Productivity Differences Between and Within Firms
Rahul Giri†
Kensuke Teshima‡
First Version: June. 2013
Preliminary
Abstract
We document how plants belonging to the same firm are heterogenous in their characteristics and document a previously undocumented margin of aggregate labor productivity
changes: within-firm across-plant reallocation of resources. We draw on newly constructed
Mexican manufacturing plant-level panel data from 2003 to 2010, which allow us to identify which plants belong to which firms, and thus to compare across plants within firm.
We find that plants that have a bigger size within firm (i) are more productive, (ii) pay
higher wages, (iii) are more likely to be export-oriented, and (iv) depend more on imported
intermediate inputs, implying that plant-level heterogeneity documented in the trade literature also holds within firms. We find evidence that reallocation of resources across plants
within firms is a non-negligible part of firm-level labor productivity changes, at least forsome important industries.
Then, we explore the implication of within-firm across-plant heterogeneity on empiricalstudies that use firm-level data or plant-level data without distinguishing firm-plant structure. We find that non-exporting plants within exporting firms enjoy same productivity
levels as exporting plants, suggesting the link between exporting and productivity arises at
the firm level, but not additionally at the plant level. We find that non-exporting plantsof exporting firms did not suffer at all from the trade crisis. These factors induce firmlevel analysis and plant-level analysis on these topics to reach different conclusions, whichsuggests that failing to recognize plant-firm ownership structure could lead to misleading
conclusions in some important questions in international economics.

—————————— ——————————†‡

CIE-ITAM, email: rahul.giri@itam.mx
CIE-ITAM, email: kensuke.teshima@itam.mx

We thank Gerardo Durand, Santiago Avila, Andres Gonzales and Victor Acosta of INEGI for theirtireless assistance with the data. We thank Enrique Seira, Lorenza Martinez and Cesar Hernandez for theircrucial support in early stages of this project, without which this project would not have been possible.
We thank Yoichi Sugita, Akihisa Shibata and seminar participants at KIER and Kyoto Summer Workshop
on Applied Economics for their useful comments.

1

Introduction
Heterogeneity in productivity at the level of firms has been a central focus of recent

research in many fields, in particular international trade and economic growth.1 Firmheterogeneity and its implications on the effects of international trade on industry productivity, individual wages and aggregate welfare have been the most important recent development in international trade since the seminal work by Melitz (2003).2 The literature of
misallocation of resources across heterogenous firms has also exploded since Restuccia andRogerson (2008) and Hsieh and Klenow (2009).3
In most of the empirical applications, researchers have used two types of data: firmlevel data and plant-level data. They use the word “firm” and “plant” interchangeably,
and researchers compare the numbers across studies or statistics that come from firm-level
data and plant-level data.4 This is mostly due to data restrictions: most plant-level data
do not recognize firm-plant structure.5
Recognizing firm-plant ownership structure could be important at least for two related
reasons. First, we could observe what is happening within the firm. In most firm-levelor plant-level data, at least for the ones that researchers in international trade use, one
observation typically corresponds a firm or a plant. The ability to look at plants within afirm allows us to investigate the re-allocations across plants within firms. This re-allocation
within firms is something that is being emphasized in the emerging literature on multiproduct firms either in theory or with calibration exercises (for example, Bernard, Redding
and Schott (2011) and Mayer, Melitz and Ottaviano (2011)), though not directly with
firm-plant linked data.
Second, because of within-firm adjustment, failing to recognize firm-plant ownership1

See Syverson (2011) for a survey on the literature on productivity.
The number of surveys and introductions have also been already many. For example, see Melitz andRedding (2012) for a comprehensive survey and Melitz and Trefler (2012) for introduction of the topic.
3
See Restuccia and Rogerson (2013) for an introduction of the topic and see other papers in the same
volume of the Review of Economic Dynamics.
4
For example, in Hsieh and Klenow (2009), the Chinese data are firm-level data, while the Indian andthe U.S. data are plant-level data.
5
There are studies that use data with firm-plant structure, but they do not exploit within-firm acrossplant heterogeneity.
21

structure and running regressions either at the plant level or at the firm level may lead tomisleading conclusions. For example, what has been regarded as across-plant reallocation
may really be within-firm reallocation. Also, response to a shock may be different at theplant level versus at the firm level.
We draw on newly constructed Mexican manufacturing plant-level panel data from2003 to 2010, which allow us to identify which plants belong to which firms, and thus tocompare across plants within firm. We document several facts that show the importanceof multi-plant firms and within-firm across-plant heterogeneity. Then, we go on to explore
the implication of the failure of recognizing firm-plant ownership structure in analyzing theimpact of trade crisis on employment adjustment.
In terms of the facts, we document the following. First, multi-plant firms are not manybut important. Second, there is a substantial degree of systematic heterogeneity acrossplants within firms. We find that plants that have a bigger size within firm are (i) are moreproductive, (ii) pay higher wages, (iii) are more likely to be exporters, and (iv) depend
more on imported intermediate goods. This pattern is remarkably similar across years.
This finding gives support to models of multi-product firms in international trade such as
Bernard, Redding and Schott (2010) and Bernard, Redding and Schott (2011).
In terms of the implication of this within-firm across-plant heterogeneity on the aggregate labor productivity changes, we find that reallocation of resources across plants withinfirms contributes positively by eight percent to the aggregate labor productivity changes
observed in our data from 2003 to 2008. We show that there is a substantial industrylevel heterogeneity in the importance of this reallocation of resources across plants withinfirms and that the importance is indeed high for industries in which the mechanism could
potentially operate.
Recognizing the firm-plant structure has an important implication in studying the issue
of exporter productivity premium, which is one of the central topics of trade theories
with firm-heterogeneity. We show that non-exporting plants of exporting firms enjoy thesame productivity level as exporting plants of the same firm. The exporter productivity
premium is vastly underestimated in plant-level regressions without recognizing the firm-2

plant structure because such plant-level regressions would not be able to distinguish between
non-exporting plants of exporting firms and non-exporting plants of non-exporting firms.
This raises caution against using only plant-level data in estimating exporter productivity
premium.6
Finally, for the trade crisis period of 2008-2009, firm-level regressions suggest that firmsthat were more export oriented as a whole did not suffer more, while plant-level regressions
suggest that plants that were more export oriented within firms did suffer more than plantsthat were less. Thus, conclusions drawn on the impact of the trade crisis are starkly different
between firm level data and firm-plant level data. This implies that a failure to accountfor firm-plant ownership structure may lead to a misleading conclusion in studies on theimpact of trade and financial crisis on employment adjustment. Importantly, the results
suggest that there is no risk sharing between export-oriented plants and domestic-marketoriented plants within firms. This is consistent with the story that export-market-oriented
plants and domestic-market-oriented plants within firms produce very different products
so a demand shock to one of them cannot be coped at the level of firms.
This paper is related to papers on Multi-product firms. Bernard, Redding and Schott(2010) document the extent of product switching for Multi-product firms. Bernard, Redding and Schott (2011) analyze the impact of trade liberalization on product composition.
Baldwin and Gu (2009) examine product diversification and Arkolakis and Muendler (2010)
analyze multi-destination multi-product firms. To our knowledge, we are the first to document across-plant within-firm heterogeneity of multi-product firms and its implication on
the firm-level and the aggregate labor productivity changes.
[More Literature Review Coming]
This paper is organized as follows. The next section describes the data, and presents
descriptive statistics of plant-level variables and firm-level variables. Section 3 documents
several facts about the importance of multi-plant firms. Section 4 provides evidence ofthe contribution of within-firm across-plant reallocation on aggregate labor productivity.
6

This also suggests that within-firm across-plant heterogeneity in labor productivity may not be comingfrom the export decision, but more analysis exploiting multi-product multi-plant firms and single-productmulti-plant firms is necessary to link the results to theories of multi-product firms.

3

Section 5 presents the results of the analysis of the exporter premium. Section 6 presents theresults of the analysis on how firm-level data and plant-level data provide different answers
for the analysis of the impact of the trade crisis 2008-2009 on employment adjustment.
Section 7 concludes.

2

Data
The data come from the project Statistics of Exporting Firms by the Instituto Nacionalde Estadı́sticas, Geografı́a (INEGI) [National Institute of Statistics and Geography] of
Mexico. This project links plant survey data, namely the Encuesta Industrial Anual (EIA)[Annual Industrial Survey] with the custom transaction data in order for the INEGI tocalculate various statistics of firms that trade and therefore the Mexican government tobetter understand the characteristics of firms that engage in international trade. The EIA
is a longitudinal plant level dataset manufacturing industries, in which plants were thenselected in decreasing order of value of output until the set of selected plants made up 85% of the total value of output (not including maquiladoras, which we turn below) of each6-digit industry covered. The custom transaction data are administrative records of the
Mexican customs agency on every transaction crossing the Mexican border.7 The former
is at the plant level while the latter is at the firm (tax payer id) level. As a by-product,
there is a concordance between firms and plants. The official data span from 2007 to 2010.
We use test data that span from 2003 to 2010, excluding so-called maquiladora plants.8
The link between the custom transaction data and the establishment survey is constructed by the INEGI by the following procedure. First, the Economic Census of 2009carried out by INEGI asks tax payer id. Therefore, for the establishments that existed in
7

The custom transaction data part of the linked data include yearly export and import values for each8-digit tariff classification code for each destination country (origin country in case of imports) for eachfirm, though the current version of this paper does not use the feature of the data yet.
8
Maquiladora plants are assembly plants that participate in a Mexican government export-promotion
program. They are typically selling the most, if not all, of their products to foreign countries, in particular
to the U.S. The reason that the official data start from 2007 is that INEGI had separate surveying systems of non-Maquiladora plants and Maquiladora plants prior to 2007. Therefore, incorporating data on
Maquiladora plants before 2006 in a consistent manner would not be easy. The reason that the test data
start from 2003 is that the sampling scheme of the EIA was refreshed that year.

42009 that provided a tax payer id in the 2009 Economic Census, the concordance between
firm ID and plant ID exists. For the rest of the establishments, INEGI did the linking between the two data using name, address and industry from the both data. The data coverplants that appeared at least once in the custom transaction data either as an exporter oran importer.
The data are not representative in many ways. First, by construction data are limited to firms that have exported or imported at least once in the data period. For big
firms, however, not importing is almost impossible for firms that are more than medium
size. Therefore the data end up covering most of firms with certain size. Second, thedata may be missing for smaller plants of multi-plant firms. However, if anything, theimportance of multi-plant firms and within-firm heterogeneity would be underestimated.9
Third, Maquiladora plants are missing. However, they are very different in terms of theircharacteristics and of responses to trade shocks (Verhoogen, 2008), so we find it reasonable
to focus on non-Maquiladora firms as a first analysis. To sum up, the current data arepractically panel data of medium and large plants excluding Maquiladora plants.
In the following analysis, we regard three-digit Mexican industry code as the unit ofindustry and six-digit Mexican industry code as the unit of product.10 Each plant in
the data report one six-digit industry (product) code. One weakness of the data of thecurrent paper compared to the standard in the multi-product firms literature is that we do
not know what plants produce in detail. Therefore, we regard a firm as a multi-productfirm if it contains more then one plant that report different six-digit industry (product)codes. Our definition of multi-product firms is more conservative than the standard in theliterature in that multi-product firms by our definition would be also classified as multiproduct firms by the standard in the literature while the opposite is not true as we cannot
capture the cases a plant produces products other than what they report as their main
9

For 2009, we cross-checked with the Economic Census and the importance of multi-plant firms is indeed
bigger. The results are available upon request.
10
Mexican industry code is based on Sistema de Clasificación Industrial de América del Norte (SCIAN),
which is consistent with North American Industry Classification System (NAICS), which is a joint effort
to harmonize industry classifications among the US, Canada and Mexico. A three-digit Mexican industrycode is called a subsector (subsectro) and a six-digit Mexican industry code is called a clase de actividad(activity class) in the SCIAN system.

5

product. We believe that the numbers we calculate give lower bounds for the importanceof multi-product firms and the mechanism that are specific to them, such as reallocationof resources with firms across plants that produce different products. Table 1 shows anexample of how disaggregated each digit is.
Table 2 shows the summary statistics of key variables in 2003, the initial year of thedata.11 The variables shown are the number of workers, exporter dummy, export sales
divided by total sales, importer dummy (1 if a plant reports non-zero imported intermediatecost), and imported material cost divided by total cost.12 We sum up the values at theplant level to create variables at the firm level. The number of plants is 2629 while thenumber of firms is 2289, suggesting that the number of multi-plants firms is not large. In
terms of the number of workers, the mean from the plant-level data is around 300 whilethat from firm-level data is around 350, implying that plants belonging to multi-plant firms
are relatively large. The mean of the exporter dummy, the fraction of exporting plants orfirms is 50 % for the plant-level data and 53% for the firm-level data, suggesting that there
are instances in which a firm has at least non-exporting plants and exporting plants. The
same is true for importers.
Table 3 shows the same summary statistics for plants single-plant firms and multi-plantfirms separately. For the latter, the statistics both at the plant level and firm level arepresented, allowing us to see the difference between the plant-level statistics and firm-levelstatistics for the subset of the sample that the difference could potentially arise. Comparing
Columns (1) and (3), which is a comparison at the firm level, multi-plant firms hire more,
and are more likely to export and import than single-plant firms. However, comparing
Columns (1) and (2), which is a comparison at the plant level, the same is true only forthe number of workers. Columns (2) and (3) show that the statistics from the plant level
and at the firm level are very different, in particular for exporter and importer dummies.
The fraction of exporting plants or firms is 43% for the plant-level data and 64% for thefirm-level data, and the fraction of importing plants or firms is 57% for the plant-level11

The pattern is similar across years except that the ratio of plants and firms that use imported intermediate is declining over years.
12
In constructing the exporter and importer dummies, we used the EIA.

6

data and 77% for the firm-level data. This implies that there are many non-exporting or
non-importing plants belonging to firms with at least one exporting or importing plants.
Related to this point, in Section 6, we present the results of the analysis on how firm-level
data and plant-level data provide different answers for the analysis of the impact of the
trade crisis 2008-2009 on employment adjustment.
Table 3 shows also that multi-plant firms are really large in size: the average number ofworkers at the firm level is 1911. In order to see the implication of this, Table 4 shows theshare of top 5 plants and 5 firms in the industry-level employment. We can see that there
is an important difference for some industries, in particular, the food industry (311), thepaper industry (322), the chemical product industry (325), the fabricated metal productindustry (332) and the transportation equipment industry (336). This raises caution against
calculating concentration measures with plant-level data to use in the analysis.

3

Facts
Fact 1: Multi-plant firms are not many, but important.
Table 5 shows that multi-plant firms are not many-about 20 % total number of plants.

However, they occupy 40 percent of total employment and 60 percent of total productionin our data. This means that their behavior is important economically, and their withinfirm across-plant adjustment behavior could potentially have important implications. Thispattern is stable across years.
Table 6 shows the similar statistics within multi-plant firms, distinguishing between
multi-plant single-product firms and multi-plant multi-product firms.13 Among 40-50 %of the about 500 plants that belong to multi-plant firms are multi-industry firms. Amongthe multi-plant firms the share of multi-product firms in employment and production isabout half. However, their share in exports is 75 percent to 85 percent, suggesting thatmulti-industry firms are concentrated in exporting industries.
13

As is noted in the data section, we regard firms are multi-product firms if they contain at least twoplants that report different products as their main products.

7

Fact 2: Even for the case of Multi-plant firms, their main industry activity occupies avery high share.
Table 7 shows that even for multi-plant multi-product firms, their main product (the6-digit industry code that occupies the largest share in the firm-level total sales) occupies
75 percent to 80 percent of firm employment and firm sales and 90 percent of export
sales. This suggests that on average and on aggregate their activities are concentrated
to the most important activities. This is consistent with the idea of core competency inthe multi-product models (Bernard, Redding and Schott (2011) and also Arkolakis andMuendler (2010)). Again, this pattern is stable across years.
Fact 3: Plants within Multi-plant firms exhibit substantial degree of heterogeneity inlabor productivity both across and within industry.
Table 8 reports R2 of the following regressions.

LogLaborP roductivityijst = λst + ijst(1)

LogLaborP roductivityijst = µit + ijst(2)

where i, j, s and t denote firm, plant, sector (or product) and year, respectively. For
the first regression, we use the three-digit-industry-code (what we call industry)- year fixed
effects, four-digit-industry-code-year effects and six-digit-industry (what we call product)code-year effects. The idea of these regressions is to know how much the variation inplant-level labor productivity can be explained by industry-level factors and firm-levelfactors. Columns (1) (2) and (3) report that three-digit industry, four-digit industry andsix-digit-industry (product) effects explain 21 %, 31% and 50% of the variation in plantlevel labor productivity. This means that more than half of the variation in plant-level
labor productivity comes from plant-specific factors within industry or within product.
Columns (4) reports that firm effects explain 78 % of the variation in plant-level labor8

productivity. This explanatory power is much better than any of industry or product fixed
effects. However, this also means that 22 % of the variation in plant-level labor productivity
cannot be explained by firm-level factors.
In order to show further the degree of within-firm across-plant heterogeneity in laborproductivity, Table 9 shows the ranking of the most productive and not most productive(in terms of labor productivity) plants, within firms, in the product distribution of several
key variables. This comparison is done separately for single-product and multi-productmulti-plant firms. We first construct percentile for each plant’s variables within product,
then compare them between the most labor productive plants within firm and not themost labor productive plants within firms. For single-product multi-plant firms, plantsthat are not the most productive plants within firms are at 55th percentile in terms of theirproduction, which means that these plants’ production is on average just slightly bigger
than the median of the plants that produce the same product. Plants that are the mostlabor productive plants within firms are at 68th percentile, which means that these plants’production is on average close to top 30 percent of the industry. The most remarkabledifference can be seen in labor productivity itself. For both single-product multi-plantfirms and multi-product multi-plant firms, plants that not most labor productive withinfirms are just above the median of the plants producing the same product, while plantsthat are most labor productive within firms are on average close to top 20 percent laborproductive plants within industry.
Fact 4: Bigger Plants within Multi-plant firms are more likely to be more productive,
paying higher wages, being exporters and being importers.
Table 10 shows the results of the following regression:

Yijt = βCostShareijt + λit + ijt

(3)

where i, j and t denote firm, plant and year, respectively; Yijt is the log of the average
9wage per worker, export orientation (exports divided by total sales), imported material
dependence (imported material cost divided by total material cost) and energy intensity(energy-related expenditure divided by total sales), which could arguably capture bettermachines or better technology.14 For all multi-plant firms, we find strong evidence thatplants that have a higher cost share pay higher wages, are more export oriented, are more
dependent on imported materials, and are more energy efficient. For the first three variables, the results hold both for single-product multi-plant firms and multi-product multiplant firms, though we do not have good explanations for the difference of coefficients
between them. Table 10 suggests that plant or firm-level heterogeneity documented by theinternational trade literature holds also across plants within firms.

4

Importance of Between-Plant Within-Firm Reallocation
In this section, we decompose aggregate labor productivity changes into firm-level laborproductivity changes and changes that are due reallocation of shares across firms. Furthermore, in addition to the standard practice, we decompose firm-level labor productivity
changes into plant-level labor productivity changes weighted by plants’ share in firm’s total
workforce and changes that are due reallocation of the labor shares across plants withinfirms. This will allow us to assess whether changes in labor productivity at firm level are
driven by within-plant changes in productivity or across plant reallocation of workforce
within firms. The quantitative magnitude of the latter reflects the quantitative importanceof the new mechanism highlighted in recent theories of multi-product firms.15
P
Define the following variables. Lt =
Lit ,sit = LLitt and yit = LYitit . This means that theaggregate labor in our data at time t is the sum across labor of individual firms at time t;
14

Gutierrez and Teshima (2011) relate this variable and other environmental performance measures tointernational trade.
15
Some of the labor productivity changes within plants within firms could be really across-product withinfirm changes. Therefore, our estimates would give the lower bound of the importance of the mechanism. We
also further decomposed the between-plant within-firm component into the one coming from multi-productfirms and and the one coming from single-product firms. The result is available upon request.

10

sit is the share of firm i in terms of labor; and yit is labor productivity of firm i at time t.
Then, the aggregate labor productivity is the weighted average of firm-level productivity.

yt =

X

sit yit(4)

The changes in the aggregate labor productivity can be decomposed into the threecomponents in the RHS of the following equation.

Reallocation

}|X
{
zX
X
4y =
(4yi si0 ) +(yi0 4si ) +(4yi 4si )
i

|

i

{z

}

W ithin−F irm

|

(5)

i

{z

}

Between−F irm|{z

Cross−F irm}

where yi0 is the initial labor productivity of firm i, si0 is the initial labor share of firmi, 4yi and 4si are changes in firm i’s labor productivity and labor share, respectively.
The first term in the RHS is the within-firm component, because this component comesfrom labor productivity changes of each firm. The second term in the RHS is the betweenfirm component, the component coming from the changes in shares holding the initial
productivity fixed. This term is positive if on the average labor goes to more productive
firms. The third term in the RHS is the cross-firm component, the component coming fromboth the changes in shares and the changes in labor productivity. This term is positive if
on the average labor goes to firms whose productivity is growing. We call the betweenfirm component and the cross-firm component together as reallocation component as bothinclude the component coming from the share changes.
Now, due to the advantage of our current data, we can further decompose 4yi , using asimilar argument above.

11

Reallocation

4yi =

X

(4yij sij0 ) +

j∈i

{z

|

}

W ithin−P lant

z
X

}|X
{
(yij0 4sij ) +(4yij 4sij )

j∈i

j∈i

|

{z

}

Between−P lant|{z

Cross−P lant

(6)}

Putting the two equations, above, together, we can decompose the aggregate laborproductivity changes into the following five components.

XXX
XX[ (yij0 4sij ) +(4yij 4sij )]si0[ (4yij sij0 )]si0 +

4y =

i

i

j∈i

{z

|

}

j∈i

{z

|

W ithin−F irm−W ithin−plant

W ithin−F irm−Reallocation}X(yi0 4si )|{z}
Between−F irm
XXXXX[ (yij0 4sij ) +(4yij 4sij )]4si+[ (4yij sij0 )]4si +

+

i

|

i

j∈i

{z

}

Cross−F irm−W ithin−plant

j∈i

{z

|

Cross−F irm−Reallocation}

Table 11 shows the results of the above decomposition for the three types of periods
separately: (1) from 2003 to 2008, which we call the normal period, (2) from 2008 to
2009, which we call the crisis period and (3) from 2009 to 2010, which we call the recovery
period.16 Column (1) of Table 11 suggests that the most of productivity changes is explainedby the within-firm component of which the within-firm reallocation component explainseight percent. Eight percent may not sound large, but note that this is the contribution
to the aggregate labor productivity changes in our data, of which single-plant firms forwhich the within-firm across-plant reallocation component cannot operate occupies around
60 percent of employment and 40 percent of production. Therefore this suggests thatthe magnitude is much larger for firms for which this mechanism is relevant. The signs of
Between-firm and Cross-firm components are both negative, indicating that the reallocation
16

The margin of adjustment in terms of Mexican exports for the three periods is analyzed in detail in
Giri, Seira and Teshima (2012).

12

across firms contributed negatively in aggregate labor productivity changes.17 The term
Residual captures the residual component that comes from entry and exit of firms.18 The
fact that this term is positive means that on average plants that are more labor productive
than the average entered or plants that are less labor productive than the average exited,though we would not want to emphasize this result as the data are not well suited to capture
this component. Column (2) of Table 11 suggests that within-firm reallocation component
contributes negatively to the aggregate labor productivity growth by 25 %. This suggeststhat more labor-productive plants within firms lost their employment share during the tradecrisis. This may be because that the trade crisis made exporting plants suffer more thannon-exporting plants within firms and the former is more labor-productive than the latter,as is suggested by Table 10. Column (3) of Table 11 suggests that within-firm reallocation
component is not important at all in the recovery period. The asymmetry between thecrisis period and the recover period will be analyzed in our future work.
We did the same exercise separately for each 3-digit industry, and Table 12 shows thelist of five industries in which the within-firm reallocation component occupies more than
10 % in the absolute term. We can see that the steel product industry and the food industry experience negative contributions of the within-firm reallocation component, while thetransportation equipment industry, the chemical product industry and the paper industry
experience substantially positive contributions of the within-firm reallocation component.
Again, note that this is the contribution to the aggregate labor productivity changes inour data as a whole; the magnitude could be much larger for firms for which this mechanism is relevant. These five industries are also the industries in which we documented thedifference between the share of top 5 plants and that of top 5 firms in industry-level employment in Table 4, suggesting that within-firm across-plant reallocation in important for
the industries in which this mechanism is relevant. How is the importance of within-firm
reallocation systematically correlated with industry characteristics and changes in trade
exposure is left for future work.
17

This is typical in the literature. See Pages, Pierre and Scarpetta (2009) for the cases of Latin Americancountries.
18
This term is not expressed in the above equation.

13

5

Exporter Premium
In this section, we investigate the implication of firm-plant structure on the exporter

wage and productivity premia. We estimate the following equation.

Yijpt = β1 F irmExporterDummyit + β2 P lantExporterDummyijt+ β3 M ultiP lantF irmDummyit + λpt + ijpt

(7)
(8)

where i, j, p and t denote firm, plant, product and year, respectively; Yijt is the average
wage per worker, employment, or labor productivity (all in logs). The key in this equationthat there are two exporter dummies, one at the firm level, and the other at the plant level,
which allows us to analyze whether exporting plants within exporting firms perform better
than non-exporting plants within exporting firms. By construction, the plant-level exporter
dummy is necessarily zero if the firm-level exporter dummy is zero, and the two dummies
are necessarily the same for single-plant firms. For this analysis, we use all the data, notrestricting to multi-plant firms, to make the analysis closer to the typical empirical setting.
Therefore, we control the multi-plant firm dummy.
Table 13 shows the results. Column (1) shows that plant-level employment is higher if
the firm a plant belongs to is an exporter, and is also even much higher if the plant itself is
an exporter. Column (2) shows that the plant-level average wage per worker is higher if thefirm a plant belongs to is an exporter, and is also additionally higher if the plant itself is anexporter, though this additional impact is only marginally statistically significant. Column(3) shows that the plant-level productivity is higher if the firm a plant belongs to is anexporter, but not additionally higher if the plant itself is an exporter. The point estimateof the coefficient on the plant exporter dummy is also very small (0.013), compare to thaton firm exporter dummy (0.220). The results together suggest that the correlation between
labor productivity and exports is determined at the firm level, the correlation between
employment and exports determined at the plant level, and the correlation between wages

14

and exports is in between.19 This results suggest that the productivity is first determinedat the firm level and firms decide how to allocate resources across different plants.
To further corroborate this point, we run the following equation separately at the plantlevel and at the firm level.

LogLaborP roductivityipt = β1 ExporterDummyit + (β2 M ultiP lantF irmDummyit ) + λpt + (9)iptwhere i, p and t denote firm or plant, plant, product and year, respectively.20 We
run the regressions both with and without the dummy for multi-plant firms because theregressions with it are consistent with the previous table while the regressions without it areconsistent with the typical empirical setting in which the plant-firm structure information
is not available.
Table 14 shows the results. With or without the the dummy for multi-plant firms, theexporter premium on labor productivity is substantially higher for the firm-level regressions
than for the plant-level regressions. This is consistent with the argument above that the
productivity is first determined at the firm level and that therefore non-exporting plantsof exporting firms enjoy the same productivity level as exporting plants of the same firm.
This is correctly captured in the firm-level regressions, but not in the plant-level regressions,
therefore, the exporter productivity premium is vastly underestimated in the plant-level
regressions. This raises caution against using only plant-level data in estimating exporterproductivity premium.21
19
Exporting plants may be willing to pay high wages than non-exporting plants of the same firm even
if their productivity are same if exporters produce higher-quality products than non-exporters and theformer need to pay higher wage to solicit workers’ effort. See Verhoogen (2008) for such a model.
20
Note that subscript i could denote plant in this analysis.
21
This also suggests that the substantial heterogeneity in labor productivity within firms across plants
documented earlier in this paper may not be due to the co-existence of exporter plants and non-exporting
plants within same firms. More analysis exploiting multi-product multi-plant firms and single-productmulti-plant firms needs to be done, however, to link the results of this section to theories of multi-productfirms.

15

6

Impact of the Crisis on Employment
Finally, we investigate the impact of the trade crisis 2008-2009 on employment changes

using both firm-level data and plant-level data to compare how the two data could lead todifferent conclusions. For the firm-level data, we run the following regression for multi-plantfirms.

4Employmenti2009−2008 = βExporterDummyi2008 + it(10)

ExporterDummyi2008 is one for a firm if at least one plant belonging to the firm wasexporting in 2008. Column (1) of Table 15 shows the result of this regression, and we finda statistically insignificant and small β. This suggests that exporting firms were no lessworse off than non-exporting firms. However, doing the same regression at the plant levelshows a very different picture. For the plant-level data, we run the following regression.

4Employmentij2009−2008 = βExporterDummyij2008 + (λi ) + ijt

(11)

Columns (2) (3) (4) of Table 15 show the results of this regression. Columns (2) showsthat exporting plants suffered much more than non-exporting plants and the impact isstatistically and economically significant: Exporting plants reduced more than 200 workers
than non-exporting plants. Columns (3) shows the results of the regression replacing theplant-exporter dummy with the firm-exporter dummy and shows that the analysis withthe firm-exporter dummy fails to capture this effect. Columns (4) shows the results of
the regression using plant-exporter again and with firm fixed effects. Thus, the effect of
the crisis on employment is significant and starkly different between exporting and nonexporting plants within a firm; but the effect is absent when the unit of analysis is thefirm.22
22

This is consistent with the negative contribution of the within-firm reallocation components in thecrisis period shown in the previous section.

16

To sum up, for the trade crisis period of 2008-2009, firm-level regressions suggest thatfirms that were more export oriented as a whole did not suffer more, while plant-level
regressions suggest that plants that were more export oriented within firms did suffer morethan plants that were less. This implies that a failure to account for firm-plant ownership
structure may lead to a misleading conclusion in studies on the impact of trade and financial
crisis on employment adjustment using the firm-level data. Specifically, it would be wrong
to conclude that exporter did not suffer from the trade crisis in term of employment basedon the result of the firm-level regression in our context. Also, this suggests that there is norisk sharing between export-market-oriented plants and domestic-market-oriented plants
within firms and that this finding is consistent with the story that export-oriented plants
and domestic-market-oriented plants within firms produce very different products so ademand shock to one of them cannot be coped at the level of firms.23

7

Conclusion
We document how plants belonging to the same firm are heterogenous in their charac-

teristics and illustrate how the patterns are consistent with leading models of multi-productfirms advanced by a recent strand of the international trade literature. We draw on newly
constructed Mexican manufacturing plant-level panel data from 2003 to 2010, which allow
us to identify which plants belong to which firms, and thus to compare across plants withinfirm. We find that plants that have a bigger size within firm are (i) more productive (ii)paying higher wages (iii) more likely to be export-oriented and (iv) depending more on
imported intermediate inputs, implying that plant-level heterogeneity documented in the
trade literature also holds within firms. We also find evidence that reallocation of resources
across plants within firms is a non-negligible part of firm-level labor productivity changes,
at least for some important industries. We also illustrate how failing to recognize plant-firmownership structure could lead to a misleading conclusion in the analysis of the impact of23

See Verhoogen (2008) for a model in which exporting plants and non-exporting plants end up producing
goods with different quality within industry. Our results suggest that this type of heterogeneity exists even
within firms across plants.

17

trade crisis. Our analysis on within-firm across-plant heterogeneity and its implications
on overall labor productivity changes gives support to claims that the mechanism of productivity changes highlighted by recent theories of multi-product firms is quantitatively
important.
Additionally, we show that plant-level and rm-level analysis could give different results
to the analysis of the exporter productivity premium and the impact of trade crisis, suggesting that failing to recognize plant-rm ownership structure could lead to misleading
conclusions in some important questions in international economics.

18

References
Arkolakis, Costas, and Marc-Andreas Muendler. 2010. “The extensive margin ofexporting products: A firm-level analysis.”
Baldwin, John, and Wulong Gu. 2009. “The Impact of Trade on Plant Scale,
Production-run Length and Diversification.” In producer dynamics: New Evidence frommicro data. 557–592. University of Chicago Press.
Bernard, Andrew B, Stephen J Redding, and Peter K Schott. 2010. “MultipleProduct Firms and Product Switching.” American Economic Review, 100(1): 70–97.
Bernard, Andrew B, Stephen J Redding, and Peter K Schott. 2011. “Multiproductfirms and trade liberalization.” The Quarterly Journal of Economics, 126(3): 1271–1318.
Giri, Rahul, Enrique Seira, and Kensuke Teshima. 2012. “Did Trade Crisis AffectDifferent Exporters Differently? Case of Mexico.” Unpublished.
Gutierrez, Emilio, and Kensuke Teshima. 2011. “Import Competition, Technology
and Environmental Performance: Evidence from Mexico.” Unpublished.
Hsieh, Chang-Tai, and Peter J. Klenow. 2009. “Misallocation and Manufacturing
TFP in China and India.” The Quarterly Journal of Economics, 124(4): 1403–1448.
Mayer, Thierry, Marc J Melitz, and Gianmarco IP Ottaviano. 2011. “Market Size,
Competition, and the Product Mix of Exporters.”
Melitz, Marc J. 2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica, 71(6): 1695–1725.
Melitz, Marc J., and Daniel Trefler. 2012. “Gains from Trade When Firms Matter.”
Journal of Economic Perspectives, 26(2): 91–118.
Melitz, Marc J., and Stephen J. Redding. 2012. “Heterogeneous Firms and Trade.”
National Bureau of Economic Research, Inc NBER Working Papers 18652.

19

Pages, Carman, G. Pierre, and S Scarpetta. 2009. Job Creation in Latin America
and the Caribbean : Recent Trends and the Policy Challenges. Macmillan.
Restuccia, Diego, and Richard Rogerson. 2008. “Policy Distortions and Aggregate
Productivity with Heterogeneous Plants.” Review of Economic Dynamics, 11(4): 707–
720.
Restuccia, Diego, and Richard Rogerson. 2013. “Misallocation and productivity.”
Review of Economic Dynamics, 16(1): 1–10.
Syverson, Chad. 2011. “What Determines Productivity?” Journal of Economic Literature, 49(2): 326–65.
Verhoogen, Eric A. 2008. “Trade, Quality Upgrading, and Wage Inequality in the Mexican Manufacturing Sector.” The Quarterly Journal of Economics, 123(2): 489–530.

20

Table 1: Example of Industry and Product List: Case of Lather and Shoe
Industries.
Industry Code
316
-3161
...
-3162
–316211–316212–316213–316214–316219-3169...

Industry Name
Leather Industries
...
Shoes
Leather shoes
Textile shoes
Plastic shoes
Leather shoes
Shoes made in other materials
Other leather products...

Notes: This table shows an example of the level of aggregation of 3-digit, 4-digit and 6-digit industry code of the data, taking
the leather and shoe industry as an example.

Table 2: Summary Statistics of Key Variables at the Plant Level and at the
Firm Level in 2003.

Number of Workers
Exporter Dummy
Exports/Total Sales
Importer Dummy
Imported Material Cost/Total Cost
Importer or Exporter Dummy
N

Plant
303.03
0.50
0.15
0.60
0.15
0.78
2629

Firm
348.04
0.53
0.16
0.62
0.16
0.80
2289

Notes: This table shows summary statistics of key variables in 2003 both at the plant level and at the firm level.

Table 3: Summary Statistics of Key Variables at the Plant Level and at the
Firm Level in 2003, Separated by Type of Plants

Number of Workers
Exporter Dummy
Export/Total Sales
Importer Dummy
Imported Material Cost/Total Cost
Exporter or Importer DummyN(1)Single-plant Firms
Firm=Plant
238
0.52
0.16
0.61
0.16
0.74
2139

(2)

(3)
Multi-plant Firms
Plant
Firm
583
1911
0.43
0.64
0.12
0.15
0.57
0.77
0.15
0.16
0.68
0.86
492
150

Notes: This table shows summary statistics of key variables in 2003 both by the type of plants, namely plants belonging tosingle-plant firms or plants belonging to multi-plant firms. For the latter, the summary statistics at the plant level and at thefirm level are also shown.

Table 4: Share of the top 5 Plants or Firms in the Total Industry-level Employment, by Industry. Average of 2003-2010.
Industry Code
312
313
314
315
316
321
322
323
325
326
327
331
332
333
334
335
336
337
339

Description
Beverage and Tobacco
Textile Mills
Textile Product Mills
ApparelLeather and Shoes
Wood Product
Paper
Printing Related
Chemical Manufacturing
Plastics and Rubber Products
Nonmetallic Mineral ProductPrimary Metal
Fabricated Metal Product
MachineryComputer and Electronics
Electrical Equipment
Transportation Equipment
Furniture and Related
Miscellaneous

Plant
0.29
0.32
0.39
0.21
0.22
0.40
0.17
0.26
0.18
0.10
0.27
0.39
0.18
0.25
0.66
0.29
0.23
0.27
0.27

Firm
0.37
0.37
0.39
0.22
0.23
0.40
0.37
0.26
0.29
0.12
0.30
0.47
0.25
0.25
0.66
0.40
0.34
0.29
0.27

Notes: This table shows the share of top 5 plants or firms in the total industry-level employment, for each 3-digit industry.
The table excludes the Petroleum industry because of the high concentration of the industry.

Table 5: Number of Multi-plant Firms and Its Shares in Employment and Sales.
2003-2010.
Year
2003
2004
2005
2006
2007
2008
2009
2010

Type of Firm
Single-plant
Multi-plant
2137
492
2195
443
2299
499
2340
498
2369
521
2454
473
2243
460
2126
502

N Plant
0.19
0.17
0.18
0.18
0.18
0.16
0.17
0.19

Share of Multi-plant Firms
Employment
Production
0.36
0.62
0.33
0.60
0.33
0.61
0.32
0.61
0.33
0.62
0.31
0.62
0.32
0.62
0.34
0.67

Notes: This table shows the number of plants owned by single-plant firms and by multi-plant firms, andshare of employment and production accounted for by multi-plant firms, for each year from 2003 to 2010.

Table 6: Number of Multi-Product Firms and Its Shares in Employment andSales within Multi-Plant Firms. 2003-2010.
Year
2003
2004
2005
2006
2007
2008
2009
2010

Type of Firm
Single-productMulti-product
248
244
229
214
263
236
253
245
277
244
273
200
263
197
288
214

Share of Multi-product Firms
N Plant
Employment
Production
0.50
0.54
0.51
0.48
0.56
0.48
0.47
0.56
0.45
0.49
0.56
0.47
0.47
0.54
0.50
0.42
0.49
0.41
0.43
0.50
0.42
0.43
0.53
0.43

Exports
0.84
0.83
0.79
0.82
0.86
0.77
0.84
0.87

Notes: This table shows the number of plants owned by single-product multi-plant firms and by multiproduct multi-plant firms, and share of employment, production and exports accounted for by multi-productmulti-plant firms on the sum of the respective variables of the two types of firms, for each year from 2003
to 2010.

Table 7: Importance of the Most Important Industry for Multi-product Firms..
2003-2010.
Year
2003
2004
2005
2006
2007
2008
2009
2010

Type of Product
Non Top Ind
Top Ind
102
142
84
130
88
148
86
159
90
154
75
125
70
127
84
130

Share of the Top Product: Aggregate
N Plant
Employment
Production
0.58
0.75
0.80
0.61
0.75
0.78
0.63
0.77
0.78
0.65
0.78
0.81
0.63
0.77
0.79
0.63
0.76
0.77
0.64
0.80
0.81
0.61
0.77
0.81

Exports
0.88
0.87
0.87
0.90
0.87
0.82
0.87
0.86

Notes: This table shows the number of plants belonging to multi-product multi-plant firms that produce
the top product within the firm and the non-top product within the firm, for each year from 2003 to 2010.
This table also shows the fraction of total employment, production and exports that are explained by the
top products of each firm, for each year from 2003 to 2010.

Table 8: Labor productivity (1) across and within industry and (2) across andwithin firm. 2003-2010.

R2(1)
Industry Effects (3 digit)
0.21

(2)
Industry Effects (4 digit)
0.31

(3)
Product Effects
0.50

(4)
Firm Effects
0.78

Notes: This table reports the value of R2 from the regressions of plant-level labor productivity at time
t on (1) subsector (3-digit)-year effects, (2) 4-digit-industry-year effects, (3) product(6-digit)-year effects
and (4) firm-year effects. Each number shows the variation of labor productivity explained by sector-level,or product-level or firm-level factors.

Table 9: Heterogeneity between the most labor productive plants and otherplants within firms. 2003-2010.

Type of firm

Production
Non Top
Top
Single Industry 56.0
67.8
Multi Industry 64.8
71.4

Percentile within industry
Employment
ExportNon TopTop
Non Top
Top
55.4
57.6
53.6
59.1
63.2
57.4
56.0
59.9

Labor Productivity
Non Top
Top
52.6
77.2
60.8
79.6

Notes: This table shows the ranking of the most productive and not-most productive (in terms of laborproductivity) plants, within firms, in the industry distribution of several key variables. This comparisonis done separately for single-product and multi-product multi-plant firms. We first construct percentile
for each plant’s variables within industry, then compare them between the most labor productive plants
within firm and not the most labor productive plants within firms. For example, for single-product multiplant firms, plants that are not the most productive plants within firms are at 55th percentile in termsof their production, which means that these plants’ production is on average just slightly bigger than theindustry-average. Plants that are the most productive plants within firms are at 68th percentile, whichmeans that these plants’ production is on average close to top 30 percent of the industry.

Table 10: Heterogeneity between bigger plants and other plants within firms.
2003-2010.
Average Wage
Cost share

0.159***(0.037)
Firm-year Effects Yes
N
3888

Cost share

0.154***(0.036)
Firm-year Effects Yes
N
2094
Cost share

0.168**(0.037)
Firm-year Effects Yes
N
1794

Export/Sales

Imported Materials/Cost
All Multi-plant Firms
0.108***
0.068***(0.020)(0.019)
Yes
Yes
3888
3888
Single-Industry Multi-plant Firms
0.119***
0.075***(0.021)(0.011)
Yes
Yes
2094
2094
Multi-Industry Multi-plant Firms
0.091***
0.056**(0.022)(0.023)
Yes
Yes
1794
1794

Energy Cost/Sales-0.018***(0.006)Yes
3888-0.013(0.008)Yes
2094-0.026***(0.003)Yes
1794

Notes: This table shows the results from the regression of dependent variable (average wage, exportorientation, imported intermediate products dependence or the share of energy cost) on the cost share ofplants within their firms controlling for firm-year effects. The standard errors are clustered at the firm-yearlevel. Significance: * 10 percent, ** 5 percent, *** 1 percent.

Table 11: Decomposition of Aggregate Labor Productivity Changes. Normal,
Crisis and Recovery Periods.

Within-Within
Within-Reallocation
Between
Cross-within
Cross-reallocation
Residual(1)
2003-2008
Normal Period
101 %
8%
-10 %
-13%
1%
13%

(2)
2008-2009
Crisis
150%
-25 %
266 %
-7%
-8 %
-376%

(3)
2009-2010
Recovery
113%
0%
11 %
-12%
3%
-15%

Notes: This table shows the result of the decomposition analysis of the aggregate labor productivity changes
for the three types of period: the normal period from 2003 to 2008, the crisis period from 2008 to 2009,
and the recovery period from 2009 to 2010.

Table 12: Decomposition of Aggregate Labor Productivity Changes By Industry. 2003-2008.
Industry CodeIndustry Name

2003-2008
Within-Firm Across Plant Reallocation
332
Fabricated Metal Product
-58 %
311
Food
-28 %
336
Transportation Equipment
18 %325
Chemical Products
26 %
322
Paper
32 %
Notes: This table shows the contribution of within-firm reallocation components from the decomposition
analysis of the aggregate labor productivity changes separately for each industry from 2003 to 2008, forfive industries for which this component is important.

Table 13: Exporter Premium with both Firm Exporter dummy and Plant Exporter Dummy. 2003-2008.
(1)
(2)
(3)
Employment
Average Wage
Labor Productivity
Firm Export Dummy
0.188***
0.152***
0.220***(0.059)(0.029)(0.069)Plant Export Dummy
0.318***
0.054*
0.013(0.058)(0.028)(0.066)
Multi-Plant Firm Dummy
0.292***
0.257***
0.558***(0.037)(0.019)(0.034)
R2
0.466
0.373
0.459
N
16720
16720
16720
Notes: This table shows the results from the regression of total employment, average wages and laborproductivity on firm exporter dummy, plant exporter dummy, multi-plant firm dummy and product-year
fixed effects. The data are from 2003 to 2008. The standard errors are clustered at the product-year level.
Significance: * 10 percent, ** 5 percent, *** 1 percent.

Table 14: Exporter Productivity Premium. Firm-level and Plant-level Analysis
Separately. 2003-2008.

Type of Unit
Exporter Dummy

(1)
Plant
0.207***(0.017)

Multi-Plant Firm Dummy

(2)
Plant
0.215***(0.016)(3)
Firm
0.754***(0.028)0.598***(0.033)(4)
Firm
0.698***(0.027)1.792***(0.050)

r2
0.429
0.458
0.508
0.557
N
16720
16720
14714
14714
Notes: This table shows the results from the regression of log labor productivity on exporter dummy andproduct-year fixed effects. The regressions have been run both at the plant-level and at the firm-level. The
data are from 2003 to 2008. The standard errors are clustered at the product-year level. Significance: *10 percent, ** 5 percent, *** 1 percent.

Table 15: Employment Adjustment during the 2008-2009 crisis. Firm-level andplant-level analysis.

Type of Unit
Firm Export Dummy (t-1)

Plant Export Dummy (t-1)

(1)
Firm
4Empi
-38.571(52.034)(2)-195.535**(75.921)

(3)
Plant
4Empi
-17.814(57.902)(4)-477.037**(206.463)

Firm Fixed Effects
No
No
No
Yes
N
144
458
458
458
Notes: This table shows the results from the regression of the employment change from 2008 to 2009 on adummy variable indicating whether a firm (or a plant) is an exporter, run both at the level of firm and at
the level of plant. Column (1) shows the result of the firm-level regression, while columns (2)(3)(4) shows
the results of the plant-level regressions.