to Productivity Shocks:
(1)

(2)

(3)

(4)

SRnh

SRqh

h
SRn/q

SRph

0.20∗∗∗
(0.07)
0.22∗∗∗
(0.06)

0.14∗∗
(0.06)
0.18∗∗∗
(0.05)

0.15∗∗∗
(0.06)
0.18∗∗∗
(0.05)

0.05
(0.05)
0.19∗∗∗
(0.04)

0.06

0.05

0.06

Dep. Var.
ln(n/q)i
φ̂

Note: The dependent variable SRih is an industry’s short-run response of
hours to a 1 percent permanent productivity increase in a 3-variable VAR when
the third variable is inventories (i = n), sales (i = q), inventory-sales ratio
(i = n/q), or price (i = p). The right-hand side variables are as defined in Table
1. The regressions are as described in Table 3.

Table 5. The Employment Response to Productivity Shocks:
The Eﬀects of Inventory-Sales Ratio and Demand Elasticity
(1)

(2)

ln(n/q) 0.68∗∗ 0.03
(0.32) (0.13)
φ̂

Nobs

0.12 0.53∗∗
(0.17) (0.19)

Note: See Table 3. In Column (1), the log of average service life (ln δ −1 ) is
used to instrument for ln n/q. In Column (2), the log of average service life is
used as an instrument for demand elasticity φ.

Figure 1. The Response to a Permanent Productivity Increase Without Depreciation in
Storage, δ = 0
A. Aggregate Response

Percentage Deviation from Steady State

1.2

0.8

Output y
Sales q
Employment h

0.6

0.4

0.2

Quarter

B. Individual Firms’ Response
Response of type 0 firm

Response of type 1 firm
5
y
q
h

% Dev from Steady State

-5

y
q
h

-5

Quarter

Response of type 2 firm

5
y
q
h

% Dev from Steady State

Response of type 3 firm

-5

Quarter

y
q
h

-5

Quarter

Figure 2. The Response to a Permanent Productivity Increase With Depreciation in
Storage, δ = 0.9
A. Aggregate Response
1.5

0.5

-0.5

Output y
Sales q
Employment h

-1

-1.5

Quarter

B. Individual Firms’ Response
Response of type 0 firm

Response of type 1 firm

8
y
q
h

y
q
h

% Dev from Steady State

2
0
-2
-4
-6
-8

4
2
0
-2
-4
-6
-8

Quarter

Response of type 2 firm

Response of type 3 firm

8
y
q
h

y
q
h

% Dev from Steady State

Percentage Deviation from Steady State

2
0
-2
-4
-6
-8

4
2
0
-2
-4
-6
-8

Quarter

Figure 3. Employment Responses to Productivity Shocks

A.1 Storability and price stickiness, φ=0.75
0

A.2 Storability and price stickiness, φ=1.5
0

•← J=1
•← J=2

-0.5

•← J=1
•← J=2

•← J=4

-0.5
•← J=4

-1

0.2

0.4

0.6

-1

0.8

0.2

0.4

0.6

0.8

B.1 Inventory-sales ratio and price stickiness,

φ=0.75

B.2 Inventory-sales ratio and price stickiness,

φ=1.5

0
0.2 •← J=1.00
•← J=2.00
•← J=3.00

-0.1

0.15

•← J=1.00
•← J=2.00
•← J=3.00
-0.2

0.05

0.1

0.15

0.1

0.2

0.25

0.3

0.35

0
0.05

0.4

0.1

0.15

0.2

n/q

C.1 Demand elasticity and price stickiness, δ=0.0

-0.5

0.35

0.4

0.5
•← J=4.00
•← J=2.00

•← J=1.00

-0.5

-1
-1.5

0.3

C.2 Demand elasticity and price stickiness, δ=0.9

0.5
0

0.25
n/q

•← J=2.00
•← J=1.00
•← J=4.00

-1
1

-1.5

Note: We graph the cumulative one-year response of hours to a 1 percent
permanent increase in productivity. All parameter values are set at their baseline
values with the exception of (δ, φ, J, κ) as described in the text. In Panel A, we
vary δ and J for inelastic (A.1, φ = 0.75) and elastic (A.2, φ = 1.5) demands.
In Panel B, we vary the steady state inventory-sales ratio n/q and J for inelastic
(B.1, φ = 0.75) and elastic (B.2, φ = 1.5) demands. In Panel C, we vary φ and
J for low (C.1, δ = 0) and high (C.2, δ = 0.9) depreciation rates.

Figure 4. Response to Technology from VAR
Panel A. Raw Food Manufacturing
Productivity

Hours

Inventory

0.03

0.02

0.01

-0.01

-0.02

-0.03

Year

-0.03

Year

4
Year

Panel B. Durable Goods Manufacturing
Productivity

Hours

Inventory

0.05

0.04

0.03

0.02

0.01

-0.01

4
Year

-0.01

4
Year

-0.01

4
Year

Full text of Working Papers (Federal Reserve Bank of Richmond) : Understanding How Employment Responds to Productivity Shocks in a Model with Inventories, Working Paper 06-06

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