The Effects of Foreign and Domestic Demand
Heterogeneity on Firm Dynamics with Implications to
Aggregate Productivity and Trade
Bernardo S. Blum ∗
Sebastian Claro †
Ignatius Horstmann ∗
David A. Rivers ‡
Preliminary Draft – Please do not cite
May 26, 2017
[Click here for the most recent version]
Abstract
In this paper we study the economic factors that distinguish exporters from non-exporters.
We link detailed Chilean manufacturing data with transaction-level data from customs. The
resulting dataset includes firm- and product-specific information on the prices charged and
quantity sold to each destination country, including the domestic market. We develop a new
methodology that allows us to estimate, along with productivity, markups at the firm, product,
time, and destination level. Our price data, combined with our markup estimates, allow us to
compute measures of marginal costs as well. Our results show that while exporters do have
small cost advantages relative to non-exporters, heterogeneity in the demand faced by firms
in the domestic market is strongly related to export status.
KEYWORDS: Exporting, Demand, Markups, Productivity
JEL codes: F10, F12, L11
∗
Rotman School of Management, University of Toronto
Pontificia Universidad Catolica de Chile and Banco Central de Chile
‡
Department of Economics, University of Western Ontario
†
1
1
Introduction
Ever since Bernard and Jensen (1995) documented that few U.S. firms export and that the ones
that do have higher output and sales and pay higher wages than firms that do not export, economists
have sought to understand the economic fundamentals that make exporters intrinsically different
than non-exporters. Because Bernard and Jensen also documented that exporters have higher
labor productivity, on average, than non-exporters, productivity differences became the obvious
place to look for an explanation. While productivity differences have been shown to provide a
partial explanation for differences in firm exporting decisions (see, for instance, Eaton, Kortum,
and Kramarz (2011)), it has become clear that productivity differences alone cannot fully explain
the export decision. This fact has led researchers to explore other dimensions of potential firm
heterogeneity, specifically, demand-side heterogeneities (see Crozet, Head, and Mayer (2012) and
Hallak and Sivadasan (2013)) and firm-level export entry cost differences (see Das, Roberts, and
Tybout (2007) and Roberts et al. (2017)).
A difficulty that existing studies have had in trying to determine the fundamental differences
between exporters and non-exporters is that the data available do not distinguish sales in each
market the firm serves. Studies utilizing customs data have access to exporters’ foreign sales but
no information on non-exporters (other than that they do not export) or on the domestic sales of
exporters. Out of necessity, these papers can only focus on understanding how well various types
of export firm heterogeneities explain cross-firm differences in observed exporting outcomes –
export prices, quantities, and destinations. On the other hand, studies utilizing manufacturing
survey data have information on domestic sales of non-exporters but typically only have total
worldwide sales for exporters. As such, these studies can only measure an exporter’s average
performance over the domestic and foreign markets the firm chooses to serve. Because export
firms self-select into possibly different foreign markets and may have different market power in
the domestic and foreign markets, these averages may conceal a host of important differences
between exporters and non-exporters. In either case, we have, at best, only an incomplete picture
of what makes exporting firms fundamentally different from non-exporting firms.
Our aim in this paper is to provide greater clarity on this fundamental issue by bringing to
bear information contained in a new, firm-level data set for Chile. This data set combines Chile’s
Annual Manufacturing Survey (ENIA) with Chile’s Customs Database for the years 2002-2009.
With this merged data set, we have information on each firm’s dollar and quantity sales both in
the domestic market and in every foreign market the firm serves. In addition, we have data on the
standard plant-level output and input variables available in manufacturing surveys.
To use these data to their full potential, we develop a new methodology that allows us not
2
only to estimate firm-level production functions and productivities but also markups at the firm-,
time-, product-, and destination-level. Our procedure requires no parametric assumptions on the
demand facing firms in each market and therefore allows for a nonparametric estimation of market
power (markups) across each of the above-mentioned dimensions. It builds on the framework in
Gandhi, Navarro, and Rivers (2017) and exploits our detailed destination-specific data on firmlevel prices and quantities. The key insight in our estimation procedure is that the first-order
conditions for intermediate inputs can be expressed in terms of domestic prices. This allows
us to derive expressions that depend on only the domestic markup and not on demand in other
destinations, thus avoiding the dimensionality problem that arises when the number of foreign
destinations is large. To our knowledge, ours is the first study to provide estimates of firm-level
markups separately for each destination to which a firm sells, including the domestic market.
From these markup estimates, we are able to obtain (local) estimates of the slope of the individual firm demand curves for both home and foreign markets. We use these slope estimates
to provide a linear approximation for the firm demand curve in each market. Combined with
our estimate of the firms’ marginal cost curves, we develop a domestic-market profitability index for every firm. By examining the differences in the components of this index for exporters
and non-exporters, we uncover the economic fundamentals that make exporters different than
non-exporters.
Our main findings are that: i) exporters are significantly more profitable in the domestic market despite not having markedly higher demand intercepts or lower (flatter) marginal cost curves.
Instead, their larger profitability is linked primarily to flatter domestic demands which allow them
to leverage the small cost and demand intercept advantages through larger scale. We also find
that: ii) demand and cost heterogeneity are highly correlated, with high demand associated with
high cost within the firm. This suggests that firms face a trade-off between reducing production costs and promoting their products. By and large, exporters are significantly different than
non-exporters in one of two-ways: exporters that have no clear productivity advantage over nonexporters have a significant domestic demand advantage, while exporters with no clear domestic
demand advantage have a clear productivity advantage. That being said, we still find that: iii)
there is a non-trivial set of exporters that are indistinguishable, in terms of productivity and domestic demand, from non-exporters. In this case, however, we find that these firms have abnormally high foreign demand in the foreign markets they serve. Indeed, many of these firms are
more profitable in foreign markets than in the domestic market, which is rare among the universe
of exporters.
In addition to these main findings, we have a number of other findings that are novel to the
3
literature. We find that a) within firm and product, markups are 9% smaller, on average, in foreign
markets than in the domestic market, and 22% smaller in the firms’ main foreign market than in
the domestic market; b) still within firm and product, firms charge a higher markup when selling
to larger, richer, and farther away countries, and when selling in countries that share the same
language with Chile; c) domestic and foreign profitability are positively correlated, except for
exporters with low domestic profitability, as discussed in the previous paragraph; and finally, d)
despite the positive relationship in profitability, domestic and foreign markups are not correlated
with each other. Although our estimates of domestic and foreign market power are positively
correlated, the equilibrium markups, which also depend on the quantity and pricing decisions of
firms, are not.
In addition to the large literature studying the fundamental differences between exporters and
non-exporters mentioned above, this paper also contributes to the literature on the joint estimation
of production functions and market power (see, for instance, De Loecker and Warzynski (2012)
and De Loecker et al. (2016)). Our finding that firms charge significantly different markups in the
domestic and foreign markets suggest that researchers should be cautious when using firm-level
average markups, in particular to study policy changes such as trade liberalization episodes that
can potentially lead to large changes in the composition of firms’ sales across markets.
2
Data
In order to construct the data for our analysis, we combine two very detailed datasets on manufacturing firms in Chile. The first comes from Chile’s Annual Manufacturing Survey (ENIA), which
covers all manufacturing plants in the country with at least 10 employees. While a standard version of this dataset has been used extensively in the literature (see, for instance, Pavcnik (2002)),
we utilize a restricted-access version that contains much richer information, particularly as it relates to output. The survey also includes the standard plant-level input variables. Specifically, it
provides data on employment and wages, electricity and water consumption expenditures, and expenditures on intermediate inputs. Finally, the survey provides information on plant investment,
which we use to compute a measure of the plant’s capital stock using the perpetual inventory
method.
A key advantage of these data for our purposes is that, in addition to providing value output
measures (revenues), the Manufacturing Survey data contains plant-level domestic and export
sales and the total physical quantity sold for each 3-digit Central Product Classification (cpc) good
produced in the plant. This allows us to compute prices for each product sold by the firm, both
4
for domestic and foreign sales. To allocate plants’ foreign sales to specific foreign countries, we
link the Chilean Annual Manufacturing Survey to Chile’s Customs Database, where all Chilean
export transactions are recorded. These data also measure sales of each product (in both dollars
and quantities) to each foreign destination. Export revenues (and therefore the computed prices)
are free on board (FOB) in that they are net of transportation costs.
The customs data identify the Chilean exporter at the firm level, not at the plant level, and thus
this merge is done at the level of the firm-product-year. The key characteristic of the resulting
merged dataset is that, for the years 2002 - 2009, it contains information at the firm, product,
and year level on both dollar sales and quantity sold to the Chilean domestic market and to every
foreign market the firm sells to.
A few points about these data are worth highlighting. First, the 3-digit Central Product Classification, the level at which we measure products, covers 305 products in all sectors of the economy
and 186 manufactured products. To illustrate, within the beverage industry, the data distinguish
between four products: spirits, liqueurs, and other spirituous beverages (cpc 241); wines (cpc
242); malt liquors and malt (cpc 243); and soft drinks, and bottled waters (cpc 244). Second, as
we will discuss more fully in the methodology section, we estimate production functions at the 3digit ISIC industry level, allowing for the fact that some firms are multi-product firms.1 Given the
data demands imposed by our estimation procedure, our analysis focuses on 9 industries. Table 1
shows summary statistics on these industries. We chose these industries based on the total number
of observations available, the fraction of firms that export, and the uniformity of the measure of
physical units across firms in these industries.2
3
Model
Each observation in our dataset consists of a firm f , selling a product j, to a destination n, in a year
t. Firms are allowed to produce multiple products, and we let Jf denote the number of products
produced by firm f . Firms sell the output they produce to the domestic market, and potentially
to a subset of foreign markets. We let Df jt denote the total number of destinations to which firm
f sells product j in period t. For each observation we observe a vector of quantities and a vector
of revenues corresponding to the output of each product sold to each destination, including the
R
, from
domestic market: Qf jtn , Rf jtn . We can then construct a measure of prices, Pf jtn = Qff jtn
jtn
1
In order to focus on the main products produced, in our empirical analysis we focus on products for which there
are at least 40 firm-year observations.
2
In many cases quantities are measured in a standard unit such as litres or kilograms. However, for some products,
quantities are measured simply in “units”.
5
these data.
P
The total quantity produced of product j by firm f in period t is denoted by Qf jt = n Qf jtn .
Within each industry, the product-specific production function (in logs) is given by:
qf jt = fjt (kf jt , lf jt , mf jt ) + ωf jt ,
where lower-case letters denotes logs, q denotes the output produced measured in quantities, k
denotes capital, l denotes labor, m denotes intermediate inputs, and ω is a persistent (Hicksneutral) productivity shock that is known to the firm when making its period t decisions. The
observed quantity of output is given by
yf jt = qf jt + εf jt ,
where ε is an ex-post shock to output capturing measurement error. Productivity ω is assumed to
follow a first-order Markov process:
ωf jt = h (ωf jt−1 ) + ηf jt .
(1)
Let X ∈ {K, L, M } denote a generic input of the firm. For firms that produce multiple
products, the researcher only observes the total inputs used by the firm:
Xf t =
X
Xf jt .
Jf
Capital and labor are assumed to be chosen a period ahead in period t − 1. Intermediate inputs
are chosen flexibly at period t to minimize costs.
For each product produced by a firm, the firm chooses an allocation of quantities to each
market that it serves in that period, Qf jtn , such that it maximizes profits.3 This static maximization
problem implies a series of first-order conditions which equate marginal revenue in each market
with marginal cost.4
Since firms are assumed to use the same production function to produce output, regardless of
the destination, this implies that the marginal costs are equal across markets (destinations). As a
result, firms will equate marginal revenues across markets, which implies that the ratio of prices
3
Note that we are abstracting away from the choice of which markets to participate in, although the extensive
margin decisions of exporting could be added to the model (see e.g., Roberts et al. (2017)).
4
Recall that our prices are free on board prices that net out the costs of transporting the products to the final
destination market, and therefore our marginal costs reflect the marginal cost of production only.
6
for any two markets (1 and 2) is equal to the ratio of the markups,
Pf jt1
µf jt1
=
,
Pf jt2
µf jt2
(2)
where µf jtn denotes the markup over marginal cost for firm f , product j, in period t, for destination n.
4
Estimation approach
Following De Loecker et al. (2016), we estimate the production function, which varies at the
industry level, using data on single-product firms only. The advantage of this approach is that for
these firms we do not need to make any assumptions about how they allocate inputs to different
products. For the estimation of marginal costs, markups, and productivity, which all vary at the
product level, we will use both single-product and multi-product firms.
Our estimation strategy is based on the approach developed by Gandhi, Navarro, and Rivers
(2017), henceforth GNR. In addition to allowing for multi-product firms, we also extend the
methodology to incorporate data on output prices in order to recover estimates of markups.
4.1
Single-product firms
The first stage of the estimation procedure in GNR is based on the firm’s profit maximization
problem with respect to the choice of flexible intermediate inputs. Since we want to be agnostic
about the particular form of demand, we base our first stage off of the firm’s cost minimization
problem instead.
Letting PtM denote the price of intermediate inputs, the firm minimizes expenditures on intermediate inputs, subject to the production constraint:
minMf t PtM Mf t
s.t. F (Kf t , Lf t , Mf t ) eωf t ≥ Qf t .
This yields the following first order condition
PtM
= λf t
∂Qf t
∂Mf t
,
where λf t is the Lagrange multiplier and represents the (short-run) marginal cost. This expression
7
can be re-arranged to derive an equation relating the observed share of intermediate input expenditures in total quantity of output, the elasticity of output with respect to intermediate inputs ξfMt ,
and the marginal cost:
PtM Mf t
= ξfMt × λf t .
Qf t
Adding the ex-post shocks ε, we have
PtM Mf t
= ξfMt × λf t × e−εf t .
Yf t
Let n = D denote the domestic market. If we multiply both sides of this equation above by
the price charged in the domestic market, and take logs we have
ln
PtM Mf t
Pf tD Yf t
≡ sf tD = ln ξfMt − ln (µf tD ) − εf t ,
(3)
where the LHS is total expenditures on intermediate inputs divided by the total quantity of output
P
valued at the domestic price, and µf tD = λfftDt is the domestic markup. Notice that we could have
multiplied by the price charged in any of the markets served by firm f in period t. The markup
on the right hand side would then correspond to whichever destination’s price was used. The
domestic price is a good choice here since all firms serve the domestic market, and therefore this
price is observed for all firms.
We can generally write domestic quantity demanded as a function of domestic price Pf tD ,
demand shifters zf tD , and an unobserved demand shock χf tD :
Qf tD = Q (Pf tD , zf tD , χf tD ) .
We allow for the demand shock χf tD to enter flexibly, as opposed to a standard multiplicative
demand shock, as we want to allow for firm-specific heterogeneity in markups. This implies that
domestic markups can be written as a function of domestic prices and demand shifters
µf tD = µ (Pf tD , zf tD , χf tD ) .
Since the demand shock is unobserved, we note that under the assumption that the quantity demanded is monotone in χ, we can write χf tD = Q−1 (Pf tD , zf tD , Qf tD ), which implies that the
markup can be written as
µf tD = µ̃ (Pf tD , zf tD , Qf tD )
8
Equation (3) can therefore be written as
sf tD = ln ξ (kf t , lf t , mf t ) − ln µ̃ (Pf tD , zf tD , Qf tD ) − εf t .
(4)
By regressing the modified shares sf tD on inputs, domestic price, domestic quantity, and
demand shifters (such as advertising expenditures), we recover a combined function of the (log)
output elasticity of intermediate inputs and the (log) markup, as well as the ex-post shock ε.5 Since
quantity is measured with error, we can use lagged quantity, or lagged inputs, as instruments in
the first stage.
The second stage of the estimation procedure is also based on GNR. The difference is that we
are estimating the contribution of intermediate inputs to production in the second stage instead
of the first stage. In the baseline setup of GNR of perfect competition, there are no markups to
estimate, and the output elasticity of intermediate inputs is recovered directly in the first stage.
In the standard exercise of estimating a “revenue production function” using deflated revenues as the output measure, the output of different products are all measured in the same units
(value). When using quantities of output directly, one now has to account for the fact that different
products might be measured in different units (for example, kilograms versus litres). In order to
control for this, we can re-write the production function as
qf jt = f (kf t , lf t , mf t ) + γj + ωf t + εf t ,
where γj is a unit adjustment factor for product j. This implies that we can form
ω̃f t = ωf t + γj = qf jt − f (kf t , lf t , mf t ) − εf t .
Imposing the Markovian structure on ω in equation (1) gives us
ω̃f t = h (ω̃f t−1 − γj ) + ηf t + γj .
Combining these two equations gives us:
qf jt = f (kf t , lf t , mf t ) + ε̂f t + h (qf t−1 − f (kf t−1 , lf t−1 , mf t−1 ) − ε̂f t−1 − γj ) + γj + ηf t (5)
Recall that we have already estimated εf t and εf t−1 in the first stage. Since the innovation to
5
To the extent that ex-post shocks capture unanticipated productivity shocks, these may affect the realized output
price, which causes endogeneity in equation (4). We can employ non-parametric IV techniques to address this
problem.
9
productivity is, by construction, mean independent of the firm’s information set in period t − 1,
denoted If t−1 , we have the following conditional moment restriction:
E [ηf t | If t−1 ] = 0,
where If t−1 includes all lags of inputs, all lags of output prices, as well as current capital and
labor (which are assumed to be pre-determined). We can then form a GMM criterion function
using moments in ηf t to identify h and f .
Since (kf t , lf t , qf t−1 , kf t− , lf t−1 , mf t−1 ) ∈ If t−1 , they can be used to instrument for themselves. We can use product fixed effects to control for the γj ’s. This leaves mf t which is determined in period t and correlated with the contemporaneous innovation to productivity η. Previous
work by GNR shows that without additional sources of variation, the output elasticity of intermediate inputs cannot be identified using a second-stage procedure like the one we are proposing.
Fortunately, the observed output prices in our data provide a source of identifying variation, both
across firms and over time. We focus on domestic prices since they are available for each firm,
and to avoid issues of aggregating prices across markets.
Conditional on the total quantity sold, domestic output prices will vary due to domestic demand shocks χ. In addition, variation in the number and identity of destination markets, as well as
their corresponding demand shocks, will provide further variation, as they determine the quantity
sold domestically versus to foreign markets. Overall, firms that can charge higher prices will want
to produce more, and thus will demand more intermediate inputs. To mitigate against concerns
that contemporaneous demand shocks might be correlated with contemporaneous productivity
shocks, we use lagged output prices as instruments (see Doraszelski and Jaumandreu (2013)).
Since these demand shocks are transmitted to the optimal choice of intermediate inputs, we also
use twice lagged intermediate inputs mf t−2 as an over-identifying restriction (recall that mf t−1 is
already included as a control variable).
From our second-stage estimates we recover an estimate of the output elasticity of intermedi∂f (kf t ,lf t ,mf t )
. We can then combine that with our first-stage estimates to back out a
ate inputs:
∂mf t
measure of the domestic markup
\
ln
µf tD
[
−sf tD − εc
f t + ln ξf t
[
= − ln ξ (kf t , lf t , mf t ) −\
ln µ̃ (Pf tD , zf tD , Qf tD ) + ln
ξf t .
=
Once we have an estimate of the domestic markup, we can use relationships in equation (2)
implied by profit maximization, combined with the observed data on prices to each destination,
10
to recover estimates of markups for each export destination n as
µf jtn = µf jtD
4.2
Pf jtn
Pf jtD
.
Multi-product firms
For multi-product firms, a well-known challenge is that we do not observe how firms allocate
inputs to the production of their different products. De Loecker et al. (2016) propose an iterative
procedure in which they assume that productivity for a firm is the same across all products and
use this restriction to back out the input allocations. An alternative approach is to assume that
inputs are allocated proportionally to the revenue shares of each product. For simplicity, and
since De Loecker et al. (2016) note that this alternative approach generates allocations that are
highly correlated with those derived from their iterative approach, we assume that inputs are
allocated proportionally to revenue shares, which are measurable directly from the data. Letting
R
ρf jt = Rffjtt denote the revenue share of product j for firm f in period t, for all inputs X, we have
that Xf jt = ρf jt ∗ Xf t . We can then form a share analogous to the one used in the first stage in
equation (4) for single-product firms:
sf jtD ≡ ln
PtM Mf jt
Pf jtD Yf jt
,
where Pf jtD and Yf jt are the domestic price and total quantity of product j for firm f in period t.
This yields the following first-stage equation for multi-product firms:
sf jtD = ln ξ (kf jt , lf jt , mf jt ) − ln µ̃ (Pf jtD , zf jtD , Qf jtD ) − εf jt .
(6)
This equation for multi-product firms can be estimated in the same way as the version for singleproduct firms in equation (4), with the only difference being that the arguments depend on both
firm and product. Using the estimates of the production function already obtained, we can con∂f (kf jt ,lf jt ,mf jt )
struct the output elasticity of intermediate inputs ξ=
. Using this we can recover an
∂mf jt
estimate of the domestic markup µf jtD from the estimates of equation (6) above. Finally, we can
then recover all of the foreign destination markups in the same fashion as for the single product
firms, using the relationships in equation (2).
11
5
5.1
Results
Production function estimates
For each industry, we estimate a Cobb-Douglas specification of the production function. While
we could estimate a higher-order approximation such as a translog, doing so places additional
demands on the data. In addition, the Cobb-Douglas specification allows us to derive a closedform expression for the marginal cost function which will aid in interpreting the results below.
In Table 2, we report the estimated production function elasticities. Overall the estimates
are quite reasonable, with the exception of the negative capital elasticity estimate for industry
221 (publishing) and a few labor elasticities that are a bit low. We find roughly constant returns
to scale in most industries, with mild decreasing returns in industry 153 (grain mill products,
starches, and animal feeds).
Table 3 reports median and mean firm-level markups by industry. The numbers in this table are
obtained by calculating a revenue-weighted average markup over products, markets, and years for
each firm, and then computing the median and mean across firms. The averages, across industries,
of the median and mean markups are 1.83 and 2.59, respectively—similar in magnitude to what
De Loecker et al. (2016) find for firms in India.
5.2
Markups and marginal costs
Using our estimates of markups and our data on prices, we can construct a measure of marginal
costs for each firm-time-product observation. In this section we describe the patterns of heterogeneity in the markup and marginal cost estimates. The reader should keep in mind that what we
report here are estimates at equilibrium values. As such, these estimates confound the underlying
cost and demand structures facing the firms with quantity and pricing choices made by the firms.
5.2.1
Evidence within firm and product
We first examine how markups vary across markets, for a given firm, product, and year. In Table
4, we compare markups between the domestic and foreign markets. The first column in Table 4
shows that a firm selling the same product both at home and abroad charges a 9.1% lower markup
abroad, on average. The second column compares the markup charged in the domestic market to
that charged in the firm’s main foreign market, defined here as the foreign market that accounts
for the largest share of the firm’s dollar sales. In this case, markups are 22.0% lower in the main
foreign market than in the domestic market.
12
These differences in markups between foreign and domestic markets highlight one of the
advantages of our data. Since we observe detailed information about not only each foreign market,
but also the domestic market, we are able to separately estimate markups for each. The finding
that, on average, firms charge different markups domestically than abroad implies that analyses
focused on foreign markups only, or on an average markup across all markets, can be misleading,
particularly when comparing exporters to non-exporters. Moreover, as we will discuss in the next
section, a firm’s domestic and foreign markups are not correlated, which implies that they are not
good proxies for one another.
In Table 5, we show how foreign markups are related to country characteristics, in particular
to gravity variables, controlling for firm-product-time fixed effects. We find that markups are
higher in export destinations that are larger, richer, and farther away, and in countries that speak
Spanish.
For the majority of our subsequent analysis, we focus on domestic markup/market power as
our main source of demand-side heterogeneity. We do this for several reasons. First, in contrast
to each of the foreign destinations, every firm in our data sells domestically. Therefore, we can
compute a measure of market power in the domestic market for each firm, and use this to compare
across firms. Second, the set of observed foreign markups is selected. It is likely that firms
export to destinations with stronger demand for their products. Third, to the extent that market
power varies systematically between destinations, which our estimates in Tables 4 and 5 above
suggest, then averaging across markets combines differences across firms with differences across
destinations.
5.2.2
Evidence across firms
In Tables 6 and 7, we show how the equilibrium values of both marginal cost and domestic
markups vary across firms, controlling for product and time. On average, exporters have higher
marginal costs and charge higher markups domestically than non-exporters. That being said,
the number of foreign destinations an export firm sells to is not correlated with either the firm’s
marginal cost or markup in the domestic market. The same tables show that marginal cost and
markup are not correlated across firms. Interestingly, the markups firms charge in the domestic
and in its main foreign market are not correlated with each other either. These facts seem to
suggest that domestic market power is not related to costs and does not to transfer into foreign
markets. However, it is important to keep in mind that these are equilibrium values that depend
on the quantity and pricing decisions of firms, in addition to the underlying demand parameters.
Figures 1 and 2 plot the distribution of firms’ domestic markup and marginal cost. The red
13
dashed lines in these figures represent exporters while the blue solid lines represent non-exporters.
Recall that Tables 6 and 7 showed that exporters, on average, have higher marginal costs and
charge higher markups in the domestic market. Figures 1 and 2 reveal that, despite these average
differences, there is considerable overlap between exporters and non-exporters along these two
dimensions. In Figure 3 we plot the domestic markup against the marginal cost for exporters and
non-exporters, and again there is considerable overlap.6
5.3
Demand and marginal cost curves
As mentioned earlier, the markups and marginal costs described in the previous sections are equilibrium outcomes and are potentially affected by the total quantity produced by the firms and by
the quantity sold by the firm in a given market. We would not want to conclude, for instance, that
a firm with a low markup and high marginal cost faces low demand and produces inefficiently,
as these outcomes are consistent with a firm that sells a large quantity in equilibrium and faces
downward-sloping demand and an upward-sloping (short-run) marginal cost curve.
The production function estimates in the previous sections indicate that firms face upwardsloping marginal cost curves over periods in which capital and labor cannot be fully adjusted.
In the long-run, when capital and labor are fully flexible, the estimates indicate that firms have
roughly constant marginal costs.
With respect to markups, because we have not imposed any structural assumptions on demand,
we let the data tell us the relationship between markups and quantity sold. Table 8 shows that
markups are systematically and negatively related to quantity sold. This finding is robust to
using variation across firms, markets, and time as the source of identification. For instance, in
a specification with product-firm-market fixed effects, i.e., using time variation as the source of
identification, a 1% increase in quantity sold is related to 0.32% smaller markups. While this
is admittedly just a correlation, it is worth noting that endogeneity of quantity with respect to
markup would bias this correlation towards zero, thus confirming a true negative relationship
between markups and quantity sold in a market.
5.3.1
Linear demand and marginal cost
In this section we discuss how we can translate our estimates of equilibrium markups and marginal
costs into objects that do not depend on quantity. For simplicity, we drop the time and product
subscripts and let the subscript i denote a firm-product-time combination, which we will refer to as
6
Product-year effects are netted out so we can plot all industries and years on the same figure.
14
a firm. We continue to let n index destinations. Given our estimates of markups, we can calculate
the slope of the demand function at the equilibrium point as bin = (min − 1)/min ∗ (Pin /Qin ).
Note that the parameter bin does not rely on any assumptions on demand. It gives the estimate
of the slope of the firm’s demand curve at the equilibrium price and quantity. We can, however,
use this slope estimate to create a linear approximation of the firm’s demand curve and use this
approximation to back-out consumers’ “willingness-to-pay” (the demand intercept) for the firm’s
product. We specify this approximation as:
pin = ain − bin qin − ηQ−in ,
(7)
where qin is firm i’s output in market n and Q−in is the total output of firm i’s competitors
(following Melitz and Ottaviano (2008)). Given the observed data on prices and quantities and the
measures of bin constructed from the estimated markups, we can estimate the intercept of the firm
demand curve as a0in = ain − ηQ−in . The parameter a0 gives our measure of the “willingness-topay” for a firm’s product in a given market. The slope parameter, b, provides a measure of market
thickness: smaller values of b correspond to flatter demand curves and thus thicker demand.
In a similar way, we can construct a linear approximation to firm i’s (upward-sloping) marginal
cost curve. We let this approximation be given by M C = ci qiT , where qiT denotes the total quantity
produced by the firm. Note that this imposes the Cobb-Douglas restriction that the marginal cost
curve passes through the origin. Under these linear approximations, firm i’s profit maximizing
output (to market n) is given by
T
a0in − 2bin qin = ci qiT = ci qin + ci qi−n
(8)
or
qin =
T
a0in − ci qi−n
,
2bin + ci
(9)
T
where qi−n
denotes the total quantity sold by the firm to all markets other than n. Variation in the
value of qin is thus due to variation in the parameters a0in , bin , and ci , as well as the total quantity
(1−2γ)/γ
sold to other markets. Given our Cobb-Douglas specification, we have that ci = c0i qiT
, with
1
c0i = (P M /γ)[ K α Lβ eωi ]1/γ . The term c0i depends on the productivity of the firm, as well as the
i i
scale of the firm (in terms of capital and labor). Firms with higher productivity or larger scale
have flatter marginal cost curves. Putting this together, we have a solution for qin as a function of
demand and cost parameters:
15
qin =
T
a0in − ci qi−n
2bin + c0i qiT
(1−2γ)/γ
,
(10)
Firms’ profits are given by:
Πin = bin [qin ]2 = bin [
T
a0in − ci qi−n
2bin + c0i qiT
(1−2γ)/γ
]2
(11)
As equation (11) shows, profits depend on quantities, which are equilibrium objects. If we
evaluate this equation at a specific quantity, we can examine how variation in the parameters
a0 , b, and c0 affect firm profitability. Because our ultimate goal is to uncover the fundamental
differences between exporters and non-exporters, we focus on the only market in which both
operate, the domestic market. For each product, we set qiT equal to the median quantity sold
domestically, q̄, and conduct the following thought experiment: Suppose that all firms only sold
domestically. Within the universe of (domestic) market parameters captured by firm profitability,
what would make the firms that actually are exporters look different from those that are nonexporters? Because, under this thought experiment, all firms are only selling domestically, the
T
in the above expression, is of necessity equal to zero. Thus,
quantity sold to other markets, qi−n
for the thought experiment, we can define a profitability index for the domestic market as:
ΠIdx
= bi [
i
a0i
]2
2bi + c0i q̄ (1−2γ)/γ
(12)
This index captures how heterogeneity in the fundamental demand and cost parameters drive
profit heterogeneity for a firm with marginal costs evaluated at the median quantity, were that
firm selling on the domestic market only. Our estimating procedure and the structure we propose
in this section give us estimates of the three key sources of firm heterogeneity: a0 , b, and c0 .
5.3.2
Evidence across firms
Figure 4 shows the distribution of the above domestic profitability index, after controlling for
product-year fixed effects. The red dashed line shows the distribution for exporters while the
blue solid line shows the distribution for non-exporters. Exporters have a significantly larger
profitability index than non-exporters in the domestic market. This finding is confirmed in Table
9. Indeed, exporters have, on average, a 161 log-points higher index than non-exporters. The
index also positively correlates to the number of export destinations of the firm.
In Table 10, we analyze the average difference between exporters and non-exporters for each
of the components of the profit index. We find that exporters have flatter marginal cost curves.
16
The last column indicates that this is due to the scale of the firm and not to higher productivity.7 Exporters have both larger domestic demand intercepts and flatter domestic demand curves,
indicating both a higher willingness to pay, as well as a thicker demand for their products domestically. Figures 5 to 8 show, separately for exporters and non-exporters, the estimated heterogeneity
in the domestic demand intercept and slope, in the slope of the marginal cost curve, and in productivity. Visually, it appears that heterogeneity in the slope of the domestic demand curve is the
most prominent one.
While looking at each component of firms’ profitability individually is informative, it does not
tell the full story. One reason is that demand and cost parameters are likely negatively correlated.
Roberts et al. (2017) find a correlation between firm-specific demand and cost parameters for
Chinese footwear exporters to be 0.709. We find that, after accounting for product-time effects,
the correlation between a0 and c0 is 0.64.
It can also be the case that the underlying components of the profit index interact with each
other. For example, the benefit to firms from having higher levels of demand and flatter marginal
cost curves depends on the thickness of demand (b). If a firm has a very steep demand curve, then
it is not as able to leverage these other advantages. In order to account for both the correlation of
the profitability components and their interactions, we factor the profit index in equation (12) as
2
(a0i )
ΠIdx
=
i
bi
2+
c0i (1−2γ)/γ
q̄
bi
2
(13)
As this equation highlights, the heterogeneity in the profitability of a firm depends on the two
2
(a0 )
c0
components: bii and bii . These two terms capture demand-side and cost-side heterogeneity,
normalized by the thickness of demand. In order to examine how exporters compare to nonexporters along these two dimensions, in Figure 9, we provide a scatter plot of the two, based
on export status. Consistent with our earlier results, there is a positive correlation between costside and demand-side heterogeneity, indicative of a trade-off between incurring higher costs to
produce products with higher demand. Moreover, exporters are shifted both down (lower costs)
and to the right (higher demand). This is also reflected in Table 11, which shows that conditional
on our measure of demand heterogeneity, exporters have lower costs, and conditional on costs,
exporters face higher demand.
To summarize our findings thus far, exporters are significantly more profitable than non7
This finding is similar to that of Rivers (2010) who also uses a gross output production function and models
pricing behavior. A difference here is that we have data directly on the prices charged by firms and do not have to
assume an explicit model for demand.
17
exporters in the domestic market despite not having markedly better demand intercept and cost
parameters. Instead, their larger profitability is linked to flatter domestic demands which allow
them to better leverage small cost and demand intercept advantages through larger scale.
Our analysis so far has focused on short-run profitability, holding capital and labor fixed at
predetermined values. In the long run, firms will optimally adjust their levels of capital and
labor based on their expected productivity and demand. In this case, marginal cost curves will
only differ because of productivity differences. We also have that, from Table 2, firms have
roughly constant returns to scale in the long run so that the firms will have approximately constant
marginal costs. Given these observations, we can construct a long-run profitability index similar
to the short-run one above. This long-run index is given by:
h
ΠIdx
=
i
(a0i
2
− M Ci )
=
4bi
a0
√i
bi
−
M
√Ci
bi
i2
4
where the measure of demand-side heterogeneity is the same as before,
2
,
(14)
(a0i )
bi
2
, but now the measure
of cost-side heterogeneity is given by (MbCi i ) . Under this long-run interpretation, we can see in
Figure 10 that exporting firms continue to have a substantially larger domestic profitability index
compared to non-exporters. As Figure 11 also confirms, exporters continue to be more productive
given domestic demand.
5.3.3
Quality and units
One potential issue with some of the results we have presented thus far is that, even though we
have a measure of output quantity, it may be the case that different firms produce different quality
products that generate different levels of consumption services. If we do not control for this, then
firms that produce higher quality products will appear to be less productive than they actually
are. While our measures of markups are not sensitive to this, our measures of marginal cost
heterogeneity are, as well as the estimated demand parameters (a0 and b).
Such unobserved heterogeneity in quality has the same implications as unobserved differences
in units. For example, suppose firms A and B are equally productive, but firm A produces output
in single units, whereas firm B produces output in bundles of two units, each of which are equally
as valuable as a unit from firm A. In this case, firm A will appear to be twice as productive as firm
B, and therefore with half the level of marginal costs. On the demand side, in terms of our linear
demand approximation, this will lead to a demand intercept for firm A that is half that of firm B,
and a slope that is one-quarter that of firm B.
18
Our long-run measures of cost-side heterogeneity and profitability are robust to this issue
(Figures 10 and 11), as these differences in units cancel out. However, not all of our short-run
2
(a0 )
c0
measures are. The demand measure bii is, but bii is not, and thus similarly for our short-run
profitability index. An alternative approach that is not sensitive to this issue is to use cbii as the
cost-side measure. A drawback is that ci depends on the equilibrium quantity chosen by the firm,
and thus is not an underlying parameter of the firm. Using this as our measure we can rewrite the
profit index in equation (12) as
ΠIdx
= bi [
i
a0i
]2 .
2bi + ci
(15)
In Figure 12, we plot the distribution of this new index by export status. Similar to our results
in Figures 4 and 10, we find evidence that firms that export are more profitable domestically than
non-exporters. In Figure 13, we compare the role of demand and cost heterogeneity in generating
this advantage. Consistent with our previous results, exporters seem to have both lower costs and
higher domestic demand.
5.3.4
Unremarkable at home yet selling abroad
When looking at the combination of cost and domestic demand parameters, exporters perform
significantly better than non-exporters. Yet there are still many firms that export which are not
particularly low-cost or high-demand, as the overlapping left tails of the series in Figure 4 show.
A natural question is why these firms export. One possible explanation is that these firms, which
are unexceptional domestically, face relatively high foreign demand. Our rich data on exports by
destination, and our corresponding estimates across each foreign market, allow us to investigate
this possibility.
We first examine how demand parameters vary across destinations (within firm, product, and
time). Of course this can only be done on the subsample of exporting firms. More precisely, we
compute the firm’s profitability index for each market to which it sells. As we did when building
this index for firms in the domestic market, we evaluate firms’ profits as if they were selling the
median quantity, q̄, in a single market. Column 1 in Table 12 reports results from a regression
of the (log) profit index on a dummy variable for foreign markets, controlling for firm-producttime fixed effects. Column 2 shows the results of the same regression using only observations
from the main foreign market (based on the share of the firm’s sales in dollars). In both cases,
foreign profitability, here driven exclusively by differences in demand since marginal production
costs are common across markets, is found to be lower than domestic profitability. Note that,
19
consistent with the notion that firms self-select into more profitable destinations, the difference
between domestic and foreign profitability is smaller when the foreign market is restricted to the
firm’s main foreign market.
While profitability tends to be lower in foreign markets compared to domestic markets, this
need not be the case for all firms. In order to examine this, we separate our sample of exporters
into two groups, based on whether their domestic profit index is above or below the median
profitability among exporters. We then regress the (log) profit index in each foreign market on the
(log) domestic profit index interacted with an indicator for below median domestic profitability
(controlling for product-time fixed effects). We compute the predicted values from this regression
and plot them in Figure 14 against the domestic profit index.
For both groups of firms, we find that foreign and domestic profits are positively correlated
with each other. On average, a 1% increase in domestic profitability is associated with a 0.22%
increase in foreign market profitability. However, the relationship is about 30% weaker for firms
with lower domestic profitability. In other words, exporting firms with low domestic profitability
have relatively higher foreign profitability. In fact, while for most firms the foreign profit indices
are smaller than their domestic counterparts, for exporting firms with particularly low domestic profitability their exporting profitability is actually higher (above the 45o line). These results
are consistent with the hypothesis that firms that are unexceptional domestically and yet manage
to sell in foreign markets do so because they have particularly strong demand in these foreign
markets. Note that, overall, the foreign profitability indices are still lower for these firms, compared to those of their high domestic profitability counterparts, indicating that these domestically
unremarkable firms will be smaller exporters.
In Figure 15, we show a similar plot, using our measure of domestic demand heterogeneity
(M Ci )2
, instead of domestic profitability. The figure illustrates that domestic demand heterogenebi
ity has a similar pattern, indicating that it is the demand-side that is driving this result.8
6
Conclusion
One of the important messages of this paper is that productivity alone is not a key determinant of
which firms become exporters. Rather, the important fundamental difference between exporters
and non-exporters is that exporters manage to develop products that are large sellers domestically
and do so without suffering significant cost disadvantages. While policies aimed at enhancing
firm productivity benefit all firms—both exporters and non-exporters—they are, by themselves,
8
Recall that the marginal costs of production are the same across destinations.
20
unlikely to promote increased export participation rates. Rather, policies need to focus on making it less costly for successful domestic producers to expand operations and to export products
abroad. Niche products domestically may also be made into successful exporters if the producer
can identify countries for which its product has thicker markets.
21
References
Bernard, Andrew B. and J. Bradford Jensen. 1995. “Exporters, Jobs, and Wages in U.S. Manufacturing: 1976-1987.” Brookings Papers on Economic Activity. Microeconomics 1995:67–119.
Crozet, Matthieu, Keith Head, and Thierry Mayer. 2012. “Quality Sorting and Trade: Firm-level
Evidence for French Wine.” The Review of Economic Studies 79 (2):609–644.
Das, Sanghamitra, Mark J. Roberts, and James R. Tybout. 2007. “Market Entry Costs, Producer
Heterogeneity, and Export Dynamics.” Econometrica 75 (3):837–873.
De Loecker, Jan, Pinelopi K. Goldberg, Amit K. Khandelwal, and Nina Pavcnik. 2016. “Prices,
Markups, and Trade Reform.” Econometrica 84 (2):445–510.
De Loecker, Jan and Frederic Warzynski. 2012. “Markups and Firm-Level Export Status.” American Economic Review 102 (6):2437–2471.
Doraszelski, Ulrich and Jordi Jaumandreu. 2013. “R&D and Productivity: Estimating Endogenous Productivity.” Review of Economic Studies 80 (4):1338–1383.
Eaton, Jonathan, Samuel Kortum, and Francis Kramarz. 2011. “An Anatomy of International
Trade: Evidence from French Firms.” Econometrica 79 (5):1453–1498.
Gandhi, Amit, Salvador Navarro, and David A. Rivers. 2017. “On the Identification of Gross
Output Production Functions.” Working Paper.
Hallak, Juan Carlos and Jagadeesh Sivadasan. 2013. “Product and Process Productivity: Implications for Quality Choice and Conditional Exporter Premia.” Journal of International Economics 91 (1):53–67.
Melitz, Marc J. and Gianmarco I.P. Ottaviano. 2008. “Market Size, Trade, and Productivity.” The
Review of Economic Studies 75 (1):295–316.
Pavcnik, Nina. 2002. “Trade Liberalization, Exit, and Productivity Improvements: Evidence from
Chilean Plants.” Review of Economic Studies 69 (1):245–276.
Rivers, David A. 2010. “Are Exporters More Productive than Non-Exporters?” Working Paper.
Roberts, Mark J., Daniel Yi Xu, Xiaoyan Fan, and Shengxing Zhang. 2017. “The Role of
Firm Factors in Demand, Cost, and Export Market Selection for Chinese Footwear Producers.” Working Paper.
22
Figure 1: Distribution of Domestic Markup Notes: In this figure we plot the distribution of the (log) domestic markup, separately for exporters and non-­‐exporters. The firm-­‐product-­‐year domestic markups are net of product-­‐year fixed effects. 23
Figure 2: Distribution of Marginal Cost Notes: In this figure we plot the distribution of the (log) marginal cost, separately for exporters and non-­‐exporters. The firm-­‐product-­‐year marginal costs are net of product-­‐year fixed effects. 24
Figure 3: Relationship between Domestic Markups and Marginal Cost Notes: In this figure we plot the distribution of the (log) domestic markup against the (log) marginal cost, separately for exporters and non-­‐
exporters. Both markups and marginal costs are measured at the firm-­‐product-­‐year level and are net of product-­‐year fixed effects. 25
Figure 4: Distribution of Domestic Profitability Index Notes: In this figure we plot the distribution of the (log) domestic profitability index, separately for exporters and non-­‐exporters. The index is measured at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 26
Figure 5: Distribution of Domestic Demand Intercept €
Notes: In this figure we plot the distribution of the (log) domestic demand intercept a 0 , separately for exporters and non-­‐exporters. The intercept is measured at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 27
Figure 6: Distribution of Domestic Demand Slope €
Notes: In this figure we plot the distribution of the (log) domestic demand slope b , separately for exporters and non-­‐exporters. The slope is measured at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 28
Figure 7: Distribution of Marginal Cost Curve Slope Parameter €
0
Notes: In this figure we plot the distribution of the (log) marginal cost curve slope parameter c , separately for exporters and non-­‐exporters. The parameter is measured at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 29
Figure 8: Distribution of Productivity Notes: In this figure we plot the distribution of (log) productivity, separately for exporters and non-­‐exporters. Productivity is measured at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 30
Figure 9: Relationship between Domestic Demand and Cost Heterogeneity in Profitability €
€
2
c0
(a0 ) , separately Notes: In this figure we plot the measures of cost-­‐side heterogeneity in profitability against the demand-­‐side heterogeneity b
b
for exporters and non-­‐exporters. Both measures are computed at the firm-­‐product-­‐year level and are net of product-­‐year fixed effects. 31
Figure 10: Distribution of Domestic Profitability Index (long-­‐run measure) Notes: In this figure we plot the distribution of the (log) domestic profitability index, separately for exporters and non-­‐exporters. The index is the long-­‐run version in equation (14) with constant marginal costs. It is computed at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 32
Figure 11: Relationship between Domestic Demand and Cost Heterogeneity in Profitability (long-­‐run measure) 2
2
(a0 ) , Notes: In this figure we plot the measures of cost-­‐side heterogeneity ( MC) in profitability against the demand-­‐side heterogeneity b
b
separately for exporters and non-­‐exporters. The cost-­‐side measure is based on our long-­‐run profitability index in equation (14) with constant marginal costs. Both measures are computed at the firm-­‐product-­‐year level and are net of product-­‐year fixed effects. €
€
33
€
€
Figure 12: Distribution of Domestic Profitability Index (based on c instead of c 0 ) Notes: In this figure we plot the distribution of the (log) domestic profitability index, separately for exporters and non-­‐exporters. The index is the €
€
0
version in equation (15), which uses c instead of c as the cost-­‐side parameter. It is computed at the firm-­‐product-­‐year level and is net of product-­‐year fixed effects. 34
€
€
Figure 13: Relationship between Domestic Demand and Cost Heterogeneity in Profitability (based on c instead of c 0 ) €
2
(a0 ) , separately Notes: In this figure we plot the measures of cost-­‐side heterogeneity c in profitability against the demand-­‐side heterogeneity b
b
for exporters and non-­‐exporters. The cost-­‐side measure is based on our profitability index in equation (15), which uses c instead of c 0 . Both measures are computed at the firm-­‐product-­‐year level and are net of product-­‐year fixed effects. €
€
€
35
Figure 14: Relationship between Foreign and Domestic Profit Indices Notes: This figure plots the predicted values from a regression of the foreign profitability index on the domestic profitability index, a dummy for whether the domestic profitability is below the median, and their interaction (controlling for product-­‐year fixed effects). 36
Figure 15: Relationship between Foreign and Domestic Demand €
2
(a0 ) , on the domestic counterpart, a Notes: This figure plots the predicted values from a regression of the foreign demand-­‐side heterogeneity b
dummy for whether the domestic demand is below the median, and their interaction (controlling for product-­‐year fixed effects). 37
Table 1: Descriptive Statistics
Production, processing and preservation of meat, fish, fruit, vegetables, oils and fats
4%
14%
2%
1%
25%
192
692
134
436
3
3
9
3
8
Number of
Products
151
Manufacture of grain mill products, starches and starch products, and prepared animal feeds
5%
8%
300
6
Number of
Firms
153
Manufacture of other food products
7%
0%
228
Percentage of
Manufacturing
Exports
154
Manufacture of beverages
1%
9%
Percentage of
Manufacturing
Sales
155
Manufacture of wearing apparel, except fur apparel
4%
6
Industry Description
181
Sawmilling and planing of wood
198
ISIC 3
Industry
Code
201
0%
6
1%
94
9
Publishing
18%
201
53
221
23%
2%
2,475
6
Manufacture of basic chemicals
5%
65%
275
241
63%
7%
Manufacture of other chemical products
Total
7%
242
Average
38
Table 2: Production Function Estimates
ISIC 3
Labor
Capital
Industry Elasticity Elasticity
151
0.2455
0.1026
153
0.0535
0.0654
154
0.4339
0.0760
155
0.0295
0.0526
181
0.1732
0.0133
201
0.0845
0.1001
221
0.4063
-0.0418
241
0.0122
0.1049
242
0.1142
0.0693
Intermediate
Input Elasticity
0.7053
0.7752
0.5415
0.8579
0.7743
0.8384
0.6365
0.8829
0.7754
Returns
to Scale
1.0534
0.8941
1.0513
0.9399
0.9609
1.0231
1.0009
1.0000
0.9589
39
Table 3: Summary Statistics—Median and Mean Firm-Level Markups
ISIC 3 Industry
151
153
154
155
181
201
221
241
242
Industry Average
Median
Markup
1.490
1.219
1.260
2.392
2.156
1.778
1.839
2.337
1.997
1.830
Mean
Markup
2.280
1.385
1.356
3.433
2.611
2.053
1.969
4.472
3.756
2.591
Notes: For each firm we compute a revenue-weighted markup (across markets, products, and years). In
this table, we report the median and mean of this distribution.
Table 4: Markups within Firms and across Domestic and Foreign Destinations
Dependent Variable: Log(Markup)
All Markets
Dummy (Foreign Market)
Product-Firm-Year FE
r2
N
Domestic + Main Foreign
-0.091***
(0.02)
Yes
0.76
34417
-0.220***
(0.04)
Yes
0.65
14390
Notes: In this table we report estimates from regressions of (log) markups, at the firm-product-yeardestination level, on a dummy for whether the markup is a foreign destination. In the second column we
include only the domestic market and the main foreign market, which is defined as the market with the
largest value of exports, measured in sales revenue. Both regressions include product-firm-year fixed
effects. Standard errors are reported in parentheses below the point estimates.
40
Table 5: Markups within firms and markets—Gravity
Dependent Variable: Log(Foreign Markup)
Log(GDP)
Log(GDP per capita)
Log(Distance)
Common Language
Product-Firm-Year FE
r2
N
0.005*
(0.00)
0.046***
(0.00)
0.031***
(0.01)
0.040***
(0.01)
Yes
0.86
20712
Notes: In this table we report estimates from a regression of (log) foreign markups, at the firm-productyear-destination level, on a set of gravity variables: the log of gross domestic product (GDP), the log of
gross domestic product per capita, the log of the distance between Chile and the export destination, and
an indicator for whether the main language in the destination country is Spanish. The regression
includes product-firm-year fixed effects. Standard errors are reported in parentheses below the point
estimates.
41
Table 6: Marginal Cost
Dependent Variable: Log(Marginal Cost)
Exporter
0.058**
(0.02)
Log(# Export Destinations)
Product-Year FE
r2
N
Yes
0.75
12458
0.016
(0.01)
Yes
0.72
2578
Notes: In this table we report estimates from regressions of (log) marginal costs, at the firm-productyear level, on a dummy for whether a firm exports a given product in a given year (in the first column)
and the (log) number of export destinations, conditional on exporting (in the second column). Both
regressions include product-year fixed effects. Standard errors are reported in parentheses below the
point estimates.
42
Table 7: Markup in the Domestic Market
Dependent Variable: Log(Domestic Markup)
Exporter
0.079***
(0.01)
Log(# Export Destinations)
-0.004
(0.01)
Log(Foreign Markup)
-0.004
(0.01)
Log(Marginal Cost)
Product-Year FE
r2
N
Yes
0.31
12458
Yes
0.32
12458
Yes
0.29
2578
0.012
(0.01)
Yes
0.31
12458
Notes: In this table we report estimates from regressions of the (log) domestic markup, at the firmproduct-year level, on four different control variables. In the first column we use a dummy for whether a
firm exports a given product in a given year. In the second column we use the (log) number of export
destinations, conditional on exporting. In the third column we have the (log) foreign markup, computed
as the markup for the main export destination, based on the level of export sales. Finally in the fourth
column we regress on the (log) marginal cost. All regressions include product-year fixed effects.
Standard errors are reported in parentheses below the point estimates.
43
Table 8: Markups and Quantity
Dependent Variable: Log(Markup)
Log(Quantity)
-0.130***
(0.00)
-0.117***
(0.00)
-0.328***
(0.00)
-0.079***
(0.00)
Fixed-Effects
r2
N
Product
0.24
34417
Product-Firm
0.53
34417
ProductFirm-Market
0.78
34417
ProductFirm-Year
0.78
34417
Notes: In this table we report estimates from regressions of (log) markups, at the firm-product-yeardestination level, on (log) quantity, with four different sets of fixed effects. Standard errors are reported
in parentheses below the point estimates.
Table 9: Domestic Profitability Index
Dependent Variable: Log(Domestic Profitability Index)
Exporter
1.608***
(0.04)
Log(# Export Destinations)
Product-Year FE
r2
N
0.563***
(0.03)
Yes
0.4
2461
Yes
0.48
11545
Notes: In this table we report estimates from regressions of the (log) domestic profitability index, at the
firm-product-year level, on a dummy for whether a firm exports a given product in a given year (in the
first column) and the (log) number of export destinations, conditional on exporting (in the second
column). Both regressions include product-year fixed effects. Standard errors are reported in
parentheses below the point estimates.
44
Table 10: Domestic Demand and Cost Parameters—Export Status
Dependent Variable
Exporter
Product-Year FE
r2
N
Profit
Index
1.608***
(0.04)
Yes
0.48
11545
Demand
Intercept
0.157***
(0.02)
Yes
0.71
12458
Demand
Slope
-1.775***
(0.07)
Yes
0.58
11545
Marginal
Cost Slope
-0.778***
(0.04)
Yes
0.82
12458
Productivity
-0.039
(0.02)
Yes
0.1
12458
Notes: In this table we report estimates from regressions of the (log) domestic profitability index, and its
components, on a dummy for whether a firm exports a given product in a given year. All regressions
include product-year fixed effects. Standard errors are reported in parentheses below the point
estimates.
Table 11: Relationship between Domestic Demand, Cost Heterogeneity, and Exporting
Dependent Variable
Exporter
Demand
Cost
Demand
-0.535***
(0.03)
0.839***
(0.01)
1.050***
(0.03)
Cost
r2
N
0.55
11545
0.647***
(0.01)
0.59
11545
Notes: In this table we report estimates from regressions of our measures of demand heterogeneity
(
(𝑎0 )
𝑏
2
𝑐0
) and cost heterogeneity ( ), both net of product-year fixed effects, on each other and a dummy
𝑏
variable for export status. Standard errors are reported in parentheses below the point estimates.
45
Table 12: Relationship between Domestic and Foreign Profit Indices
Dependent Variable: Log(Profitability Index)
All Markets
Dummy (Foreign Market)
Product-Firm-Year FE
r2
N
Domestic + Main Foreign
-2.817***
(0.05)
Yes
0.53
29331
-0.772***
(0.05)
Yes
0.88
12929
Notes: In this table we report estimates from regressions of the (log) profitability index, at the firmproduct-year-destination level, on a dummy for whether the markup is a foreign destination. In the
second column we include only the domestic market and the main foreign market, which is defined as
the market with the largest value of exports, measured in sales revenue. All regressions include productfirm-year fixed effects. Standard errors are reported in parentheses below the point estimates.
46