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\title{\textbf{Multiple-Product Firms and Product Switching}}
\author{Andrew Bernard, Stephen J. Redding, and Peter K. Schott\thanks{%
Bernard:\ Tuck School at Dartmouth \&\ NBER, 100 Tuck Hall, Hanover, NH
03755, andrew.b.bernard@dartmouth.edu. Redding:\ Yale School of Management
\&\ CEPR, 135 Prospect St., New Haven, CT 06520, stephen.redding@yale.edu.
Schott: Yale School of Management \ \&\ NBER, 135 Prospect St., New Haven,
CT 06520, peter.schott@yale.edu. Bernard and Schott (SES-0241474) and Schott
(SES-0550190) thank the National Science Foundation, and Redding thanks the
Centre for Economic Performance, the Leverhulme Trust and Princeton
University for research support. We thank Evan Gill and Justin Pierce for
excellent research assistance, and Jim Davis for timely disclosure. We thank
the editor, three anonymous referees and Esteban Rossi-Hansberg for insight
and suggestions. We are also grateful to Marc Melitz, Sharon Oster, Peter
Neary, John Sutton, John Van Reenen, Stephen Yeaple and seminar participants
at AEA, CEPR, Dartmouth, LSE, Princeton, Stanford and Yale for helpful
comments. Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the authors and do not necessarily
reflect the views of the NSF, NBER, CEPR, or the U.S. Census Bureau. Results
have been screened to insure that no confidential data are revealed.}}

\begin{abstract}
This paper examines the frequency, pervasiveness and determinants of product
switching by U.S. manufacturing firms. We find that one-half of firms alter
their mix of five-digit SIC products every five years, that product
switching is correlated with both firm- and firm-product attributes, and
that product adding and dropping induce large changes in firm scope. The
behavior we observe is consistent with a natural generalization of existing
theories of industry dynamics that incorporates endogenous product selection
within firms. Our findings suggest that product switching contributes to a
reallocation of resources within firms towards their most efficient
use.\bigskip

JEL: D21, E23, L11, L60

Keywords: heterogeneous firms, product differentiation, product market entry
and exit
\end{abstract}

\maketitle
\shortTitle{Multiple-Product Firms and Product Switching}
\pubMonth{Month}
\pubYear{Year}
\pubVolume{Vol}
\pubIssue{Issue}

The extent to which resources are allocated to their best use is a core
issue of economics. Until now, research into industry dynamics has addressed
this issue by focusing almost exclusively on the contribution of firm entry
and exit to resource reallocation, that is, whether newly created firms or
plants are more productive than the dying firms and plants they replace.%
\footnote{%
There is a large empirical literature in macroeconomics on firm creation and
destruction and its implications for industry dynamics and the firm-size
distribution. See, for example, Martin N. Baily, Charles Hulten and David
Campbell (1992), Timothy Dunne, Mark J. Roberts and Larry Samuelson
(1989a,b), Lucia Foster, John Haltiwanger and C. J. Krizan (2001), Foster,
Haltiwanger and Chad Syverson (2008), and Esteban Rossi-Hansberg and Mark J.
Wright (2007) among others.} This paper examines a new, \textquotedblleft
extensive\textquotedblright\ margin of firm adjustment, the reassignment of
resources that takes place within surviving firms as they add and drop
(i.e., \textquotedblleft switch\textquotedblright ) products.

Our analysis of product switching makes use of a unique longitudinal dataset
that tracks U.S. firms' product-level manufacturing output across
quinquennial U.S. Manufacturing Censuses from 1987 to 1997. In this dataset,
a \textquotedblleft product\textquotedblright\ is one of approximately
fifteen hundred five-digit Standard Industrial Classification (SIC)\
categories, e.g., \textquotedblleft Passenger Cars\textquotedblright .%
\footnote{%
We refer to two-, four- and five-digit SIC\ categories as \textquotedblleft
sectors\textquotedblright , \textquotedblleft industries\textquotedblright\
and \textquotedblleft products\textquotedblright , respectively.} We observe
the set of products each manufacturing firm produces in each census year and
analyze how incumbent firms' mix of products evolves from one census year to
the next. To our knowledge, these are the most comprehensive data on
multiple-product production yet assembled. Standard manufacturing censuses,
for example, typically record just the primary industry of each
establishment.\footnote{%
Existing empirical work on multiple-product firms typically examines product
diversification at a point in time. See, for example, Frank M. Gollop and
James L.Monahan (1991) and John Baldwin and Wulong Gu (2009). Dunne et al.
(1988, 1989b) examine product diversification as a mode of market entry
distinct from plant birth, while Dunne, Shawn D. Klimek and Roberts (2005)
investigate the empirical relationship between the mode of market entry and
plant death.}

We find product switching to be frequent, widespread and influential in
determining both aggregate and firm outcomes.\emph{\ }On average, recently
added and about-to-be dropped products each account for roughly one sixth of
a product's output, amounts that rival the shares represented by recently
created and about-to-exit firms. At the firm level, we find that more than
one half of U.S. manufacturing firms alter their mix of products between
censuses, and that one half of those firms change their mix of products by 
\textit{both} adding and dropping at least one product every five years.
Product adding and dropping also exert considerable influence on the scope
of firms, with an average of 40 percent of firms adding products outside
their existing set of four-digit SIC industries between census years. Given
the unobserved changes firms presumably make to their product mix at lower
levels of aggregation, our estimates of product switching likely
underestimate the true importance of firms' adjustments to their extensive
margins.\footnote{%
One of the attractions of our data is that information is available for the
entire manufacturing sector. Scanner data, such as those used by Judith A.
Chevalier, Anil K. Kashyap and Peter E. Rossi (2003) and Christian Broda and
David E. Weinstein (2007), offer the potential to measure products at finer
levels of disaggregation, although they are typically only available for
specific categories of goods.}

Our empirical analysis is guided by a model of endogenous product selection
that builds on existing theories of industry dynamics by Boyan Jovanovic
(1982), Hugo A. Hopenhayn (1992), Richard Ericson and Ariel Pakes (1995),
Marc J. Melitz\ (2003) and Bernard, Redding and Schott (2007).\footnote{%
These models receive empirical support from studies of firm creation and
destruction by Baily et al. (1992), Dunne et al. (1989a,b)\ and Foster et
al. (2001, 2008).} In these existing models, firms that are heterogeneous in
productivity are assumed to produce a single product, with the result that
firm and product-market entry and exit are equivalent. Here, we develop a
natural extension of such models in which firms choose to produce an
endogenous range of products in response to evolving firm and firm-product
characteristics.\footnote{%
Existing theoretical research on multiple-product firms focuses on issues
associated with managing a given range of products at a particular point in
time, e.g. William J. Baumol (1977), John C. Panzar and Robert D. Willig
(1977), James A. Brander and Jonathan Eaton (1984), Avner Shaked and John
Sutton (1990) and B. Curtis Eaton and Nicolas Schmitt (1994). More recently,
Tor Jakob Klette and Samuel Kortum (2004), Erzo G. J. Luttmer (2008) and
Satyajit Chatterjee and Rossi-Hansberg (2008) have explored the role of
innovation in determining firm scope, as discussed further below.} In our
model, firms differ in innate productivity while firms' products vary in
their attractiveness to consumers \textit{vis-a-vis} other producers of the
same product. The overall profitability of a firm depends on the interaction
of these attributes. Higher values of consumer tastes for a firm's product
raise the firm's profitability in that product, while higher values of firm
productivity increase a firm's profitability in \textit{all} products. In
equilibrium, the most productive firms manufacture the largest ranges of
products because they earn greater revenue per product for given values of
consumer tastes and can therefore cover the fixed costs of a wider set of
products.

Our framework provides a basis for understanding many of the empirical
regularities discernible in U.S. census data. In the data, we find that
multiple-product firms have higher measured revenue-based productivity than
single-product firms. In the model, this difference is due to
high-productivity firms' ability to cover the fixed costs of a greater
number of products. In the data, we find product switching and firm creation
and destruction to be commonplace and pervasive across sectors. In the
model, interactions of stochastic shocks to firm productivity and stochastic
shocks to consumer tastes fosters steady-state product adding and dropping
as well as steady-state firm creation and destruction. In the data, we
observe a positive correlation between products' add and drop rates. In the
model, this correlation arises because firms that receive positive demand
shocks add the product at the same time that some incumbent producers
drawing negative demand shocks drop it. In the data we find that the
probability that a firm drops a product declines with firm-product shipments
and firm-product tenure. In the model, this scale and age dependence arises
as a result of serial correlation in idiosyncratic shocks to firm-product
profitability. Firms' lower-volume and recently-added products are more
likely to be dropped as a result of a negative shock.

Our results also emphasize the central role of the firm in mediating product
adding and dropping. In the data, we find that product adding is positively
correlated with firms' measured revenue productivity, and that product
dropping is influenced by firm as well as firm-product attributes. In the
model, decisions to add or drop products are interdependent given the
contribution of the firm-level productivity draw to the profitability of all
of a firm's products. We also find product switching to be related to firm
outcomes, with net adding and net dropping of products being positively and
negatively correlated with measured revenue productivity, respectively. In
the model, such contemporaneous responses are driven by shocks to
productivity: firms receiving positive shocks earn greater revenue per
existing product and expand, while firms receiving negative shocks
contract.\ 

Though our model serves as a useful guide for our empirical analysis, in its
current form it is too stylized to provide an explanation for all of the
facts that we uncover. We find, for example, that some pairs of products are
more likely to be coproduced within firms than others, and that mergers and
acquisitions account for a relatively small share of the number of products
added and dropped but a larger share of their value. While these facts
transcend our basic setup, we describe how the model might be extended to
incorporate them.

The remainder of the paper is structured as follows. Sections I and II
outline our theoretical framework and describe our dataset. Sections III and
IV report our main empirical findings andtheir consistency with our
theoretical framework. Section V concludes with suggestions for future
research.

\section{Theoretical Framework}

In this section we outline a simple model of multiple-product firms and
product switching that is a natural extension of standard models of industry
dynamics by Jovanovic (1982), Hopenhayn (1992), Ericson and Pakes (1995),
Melitz (2003), and Bernard, Redding and Schott (2007). Our goal is to
introduce the simplest model necessary for useful data analysis, i.e., one
that captures the essence of a broad class of models featuring product
selection. Toward that end, we employ a number of simplifying assumptions,
for example ruling out supply- or demand-driven complementarities across
products. We return to a discussion of how the model might be generalized
and discuss alternative potential approaches after presenting our main
empirical findings. We note that a more detailed discussion of the model and
a more formal analysis of its implications is available in a web-based
technical appendix.\footnote{%
Available from http://***.}

\subsection{Endowments and Preferences}

Labor is the sole factor of production and is assumed to be in inelastic
supply $L$ (which also indexes the size of the economy). The representative
consumer's preferences are a constant elasticity of substitution (CES)
function of the consumption of a continuum of products $i\in \lbrack 0,1]$:%
\begin{equation}
U=\left[ \int_{0}^{1}\left( a_{i}C_{i}\right) ^{\nu }di\right] ^{\frac{1}{%
\nu }},\qquad 0<\nu <1,  \label{utility}
\end{equation}%
where $a_{i}>0$ is a demand parameter that allows the relative importance of
products in utility to vary. Firms are assumed to produce differentiated
varieties of products, so that $C_{i}$ is a consumption index, which also
takes the CES form:%
\begin{equation}
C_{i}=\left[ \int_{\omega \in \Omega _{i}}\left( \lambda _{i}\left( \omega
\right) c_{i}\left( \omega \right) \right) ^{\rho }d\omega \right] ^{\frac{1%
}{\rho }},\quad P_{i}=\left[ \int_{\omega \in \Omega _{i}}\left( \frac{%
p_{i}\left( \omega \right) }{\lambda _{i}\left( \omega \right) }\right)
^{1-\sigma }d\omega \right] ^{\frac{1}{1-\sigma }},\quad 0<\rho <1,
\label{cindex}
\end{equation}%
where $\omega $ indexes firm varieties within products, $\Omega _{i}$ is the
(endogenous) set of firm varieties produced within product $i$, and $P_{i}$
is the price index dual to $C_{i}$ for product $i$.

The demand parameter $\lambda _{i}\left( \omega \right) \geq 0$ determines
the representative consumer's relative demand for the varieties of different
firms within each product.\footnote{%
One interpretation of the parameter $\lambda _{i}\left( \omega \right) $ is
product quality, though this parameter also captures other more subjective
characteristics of a firm's variety that influence consumer tastes.}
Although not central to our results, we make the natural assumption that the
elasticity of substitution across varieties within products is greater than
the elasticity of substitution across products: $\sigma =\frac{1}{1-\rho }%
>\kappa =\frac{1}{1-\nu }>1$. Similarly, we assume for simplicity that the
elasticity of substitution across varieties within products, $\sigma =\frac{1%
}{1-\rho }$, is the same for all products.

\subsection{Production Technology}

Firms from a competitive fringe may enter by incurring a sunk entry cost of $%
f_{e}>0$ units of labor. Incurring the sunk entry cost creates a firm brand
and a blueprint for one horizontally differentiated variety of every
product. Only once the sunk cost has been incurred does the firm observe its
initial\emph{\ }productivity, $\varphi \in \lbrack \underline{\varphi },\bar{%
\varphi}]$, and consumer tastes for the characteristics embodied in its
blueprint for every product, $\lambda _{i}\in \lbrack \underline{\lambda },%
\bar{\lambda}]$. Productivity $\varphi $ is firm-specific but is common
across products within firms, whereas consumer tastes $\lambda _{i}$ are
firm-product specific and are therefore idiosyncratic to a particular
product made by a particular firm.\footnote{\label{footaltlambda}With CES
demand and monopolistic competition, differences in productivity across
firms have identical effects on equilibrium revenue and profits to
differences in consumer tastes. While we have modelled the component of
profitability that is firm-product specific ($\lambda _{i}$) as consumer
tastes, we could have equivalently introduced a productivity parameter that
is firm-product specific. While consumer tastes are a plausible source of
idiosyncratic shocks to firm-product profitability, the important point for
our analysis is that the profitability of a product for a firm has both a
firm and a firm-product component.}

Productivity and consumer tastes evolve stochastically over time and we
choose a specification for their evolution that is both tractable and
sufficiently general to match key features of the firm-product data.%
\footnote{%
Bernard, Redding and Schott (2006) introduce a static model of multi-product
firms without equilibrium product switching to examine the impact of trade
liberalization on firms'\ product scope.} Upon entry, productivity and
consumer tastes are drawn from the continuous distributions $g_{e}\left(
\varphi \right) $ and $z_{ei}\left( \lambda _{i}\right) $ respectively, with
cumulative distributions $G_{e}\left( \varphi \right) $ and $Z_{ei}\left(
\lambda _{i}\right) $. Once a firm observes its initial values of
productivity and consumer tastes, it decides whether to produce or exit. If
the firm exits, its production knowledge is lost, and the sunk cost must be
incurred again in order for the firm to re-enter. If the firm enters, it
faces a Poisson probability $\theta >0$ of a shock to productivity $\varphi $%
, in which case a new value for productivity $\varphi ^{\prime }$ is drawn
from the continuous conditional distribution $g_{c}\left( \varphi ^{\prime
}|\varphi \right) $, with cumulative distribution $G_{c}\left( \varphi
^{\prime }|\varphi \right) $. Similarly, the firm faces a Poisson
probability $\varepsilon _{i}>0$ of an idiosyncratic shock to consumer
tastes for its variety $\lambda _{i}$, in which case a new value for
consumer tastes $\lambda _{i}^{\prime }$ is drawn from a continuous
conditional distribution $z_{ci}\left( \lambda _{i}^{\prime }|\lambda
_{i}\right) $, with cumulative distribution $Z_{ci}\left( \lambda
_{i}^{\prime }|\lambda _{i}\right) $.\footnote{%
While the model could be extended to allow firms to make endogenous
investments in improving productivity and enhancing consumer tastes, these
extensions are not central to the model's key predictions, which are driven
by selection, and so we do not pursue them here.}

Consistent with the serial correlation in firm and firm-product shipments
observed in our data, we assume that consumer tastes and productivity are
positively serially correlated, which corresponds to the following
assumption about their conditional distributions: $\partial Z_{ci}\left(
\lambda _{i}^{\prime }|\lambda _{i}\right) /\partial \lambda _{i}<0$ and $%
\partial G_{c}\left( \varphi ^{\prime }|\varphi \right) /\partial \varphi <0$
for $\lambda _{i}^{\prime }\in \lbrack \underline{\lambda },\bar{\lambda}]$
and $\varphi ^{\prime }\in \lbrack \underline{\varphi },\bar{\varphi}]$.
Thus the probability of drawing a new value for consumer tastes
(productivity) less than $\lambda _{i}^{\prime }$\ ($\varphi ^{\prime }$) is
decreasing in the existing value of consumer tastes (productivity). To make
use of law of large numbers results, we assume that the distributions of
consumer tastes and productivity are independent across firms. For the same
reason, we also assume that the distributions of consumer tastes are
independent across products and that the distributions of consumer tastes
and firm productivity are independent of one another.\footnote{%
While the consumer taste and firm productivity distributions are independent
of one another, there is interdependence in a firm's profitability across
products, because firm productivity is common across products. We discuss
extending the model to introduce other forms of interdependence in Section
IV below.} Firms also face a Poisson probability of death $\delta >0$ due to 
\textit{force majeure} events unrelated to profitability.

The production technology takes the following form. There is a fixed
corporate headquarters cost of $f_{h}>0$ units of labor, which the firm must
incur irrespective of the number of products that it chooses to produce, and
a fixed production cost of $f_{pi}>0$ units of labor for each product $i$
that is produced. In addition, there is a constant marginal cost for each
product, which depends upon the firm's productivity. Total labor employed by
a firm with productivity $\varphi $\ is thus:%
\begin{equation}
l\left( \varphi \right) =f_{h}+\int_{0}^{1}I_{i}\left[ f_{pi}+\frac{%
q_{i}\left( \varphi ,\lambda _{i}\right) }{\varphi }\right] di,
\label{prodtech}
\end{equation}%
where $I_{i}$ is an indicator variable which equals one if a firm produces
product $i$ and zero otherwise, and $q\left( \varphi ,\lambda _{i}\right) $
denotes output of product $i$ by a firm with productivity $\varphi $ and
demand $\lambda _{i}$.

\subsection{Equilibrium Entry and Production Decisions}

The key economic decisions of a firm in the model are whether to enter or
exit and in which product markets to participate. We begin by considering
the decision of whether to participate in a product market. If a firm
produces a product, it supplies one of a continuum of varieties each with
measure zero relative to the product market as whole. As this is true for
each of the continuum of products, the firm's profit maximization problem
reduces to choosing the price of each product variety separately to maximize
the profits derived from that product variety. This optimization problem
yields the standard result that the equilibrium price of a product variety
is a constant mark-up over marginal cost:%
\begin{equation}
p_{i}\left( \varphi ,\lambda _{i}\right) =\frac{1}{\rho }\frac{w}{\varphi },
\label{varprice}
\end{equation}%
where we choose the wage for the numeraire and so $w=1$.

Under our assumption of CES preferences, equilibrium prices are inversely
related to firm productivity. As $\varphi $\ rises, variable labor input and
output rise, but prices fall, leaving revenue per variable input unchanged.
Nevertheless, the model features dispersion in revenue-based measures of
productivity across firms, as examined in our empirical analysis below,
because of the assumption of fixed production costs. As $\varphi $\ rises,
variable labor input and revenue increase, with the result that the fixed
labor input is spread over more units of revenue.\footnote{%
We follow Foster, Haltiwanger and Chad Syverson (2008) in differentiating
between revenue- and quantity-based measures of productivity. As we show in
the web-based technical appendix, both measures are monotonically related to
the firm productivity draw ($\varphi $) in the model. We note that a
monotonic relationship between $\varphi $\ and revenue-based measures of
productivity can also be achieved via a demand system with a variable
elasticity of substitution, such as the quasi-linear preferences of Melitz
and Gianmarco I. P. Ottaviano (2008). In that setting, equilibrium prices
fall less than proportionately with productivity due to variable mark-ups.}

As there is a fixed production cost for each product, there exists a \textbf{%
zero-profit consumer taste cutoff }$\lambda _{i}^{\ast }\left( \varphi
\right) $ such that a firm with productivity $\varphi $ will only produce
product $i$ if it draws a consumer taste greater than or equal to $\lambda
_{i}^{\ast }\left( \varphi \right) $. The zero-profit consumer taste cutoff
is defined as follows:%
\begin{equation}
\pi _{i}\left( \varphi ,\lambda _{i}^{\ast }\left( \varphi \right) \right) =%
\frac{R_{i}\left( \rho P_{i}\varphi \lambda _{i}^{\ast }\left( \varphi
\right) \right) ^{\sigma -1}}{\sigma }-f_{pi}=0,  \label{zppp}
\end{equation}%
where $\pi _{i}\left( \varphi ,\lambda _{i}\right) $ denotes equilibrium
profits from a variety of product $i$ with consumer taste $\lambda _{i}$ and
firm productivity $\varphi $.

From equation (\ref{zppp}), the higher a firm's productivity $\varphi $, the
lower the zero-profit cutoff for consumer tastes $\lambda _{i}^{\ast }\left(
\varphi \right) $, and so the greater the probability of having a value for
consumer tastes sufficiently high to profitably produce the product. With a
continuum of products and independent distributions for consumer tastes, the
law of large numbers implies that the fraction of products produced by a
firm equals the sum of its probabilities of producing each product.
Therefore, as the probability of producing each product is increasing in
firm productivity, a key implication of the model is that a firm's product
range is increasing in its productivity.

We now consider a firm's decision of whether to enter or exit. With a
continuum of products and independent distributions for consumer tastes, a
firm's expected profits across the continuum of products equals the sum of
its expected profits from each product minus the fixed headquarters costs:

\begin{equation}
\pi \left( \varphi \right) =\int_{0}^{1}\left[ \int_{\lambda _{i}^{\ast
}\left( \varphi \right) }^{\bar{\lambda}}\pi _{i}\left( \varphi ,\lambda
_{i}\right) \gamma _{zi}\left( \lambda _{i}\right) d\lambda _{i}\right]
di-f_{h}.  \label{expfirmprof}
\end{equation}%
where $\gamma _{zi}\left( \lambda _{i}\right) $ is the stationary
distribution for consumer tastes, which as discussed further in the
web-based technical appendix is endogenously determined as a function of the
entry and conditional distributions, $z_{ei}\left( \lambda _{i}\right) $ and 
$z_{ci}\left( \lambda _{i}\right) $ respectively.

Although consumer tastes for a firm's variety of a product are stochastic,
the law of large numbers implies that all firms with the same productivity
experience the same flow of total profits across the continuum of products
in equation (\ref{expfirmprof}). Stochastic shocks to consumer tastes
generate fluctuations in the profitability of individual products, which
lead them to be added and dropped over time. However, these fluctuations in
the profitability of individual products average out at the level of the
firm, so that the evolution of total firm profits over time is determined
solely by stochastic shocks to firm productivity.

The value of a firm with productivity $\varphi $ equals the flow of current
profits plus the expected value of capital gains or losses as a result of a
stochastic productivity shock, discounted by the probability of firm exit:

\begin{equation}
v\left( \varphi \right) =\left\{ 
\begin{array}{l}
\frac{\pi \left( \varphi \right) +\theta \left[ \int_{\varphi ^{\ast }}^{%
\bar{\varphi}}\left[ v\left( \varphi ^{\prime }\right) -v\left( \varphi
\right) \right] g_{c}\left( \varphi ^{\prime }|\varphi \right) d\varphi
^{\prime }\right] }{\delta +\theta G_{c}\left( \varphi ^{\ast }|\varphi
\right) }\hspace{0.7in}\text{for }\varphi \geq \varphi ^{\ast } \\ 
0\text{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
otherwise}%
\end{array}%
\right. ,  \label{bellvalfirm}
\end{equation}%
where the denominator on the right-hand side of equation (\ref{bellvalfirm})
is the probability of firm exit, which equals the exogenous probability of
firm death $\delta $ plus the endogenous probability of experiencing a
productivity shock that induces exit $\theta G_{c}\left( \varphi ^{\ast
}|\varphi \right) $.

The presence of a continuum of products in the model implies that each firm
draws a value for consumer tastes above the zero-profit cutoff $\lambda
_{i}^{\ast }\left( \varphi \right) $ in a positive measure of products.
However, for entry to be profitable, the value of the current profits across
this positive measure of products plus the expected value of capital gains
or losses must exceed the fixed headquarters costs. As total firm profits
across the continuum of products $\pi \left( \varphi \right) $ are
increasing in $\varphi $, and the probability of experiencing a productivity
shock that induces exit $G_{c}\left( \varphi ^{\ast }|\varphi \right) $ is
decreasing in $\varphi $, the value of the firm in equation (\ref%
{bellvalfirm}) is increasing in its productivity. Therefore, there is a
zero-value cutoff productivity $\varphi ^{\ast }$ below which firms exit,
which is defined by $v\left( \varphi ^{\ast }\right) =0$.

In an equilibrium with positive entry, the expected value of entry must
equal the sunk entry cost, which requires the following free entry condition
to hold:%
\begin{equation}
V=\left[ 1-G_{e}\left( \varphi ^{\ast }\right) \right] \bar{v}=f_{e},\qquad 
\bar{v}\equiv \int_{\varphi ^{\ast }}^{\bar{\varphi}}v\left( \varphi \right)
\left( \frac{g_{e}\left( \varphi \right) }{1-G_{e}\left( \varphi ^{\ast
}\right) }\right) d\varphi ,  \label{freeentry}
\end{equation}%
where $\left[ 1-G_{e}\left( \varphi ^{\ast }\right) \right] $ is the \textit{%
ex ante} probability of drawing a productivity above the zero-value cutoff $%
\varphi ^{\ast }$ upon entry, $g_{e}\left( \varphi \right) $ is the
probability of drawing productivity $\varphi $\ upon entry, and $v\left(
\varphi \right) $ is the solution to the Bellman equation (\ref{bellvalfirm}%
).

General equilibrium is referenced by the following six variables and
functions: the zero-value cutoff productivity below which firms exit $%
\varphi ^{\ast }$, the zero-profit cutoff consumer taste for each product
for a firm with the zero-value cutoff productivity $\lambda _{i}^{\ast
}\left( \varphi ^{\ast }\right) $, the endogenous stationary distribution
for firm productivity $\gamma _{g}\left( \varphi \right) $, the endogenous
stationary distribution for consumer tastes for each product $\gamma
_{zi}\left( \lambda _{i}\right) $, the price index for each product $P_{i}$,
and aggregate revenue for each product $R_{i}$. As shown in the web-based
technical appendix, these six variables and functions are determined by the
following equilibrium conditions: consumer and producer optimization, goods
and labor market clearing, free entry, the zero-profit cutoff condition for
consumer tastes for each product, the equality of the mass of successful
entrants and the mass of exiting firms, the equality of the outflow and
inflow of firms from each value of consumer tastes, and finally the equality
of the outflow and inflow of firms from each value of productivity.

The general equilibrium of the model features both steady-state product
switching and steady-state firm entry and exit. Each period a measure of new
firms incur the sunk entry cost, and those with productivity draws above the
zero-value cutoff enter, while those with productivity draws below the
zero-value cutoff exit. A surviving firm with unchanged productivity
produces a constant range of products, but idiosyncratic shocks to consumer
tastes for individual products induce surviving firms to drop a measure of
the products previously produced and add an equal measure of products not
previously produced. As stochastic shocks to a surviving firm's productivity
occur, the range of products produced expands with an increase in
productivity and contracts with a decrease in productivity. Firms exit
endogenously when their productivity falls below the zero-value cutoff or
exit exogenously when death occurs as a result of \textit{force majeure}
considerations.

As discussed further below, these and other features of the model are used
to guide our empirical analysis. Before beginning that analysis, we describe
our data.

\section{Data Description\label{s_data}}

As part of its quinquennial Census of Manufactures (CMF), the U.S. Census
Bureau (hereafter \textquotedblleft Census\textquotedblright ) collects
information on the set of Standard Industrial Classification (SIC)
categories produced by U.S. manufacturing establishments (i.e.,
\textquotedblleft plants\textquotedblright ). This information is obtained
from questionnaires plants are required to fill out by law under Title 13 of
the United States Code. Each questionnaire has two parts. The first is
common to all establishments and solicits general information about their
operation, including their overall shipments (i.e., \textquotedblleft
output\textquotedblright ), use of inputs (capital, production and
non-production workers and materials) and wagebills.\footnote{%
CMF questionnaires define shipment value as goods' \textquotedblleft net
selling value f.o.b. plant to the customer after discounts and
allowances,\textquotedblright\ and excluding freight charges and excise
taxes. Questionnaires used as part of the 1997 CMF are available at
www.census.gov/epcd/www/econ97.html. All dollar-value data collected in the
CMF\ are nominal.} We use this information to examine differences between
single- and multiple-product firms, and, along with industry price deflators
provided by Eric J. Bartelsman, Randy A. Becker and Wayne B. Gray (2000), to
compute revenue-based measures of firms' labor and total factor productivity
(TFPR).\footnote{%
We measure firm TFPR\ as the shipment-weighted average TFPR\ of its plants.
Plant TFPR\ in a given census year is measured relative to other plants in
its main industry in percentage terms using the multi-factor superlative
index number of Douglas W. Caves, Laurits R. Christensen, and W. Erwin
Diewert (1982). This index accounts for plants' use of capital, production
workers, non-production workers and materials. Plant shipments, capital and
materials are deflated according to the four-digit SIC deflator of its major
industry using deflators provided by Bartelsman et al. (2000). Wages are
deflated by regional U.S. consumer price indexes available at www.bls.gov. A
plant's main industry is the four-digit SIC\ in which it has the largest
value of shipments.} As noted in Section I.C and discussed further in the
web-based technical appendix, both revenue- and quantity-based measures of
productivity are monotonically related to the firm productivity draw ($%
\varphi $)\ in the model.\footnote{%
We focus on revenue-based measures of productivity because data on physical
units of output is not available for all products and because physical units
of output are not comparable across firms for many products, e.g., cars. We
note that Foster, Haltiwanger and Syverson (2008) find a positive
correlation between revenue- and quantity-based measures of productivity for
a sample of 11 products for which it is possible to compute and compare both
measures across firms.}\emph{\ }

The second part of each questionnaire varies depending upon the industry in
which the establishment operates. It lists the set of products
establishments in the industry typically produce as well as a verbal
description of each product.\footnote{%
Questionnaires also collect information on establishments' \textquotedblleft
other\textquotedblright\ activities, such as \textquotedblleft tasks
performed for others using others' materials\textquotedblright , that cannot
be associated with a particular manufacturing product. We exclude these
categories from our analysis.} Establishments are instructed to record their
total shipments of each product.\footnote{%
We note that the census does not collect information on firms' input use by
product, and also that output deflators for five-digit SIC\ products are not
available. As a result, measurement of establishments' use of inputs or
revenue productivity within individual products is not possible.} In the
event that an establishment also ships products not listed on the form, the
questionnaire provides space for them to record any shipments in additional
product codes. Establishments are assigned to industries according to
information collected from previous censuses as well as other Census
surveys. Very large plants with substantial activity in a number of
industries may receive more than one form. Very small plants, referred to as
\textquotedblleft administrative records\textquotedblright , are not
required to report output at the product level. These establishments
represent a very small share of overall U.S. manufacturing output and are
typically ignored in U.S. microdata research; we drop them here as well.

We analyze product switching in the 1987 through 1997 censuses. We use a
five-digit SIC\ category as our definition of a product and refer to two-
and four-digit SIC\ categories as \textquotedblleft
sectors\textquotedblright\ and \textquotedblleft
industries\textquotedblright , respectively.\footnote{%
Output at the five-digit SIC\ level is the most disaggregate data available
for all plants. While CMF\ questionnaires solicit information at the
seven-digit SIC level, establishments also surveyed for other programs
(e.g., Census' Current Industry Reports) are permitted to report information
at the five-digit level to alleviate their reporting burden.} As described
in United States Department of Commerce (1989), manufacturing encompasses 20
sectors, 455 industries and 1440 products. As product-mix decisions are made
at the level of the firm, we aggregate plants to firms to create a firm by
product by census year dataset.\footnote{%
Firm identifiers are derived from firms' legal identities, and firms can
consist of one or many establishments. Census uses an annual Company
Organization Survey both to determine how new firms are organized and to
keep track of changes in incumbent firms' ownership structure over time,
e.g., the buying and selling of plants, the creation of new plants or the
closing of existing plants.} Using this dataset we track the products that
firms add and drop across census years.\footnote{%
SIC\ categories undergo minor revisions in each census year but experienced
a major revision in 1987. Census uses an internally generated concordance to
map product codes collected in censuses after 1972 to the 1987 revision. We
focus on the 1987 to 1997 censuses because they are less sensitive to this
concordance and exhibit high product-code consistency over time. To be
conservative, we drop the roughly 1 percent of five-digit codes
(representing roughly 5 percent of total value) that do not appear in all
three censuses. We note that our findings are not sensitive to this
procedure, and that we find (but do not report) similar results for other
sample periods, e.g., the 1972 to 1982 censuses, where the concordance of
collected and 1987-revision product codes is less precise.} Given that a
considerable body of research already examines firm creation and
destruction, we focus on the features of product switching by surviving
firms highlighted by our model. In particular, we neither treat exiting
firms as those who drop all their products, nor entering firms as whose who
add all their products. For convenience, we often refer to firms that
produce multiple products as \textquotedblleft MP\ firms\textquotedblright\
and firms that produce a single product as \textquotedblleft SP
firms\textquotedblright .

To provide a sense of the relative level of detail between sectors,
industries and products, consider \textquotedblleft Nonferrous Wiredrawing
and Insulating\textquotedblright\ (SIC\ 3357), which is one industry inside
the \textquotedblleft Primary Metal Industries\textquotedblright\ (SIC\ 33)
sector. The thirteen products in this industry range from copper wire (SIC\
33571) to fiber optic cable (SIC 33579), and are listed in Table A1 of the
web-based technical appendix. Though these products share a grossly similar
end use, they can differ substantially in terms of the materials and
technologies required to manufacture them.

For the manufacturing sector as a whole, the typical two-digit sector has 24
four-digit industries and 76 five-digit products, as reported in Table A2 of
the web-based technical appendix. The number of products per sector ranges
from a low of 12 in Leather (SIC\ 31)\ to a high of 178 in Industrial
Machinery (SIC 35). Similarly, the average number of products per industry
within sectors ranges from a low of 1.1 in Leather to a high of 5.1 in
Printing and\ Publishing (SIC 27).\footnote{%
There is substantial variation in the precision of industry and product
classifications. For example, Passenger Cars (SIC 37111) and Combat Vehicles
(SIC 37114) are examples of products in the Motor Vehicle industry (SIC
3711), while Textbook Binding and Printing (SIC 27323) and Religious Books,
Binding and Printing (SIC 27323) are examples of products in the Book
Printing industry (SIC 2732).} Nonferrous Wiredrawing and Insulating (SIC\
3357), the industry highlighted above, is just one of 26 Primary Metal
Industries, and its products represent 14 percent (13/90) of the total
number of products in that sector. Products vary substantially in terms of
how they are produced both within and across sectors, as shown in the last
four columns of Table A2, which report products' 1997 capital and skill
intensity by sector.\footnote{%
As the CMF\ does not collect information on input usage (or wages) by
product, we measure a product's capital and skill intensity as the
shipment-weighted average of all plants producing it.}

We interpret the Standard Industrial Classification (SIC) categories used to
record U.S. manufacturing output as discrete partitions of the model's
continuum of products, which become coarser as one increases the level of
aggregation. With this interpretation, the model provides a natural
explanation for the coexistence of single- and multiple-product firms. We
think of firms producing a single product as those whose range of products
falls within a single five-digit category. MP firms, on the other hand, are
those whose product range is wide enough to span several five-digit SIC
categories.

Table \ref{t_mpmi} reports an average breakdown of SP\ and MP\ firms across
the 1987 to 1997 census years in our sample, and also reports the average
number of products, industries and sectors MP\ firms produce. As indicated
in the table, MP\ firms dominate:\ though they represent a minority of firms
(39 percent), they account for a strong majority (87 percent) of shipments.
Multiple-industry and multiple-sector firms are similarly influential,
responsible for 28 and 10 percent of firms but 81 and 66 percent of output,
respectively. The final column of Table \ref{t_mpmi} reveals that the
average MP firm produces 3.5 products, that the average multiple-industry
firm manufactures in 2.8 industries and that the average multiple-sector
firm is present in 2.3 sectors.\footnote{%
On average across the census years 1987 to 1997, the share of MP firms with
a single plant is 84 percent compared to a share of 93 percent for all
firms. Therefore, MP firms are more likely to operate several production
facilities than SP firms, but multiple products are frequently produced
within the same production facility.}

\begin{center}
TABLE\ 1 ABOUT\ HERE
\end{center}

\section{Empirical Evidence}

Our model highlights a number of features of product switching that operate
at the level of firms, products and firm-products. We organize our empirical
investigation of product switching in this section according to these levels
of analysis. We note that the formal derivation of the model's implications
is available in the web-based technical appendix.

\subsection{Firm-Level Evidence}

In the model, firms with higher productivity produce a wider range of
products than firms with lower productivity because their higher revenues
per product allow them to cover the fixed costs of a larger measure of
products. Idiosyncratic shocks to firm-product profitability drive
steady-state adding and dropping of products within firms, while
idiosyncratic shocks to firm productivity induce changes in the measure of
goods firms produce.

\subsubsection{The Relative Productivity of Multiple-Product Firms\emph{\ }}

Table \ref{t_mp} compares the characteristics of single- and
multiple-product firms in the 1997 census, though we note that results are
similar in previous census years. The table reports the results of OLS
regressions of the natural log of the noted firm characteristic on a dummy
variable equal to unity if the firm produces multiple products as well as
main-industry fixed effects. As indicated in the table, MP\ firms are larger
than SP\ firms in the same industry in terms of both shipments (0.66 log
points) and employment (0.58 log points). We also find that MP firms have
higher revenue-based labor and total factor productivity (TFPR)\ than SP\
firms in the same industry.\emph{\ }

\begin{center}
TABLE\ 2 ABOUT\ HERE
\end{center}

Similar differences are found with respect to firms producing in multiple
industries and in multiple sectors, except for the TFPR\ differential
between single- and multiple-sector firms. That difference is statistically
indistinguishable from zero, perhaps due to the difficulties of measuring
productivity in firms with disparate products that span two-digit sectors.%
\footnote{%
Our model implies that measurement of TFPR for multiple-product firms is
problematic if, as is the case here, data on inputs at the firm-product
level are unavailable. See also Bernard, Redding and Schott (2005) and Jan
De Loecker (2008). \label{foot_tfp}} All remaining differences displayed in
the table are statistically significant at the 1 percent level.

While our analysis is based on U.S. Census data, we note that other datasets
are amenable to analyzing firms' product scope at various levels of
aggregation. The publicly available Amadeus database published by Bureau Van
Dijck, for example, contains information on EU\ firms' primary and secondary
industries. We note that differences among single- and multiple-industry
firms in those data are similar to the results reported in the second column
of Table 4 below. Unfortunately, the manner in which Amadeus tracks changes
in firms' industries over time makes it difficult to undertake comparisons
of product-mix dynamics across U.S. and EU\ firms.

\subsubsection{Product Switching Within Firms}

We examine product switching by dividing surviving firms into four
exhaustive and mutually exclusive groups based on the manner in which they
alter their mix of products between census years. Possible actions are: (1) 
\textit{None} - the firm does not change its mix of products; (2)\ \textit{%
Drop} - the firm only drops products; (3)\ \textit{Add} - the firm only adds
products; and (4)\ \textit{Both} - the firm both adds and drops products,
i.e., \textquotedblleft churns\textquotedblright\ products.

Table \ref{t_nadb} reports firm activity across these dimensions for the
pooled 1987 to 1997 censuses. Cells in the top panel of the table report the
average percent of firms reporting each activity across five-year census
intervals, while cells in the bottom panel report percentages weighted by
firm output.\footnote{%
Though the figures reported in the table correspond to the probabilities of
product switching conditional on firm survival, it is straightforward to
evaluate the unconditional probabilities of product switching for all firms
by multiplying the figures in the table by the average probability of firm
survival, which is roughly two-thirds.} The five columns in each panel
report results for all firms, MP\ firms, firms that export, firms whose
shipments are above the 75th percentile (\textquotedblleft large
firms\textquotedblright ) and firms with more than one manufacturing plant.

\begin{center}
TABLE\ 3 ABOUT\ HERE
\end{center}

As indicated in the upper panel of the table, an average of 54 percent of
surviving firms alter their mix of products every five years, 15 percent by
dropping at least one product, 14 percent by adding at least one product and
25 percent by both adding and dropping at least one product. Comparing the
results for all firms in the first column with those for MP firms in the
second column, we find implicitly that SP\ firms are more likely to leave
their product mix unchanged than MP\ firms. From the third column of the
table, we find that exporters are more likely to change their product mix
than non-exporters. Finally, from the remaining columns of the table, we see
that large firms and multiple-plant firms also have above-average rates of
product switching.\footnote{%
Results for SP\ firms, non-exporters, \textquotedblleft
small\textquotedblright\ firms and single-plant firms are available upon
request. An alternate decomposition of activity according to whether firms
do not change their product mix, change their mix but do not net add or drop
any products, change their product mix and net add products or change their
product mix and net drop products indicates that these actions on average
occur 46, 12, 22 and 20 percent of the time, respectively, across census
years.}

The frequency and pervasiveness of product switching displayed in the upper
panel of Table \ref{t_nadb} is consistent with our model. In the lower panel
of the table we report output-weighted results, which reveal that firms
accounting for relatively large shares of output are more likely to add and
drop products than smaller firms across columns. This behavior is also
understandable in light of our theoretical framework, as more productive
firms are more likely to have product ranges wide enough to span five-digit
SIC categories, rendering them more likely to add and drop products. Since
more productive firms in the model also produce more of each product and
have larger total output, firms that switch products are likely to account
for a larger share of output than of the number of firms. As indicated in
the table, an average of 89 percent of all manufacturing output is produced
by firms that change their mix of products across census years. Firms that
both add and drop products account for the largest share of output, at 68
percent.

\subsubsection{Product Switching and Firm Characteristics}

We examine the relationship between product switching and firm outcomes via
OLS\ regressions of log changes in firm characteristics between census years
on dummy variables capturing contemporaneous product-switching behavior,%
\emph{\ }%
\begin{equation}
\Delta Z_{jt}=\alpha _{mt}+\beta _{1}NetDrop_{jt}+\beta
_{2}NetAdd_{jt}+\varepsilon _{jt}.  \label{Outcome}
\end{equation}%
where $\Delta Z_{jt}$\ represents the log difference in a firm outcome
between census years $t-5$\ and $t$; $\alpha _{mt}$ represents a full set of
product-mix by year fixed effects; $NetDrop$ is a dummy variable that is
equal to one if a firm reduces its net number of products and zero
otherwise; and $NetAdd$ is a dummy variable that is equal to one if a firm
increases its net number of products and zero otherwise.\footnote{%
The left out category encompasses firms that undertake no product switching
or, if they do switch products, experience no net change in the number of
products they produce. Similar results are obtained if an additional dummy
variable is included for firms that engage in product switching but
experience no net change in products. Though our regression focuses on net
adding and dropping because these relate most closely to the predictions of
the model, we note that an analogous specification using the \textit{Add}, 
\textit{Drop} and \textit{Both} measures defined above also reveals
statistically significant correlations between product switching and changes
in measured firm characteristics.} The firm characteristics we consider are
real output, employment, and real revenue-based labor and total factor
productivity.\footnote{%
Results for nominal output and nominal output per worker are similar. Due to
the unavailability of product-level price indexes, firms' product-level
shipments are deflated by their corresponding industry-level deflators. The
inclusion of product-mix-by-year fixed effects in the regression helps to
alleviate concerns about product-year variation in prices.} The regression
results, reported in Table \ref{t_firmout}, include all surviving firms
between the 1987 to 1992 and 1992 to 1997 censuses. The regression
coefficients therefore capture the correlation between changes in the net
number of products and changes in firm characteristics conditional on firm
survival. Each row of the table reports results for a different firm-outcome
regression. Standard errors adjusted for clustering at the industry level
are reported in parentheses below coefficients. The number of firm-year
observations included in each regression as well as each regression's $R^{2}$%
\ are reported in the final two columns of the table.

\begin{center}
TABLE\ 4 ABOUT\ HERE
\end{center}

As indicated in the table, we find that product switching is related to
changes in firm characteristics in the way suggested by the model. We find
that net product adding is associated with an increase in firm size (whether
measured by output or employment) as well as revenue-based labor and total
factor productivity (TFPR). Similarly, we find that net product dropping is
associated with a decrease in firm size and TFPR. Although the correlation
between net product dropping and revenue-based labor productivity is
positive rather than negative, the estimated coefficient is roughly an order
of magnitude smaller than those for the other variables. As noted above, the
structure of our model implies that measuring the productivity of
multiple-product firms is problematic when data on inputs are unavailable at
the firm-product level.

While the regression results in Table \ref{t_firmout} establish that product
switching is accompanied by changes in observed firm characteristics, we
emphasize that they are correlations capturing an equilibrium relationship
between endogenous variables. As product choice is endogenous, the
regression coefficients capture both the non-random decision to change the
net number of products and the impact of this decision on observed firm
characteristics.

\subsubsection{Potential Product-Category Mismeasurement}

Census devotes considerable resources to the accurate collection and
verification of establishments' product-shipment data. As noted above, forms
are designed to minimize measurement error by being tailored to the industry
in which establishments operate, by listing the SIC categories (and
descriptions) that establishments in the industry commonly produce, and by
offering establishments space to record output in unlisted categories. After
forms are collected, Census verifies the consistency of current responses
with past responses and re-contacts establishments whose data appears
erroneous. Nevertheless, our analysis of product switching is susceptible to
establishments' inaccurate transcription of SIC codes.

We believe our results to be robust to product-category mismeasurement for
several reasons. First, we note that our use of five-digit SIC categories to
define products requires only that firms correctly record the first five
digits of the seven-digit SIC\ categories listed on the Census
questionnaire. Second, we find little evidence of spurious product switching
in the data:\ less than two percent of firms across the 1987 to 1997
censuses, for example, are observed producing, not producing, and again
producing the same product. Third, the results reported in Table \ref%
{t_firmout} indicate correlations between product-switching behavior and
separately recorded measures of firm characteristics such as size and input
usage that are systematic and consistent with our model. The consistency of
these and other empirical results with the predictions of the model is hard
to square with simple explanations of mismeasurement based on classical
measurement error.

Fourth, we note that we observe similar switching behavior with respect to
even more easily identified four-digit SIC\ industries and two-digit SIC\
sectors. Table \ref{t_nadb_out42} compares firms' extensive-margin
adjustments for products (column 1; reproduced from Table \ref{t_nadb}),
industries (column two) and sectors (column three) using the same typology
of activities as in Table \ref{t_nadb}. The first row of the table records
the average share of firms making no adjustments between census years. Not
surprisingly, product switching (54 percent)\ is more likely than industry
switching (41 percent), and industry switching is more prevalent than sector
switching (16 percent). Even so, product adding induces an average of 27
percent of firms to enter at least one new industry and 9 percent of firms
to break into at least one new sector every five years. To the extent that
adding industries and sectors requires adopting unfamiliar production and
distribution technologies, these findings also suggest that firms'
extensive-margin adjustments involve considerable changes in the nature and
scope of firms.

\begin{center}
TABLE\ 5 ABOUT\ HERE
\end{center}

As a final check, we also examine how product switching varies depending on
the main two-digit manufacturing sector of a firm. We find that the average
percent of firms that alter their mix of products every five years varies
from a low of 33 percent in Stone \&\ Concrete (SIC\ 32) to a high of 71
percent in Printing \& Publishing (SIC\ 27), as reported in Table A4 in the
web-based technical appendix. Product switching therefore appears to be a
pervasive feature of the U.S.\ manufacturing sector that is not driven by
behavior in a few influential sectors.

\subsection{Product-Level Evidence}

In the model, there is a positive correlation between products' add and drop
rates:\ while some firms not producing a product receive a positive demand
shock and therefore add it, some of the incumbent producers receive a
negative demand shock and hence drop it. Variation in product add and drop
rates is governed by the probability of receiving a shock. \textquotedblleft
Turbulent\textquotedblright\ product markets, where idiosyncratic shocks are
more likely, exhibit more frequent adding and dropping, other things equal,
than \textquotedblleft stable\textquotedblright\ products where shocks are
less prevalent. A related feature of product switching at the product level
concerns gross versus net changes in product output. As idiosyncratic shocks
lead different sets of firms to add and drop the same product
simultaneously, the model has gross changes in product output dominating net
changes.

\subsubsection{Product Add Versus Drop Rates}

Figure \ref{f_adddrop} displays the mean rate at which five-digit SIC\
products are added and dropped by U.S. manufacturing firms across the 1987
to 1997 censuses. A product's add rate in year $t$ is computed as the number
of firms adding the product between census years $t-5$ and $t$ divided by
the average number of firms producing the product in both years. Drop rates
are computed analogously. As shown in the figure, there is a clear positive
correlation between the rates at which products are added and dropped. This
correlation is statistically significant at conventional levels.\footnote{%
Existing research on plant creation and destruction finds a positive
correlation between plant entry and exit rates. See for example Dunne et al.
(1989a) for the United States.}

\begin{center}
FIGURE\ 1 ABOUT\ HERE
\end{center}

The positive correlation between the rates at which U.S. manufacturing
products are added and dropped indicates that the extensive-margin
adjustments we observe in the data cannot be explained solely in terms of a
net reallocation of economic activity from one group of products to another.
Such a net reallocation would imply a negative correlation between the rates
of product adding and dropping, as growing products are frequently added and
infrequently dropped, and declining products are frequently dropped and
infrequently added. Although the fact that add and drop rates do not lie
perfectly along a 45 degree line indicates that there is some net transfer
of output across products in the data, other forces are also clearly at work.%
\footnote{%
In the model, a turbulent product with a high probability of idiosyncratic
shocks to demand not only has high rates of product adding and product
dropping but also displays a high volatility of shipments at firms that
continue to produce it. Consistent with this implication, we find a positive
correlation in the data between a product's rate of adding or dropping and
its mean standard deviation of log shipments over time at firms that
continue to produce the product.}

We note that while the positive correlation in Figure \ref{f_adddrop} is
hard to reconcile with pure net reallocation \textit{across} products, it
does not rule out unobserved net reallocation \textit{within} products.
Indeed, in the model, net reallocation within products occurs because some
firms add a product as other firms drop it.

\subsubsection{Product Switching and Aggregate Output}

Our model points to product switching as a new dimension of resource
reallocation that complements the more widely-studied margin of plant or
firm entry and exit. To assess the relative importance of this new dimension
at the product and aggregate level, we decompose a product's output
according to the type of firm producing it. In our first decomposition, we
look backward in time to divide product output in year $t$ according to
firms that produce the product in both $t$ and $t-5$ (\textquotedblleft
incumbents\textquotedblright ), surviving firms that do not produce the
product in $t-5$ but do produce it in $t$ (\textquotedblleft
adders\textquotedblright ), and firms that do not exist in $t-5$ but produce
the product in $t$ (\textquotedblleft entering firms\textquotedblright ), 
\begin{equation}
Y_{tp}=\sum_{j\in B_{tp}}Y_{tpj}+\sum_{j\in A_{tp}}Y_{tpj}+\sum_{j\in
N_{tp}}Y_{tpj},  \label{a_decomp}
\end{equation}%
where $p$ indexes products; $j$ denotes firms; and $B_{tp}$, $A_{tp}$ and $%
N_{tp}$ represent the set of incumbents, adders and entering firms,
respectively.

Our second decomposition is forward-looking and divides a product's output
in year $t$ according to firms that produce the product in both $t$ and $t+5$
(\textquotedblleft incumbents\textquotedblright ), surviving firms that
produce the product in $t$ but not in $t+5$ (\textquotedblleft
droppers\textquotedblright ), and firms that produce the product in $t$ but
die between $t$ and $t+5$ (\textquotedblleft exiting firms\textquotedblright
),

\begin{equation}
Y_{tp}=\sum_{j\in B_{tp}}Y_{tpj}+\sum_{j\in D_{tp}}Y_{tpj}+\sum_{j\in
X_{tp}}Y_{tpj},  \label{d_decomp}
\end{equation}%
where $D_{tp}$ and $X_{tp}$ denote the sets of dropping and exiting firms,
respectively.

The decompositions in equations (\ref{a_decomp}) and (\ref{d_decomp}) are
attractive for our analysis for two reasons. First, because they are based
on the nominal value of output in year $t$, they do not require
product-level price deflators. Second, they can be converted into percentage
decompositions for each product by dividing through by $Y_{pt}$. As a
result, they do not require comparisons of output value across products and
so avoid the problems associated with such comparisons.

The upper panel of Table \ref{t_newdecomp} reports the mean product-value
decompositions in percentage terms across all products. Each row of the
panel reports the average decomposition for a particular census year, with
the first three columns looking backward (adding versus entering) and the
final three columns looking forward (dropping versus exiting). In both cases
we find that roughly two-thirds of the average product's output is produced
by incumbents. The remaining output is more or less evenly split between
firms adding or dropping the product and entering or exiting firms. In 1992,
the only year of the sample for which both decompositions can be performed,
adders and entrants are responsible for an average of 14 and 19 percent of
products' output, respectively, while droppers and exiters account for 15
and 18 percent, respectively.

\begin{center}
TABLE\ 6 ABOUT\ HERE
\end{center}

In Table A3 in the web-based technical appendix, we report the results of a
similar decomposition for the share of firms producing a product in a census
year. While incumbents again make the greatest single contribution, their
average share of firms, at 40 to 45 percent, is lower than their average
share of output. Of the remaining 55 to 60 percent of producers, 29 to 37
percent are entering or exiting firms and 23 to 27 percent are adders or
droppers. In Table A4 in the web-based technical appendix, we report the
results of these decompositions by two-digit sector. While there is some
variation across sectors, we find substantial contributions of roughly equal
magnitude from adders and droppers and entering and exiting firms in each
two-digit manufacturing sector.

The breakdowns reported in Table \ref{t_newdecomp} also highlight the fact
that gross changes in product output are substantially larger than the
associated net changes, an \textquotedblleft excess
reallocation\textquotedblright\ that is similar in spirit to the one found
in job creation and destruction by Stephen J. Davis and Haltiwanger (1992).
Indeed, comparison of the forward-looking 1992 decomposition with the
backward-looking 1997 decomposition reveals that 15 percent of the average
product's 1992 output is accounted for by firms that subsequently drop the
product, while 15 percent of 1997 output is due to firms that just added it.
Over the same period, the change in the average share of output represented
by incumbents was just 3 percent (from 67 to 70 percent).\footnote{%
We find a similar dominance of gross versus net product switching in a
decomposition of\ real U.S. manufacturing growth that separates real output
changes according to firm entry and exit, incumbents' product adding and
dropping and incumbents' continuing-product growth and decline. A
disadvantage of that decomposition relative to the one presented here is its
reliance on industry-level price indexes to deflate the output of all
products within the same industry.}

\subsection{Firm-Product Level Evidence}

In the model, a firm's profitability in a particular product is the result
of an interaction between firm-wide productivity and consumers' taste for
particular firm-products. As a result, firms adding products are likely to
have higher values of firm productivity than firms whose product range
remains constant. Likewise, because consumer tastes are serially correlated
and so are positively correlated with firm-product shipments and the length
of time for which a firm has produced a product, firms are more likely to
drop products that are small (scale dependence) or relatively new to the
firm (age dependence). Finally, variation in consumer taste across products
within firms results in differences in the size of shipments across products
within firms.

\subsubsection{Product Adding}

Firms' product adding decisions are systematically related to their
revenue-based productivity in existing products in the way suggested by the
model. We find a positive association between initial firm revenue-based
productivity and subsequent product adding among firms producing the same
initial mix of products. Table \ref{t_fadd} reports the results of OLS\
regressions of a dummy variable indicating product adding by either SP\
(right panel)\ or MP\ firms (left panel) between 1992 and 1997 on firm
revenue-based productivity in 1992,

\begin{equation}
Add_{jt}=\alpha _{m}+\beta _{1}\text{\textit{Productivity}}_{jt}+\varepsilon
_{jt},  \label{fadd}
\end{equation}%
where $\alpha _{m}$ represents a set of product-mix fixed effects and 
\textit{Productivity}$_{jt}$ is measured in terms of either revenue-based
labor productivity or TFPR. We employ a linear probability model so that
product-mix fixed effects, which allow for a comparison of behavior among
firms producing the same initial set of products, can be included in the
regression. Given that we estimate the regression for a single
cross-section, the product-mix fixed effects control for the level and
change of any product-mix-specific characteristic that influences the
probability of adding a product between 1992 and 1997.\footnote{%
We find similar results for earlier census periods. The analogous
specification when census periods are pooled involves including a full set
of interactions between product mix fixed effects and time fixed effects.
This specification also yields similar results.}

As shown in the two panels of Table \ref{t_fadd}, subsequent product adding
is positively and statistically significantly correlated with both initial
TFPR\ and initial revenue-based labor productivity for both SP\ and MP\
firms. As also shown in the table, this positive correlation remains when
controls for firm size (i.e., employment) and age are included in the
regression. These results are subject to the aforementioned caveats about
the problems of measuring firm productivity when separate data on inputs are
not available by product within firms. Nonetheless, they suggest that the
revenue-based productivity advantage of MP\ firms observed above in Table %
\ref{t_mp}\ is due at least in part to selection:\ SP\ firms who
subsequently become MP\ firms have on average higher revenue-based
productivity than other SP\ firms.\footnote{%
Our finding of a positive correlation between a firm's revenue-based
productivity given its existing product mix and its decision to add a new
product is hard to reconcile with a model in which products are randomly
assigned to firms (see for example Roc Armenter and Mikos Koren 2008). Under
random assignment, there would be no correlation between existing producer
characteristics and the addition of a new product.}

\begin{center}
TABLE\ 7 ABOUT\ HERE
\end{center}

\subsubsection{Product Dropping}

We also find evidence of scale and age dependence in firms' decisions to
drop products in line with the process of selection within firms emphasized
by the model. Table \ref{t_fpdrop} reports OLS\ regressions of a dummy
indicating the dropping of one of a surviving firm's products between census
years 1992 and 1997 on firms' 1992 relative product size (\textit{Size}$%
_{jit}$) and relative product tenure (\textit{Tenure}$_{jit}$) as well as
both firm and product fixed effects:

\begin{equation}
Drop_{jpt}=\alpha _{j}+\alpha _{p}+\beta _{1}\ln (\text{\textit{Size}}%
_{jpt})+\beta _{2}\ln (\text{\textit{Tenure}}_{jpt})+\varepsilon _{jpt},
\end{equation}%
where $j$ and $p$ index firms and products respectively and $\alpha _{j}$
and $\alpha _{p}$ represent firm and product fixed effects, respectively.
The variables \textit{Size}$_{jpt}$ and \textit{Tenure}$_{jpt}$ are defined
in terms of shipments and the length of time for which a firm has produced a
product respectively. Both size and tenure are measured relative to their
averages for the product via log differencing in each census year. As a
result, these variables control for differences across products in output
and tenure, both at a point in time and over time. We note that we examine
the model's firm-product predictions in the context of product dropping
because construction of an analogous adding sample is impractical given the
size of our dataset. Our sample consists of surviving firms and therefore
the estimated coefficients capture the determinants of a firm's decision
whether to drop products conditional on firm survival.

As our regression specification is estimated for a single cross-section of
data based on the decision whether to drop a product between 1992 and 1997,
the firm fixed effects control for any firm characteristic that is common
across products and affects the decision whether to drop a product over this
period (e.g., total firm shipments, the growth of total firm shipments, firm
age, firm productivity, whether a firm is an exporter or enters/exits export
markets, whether a firm has multiple plants). Similarly, the product fixed
effects control for any product characteristic that is common across firms
and influences the decision whether to drop a product (e.g., an aggregate
change in relative demand or supply across products). The coefficients $%
\beta _{1}$\ and $\beta _{2}$ are therefore identified solely from the
variation in shipments and tenure that is idiosyncratic to individual pairs
of firms and products.\footnote{%
We find similar results for earlier census periods. The analogous
specification when census periods are pooled involves including a full set
of interactions between firm and time fixed effects and between product and
time fixed effects. This specification also yields similar results.}

Results are reported with and without firm and firm-plus-product fixed
effects. In all three cases, coefficient estimates indicate that firms are
less likely to drop a product if their shipments and tenure are large
relative to firms producing the same products.\footnote{%
In the model, consumer tastes follow a first-order Markov process, so that
the probability of drawing a new value for consumer tastes depends only on
the current value of consumer tastes. Furthermore, controlling for firm and
product fixed effects, log firm-product shipments are proportional to the
current value of consumer tastes. Therefore, as in much of the firm entry
and exit literature, age or tenure should become insignificant in a
specification that controls appropriately for scale. One natural explanation
for the significance of firm-product tenure in such a specification is that
consumer tastes follow a higher-order Markov process, and the model could be
extended to allow for this possibility.} To the extent that relative
firm-product size and tenure are positively correlated with firm-product
revenue-based productivity, the results in Table \ref{t_fpdrop}~suggest a
systematic reallocation of economic resources within firms towards
activities that generate more revenue per unit of factor input. As a result,
studies of industry dynamics that ignore firms' extensive margins likely
underestimate the role of reallocation in both output and revenue-based
productivity growth.

\begin{center}
TABLE\ 8 ABOUT\ HERE
\end{center}

\subsubsection{Product Switching and Firm Output}

We find that the process of reallocation within firms captured in the model
is quantitatively important at the firm level as well as at the aggregate
level. To illustrate this, we decompose the output of surviving firms in a
given census year according to whether the products are continuously
produced versus recently added or about to be dropped. These backward- and
forward-looking firm-level decompositions are analogous to those used for
products in equations (\ref{a_decomp}) and (\ref{d_decomp}), respectively,
above. Here, however, there is no contribution from firm entry or exit
because the decompositions are undertaken for surviving firms.\footnote{%
We note that the product-level decompositions reported earlier are not
simple averages of the firm-level decompositions reported here for
additional reasons besides the focus on surviving firms. In particular, the
weight of firms in the product-level decompositions varies substantially
depending on their size, and the firm-level decompositions include a firm's
output across all products.} As shown in Table \ref{t_fdecomp}, we find that
on average 26 and 31 percent of firm output in 1992 and 1997, respectively,
is represented by products firms added within the previous five years. A
comparable average share of firm output, 29 and 26 percent for 1987 and
1992, respectively, is accounted for by about-to-be-dropped products. These
shares suggest that product switching exerts considerable influence on firm
activity, and that gross changes in firm output are substantially larger
than net changes.

\begin{center}
TABLE\ 9 ABOUT\ HERE
\end{center}

\subsubsection{Distribution of Product Shipments Within Firms}

To provide evidence on the product heterogeneity within firms featured in
the model, Table \ref{t_pvshare} reports the average share of firm output
represented by each of a firm's products, with products sorted from largest
to smallest. To conform with Census disclosure requirements, we report these
average shares for firms producing up to ten products. We note that firms
producing ten or fewer products represent roughly 99 percent of firms and
roughly half of U.S. manufacturing shipments in our sample. As shown in the
table, the distribution of output across products is highly skewed, with the
average share of firm output attributable to a firm's largest product
declining from 80 percent for firms that produce two products to 46 percent
for firms that produce 10 products.

\begin{center}
TABLE\ 10 ABOUT\ HERE
\end{center}

A commonly used benchmark in the literature on firm size distributions is
the Pareto distribution, which predicts a log linear regression relationship
between the log rank of firm shipments and log firm shipments. To similarly
assess the product-size distribution within firms producing a like number of
products, we estimate an analogous regression of the log rank of
firm-product size on the log of their share of firm shipments.\footnote{%
If the distribution of shipments, $x$, across products within firms shown in
Table \ref{t_pvshare} is Pareto with minimum value $k$ and shape parameter $%
a $, we have Prob$\left( x>x^{\prime }\right) =\left( k/x^{\prime }\right)
^{a} $. Taking logarithms in this expression and rearranging terms yields
the following relationships: $\log \left( Rank_{p}\right) =A-a\log \left(
x_{p}\right) =B-a\log \left( Share_{p}\right) $, where $Rank_{p}$ is the
rank of $x_{p}$, $Share_{p}=x_{p}/X$, and $A$, $B$ and $X=\sum_{p}x_{p}$ are
constants.} We estimate this regression separately for firms producing four,
six, eight and ten products using the data on the average shares of products
in firm output reported in Table \ref{t_pvshare}. The fitted and actual
values for firm-product rank and size in these regressions are displayed in
Figure \ref{fig_withinsize}. As indicated in the figure, actual values lie
above the regression line in the middle of the distribution and below the
regression line in the tails, implying thinner tails than the Pareto
distribution.\footnote{%
Including a quadratic term in log product size in the regression, we find
that a null hypothesis of linearity is strongly rejected at conventional
levels of statistical significance. From a comparison of the tails across
the panels of Figure \ref{fig_withinsize}, the departures from a Pareto
distribution increase with the number of products that firms produce.}
Therefore the heterogeneity across products within firms stressed in our
model displays the same features as the heterogeneity across firms examined
in the firm-size distribution literature (see, for example, Rossi-Hansberg
and Wright 2007).

\begin{center}
FIGURE\ 2 ABOUT\ HERE
\end{center}

\subsection{Alternate Explanations}

Our empirical analysis of product adding and dropping thus far accords well
with features of product switching highlighted by our model of endogenous
product selection. Here, we discuss potential alternate explanations for the
facts we uncover and the extent to which they receive support from the data.

Explanations of product switching fall into three broad categories according
to whether they focus on factors that are specific to products, on factors
that are specific to firms, or on factors that are idiosyncratic to
firm-product pairings. The first category of explanations emphasizes forces
that are product-specific but common to all firms, such as changes in
relative demand (e.g., changing fashions) or relative supply (e.g., changing
technology). Explanations of this form that involve a net reallocation of
economic activity across products, e.g., from \textquotedblleft
cold\textquotedblright\ to \textquotedblleft hot\textquotedblright\
products, are hard to reconcile with the positive correlation between
products' add and drop rates observed in Figure \ref{f_adddrop}.

A second class of explanations for product switching focuses on factors that
are specific to firms but common to products. Positive shocks to a firm's
productivity, for example, might increase the profitability of all products
it could produce, thereby inducing the firm to add previously unprofitable
products. This class of explanations, however, is hard to reconcile with the
fact that firms simultaneously add and drop products across census years.
Such switching suggests that any firm-specific shocks differentially affect
its products, and are therefore firm-product specific. A more fundamental
challenge for both firm- and product-specific explanations of product
switching is our finding that firm-product characteristics are influential
determinants of product switching even after controlling separately for firm
and product characteristics.

The model developed in Section I falls into the third category of
explanations, which concentrates on the role of firm-product attributes in
influencing product switching. In our model, the interaction of
idiosyncratic shocks to firm productivity and firm-product demand fosters
both self-selection of firms and self-selection of products within firms.
Klette and Kortum (2004) -- hereafter KK -- offer an alternate firm-product
approach that emphasizes innovation.\footnote{%
See also Rasmus Lentz and Dale T. Mortenson (2005), Luttmer (2008) and
Chatterjee and Rossi-Hansberg (2008) for other innovation-based models of
firm scope.} In the KK model, products cycle across firms as they exchange
technological dominance. While this model is consistent with some of the
stylized facts we present (e.g., product switching across census years), it
fails to capture others. In KK, for example, the firm-size distribution is
determined entirely by variation in the extensive margin of the number of
products firms produce. In the data, however, we find that the intensive
margin of output per product is quite influential in determining variation
in firm size.\footnote{%
Regressing the log of firm average output per product (the intensive margin)
and the log of firm number of products (the extensive margin) on the log of
firm total output, we find that the intensive margin accounts for around 90
percent of the cross-section variation in firm size.} The KK\ model also
predicts a constant hazard rate -- equal to the economy-wide rate of
creative destruction -- for firms' dropping of products. Here, however, we
find that the probability that a firm drops a product is decreasing in
firm-product shipments and the length of time for which the firm has
produced the product. Though our data motivate the development of the
selection model described above, we believe that extending innovation-based
models to match our new stylized facts is another interesting avenue for
further research.

\section{Extending the Basic Selection Model}

In this section we highlight several dimensions of the data that are less
well captured by either our model or the alternative potential explanations
discussed above, but which point to potentially fruitful lines of future
theoretical and empirical research.

\subsection{Product Coproduction}

Our first set of additional results relates to the types of goods firms tend
to produce together. Table \ref{t_coprod} reports the average annual
frequency, in thousands, with which firms coproduce products within and
across sectors from 1987 to 1997. Dark shading indicates coproduction that
is significantly more frequent than expected based on the individual
probabilities of producing each product, while light shading indicates
significantly less coproduction.\footnote{%
We assess statistical significance by comparing the observed co-production
frequencies to those that would be expected under a null hypothesis that the
decisions to produce row and column product lines are independent. Under
this null, the expected frequency with which a particular pair of major
sectors is co-produced follows an independent Poisson distribution. An
individual cell's deviation from random co-production therefore follows a
standard normal distribution, $\frac{o_{rc}-e_{rc}}{\sqrt{e_{rc}}}\sim
N\left( 0,1\right) ,$ where \thinspace $o_{rc}$ and $e_{rc}$ are the
observed and expected frequencies in row $r\,$\ and column $c$,
respectively. Summing across cells, the statistic for testing whether the
entire matrix of frequencies is generated by random co-production, $%
\dsum\nolimits_{r,c}\frac{\left( o_{rc}-e_{rc}\right) ^{2}}{e_{rc}}$, is
distributed chi-squared.} As shown in the table, the probability that a firm
produces a product in the row sector conditional on production of a product
in the column sector is relatively high within sectors as well as between
sectors that appear related (e.g., Apparel and Textiles, or Electronics and
Industrial Machinery). Furthermore, the matrix of data as a whole rejects
the null hypothesis that the probability a firm produces a product is
independent of the firm's other products (p-value \TEXTsymbol{<} 0.01).

\begin{center}
TABLE\ 11 ABOUT\ HERE
\end{center}

In developing our model, we assumed for simplicity that consumer tastes $%
\lambda _{i}$ were independently distributed across products. As a result,
the only interdependence in firm sales across products arises from firm
productivity $\varphi $, which raises or reduces a firm's sales across all
products proportionately. However, the findings in Table \ref{t_coprod}
suggest richer forms of interdependence, where some pairs of products are
systematically coproduced within firms, while other pairs of products are
systematically produced in separate firms.\footnote{%
Similarly, the co-production findings in Table \ref{t_coprod} sit awkwardly
with the assumption in the innovation-based model of Klette and Kortum
(2004) that the identity of the product to which a firm's innovation applies
is drawn randomly from the set of potential products.} One way of extending
the model to capture richer forms of interdependence is to allow consumer
tastes (or equivalently a product-specific component of productivity) to be
correlated across products. For example, product characteristics that are
highly valued in one product market (e.g., apparel) may be highly valued in
another product market (e.g., textiles). While such an extension would bring
the model closer to the data, this would come at the cost of making the
model considerably less tractable. Nevertheless, achieving greater
understanding of the sources of interdependence in demand or production
technology across products within firms would be useful.

\subsection{Modes of Product Switching}

Our second set of additional results relates to the mode by which firms add
and drop products. There are a variety of ways in which firms can add a
product:\ at existing facilities, at newly constructed plants, or by
acquiring an existing plant from another firm. Similarly firms can drop
products at continuing plants, by closing plants or by selling plants to
another firm.

Table \ref{t_ma} reports the distribution of product adds (top panel) and
drops (bottom panel)\ according to how they are accomplished. As indicated
in the first column of each panel, roughly 85 percent of added and dropped
products, respectively, are added and dropped at existing plants. The share
of the number of products added and dropped through mergers \& acquisitions
(M\&A) is relatively small: less than 10 percent of both adds and drops
involve plant acquisitions or divestitures whether by themselves or in
combination with another mode of product switching. However, as shown in the
second column of each panel, M\&A activity is substantially more important
as a share of the value of products added and dropped, indicating that the
products added and dropped through plant acquisitions or divestitures are on
average larger than those added and dropped through other modes of product
switching. Columns three and four of each panel show that a similar pattern
is observed for the share of firms that add and drop products.

\begin{center}
TABLE\ 12 ABOUT\ HERE
\end{center}

A distinct but related issue is the extent to which M\&A is accompanied by
any of the modes of products switching. Comparing product and
sector-switching according to whether or not firms concomitantly acquire or
divest a plant, we find that firms involved in an ownership change are
relatively more likely to change their mix of products, as reported in Table
A5 in the web-based technical appendix. An average of 94 percent of firms
that engage in M\&A\ activity also alter their mix of products, compared
with an average of 53 percent for firms that do not participate in an
acquisition or divestiture. For sector switching, the importance of M\&A\ is
even more stark: the analogous percentages are 67 and 15 percent.

While our finding that product switching frequently occurs within firms'
existing plants motivates the model's abstraction from M\&A and the creation
of new plants, the introduction of these complementary modes of product
switching is an interesting area for further research.

\section{Conclusions}

The extent to which resources are allocated to their best use is a primary
concern of economics. Virtually all empirical research on reallocation as a
source of industry output and measured productivity growth focuses on plant
or firm entry and exit or changes in the composition of output across plants
or firms. This paper identifies product switching as an important source of
reallocation within firms and analyzes its determinants and consequences.

Guided by a natural extension of existing models of industry dynamics that
allows firms to produce an endogenous range of products in response to
evolving firm and product characteristics, we develop a body of evidence
about this new dimension of firm behavior. Using a novel dataset that tracks
U.S.\ manufacturing output at the level of five-digit products within firms,
we find that firms add and drop products with surprising intensity and
frequency. On average, 54 percent of US\ manufacturing firms alter their mix
of five-digit products every five years, and these adjustments lead an
average of 41 percent of firms to enter new or exit existing four-digit
industries, and 16 percent of firms to extend or contract their set of
two-digit sectors. Overall, we find that the gross contributions of product
adding and dropping to the evolution of aggregate manufacturing output are
as large as the gross contributions of firm entry and exit.

We demonstrate that observed patterns of product switching are inconsistent
with explanations based purely on net reallocation across products and are
more generally hard to reconcile with explanations based on firm or product
shocks alone. In contrast, we find support for the central features of our
extended model of industry dynamics, which emphasizes selection within as
well as across firms. In particular, the model accounts for the positive
correlation across products between the rate of product adding and dropping
and the age and scale dependence observed in the probability a product is
dropped.

Though our basic framework is a good match for key features of the census
data, additional empirical analysis reveals areas in which it might be
extended. In the current version of the model, for example, the only source
of dependence in profitability across a firm's products is the firm's
overall productivity: higher firm productivity raises the profitability of
all products. Empirical examination of firms' product mix, however, reveals
that firms are more likely to co-manufacture products within the same
industry, or within \textquotedblleft linked\textquotedblright\ industries,
e.g., lumber and furniture or electronics and instruments. An extended
version of our model might incorporate demand- or supply-side
complementarities that rationalize these links. Similarly, extending the
model to allow firms to endogenously choose between various modes of product
switching, such as plant creation and M\&A, is another interesting avenue
for future research.

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\noindent \textbf{Ericson, Richard and Ariel Pakes. 1995.} \textquotedblleft
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\noindent \textbf{Foster, Lucia, John Haltiwanger and C. J. Krizan.} 2001.
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\noindent \textbf{Foster, Lucia, John Haltiwanger and Chad Syverson. 2008.}
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\noindent \textbf{Gollop, Frank M. and James L. Monahan. 1991.}
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\noindent \textbf{Jovanovic, Boyan. 1982.} \textquotedblleft Selection and
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\textquotedblleft Productivity Growth and Worker
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\noindent \textbf{Melitz, Marc J. 2003.} \textquotedblleft The Impact of
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Multi-product Firms and Market Structure.\textquotedblright\ \textit{RAND
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Office.

\pagebreak

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