Flexibility and Productivity:Towards the Understanding of Firm Heterogeneity for

Multi-product Exporters∗

Luca Macedoni†

Aarhus University

Mingzhi (Jimmy) Xu‡

INSE at Peking University and NBER

October 2018

Abstract

We study the heterogeneity in scope and sales across multi-product exporters. Guidedby new firm-level evidence using China’s customs data, we build a general-equilibrium modelfeaturing firm heterogeneity in productivity and in flexibility, namely the ability to introducenew varieties in a destination at low costs. We estimate our model, finding suggestive evi-dence of a trade-off between productivity and flexibility: more productive firms are likely tobe less flexible, as they pay higher fixed costs to introduce new varieties. The properties ofsuch trade-off between productivity and flexibility are heterogeneous across industries. In thespirit of Hottman et al. (2016), we find firms’ flexibility accounts for 65 to 75% of the totalvariation in scope across firms and destinations, and 12 to 16% of the total variation in sales.

Keywords: International trade; Multi-product firms, Flexible manufacturing, Firm hetero-geneity, Firm-level data, China.

JEL Code: F12, F14, L11

∗We thank Ina Simonovska and Robert Feenstra for early suggestions and support. We also thank CostasArkolakis, Sharat Ganapati, Deborah Swenson, Frederic Warzynski, and seminar participants at Aarhus University,European Trade Study Group 2017, Midwest Spring International Trade Meeting 2018, Ljubljana Empirical TradeConference 2018, North American Summer Meeting of the Econometric Society 2018, and IFN.†lmacedoni@econ.au.dk‡mzhxu@ucdavis.edu. Financial support from the China Scholarship Council is gratefully acknowledged.

1 Introduction

Standard models of multi-product firms assume that one attribute of the firm, i.e., productivity,

drives both the ability to produce a good efficiently and the ability to produce many goods. More

productive firms export a larger number of varieties, or scope, and enjoy larger sales (Bernard

et al., 2011; Mayer et al., 2014). The positive relationship between productivity, sales, and scope

is intuitive: a rise in a firm’s productivity increases the sales of each existing variety and restores

the profitability of discontinued varieties. This study provides new evidence suggesting that firms

differ in their productivity and in the ability to introduce new varieties at low costs. Our goal is to

investigate the determinants of firms’ ability to introduce new varieties and study its consequences

on firms’ scope and sales. As multi-product firms dominate trade flows (Bernard et al., 2007), such

a two-dimensional heterogeneity has major implications for the margins of trade.

Our main empirical contribution is to document three new stylized facts for Chinese exporters,

using data from the China Customs Dataset and the Annual Surveys of Industrial Production

(Brandt et al., 2014). First, we find that firm-destination specific shocks explain more than 50%

of the variation in scope across firms and destinations. Models of multi-product firms predict that

destination characteristics such as size (Bernard et al., 2007), per capita income (Macedoni, 2017),

competition (Mayer et al., 2014), and firms’ productivity determine the scope of exporters. Our

evidence suggests that firm-destination specific shocks, as those modeled by Arkolakis et al. (2015)

and Mayer et al. (2016), are quantitatively relevant determinants of scope.

Second, we document a disconnect between total sales of firms and their scope in a given

destination. Standard models of multi-product firms predict a positive relationship between sales

and scope driven by productivity (Bernard et al., 2011). However, there are several single-product

and wide-scope Chinese firms at any level of sales. A similar pattern emerges when we study

the relationship between productivity and scope. At any level of productivity, there are several

single-product and wide-scope firms.

While any kind of firm-destination specific shocks could explain the first stylized fact, only

shocks to the within-firm extensive margin can rationalize the disconnect between sales and scope.

To generate the disconnect between sales and scope, a model needs firm-destination specific shocks

that affect the choice of scope but leave the sales per variety unchanged. Shocks that directly affect

the intensive margin, namely the sales per variety, such as quality or appeal, fail to rationalize

this stylized fact. Although there could potentially be several shocks to the within-firm extensive

margin, we choose to model them with a random fixed cost per variety and destination.

For our third stylized fact, we investigate whether firms’ observable characteristics can explain

the documented disconnect between sales and scope to understand the determinants of the shock

to the within-firm extensive margin. In the spirit of Hallak and Sivadasan (2013), we study the

relationship between exporter’s scope, conditional on sales, and other firm-level characteristics.1

1Hallak and Sivadasan (2013) study the exporter premia conditional on sales. We refer to the scope conditional

1

The conditional scope of Chinese exporters is affected by productivity, capital stock, capital in-

tensity, R&D spending, experience, and ownership. The signs of the relationships vary across

industries, suggesting that the determinants of the shock to the within-firm extensive margin dif-

fer significantly across industries. For instance, the conditional scope of textile firms declines with

productivity: taking two firms with the same sales, the firm with lower productivity has the wider

scope. However, such a relationship is absent or even positive in other industries.

We rationalize the three stylized facts in a general equilibrium, multi-country model of heteroge-

neous multi-product firms. The model shares standard assumptions from the literature: consumers

have CES preferences (Bernard et al., 2011), firms are monopolistically competitive and have a

core competence (Eckel and Neary, 2010; Arkolakis et al., 2015). Our main point of departure

from single-attribute models of multi-product firms is that, in addition to productivity, firms differ

in the ability to introduce a new variety in a destination at low costs. Expanding the scope in a

destination requires the payment of a fixed cost to adapt production and distribution processes to

the new variety. The fixed cost per variety is subject to firm-destination specific shocks. Such a

shock rationalizes our first two stylized facts: a firm’s productivity is not the only determinant of

the firm’s scope, and firms with the same level of sales export a different scope depending on the

realization of the fixed cost shock.

We interpret the heterogeneity in the fixed cost as heterogeneity in the flexibility of firms’

production processes. Eckel and Neary (2010) define flexible manufacturing as the ability of firms

to introduce new varieties with minimal adaptations to production processes.2 While in Eckel and

Neary (2010) firms are fully flexible, and the fixed cost per variety is absent, in our framework

a firm’s flexibility is subject to shocks: the higher the fixed cost per variety, the lower the firm’s

flexibility.

We are not the first to introduce two layers of heterogeneity across firms to rationalize empirical

evidence, as the literature has considered, in addition to productivity, demand shocks (Kee and

Krishna, 2008; Eaton et al., 2011; Demidova et al., 2012; Roberts et al., 2018; Cherkashin et al.,

2015) and shocks to fixed costs (Das et al., 2007; Eaton et al., 2011; Armenter and Koren, 2015;

Arkolakis et al., 2015). Our main theoretical contribution is to systematically evaluate the rela-

tionship between flexibility and productivity and quantify the effects of flexibility heterogeneity

on the scope and sales heterogeneities for Chinese exporters.

In our model, the variance of the shock to the fixed cost across destinations reflects the het-

erogeneous ability of a firm to adapt to foreign non-tariff barriers. Namely, a Chinese firm may

find it less costly to adapt product standards and packaging for the South Korean market than

on firm’s sales as conditional scope. The conditional scope is the residual of a regression of log(scope) on log(sales)and a constant, and, thus, represents the variation in scope not explained by sales.

2Flexible manufacturing was first addressed by the IO literature (Eaton and Schmitt, 1994). A more generaldefinition by Milgrom and Roberts (1990) states that flexible manufacturing allows for a quick response to changes inmarket conditions. Thesmar and Thoenig (2007) study how vertical integration or separation affect such flexibility.Other definitions of flexibility used in the literature are the ability of reducing delivery times (Tseng, 2004) and ofchanging production scale with minor adjustment costs (Gal-Or, 2002).

2

for the French market. Although there is little evidence on the determinants of fixed costs of

exporting, a documented reason for the variance of flexibility across destinations could be the

exporting experience of firms’ managers (Mion et al., 2016). Moreover, we allow for a correlation

between flexibility and firms’ productivity. As we leave the sign of such correlation unspecified,

our theory nests the alternative frameworks of multi-product firms (Arkolakis et al., 2015; Nocke

and Yeaple, 2014) and of flexible manufacturing (He, 1992).3 The model also shed some light on

industry-specific determinants of flexible manufacturing that can range from cash flows to R&D

expenditures, as we document in our third stylized fact.

We estimate the parameters of our model by matching moments from the distribution of sales

and scope of Chinese exporters. To estimate the model, we follow the conventional assumptions

on the functional forms for the distributions of productivity as well as the production technology

within firms. In particular, we assume that productivity follows a Pareto distribution as Chaney

(2008). Moreover, flexibility also follows a Pareto distribution to match the distribution of scope

conditional on productivity that we observe in the data. In line with our evidence, the corre-

sponding distribution of sales resembles a log normal distribution, and the distribution of scope

resembles a Pareto distribution.

The estimation highlights two main results. First, the distribution of firms’ flexibility is nega-

tively correlated with the distribution of productivity: more productive firms tend to be less able

to introduce new varieties at low costs. Second, there is a high degree of heterogeneity across

industries, both in the dispersion of the flexibility shocks and in the magnitude of the correlation

between productivity and flexibility. The result suggests that the determinants of firms’ scope and

sales are heterogeneous across industries.

To the extent that flexibility and productivity are endogenous choices of firms, the estimation

suggests a negative trade-off between the two sources of heterogeneity. If firms are able to invest

in improving their productivity, they might do so at the expense of flexibility, and vice versa.

Although our study finds that both flexibility and productivity are determinants of scope and

sales, the recent increases in tariffs between China and US highlight a potentially important role

for flexibility. In fact, more flexible firms would likely be able to respond to higher tariffs by

introducing new products not subject to the tariff hikes.

For firms selling in US supermarkets, Hottman et al. (2016) find that heterogeneity in product

scope is the second most important factor, after product appeal, in explaining firm sales hetero-

geneity.4 In the spirit of Hottman et al. (2016), we further extend the understanding of firm

heterogeneity by quantifying how much the heterogeneity in product scope and sales can be at-

tributed to the heterogeneity in flexibility. Our quantification exercise highlights two main results.

3For instance, when we specify a negative correlation between flexibility and productivity, our framework issimilar to the diseconomies of scope of Nocke and Yeaple (2014).

4The authors find that 50-70% of the sales variance can be attributed to firms’ appeal, or quality, and 20-25%to firms’ scope. Similarly, by examining the universe of buyer-supplier relations in Belgium, Bernard et al. (2018)document that downstream, or demand, factors explain most of firm heterogeneity.

3

First, heterogeneity in flexibility is the major determinant of product scope for Chinese ex-

porters. When using the parameters calibrated for the entire sample of manufacturing firms, we

find that the heterogeneity in flexibility explains 76% of the variation in scope across firms and

destinations. The explanatory power of flexibility is mainly driven by the correlation between

flexibility and productivity rather than the dispersion of flexibility. Moreover, allowing for hetero-

geneity in the parameters at the industry-level, we find that heterogeneity in flexibility explains

up to 64% of the variation in scope across firms and destinations.

Second, heterogeneity in flexibility accounts for 12-16% of the heterogeneity in Chinese firms’

sales. The result highlights similarities with those of Hottman et al. (2016). In fact, flexibility

affects sales indirectly through the product scope decisions made by firms. We use our results and

back out that 18-21% of the variation in sales is explained by product scope, which is analogous

to the findings of Hottman et al. (2016).

Our paper is closely related to the work of Arkolakis et al. (2015) and Nocke and Yeaple

(2014). Arkolakis et al. (2015) augment the Bernard et al. (2011) model with firm-destination

specific shocks that improve the ability of the model to fit the data. Our empirical work further

supports the authors’ assumption. In fact, the firm-destination specific shock to the fixed cost per

variety generates the observed sales and scope disconnect. While Arkolakis et al. (2015) interpret

the shock as an i.i.d. random cost of market access, our study argues that the shock affects firms’

flexibility in production. In support of our assumption, the evidence shows that the shock is

related to firms’ observable characteristics, and the estimation of the model highlights a negative

relationship between flexibility and productivity. Finally, our paper generalizes the theoretical

implications of Nocke and Yeaple (2014). The authors assume that firms’ technology exhibits

dis-economies of scope, which can be achieved in our model by a negative correlation between

flexibility and productivity.

The remainder of the paper is organized as follows. Section 2 documents three new empirical

regularities for Chinese exporters. Section 3 presents our model of multi-product firms, which we

estimate in section 4. Section 5 concludes the paper.

2 Stylized Facts for Multi-product Exporters

We use firm-level data from two sources. The first is the China Customs Dataset that provides data

on export values at the product-firm-destination-year level for all international transactions from

China. A product is a Harmonized System (HS) eight-digit code. To understand which firms’

characteristics influence the scope decisions of firms, we use the Annual Surveys of Industrial

Production (ASIP) that is conducted by the National Bureau of Statistics of China (Brandt et al.,

2014). The dataset covers manufacturing firms with more than five million RMB in annual sales

(≈ $700k). For each firm, the ASIP provides data on employment, output, and elements of

accounting statements.

4

We use name, location, zip code, and telephone number to match the firms in the two datasets.

We match 30% to 40% of exporters involved in ordinary trade to the information provided in

ASIP.5 The China Customs Dataset ranges from 2000 to 2006 while the ASIP from 1998 to 2007.

While the results of our paper hold for each year separately, for the sake of exposition we focus

on 2006, which has the largest number of matched firms.6 Moreover, we refine our sample to the

firms involved in ordinary trade only.7

Chinese multi-product firms dominate the country’s exports: 77% of exporters sell at least two

products in a destination, and they account for 94% of total export value. Such results are in line

with the evidence documented for several other countries by Bernard et al. (2007), Mayer et al.

(2014), Arkolakis et al. (2015), and Macedoni (2017). Our sample of matched firms exhibits a

similar distribution: 78% of the firms in the sample are multi-product, and they account for 96%

of the sample’s total exports.

As our main empirical results focus on the distribution of firms’ scope, sales, and productivity

within a destination, we focus on the US market, the most popular destination for Chinese exports.

Figure 1 illustrates the distribution of the number of HS eight-digit goods per firm that Chinese

exporters sell to the US. The first graph uses all exporters while the second focuses on the sample

of firms with matched characteristics from ASIP. The two distributions are remarkably similar as

they both exhibit the largest mass for a scope of one. In particular, 36% of all Chinese exporters

and 40% of our matched sample export a single HS eight-digit good to the US. However, matched

firms have a wider scope, on average, than the firms in the entire sample.

Figure 1: Distribution of Product Scope in the U.S. (2006)

(a) All Sample (b) Matched Sample

While the scope distribution across firms resembles a Pareto distribution, sales appear to be

log-normally distributed. Figure 2 shows the distribution of log sales within the US, for the entire

5We follow the conventional method to match firms from the China Customs Data to the ASIP (Feenstra et al.,2014; Yu, 2015; Manova and Yu, 2016).

6In Appendix B, we also use the 2000 customs data to carry on empirical investigation.7The code for ordinary trade mode is 18. According to Dai et al. (2016), firms involved in processing exports

behave abnormally in China. The performance of matching process and the summary statistics are in Appendix A.

5

sample of firms and the matched sample. Although the average sale is larger for the matched

sample, the two distributions look virtually identical.

Figure 2: Distribution of ln(Export Sales) in the U.S. (2006)

(a) All Sample (b) Matched Sample

2.1 Exporter Scope Across Firms and Destinations

“Single attribute” models of multi-product firms, in which productivity is the only determinant

of the firms’ performances, predict that the scope of an exporter f , from China to a destination

j, depends on two fixed effects. The first component is a firm fixed effect that captures firm’s f

productivity and costs of production common for all destinations reached. The second one, is a

destination fixed effect that captures characteristics of the destination j, such as aggregate size

(Bernard et al., 2011), level of development (Macedoni, 2017), and intensity of competition (Mayer

et al., 2014), as well as bilateral trade costs. How much do these margins explain the variation of

scope across firms and destinations?

To answer this question, we regress the number of products that a firm f exports to a destination

j on a firm fixed effect af and a destination fixed effect dj:

ln(# Productsfj) = af + dj + cfj (1)

where the error cfj captures firm-destination specific shocks to the scope.

Table 1: Decomposition of Product Scope Variation

Sample Model Fit (R2) af dj

All Exporters 0.37 0.36 0.01

Matched Exporters 0.44 0.42 0.02

R2 from (1), and from regressing the log of the scope on

firm (af ) and destination (bj) fixed effects only.

6

In Table 1, we show the R2 of the regression and the contribution to the model fit of the firm

and destination fixed effects. The simple model (1) explains 37% of the scope variation for all

exporters and 44% for the sample of matched exporters. More than a half of the variation in the

scope of Chinese exporters is explained by firm-destination specific shocks. Firm characteristics

account for almost all the explanatory power of standard models, since destination features have

a smaller impact as they mainly affect the within-firm R2 of the scope regression.

The results are robust to analyzing the additional years available, and the R2 becomes even

smaller as we consider years prior to 2006 as shown in appendix B.

2.2 Sales and Scope Disconnect

Let us now focus on the within-destination distribution of product scope, sales, and productivity.

Standard models of multi-product firms predict a positive relationship between the number of

products exported by a firm f in j and its sales:

(# Products)fij = G(dij,Revenuefij) (2)

where dij, depending on the model, captures destination characteristics and bilateral trade costs.

Moreover, since the firm’s revenues are proportional to the firm’s productivity, (2) can be written

as:

(# Products)fij = G(dij,Productivityf ) (3)

How do (2) and (3) perform in the data? Choosing the US as destination, we plot the scope of

Chinese exporters, normalized by the industry average, against the log of their sales, demeaned by

the industry average, in Figure 3. Panel (a) displays the pattern for entire Chinese exporters to

the US, and Panel (b) is for the matched ones.

On average, there is a positive relationship between sales and scope, as the standard models

would predict. The regression coefficient is positive and significant and exhibits a similar magnitude

for both samples. However, Figure 3 highlights that such a relationship is far from perfect. In

fact, the R2 of the line of best fit is 11%. At any level of sales, there are single-product firms

and multi-product firms. Consistent with the standard models, at medium-high level of sales it

is possible to observe wide-scope multi-product firms. However, contrary to the standard models,

there are also single and narrow scope firms at medium-high level of sales.

To evaluate the relationship between scope and firm productivity, we focus on the sample of

matched exporters, for which ASIP provides firm information on employment, value added, cap-

ital, and intermediate inputs. We follow Levinsohn and Petrin (2003) and estimate productivity,

excluding firms whose productivity values are ≤ 1% or ≥ 99%.8 The relationship between produc-

tivity and scope (Figure 4) is similar to that between sales and scope (Figure 3). In fact, there

8Appendix C provides the detailed procedure for estimating firms’ productivity.

7

Figure 3: Product Scope and Sales of Exporters in the U.S. (2006)

(a) All Sample (b) Matched Sample

is a positive and statistically significant relationship between productivity of a firm and scope

in a destination. At any level of productivity, there are single- and multi-product firms. More-

over, wide-scope firms are spread across all ranges of productivity. “Single attribute” models of

multi-product firms can hardly be reconciled with this evidence.

Figure 4: Product Scope and Productivity of Exporters in the U.S. (2006)

If the presence of single-product firms at any level of sales and productivity is simply an outlier

event, the case for adding an additional layer of firms’ heterogeneity to the standard model would

be weakened. To address such a concern, we divide firms in quartiles by productivity and plot

the distribution of product scope conditional on the firm belonging to a certain quartile of the

productivity distribution.

Figure 5 shows that, in each quartile, the majority of firms exports a single-product to the US.

The distribution of scope conditional on productivity resembles a Pareto distribution, and it is

similar to that arising when we divide firms in quartiles by their sales or using the entire sample.

The result is in stark contrast to a standard model of multi-product firms that would predict

that the peak of the distribution would be shifting to higher scope as productivity increases, even

allowing for some noise in the data.

8

Figure 5: Scope Distribution by Productivity Quartiles

We perform a number of robustness checks, and the results are shown in appendix B. The

disconnect between sales and scope and between productivity and scope hold when using 1) the

level of scope without the normalization by industry averages, 2) the logarithm of the scope, 3)

value added per worker as a measure of productivity, and 4) excluding single-product exporters.

The only relevant difference is that the relationship between scope and productivity measured by

value added per worker becomes insignificant.

The positive slope of the line of best fit still persists when using nonparametric methods such

as the locally weighted scatter-plot smoothing. The disconnect is also robust to analyzing each

industry separately. The R2 of regressing number of products on the log of sales ranges from 4%

in plastic & rubber to 20% in textile. Moreover, the pattern uncovered for the US market also

holds across all the major destinations for Chinese exporters: Germany, India, Italy, and Japan.

Although disaggregate, each HS eight-digit code can potentially include a large number of

products. A concern may arise if the classification of products within each HS code is artificially

driving the disconnect. Namely, two firms with the same sales may have the same number of

products, but one firm’s product are classified within one HS code while the other firm’s product

cover several HS codes. We cannot fully dismiss such a concern without access to bar code data.

However, we verified that the disconnect still emerges when we consider more aggregate definitions

of products (HS six- and four-digit codes). Thus, the way products are classified within HS codes

does not appear to be driving the result.

Finally, results are robust to dividing firms between those that produce homogeneous and

differentiated goods according to the definition introduced by Rauch (1999).

9

2.3 What Explains the Disconnect?

In this section, we investigate whether the deviations of the exporter’s scope from the value pre-

dicted by export values are random, or if they depend on other observable characteristics of firms.

Such hypothesis is motivated by the literature, which suggests that the scope of firms may depend

on several firms’ characteristics. Using Italian data, Parisi et al. (2006) find that R&D expenditure

and cash flows increase the likelihood of product innovation by firms. Timoshenko (2015) finds

that product switching occurs more often in new exporters, suggesting that firms’ learning could

affect the scope decisions of firms.

We first run the following regression for Chinese exporters in the US:

ln(# ProductsfUS) = b0 + b1 ln(RevenuefUS) + εf (4)

and record the residual εf . The residual is the variation of scope not explained by revenues. Next,

we run univariate regressions of εf on the following firm’s level variables: capital stock, employment,

capital intensity, assets, liabilities, value added per worker, R&D expenditures, advertisement

expenditures, firm’s age, and equity share owned by the state and owned by foreign parties. Since

the results are industry-specific, we apply the procedure for each industry separately. Moreover, we

focus on the sample of matched firms as only for those do we have information on the explanatory

variables.

For the sake of exposition, let us focus on the two largest export industries by value: textile

and machinery (Table 2). The residuals from (4) are correlated to several firm-level characteristics

although there is heterogeneity in the industry-specific coefficients. Conditional on sales, the scope

of textile exporters declines in value added per worker, capital stock, and capital intensity. This

means that given two firms with the same level of sales, the firm with higher value added per worker,

capital stock, or capital intensity exports fewer varieties. On the other hand, the conditional scope

of machinery exporters increases with value added per worker and capital stock. Similarly, larger

expenditures on R&D are correlated with a decline in the conditional scope for textile firms, but

with an increase for machinery producers. Advertisement and firms’ age increase the conditional

scope of machinery firms but have no effects on textile firms.

There is considerable heterogeneity in the relationship between conditional scope and firm’s

characteristics across industries. All the firm-level characteristics we consider can improve, reduce

or have no effect on the conditional scope depending on the industry considered. In tables B.2 and

B.3 of the appendix, we report the industry-level correlations as well as the results of a regression

in which we pool all explanatory variables together. Total capital stock improves the conditional

scope for chemicals, footwear, plastic, leather, transportation, and wood products while it reduces

the conditional scope of firms producing foodstuffs, metals, and mineral products. A positive

relationship between capital stock and conditional scope may suggest the presence of economies of

10

scope (Arkolakis et al., 2015): the larger the capital stock, the lower the fixed cost per product.

A negative relationship, on the other hand, suggests the presence of diseconomies of scope (Nocke

and Yeaple, 2014).

Table 2: Correlation Between Residual andFirm Characteristics

Firm Characteristics Textile Machinery

VA per Worker -0.09*** 0.02***

Capital Stock -0.03*** 0.01***

Capital Intensity -0.45*** -0.08***

R&D Fee -0.01*** 0.01***

Advertisement Fee 0.00 0.02***

Firm Age 0.00 0.01***

Coefficients from regressing ln εf from (4) on

firm characteristics. *** p<0.01, ** p<0.05, *

p<0.1.

Expenditures on R&D improve the conditional scope in the production of chemicals, foodstuffs,

footwear, plastic, leather, stone, wood, and miscellaneous goods, and have insignificant or negative

effects for the remaining industries. The heterogeneous effects of R&D on scope may reflect

industry heterogeneity in R&D intensity (Klette and Kortum, 2004). In some industries, R&D

may favor process innovation, which increases revenues. In other industries, R&D may favor

product innovation, which might increase scope relative to the increases in revenues.

A similar argument could apply to expenditures on advertisement, which proxy marketing

activities. Advertisement expands firms’ customer base and, thus, sales. A negative effect of

advertisement on the conditional scope may suggest that the advertisement strategies are focused

for fewer products. A positive effect may suggest advertisement strategies that favor the entire

product range.

3 Model

3.1 Consumer’s Problem

Consider a world of I countries: subscript i denotes an origin and j a destination. In each country

j, Lj consumers, with per capita income yj, enjoy the consumption of varieties of a differentiated

good. Consumers in each country j have the same CES preferences:

Uj =

[I∑i=1

∫Ωij

qij(ω)σ−1σ

] σσ−1

(5)

11

where σ > 1 is the elasticity of substitution across varieties, and Ωij is the set of varieties exported

from i to j. As in Bernard et al. (2011) and Mayer et al. (2014), varieties are horizontally differen-

tiated, and the elasticity of substitution within firms is the same as the elasticity of substitution

across firms. Thus, we assume away cannibalization effects that would be generated by a nested

preference structure, which only quantitatively affects the results of this model.9

Let xij(ω) = Ljqij(ω) be the aggregate demand for variety ω from i to j. Solving the consumer’s

problem and aggregating across consumers yield the following inverse demand function:

pij(ω) = Ajxij(ω)−1σ (6)

where Aj = yjLj

[∑Ii=1

∫Ωijxij(ω)

σ−1σ

]−1

is a demand shifter.

3.2 Firm’s Problem

Each firm produces a continuum of varieties indexed by ω. Labor is the only input and is paid

a wage wi. To produce and deliver a given variety in a destination, a firm pays a constant

marginal cost and a fixed cost. Varieties within-firm differ in their marginal costs: firms have a

core competence and marginal cost rise as firms introduce varieties farther from the core (Eckel

and Neary, 2010). The production costs of firms are subject to two random shocks. The first one

is firm-specific and, as in the standard literature, it affects the marginal costs of the firm. The

second one is firm-destination specific, and it affects the fixed cost per variety.

The marginal cost to produce a unit of variety ω from i to j is τijwich(ω), where τij is the

iceberg trade cost, and τii = 1. Each firm produces the first variety, or core, with the lowest

variable cost, and the variable cost of new varieties increases with their distance from the core.

Hence, we assume that h′(ω) is increasing in ω. Moreover, we normalize h(0) = 1 so that c is the

marginal cost of the core variety, and it is randomly drawn by firms.

To introduce a new variety in a destination j, each firm pays a fixed cost fijβ where fij is

the deterministic component while β is subject to firm-destination specific shocks. The fixed cost

represents the costs of adjusting production and distribution processes to the new variety (Bernard

et al., 2011; Arkolakis et al., 2015). We interpret the fixed cost per variety as a measure of a firm’s

flexibility: the lower the fixed cost, the higher the flexibility (Eckel and Neary, 2010). Thus, the

two random shocks to the marginal cost of the core variety c and to the fixed cost β generate two

layers of heterogeneity across firms: in productivity and flexibility.

The variance of the shock to the fixed cost across destinations reflects the heterogeneous ability

of a firm to adapt to foreign non-tariff measures that affect distribution, packaging, and product

standards. Namely, the same firm may be more or less flexible depending on the destination:

a Chinese firm may find it less costly to adapt product standards and packaging for the South

9See Macedoni (2017) for details on cannibalization effects.

12

Korean market than for the French market. Although there is little evidence on the determinants

of fixed costs of exporting, a documented reason for the variance of flexibility across destinations

could be manager’s experience. Mion et al. (2016) show that that firms hiring managers with

export experience are more likely to export, especially to the destinations in which managers have

previous experience.

To the extent that flexibility is a feature of the design and production of goods by a firm,

we might expect the draws of the shock to the fixed cost to be correlated across destinations

within-firm. This possibility is suggested by our evidence that several characteristics of the firm

explain the scope conditional on sales. To reflect this channel, our model features a distribution

of the fixed cost shock which is correlated with the firm’s productivity. We leave the sign of the

correlation unspecified and will determine it with the estimation of the model. For instance, a firm

may have designed its products in order to easily adapt them to regulations and standards of any

destination. Such a design may come at the cost of reducing the total volumes that the firm can

produce, or it may increase them.

Firms pay a (sunk) fixed cost of entry to discover their productivity and another (sunk) fixed

cost per destination to discover their flexibility.10 The timing of firms’ decisions is as follows. In

each country there is a pool of potential entrants. Upon entry, a firm pays a fixed cost fE in

domestic labor unit and discover the productivity 1c

of its core variety, where c is drawn from a

distribution Gi(c), with pdf gi(c) and support [0, ci]. Only a mass Ni of firms pays the fixed cost

of entry. Free entry drives the expected profits to zero and, hence, yi = wi.

To export to a destination j, a firm faces a two-stage problem similar to Demidova et al.

(2012) and Cherkashin et al. (2015). In the first stage, the firm decides whether to pay a fixed

cost Fij to discover its realization of the fixed cost β per variety in j. Only a subset of firms

pays Fij. The firm draws β from a distribution Bc(β) with pdf bc(β) and support [0, βmax,c]. The

distribution of β could be firm specific since we documented that the conditional scope is related

to observable characteristics of the firm. In the second stage, given c and β, each firm chooses

quantity xij(ω, c, β) for each produced variety ω ∈ [0, δij(c, β)] and scope δij(c, β). Firms are

monopolistically competitive.

3.2.1 Second Stage

To solve the firm’s problem we proceed backwards, starting from the second stage. The profits of

a firm from i to j are given by:

Πij(c, β) =

∫ δij(c,β)

0

[(pij(ω)− τijwich(ω))xij(ω)− fijβ]dω (7)

10According to the estimates of Das et al. (2007), the fixed cost of entry in a foreign market is quite large.

13

with pij(ω) from (6). Profit maximization yields the standard constant markup pricing rule:

pij(ω, c) =σ

σ − 1τijwich(ω) (8)

It is convenient to re-write the profits of a variety ω as follows:

πij(ω, c, β) =1

σ − 1

[Ajσ − 1

σ

]σ(τijwich(ω))1−σ − fijβ

Given that h′(ω) > 0, there exists a value of the fixed cost shock β∗ij(c) such that a firm with cost

draw c makes zero profits by selling its core variety ω = 0. If a firm with productivity 1c

draws

β < β∗ij(c), it sells a positive scope to consumers in j. Otherwise, if β > β∗ij(c) the firm is inactive

in j. The fixed cost cutoff declines with the marginal cost of production and delivery:

β∗ij(c) =1

fij(σ − 1)

[Ajσ − 1

σ

]σ(τijwic)

−(σ−1) (9)

Less productive firms need to be more flexible in order to be active in j. Moreover, the cutoff

declines in the iceberg trade cost: for a given productivity, less flexible firms can sell a positive

scope in closer destinations.

Let us rewrite per variety profits as a function of the fixed cost cutoff β∗ij(c) and β:

πij(ω, c, β) = fijβ

[β∗ij(c)

βh(ω)1−σ − 1

]The firm introduces new varieties until the profits of the last variety δij(c, β) drop to zero. The

optimal scope of the firm is then implicitly defined by:

h(δij(c, β)) =

(β∗ij(c)

β

) 1σ−1

(10)

The left-hand side of (10) is increasing in the scope of the firm by the core competence assump-

tion. The right-hand side is increasing in firm’s productivity (1c). However, because of the shock

β, a given scope can be attained by a high productivity firm with low flexibility and by a low

productivity firm with high flexibility.

Following the notation of Arkolakis et al. (2015), let H(δij(c, β)) =[∫ δij(c,β)

0h(ω)1−σdω

] 11−σ

be

a measure of the productivity of the firm across its varieties. H(δij(c, β)) is declining in scope: as

the firm introduces new varieties far from the most productive core, its average productivity falls.

The total sales of a firm are:

Rij(c, β) = σfijβ∗ij(c)H(δij(c, β))1−σ (11)

14

Using our definition of scope (10) we can rewrite (11) as:(h(δij(c, β))

H(δij(c, β))

)σ−1

=Rij(c, β)

σfijβ(12)

which represents the sales and scope disconnect illustrated in the previous section. The left-

hand side is increasing in the scope. Hence, there is a positive relationship between scope and

sales which is, however, disconnected by the shock β. In standard models of multi-product firms

(Bernard et al., 2011; Mayer et al., 2014), β is constant across firms, and, therefore, these models

predict a positive relationship between scope and sales. In our model, for a given level of sales the

scope is determined by the realization of β. Since β is drawn from a firm-specific distribution, it

may be related to the firm’s characteristics as the evidence suggests.11

3.2.2 First Stage

Given β and c a firm chooses prices and scope according to (8) and (10). Its profits are given by:

Πij(c, β) = fijβ

[(h(δij(c, β))

H(δij(c, β))

)σ−1

− δij(c, β)

](13)

which are declining in c, provided that ddδ

(h(δ)H(δ)

)σ−1

> 1. The firm’s expected profits in j equal:

E[Πij(c)] =

∫ β∗ij(c)

0

Πij(c, β)bc(β)dβ (14)

A firm with cost draw c enters a destination j as long as its expected profits over the possible

realizations of the fixed cost shock exceed the fixed cost of entry Fij.12 Hence, there exists a

marginal firm with cost draw c∗ij such that:

E[Πij(c∗ij)] = Fij (15)

Figure 6 summarizes the entry and production decisions of firms. A firm with cost draw c > c∗ij

does not pay the fixed cost Fij and, thus, decides not to enter the destination. On the other hand,

a firm with c < c∗ij pays the fixed cost Fij and discovers its draw of β. If β > β∗ij(c) the firm does

not produce any variety. If β equals the cutoff, the firm is indifferent between producing the core

variety and not producing, thus, having a scope of zero. For β below the threshold, the firm has

a positive scope and sales. For a given c, firms with low β have a higher scope δij(c, β).

11As previously argued, only shocks to the extensive margin can explain the disconnect between sales and scope.In appendix D.3, we outline extensions of the model in which firms are subject to shocks to their product qualityand show that such extensions fail to rationalize the disconnect between sales and scope.

12The expected profits are declining in c if∫ β∗

ij(c)

0

[∂Πij(c,β)

∂c bc(β) + Πij(c, β)∂bc(β)∂c

]dβ < 0.

15

Figure 6: Entry and Production Decisions

𝛽

𝑐𝑐𝑖𝑗∗

No EntryEntry

No Production

Production

𝛽𝑖𝑗∗ (𝑐)

𝛽𝑖𝑗∗ (𝑐𝑖𝑗

∗ )

3.2.3 Firms’ Entry

Firms pay the fixed cost fE if their expected profits across all destinations exceed the fixed cost

of entry. In particular, ex-ante expected profits across all destinations are given by:

πi =I∑j=1

Gi(c∗ij)

∫ c∗ij

0

E[Πij(c)]µi(c)dc (16)

where E[Πij(c)] is defined in (14), and µc(c) is the distribution of cost draws conditional on c being

below the threshold c∗ij. In particular µi(c) = gi(c)Gi(c∗ij)

if c < c∗ij and zero otherwise. Free entry

implies that firms’ expected profits equal the fixed cost of entry:

πi = wifE (17)

3.3 Equilibrium

Following Cherkashin et al. (2015), we compute the mass of firms Nij that sell to a destination j

by integrating the probabilities over the white area (labeled “Production”) of figure (6):

Nij = Ni

∫ c∗ij

0

∫ β∗ij(c)

0

dBc(β)dGi(c) (18)

The total revenues from i to j are:

Tij = Ni

∫ c∗ij

0

∫ β∗ij(c)

0

Rij(c, β)bc(β)gi(c)dβdc (19)

16

where the firm’s revenues are defined in (11). Goods market clearing implies that:

I∑i=1

Tij = wjLj (20)

In equilibrium, firms choose scope and prices according to (10) and (8), free entry drives

expected profits equal to the fixed cost of entry (17), goods markets clear (20), and trade is

balanced, namely Tij = Tji.

4 Estimation

In this section, we parametrize the model and use a simulated method of moments (SMM) algo-

rithm to estimate the parameters controlling the distribution of productivity and flexibility.

4.1 Parametrization of the Model

To derive the model’s predictions, we choose the following functional forms for the distributions

of productivity, flexibility and within-firm marginal costs. Following a long literature started by

Chaney (2008), the inverse of a firm’s productivity c is drawn from a Pareto distribution with CDF

Gi(c) =(cci

)κ, where c ∈ [0, ci], κ is the shape parameter, common across all countries, and ci is

an origin specific location parameter.

The distribution of the fixed cost shock β follows a Pareto distribution with CDF Bc(β) =(β

βmcα

)γ, where β ∈ [0, βmc

α], γ is the shape parameter and βmcα is a firm-specific location pa-

rameter. We chose a Pareto distribution to replicate the observed distribution of scope conditional

on firms’ productivity (Figure 5). If α > 0, the fixed cost shock is positively correlated with the

cost draw, and, thus, productivity and flexibility are positively correlated. If α < 0, productivity

and flexibility are negatively correlated while they are uncorrelated if α = 0.13

The firm-specific location parameter is a shorthand that captures alternative ways with which

firms’ characteristics affect firms’ flexibility. The evidence, in fact, suggests that several firm-level

variables, from capital stock to R&D expenditures, influence the conditional scope. Assuming

an exogenous firm-specific location parameter for the distribution of the fixed cost generalizes

alternative endogenous mechanisms that explain firms’ heterogeneity in the ability to introduce

new varieties. Our model can be thought of as a reduced-form expression of He (1992), in which

firms can choose between an output-specific or a flexible technology. If the cost for the flexible

technology is constant, more productive firms are endogenously more flexible too. In contrast,

if choosing the flexible technology reduces the efficiency of production, the opposite case would

occur. Moreover, the model of economies of scope in Arkolakis et al. (2015) can be represented by

13In Arkolakis et al. (2015), α equals zero while the fixed cost fij is a declining function of the scope.

17

α > 0 while the presence of diseconomies of scope of Nocke and Yeaple (2014) by α < 0.

Finally, our marginal cost per variety ω is h(ω) = exp(θω), which has the desired properties of

h(0) = 1 and h′(ω) > 0. The implication of such functional form is that firms with wider scope

respond less to trade shocks than narrow scope firms. We derive the closed-form expressions for

scope and revenues, and the equilibrium conditions for the parametrized model in appendix D.1.

4.2 Estimation Strategy

Our goal is to estimate the set of parameters Θ = [θ, σ, γ, α, βm, κ], which fully characterizes

the technology of multi-product firms and the distribution of productivity and flexibility across

firms. Given the candidate parameters Θ, we design an algorithm that simulates the revenues

and scope across destinations of 1, 000, 000 hypothetical Chinese firms. We focus on the eighteen

most popular destinations for Chinese exporters. To maximize the number of observations we use

for the simulation, we condition our sample to contain only exporters that enter a given reference

destination r. We use r = China, namely firms that sell in the domestic economy (or all Chinese

exporters) and r = US, namely the firms that export to the US.14 The algorithm finds the values of

Θ that minimize the weighted sum of squared difference between the simulated vector of moments

to the vector of moments in the data.

We follow Arkolakis et al. (2015) and focus on 118 moments, which are divided into the following

five sets:

1. We consider moments from the distribution of product sales, within-firm and within-destination.

The distribution of sales within-firm is regulated by firms’ technology and by consumers’ pref-

erences. Higher elasticity of marginal costs with respect to the distance of a variety from the

core (θ) causes product sales to decline faster the farther from the core they are. A similar

relationship arises between product sales and the elasticity of substitution σ.

2. We match moments from the distribution of the sales of core products within-destination. As

we focus on the core products, the distribution of sales is independent of the ability of firms

to expand their scope. Absent any heterogeneity in flexibility, the distribution of the core

products sales would reflect the distribution of productivity and the degree of substitutability

between products. The presence of heterogeneity in flexibility affects the extensive margin

of the distribution of core sales.

3. We include the distribution of exporters’ scope within-destination. In “single attribute mod-

els”, such a distribution would only depend on the distribution of firms’ productivity and

on the distribution of within-firm’s productivity, which we targeted in the previous two sets

of moments. In our framework, the scope distribution within-destination is affected both

14We focus on exporters, as our dataset does not cover the domestic scope of Chinese firms.

18

by the degree of dispersion of the shock to firms’ flexibility and by the correlation between

flexibility and productivity.

4. The fourth set of moments takes into account the distribution of firms’ total sales within-

destination. Combined with the third set of moments, the fourth set exploits the observed

disconnect between sales and scope, which is explained by the presence of heterogeneity in

flexibility. Without such a heterogeneity, given the distribution of productivity and scope,

the distribution of sales would be easily determined. However, in our framework, there is a

disconnect between sales and scope that is informative of the heterogeneity in flexibility.

5. The fifth set of moments considers the distribution of firms’ scope across destinations. Absent

any flexibility shocks, controlling for firms’ and destinations’ characteristics, the distribution

of scope across destinations should be identical across firms. Any deviations from the pre-

dictions of “single attribute models” are captured by the shock to firms’ flexibility.

Our estimation procedure closely follows Arkolakis et al. (2015). The detailed description of the

algorithm, moments, and the statistical inference are provided in appendix E.

4.3 Estimation Results

Table 3 shows the estimated parameters for the full sample of manufacturing firms. All parameters

are statistically significant. Moreover, a regression of the calibrated moments against the moments

in the data yields an overall R2 of 80%, and 45% to 97% across the five sets of moments we

consider. Details are in appendix E.5. We use both the United States and China as the reference

country, and the estimates remain similar.15

The shape parameter of the distribution of the fixed cost γ approximately equals 3.1, which

suggests a large degree of dispersion in the shock. Without heterogeneity in the fixed cost per vari-

ety and destination, such a parameter would be assuming larger values. Moreover, the correlation

between the productivity and flexibility distribution is negative: more productive firms are more

likely to draw unfavorable draws of flexibility. The result suggests that, to the extent by which

flexibility and productivity are endogenous choices of firms, there is a trade-off between the ability

to increase volumes at low costs and the ability to expand the scope at low costs.

The estimated trade elasticity with respect to iceberg trade costs has a value of 3.3 (US as

reference) and 4.28 (China as reference) not far from the consensus in the literature (Caliendo

and Parro, 2015; Simonovska and Waugh, 2014). In “single attribute” models, the trade elasticity

would equal the shape parameter of the distribution of productivities κ while in our model it

also depends on γ and α. As our estimated trade elasticity is in line with the consensus in

the literature, we can conclude that ignoring the heterogeneity in flexibility would yield biased

15In the counterfactual analysis, we use the estimates from column (1) of Table 3, which uses the United Statesas reference country.

19

estimates of the distribution of firms’ productivity. In particular, ignoring flexibility would cause

an underestimation of productivity dispersion. The derivations are in appendix D.2.

As the distribution of sales within a firm is controlled by the parameters θ(σ−1), the relatively

small value of θ suggests that the skewness of within-firm sales is mainly driven by the demand

rather than the marginal cost schedule of firms. In other words, although marginal cost rises

relatively slowly with the scope, the differences in demand are magnified by the demand elasticity

of substitution.

Table 3: Estimation of Θ (SMM)

Pooling Sample Estimation

Description \Reference Country (1) United States (2) China

κ Shape par. of productivity distr1.011*** 1.088***

(0.032) (0.031)

α Correlation productivity fixed cost-0.744** -0.742***

(0.291) (0.200)

βm Shift par. of fixed cost distr.1.160** 1.111***

(0.476) (0.690)

γ Shape par. of fixed cost distr.3.119** 4.899***

(1.147) (0.690)

θ Elas. of m.cost with distance from core0.205*** 0.131***

(0.068) 0.013

σ Elasticity of substitution1.812*** 1.826***

(0.222) (0.142)

United States as the reference country. Bootstrapped standard errors are reported

in parentheses; *** p<0.01, ** p<0.05, * p<0.1.

As displayed in our third stylized fact, the determinants of firms’ flexibility might be heteroge-

neous across industries. As a result, our estimated parameters are likely to be industry specific. To

test this hypothesis, we estimate the parameters at the industry-level. As our moments require the

presence of firms selling a sufficient number of products (32 in our case), we focus on the following

eight industries out of fifteen: Vegetable Products, Foodstuffs, Metals, Transportation, Chemicals

& Allied Industries, Machinery & Electrical, Textile, and Miscellaneous. Results are provided in

Table 4. Given that the sample size of each industry becomes much more limited, and that firms

exporting a sufficient number of products also become less ubiquitous within each industry, the by-

industry parameters are less precisely estimated relative to our baseline specification, particularly

so for Foodstuffs and Transportation.

The shape of the distributions of productivity and flexibility, and their correlation, exhibit a

large degree of heterogeneity across industries. In particular, γ ranges between 1.6 to 4.5, which

highlights higher dispersion in the flexibility shock at the industry-level relative to the sample

of all manufacturing firms. The correlation between productivity and flexibility, captured by the

parameter α, ranges between −1.4 and −0.6. Though for many industries we cannot reject the

null hypothesis that α = 0, we detect the statistical significance for Machinery & Electrical and

20

Miscellaneous industries. The prevalent negative sign on α suggests that more productive firms

are likely drawing unfavorable levels of flexibility.

Such a result highlights industry heterogeneity in the determinants of the trade-off between

sale and scope decisions of firms. For instance, in the metals industry, the most productive firms

are also likely to pay high fixed costs in order to introduce new products in the destination while

the least productive firms pay low fixed costs. In the textile industry, the estimated value of α is

not statistically different from zero. In this case, productivity and flexibility are uncorrelated: the

likelihood of being flexible is not related to the productivity of the firm.

Table 4: Estimation of Θ by Subset of Industries

Industry Category HS-Code κ α βm γ θ σ

Vegetable Products 6 - 15 1.157*** -0.678 1.067*** 2.966* 0.258*** 1.777***

(0.395) (0.614) (0.365) (1.639) (0.052) (0.315)

Foodstuffs 16 - 24 1.003 -0.807 1.531*** 2.372 0.258*** 1.844**

(1.729 ) (1.162) (0.389) (2.015) (0.057) (0.665)

Chemicals & Allied Industries 28 - 38 2.071*** -1.183 1.019*** 4.458*** 0.103*** 2.729**

(0.431) (1.320) (0.253) (1.562) (0.036) (1.015)

Textile 50 - 63 1.270*** -0.596 1.053** 3.481*** 0.254*** 1.685**

(0.059) ( 0.900) ( 0.429) (0.897) (0.068) ( 0.627)

Metals 72 - 83 1.024*** -0.858 1.356*** 1.836* 0.237*** 1.913***

(0.281) (0.595) (0.279) (1.083) (0.069 ) (0.422 )

Machinery & Electrical 84 - 85 1.003*** -1.456*** 0.534* 1.595** 0.195*** 2.252***

(0.209) (0.307) (0.280) (0.658) ( 0.033 ) (0.195)

Transportation 86 - 89 1.491 -0.810 0.996** 2.142* 0.258*** 2.000***

(1.284) (0.827) ( 0.436) ( 1.146) (0.014) (0.521 )

Miscellaneous ≥90 1.012*** -0.719*** 1.151** 2.826*** 0.261*** 1.746***

(0.175) (0.227 ) ( 0.451) ( 0.638 ) (0.043) ( 0.163)

United States as the reference country. The estimates using China as reference country are similar. Bootstrapped

standard errors are reported in parentheses; *** p<0.01, ** p<0.05, * p<0.1.

4.4 Model and Stylized Facts

This section shows how the parametrized model explains the three stylized facts we document. To

use our calibrated model for replicating the plots and figures shown in section 2, we simulate the

behavior of 1, 000, 000 firms using the industry-specific parameters as provided in Table 4.

4.4.1 Exporter Scope across Firms and Destinations

Let θ = θ(σ − 1) and γ = (γ + 1)(σ − 1). The scope (10) of the firm with cost draw c and fixed

cost shock β becomes:

δij(c, β) = δ +αγ + γ

θ(γ + 1)ln ci −

1

θ(γ + 1)ln

(fijwj

)+

αγ + γ

κθ(γ + 1)ln

(λijLjLi

)− 1

θln c− 1

θln β (21)

where δ is a positive constant that depends on the parameters of the model, and λij is the trade

share of country i’s exports over total expenditures in j. The scope of an exporter is decomposed

21

into several determinants. The scope declines with firm-specific marginal cost c and the firm-

destination specific fixed cost β.

Both the origin size Li and the shift parameter of the productivity distribution ci affect the

scope of exporters. In line with the evidence of Macedoni (2017), exporter’s scope increases with

the size of the destination Lj and with its per capita income wj.16 Since the fixed cost of entry is

expressed in foreign labor units, as wj increases, only firms with high enough productivity - and,

thus, larger scope - are active in the destination. Firms enjoy higher total and per product sales

in larger destinations, which in turn make them better able to cover the fixed costs per product

and the fixed entry cost. Finally, product scope depends on two bilateral variables: fij and the

export trade share λij. The easier it is to reach a destination j, the larger the scope of the firm.

The model is consistent with the first stylized fact. The scope of exporters from an origin

depends on firm specific and destination specific characteristics that would be captured by firm

and destination fixed effects. Moreover, the presence of the fixed cost shock β introduces the

firm-destination specific component that is suggested by data.

4.4.2 Sale and Scope Disconnect

Figure 7a illustrates the disconnect between productivity and scope arising in our calibrated model.

The model can replicate the disconnect observed in the data: for any level of productivity, there

are several narrow and wide-scope firms. Similarly, Figure 7b shows the simulated relationship

between scope and sales, which is similar to the relationship uncovered in the data. Narrow scope

firms are present at any level of sales, and there are wide-scope firms for medium to high levels of

sales.

Figure 7: Sale and Scope Disconnect

(a) Productivity and Scope (b) Sales and Scope (c) Demeaned Sales and Scope

The dispersion in flexibility γ and the correlation between productivity and flexibility α both

affect the disconnect. Larger values of γ increase the slope of the line of best fit between scope and

productivity because, as γ increases, favorable fixed cost shocks become rarer, and, thus, there are

16The mechanism is different than Macedoni (2017), in which non-homothetic preferences drive the positive rela-tionship between per capita income and scope. If fij is expressed in foreign labor units, such a positive relationship,however, disappears.

22

fewer low-productivity firms. Moreover, larger values of γ reduce the dispersion around the line of

best fit. The parameter α positively affects the sign of the slope of the line of best fit. For positive

values of α more productive firms are also more likely to receive low values of β: the correlation

between scope and productivity improves.

The distribution of the scope, conditional on the realization of c, follows a distribution that

is similar to the distribution observed in the data. The larger the γ, the larger the mass of firms

producing a narrow scope. The larger the α, the larger the average productivity in a destination,

and the smaller the skewness of the simulated distribution.

Figure 8: Distribution of Scope Conditional on Productivity

4.4.3 What Explains the Disconnect?

In the empirical analysis, we found that the scope conditional on sales is related to firms’ charac-

teristics. In the model, the conditional scope of active firms depends on the realization of the fixed

cost shock. The relationship uncovered in the data between conditional scope and firms’ character-

istics mainly depends on how the flexibility shock affect the selection of firms into export markets.

Hence, through the lens of the model the third stylized fact suggests that firms’ characteristics

other than productivity affect the scope of firms, but it does not indicate a causal relationship.

To gather some intuition, let us consider the expected realization of the fixed cost shock β for

active firms, conditional on a firm drawing c. In other words, let us compute the expected value

of β conditional on a firm being active (i.e. β ≤ βij∗(c)) and weight it by the probability of a firm

with cost c being active:

E[β|c] =γ

γ + 1

β∗ij(c∗ij)

γ+1c∗σ−1ij

βγmc−αγ−γ (22)

The expected value of β depends on productivity 1c

with an elasticity of (αγ) + γ. The reason why

23

the expected realization of the fixed cost shock varies with productivity is twofold. First, there is

a selection effect (γ), which is independent of the correlation between β and c. Since only firms

with high productivity are able to remain active despite high fixed cost shocks, we observe that,

on average, more productive firms experience higher shocks.

The correlation between fixed cost draw and marginal cost draw, represented by the parameter

α, drives the second mechanism. With positive values of α, more productive firms are likely more

flexible. Hence, they are more likely to be active, thus, increasing the positive relationship between

average shock and productivity. On the other hand, with a negative α, more productive firms are

more likely to draw high fixed cost shocks. As more productive firms are then more likely to be

inactive, the relationship between E[β|c] and productivity flattens.

4.4.4 Scope and Sales Distributions

Using Chinese data, we document distributions for firms’ scope and sales that approximate a

Pareto and a log-normal distribution. Figure 9 shows that the model generated distributions of

scope and sales are consistent with what we observe in data.

Figure 9: Distribution of Scope and Sales

In “single attribute” models with CES preferences, the distribution of sales follows the distri-

bution of productivities (Mrazova et al., 2017). Hence, if productivity is Pareto distributed, so

are the sales. In our model, the two Pareto distributions of productivity and flexibility generate a

distribution of sales that resembles a log-normal distribution. To understand the result, consider

the firms at the bottom of the productivity distribution. As the Pareto distribution has a large

mass at the bottom, there is a large mass of less productive firms with low sales. The shock to

the fixed cost per variety causes some of these firms to not produce and others to produce more

varieties than a “single attribute” model would predict. Both channels reduce the mass of firms

at low sales and shift it towards higher levels of revenues.

24

4.5 Towards the Understanding of Firm Heterogeneity

This section illustrates the quantitative relevance of heterogeneity in firms’ flexibility. In the spirit

of Hottman et al. (2016) we compute how much of the variation in product scope and sales across

firms and destination could be attributed to variation in firms’ flexibility.

Flexibility and Scope

How much does the heterogeneity in flexibility explain the scope decisions of firms? To answer

this question, we consider the following counterfactual analysis. We simulate 1, 000, 000 Chinese

firms following the procedure described in the previous section. We choose alternative values for

our parameters to quantify the role of the correlation between productivity and flexibility, the

dispersion in flexibility, and the heterogeneity across industries. Using the simulated sample of

firms, we then compare the goodness of fit (R2) resulting from the following two regressions:

1) ln(# Productsfj) = af + dj + cfj

2) ln(# Productsfj) = af + dj + ln βfj + cfj

where af and dj are firm and destination fixed effects, cfj is the error term, and ln βfj is the log

of the simulated fixed cost per variety and destination j of firm f . We consider the difference

between the two goodness of fit (R22−R2

1) as a measure of the explanatory power of the fixed cost

shock β. We discretize the continuous scope of our model, hence, the R2 in regression 2) is less

than one.

Table 5: Role of Flexibility in Scope Decisions of Exporters

Sample Parameters R21 R2

2 R22 −R2

1

(1) Pooled Manufacturing Sample Original Estimates 0.11 0.87 0.76

(2) Pooled Manufacturing Sample α = 0 0.70 0.90 0.20

(3) Pooled Manufacturing Sample High γ 0.16 0.87 0.71

(4) Pooled Manufacturing Sample Low γ 0.08 0.82 0.74

(5) By Industry Sample Industry-level Estimates 0.18 0.82 0.64

Detailed explanation in the text. The calibrated parameters for (1) to (4) are obtained from the sample of

manufacturing firms with the United States as the reference country. In row (2), we set α = 0. In row (3),

we set γ two times as big as our calibrated value, and set it as half as big in row (4). Parameters for (5) are

separately estimated for each industry.

As an example, consider the first row of Table 5. We simulate the behavior of Chinese firms

using the parameters estimated in the column (1) of Table 3. Then, we regress the simulated scope

of exporters against firm fixed effects and destination fixed effects. When, in addition to the firm

and destination fixed effects, we include our fixed cost shock β, the R2 of the regression has an

25

absolute increase of 76%. We then conclude that the heterogeneity in the fixed cost shock explains

about 76% of the variation in scope across firms and destination.

A more conservative prediction of the quantitative effects of heterogeneity in flexibility on scope

is the following. In our first stylized fact, we showed that firm fixed effects and destination fixed

effect accounted for 37-44% of the variation in scope, a larger number than the 11% obtained in

the row (1) of Table 5. Assuming that R21 = 37%, the explanatory power of flexibility becomes

87%− 37% = 40%, which is still a larger number than both firm and destination fixed effects.

We further decompose the sources of the explanatory power of the fixed cost shock with the

following two exercises. First, we repeat the analysis using the originally estimated parameters

but setting α = 0. When we impose that the distributions of productivity and flexibility are

independent, the explanatory power of β falls from 76% to 20%. Second, we use the original

estimated parameters but we set a high value for γ. A high value of γ reduces the dispersion in the

fixed cost, which is equivalent to reducing the degree of heterogeneity in flexibility. In such a case,

the explanatory power of β falls from 76% to 71%. On the other hand, a lower value of γ reduces

the explanatory power of flexibility to 74%. These counterfactual exercises highlight the role of α.

The quantitatively relevant effect of flexibility on the product scope of exporters is mainly due to

its correlation with productivity rather than the degree of dispersion of the shock.

Finally, we repeat the analysis using our industry-level estimates from Table 4. Heterogeneity

in flexibility explains 64% of the variation in scope across firms and destination.

Flexibility and Sales

We now turn to evaluate how well firm flexibility could explain the heterogeneity in firm sales.

Similar to the previous exercise, we simulate 1, 000, 000 Chinese firms, choosing alternative values

for our parameters. Using the simulated sample of firms, we then compare the goodness of fit (R2)

resulting from the following two regressions:

1) ln(Salesfj) = af + dj + cfj

2) ln(Salesfj) = af + dj + ln βfj + cfj

where af and dj are firm and destination fixed effects, cfj is the error term, and ln βfj is the log

of the simulated fixed cost per variety and destination j of firm f . We consider the difference

between the two goodness of fit (R22−R2

1) as a measure of the explanatory power of the fixed cost

shock β. Results are in table 6.

Heterogeneity in the fixed cost shock explains about 16% of the variation in sales across firms

and destination. Similar to the previous results, the explanatory power of flexibility is mainly

driven by the correlation between flexibility and productivity. When we set such a correlation to

zero, we find that the R2 improves only by 4%. However, the dispersion in the flexibility shock,

which is inversely related to γ, has a larger effect on sales. Doubling γ reduces the explanatory

26

power by half. Finally, using the industry-specific estimates, flexibility improves R2 by 12%.

In standard models of multi-product firms, total sales of an exporter only depend on firms’

characteristics, such as productivity, product appeal, and scope (which could be determined by

the firms’ attributes), and destination characteristics. Through the lens of our model, firm and

destination characteristics explain a large portion of the variation in export sales. However, het-

erogeneity in flexibility, through its effect on firms’ selection into export markets and the level of

scope, further improves our understanding of export sales heterogeneity.

Table 6: Role of Flexibility in Export Sales

Sample Parameters R21 R2

2 R22 −R2

1

(1) Pooled Manufacturing Sample Original Estimates 0.79 0.95 0.16

(2) Pooled Manufacturing Sample α = 0 0.92 0.96 0.04

(3) Pooled Manufacturing Sample High γ 0.89 0.97 0.08

(4) Pooled Manufacturing Sample Low γ 0.71 0.90 0.19

(5) By Industry Sample Industry-level Estimates 0.80 0.92 0.12

Detailed explanation in the text. The calibrated parameters for (1) to (4) are obtained from the sample of

manufacturing firms with the United States as the reference country. In row (2), we set α = 0. In row (3),

we set γ two times as big as our calibrated value and set it as half as big in row (4). Parameters for (5) are

separately estimated for each industry.

We can draw a parallel with the results of Hottman et al. (2016). The authors, in fact,

documented that the sales heterogeneity of firms selling to the US is due mainly to product

appeal, which explains 50%-75% of the variation in sales, and to product scope, which explains

20%-25% of the variation. Our result differs in that we consider Chinese exporters and study the

heterogeneity across firms and destination. Moreover, we do not explicitly model firms’ product

appeal, which is captured by the firm productivity 1/c, as the two concepts are isomorphic in our

model and our moments. Yet, as flexibility accounts for 65%-75% of the variation in scope, and

12%-16% of the variation in sales, we can infer that scope explains between 12/65 = 18% and

16/75 = 21% of total sales. Such a result is in line with the findings of Hottman et al. (2016).

5 Conclusions

We have argued that “single attribute” models, in which productivity is the only source of firms’

heterogeneity, fail to explain several new stylized facts for multi-product exporters. We build a

model in which firms differ in productivity and flexibility - the ability with which they introduce

new varieties at low costs. Firms’ flexibility explains between 65% to 75% of the total variation of

scope across firms and destinations, and between 12% to 16% of the variation of firms’ sales.

The literature has considered several theories that explain firms’ decisions to improve produc-

tivity or flexibility (He, 1992). The firms’ choices are, ultimately, depending on the presence of

27

economies or diseconomies of scope (Arkolakis et al., 2015; Nocke and Yeaple, 2014). The results of

our model shed some light on the topic. First of all, we find that, on average, firms face a trade-off

between productivity and flexibility: more productive firms are likely to face higher fixed cost per

variety when exporting, while the fixed costs are lower for less productive firms. Moreover, the

trade-off appears to be heterogeneous across industries. While in some industries flexibility and

productivity are negatively correlated, the opposite is true for other industries.

References

C. Arkolakis, S. Ganapati, and M.-A. Muendler. The extensive margin of exporting products: Afirm-level analysis. Mimeo. Previously NBER Working Paper 16641, 2015.

R. Armenter and M. Koren. Economies of Scale and the Size of Exporters. Journal of the EuropeanEconomic Association, 13(3):482–511, 2015.

A. B. Bernard, J. B. Jensen, S. J. Redding, and P. K. Schott. Firms in International Trade. Journalof Economic Perspectives, 21(3):105–130, 2007.

A. B. Bernard, S. J. Redding, and P. K. Schott. Multiproduct Firms and Trade Liberalization.The Quarterly Journal of Economics, 126(3):1271–1318, 2011.

A. B. Bernard, E. Dhyne, G. Magerman, K. Manova, and A. Moxnes. The Origins of FirmHeterogeneity: A Production Network Approach. Mimeo, 2018.

L. Brandt, J. Van Biesebroeck, and Y. Zhang. Challenges of working with the Chinese NBSfirm-level data. China Economic Review, 30:339–352, 2014.

L. Caliendo and F. Parro. Estimates of the Trade and Welfare Effects of NAFTA. Review ofEconomic Studies, 82(1):1–44, 2015.

T. Chaney. Distorted Gravity: The Intensive and Extensive Margins of International Trade.American Economic Review, 98(4):1707–21, 2008.

I. Cherkashin, S. Demidova, H. L. Kee, and K. Krishna. Firm heterogeneity and costly trade:A new estimation strategy and policy experiments. Journal of International Economics, 96(1):18–36, 2015.

M. Dai, M. Maitra, and M. Yu. Unexceptional exporter performance in China? The role ofprocessing trade. Journal of Development Economics, 121:177–189, 2016.

S. Das, M. J. Roberts, and J. R. Tybout. Market Entry Costs, Producer Heterogeneity, and ExportDynamics. Econometrica, 75(3):837–873, 2007.

S. Demidova, H. L. Kee, and K. Krishna. Do trade policy differences induce sorting? Theory andevidence from Bangladeshi apparel exporters. Journal of International Economics, 87(2):247 –261, 2012.

B. C. Eaton and N. Schmitt. Flexible Manufacturing and Market Structure. American EconomicReview, 84(4):875–88, 1994.

28

J. Eaton, S. Kortum, and F. Kramarz. An Anatomy of International Trade: Evidence From FrenchFirms. Econometrica, 79(5):1453–1498, 2011.

C. Eckel and J. P. Neary. Multi-Product Firms and Flexible Manufacturing in the Global Economy.Review of Economic Studies, 77(1):188–217, 2010.

R. C. Feenstra, Z. Li, and M. Yu. Exports and credit constraints under incomplete information:Theory and evidence from China. Review of Economics and Statistics, 96(4):729–744, 2014.

E. Gal-Or. Flexible manufacturing systems and the internal structure of the firm. InternationalJournal of Industrial Organization, 20(8):1061 – 1096, 2002.

J. C. Hallak and J. Sivadasan. Product and process productivity: Implications for quality choiceand conditional exporter premia. Journal of International Economics, 91(1):53–67, 2013.

H. He. Investments in flexible production capacity. Journal of Economic Dynamics and Control,16(3):575–599, 1992.

C. Hottman, S. J. Redding, and D. E. Weinstein. Quantifying the sources of firm heterogeneity.The Quarterly Journal of Economics, 131:1291––1364, March 2016.

H. L. Kee and K. Krishna. Firm-Level Heterogeneous Productivity and Demand Shocks: Evidencefrom Bangladesh. American Economic Review, 98(2):457–62, May 2008.

T. J. Klette and S. Kortum. Innovating Firms and Aggregate Innovation. Journal of PoliticalEconomy, 112(5):986–1018, October 2004.

J. Levinsohn and A. Petrin. Estimating Production Functions Using Inputs to Control for Unob-servables. The Review of Economic Studies, 70(2):317–341, 2003.

L. Macedoni. Large multiproduct exporters across rich and poor countries: Theory and evidence.Working Paper, 2017.

K. Manova and Z. Yu. How firms export: Processing vs. ordinary trade with financial frictions.Journal of International Economics, 100:120–137, 2016.

T. Mayer, M. J. Melitz, and G. I. P. Ottaviano. Market Size, Competition, and the Product Mixof Exporters. American Economic Review, 104(2):495–536, 2014.

T. Mayer, M. J. Melitz, and G. I. Ottaviano. Product Mix and Firm Productivity Responses toTrade Competition. NBER Working Paper 22433, 2016.

P. Milgrom and J. Roberts. The Economics of Modern Manufacturing: Technology, Strategy, andOrganization. American Economic Review, 80(3):511–528, June 1990.

G. Mion, L. D. Opromolla, and A. Sforza. The Diffusion of Knowledge via Managers’ Mobility.CEPR Discussion Paper 11706, 2016.

M. Mrazova, J. P. Neary, and M. Parenti. Sales and Markup Dispersion: Theory and Empirics.CEPR Discussion Paper 12044, 2017.

V. Nocke and S. Yeaple. Globalization and multiproduct firms. International Economic Review,55(4):993–1018, 2014.

29

M. L. Parisi, F. Schiantarelli, and A. Sembenelli. Productivity, innovation and R&D: Micro evi-dence for Italy. European Economic Review, 50(8):2037–2061, November 2006.

J. E. Rauch. Networks versus markets in international trade. Journal of International Economics,48(1):7–35, 1999.

M. J. Roberts, D. Y. Xu, X. Fan, and S. Zhang. The Role of Firm Factors in Demand, Cost, andExport Market Selection for Chinese Footwear Producers. Review of Economic Studies, 85(4),October 2018.

I. Simonovska and M. Waugh. Trade models, trade elasticities, and the gains from trade. NBERWorking Paper 20495, 2014.

D. Thesmar and M. Thoenig. From Flexibility to Insecurity: How Vertical Separation Ampli-fies Firm-Level Uncertainty. Journal of the European Economic Association, 5(6):1161–1202,December 2007.

O. Timoshenko. Product switching in a model of learning. Journal of International Economics,95(2):233–249, 2015.

M.-C. Tseng. Strategic choice of flexible manufacturing technologies. International Journal ofProduction Economics, 91(3):223 – 227, 2004.

M. Yu. Processing trade, tariff reductions and firm productivity: evidence from Chinese firms.The Economic Journal, 125(585):943–988, 2015.

30

Appendix

A Summary Statistics for ASIP and Customs Data

Table A.1: Match Statistics Between ASIP and China Custom Data

Year # Matched Firms % of Total Number % of Total Export2000 16,596 35.32% 20.91%2001 19,597 37.44% 24.41%2002 23,112 37.51% 27.17%2003 27,333 35.49% 26.35%2004 41,955 41.52% 37.95%2005 44,212 35.62% 35.61%2006 50,648 33.42% 36.28%

Match Statistics from matching firms in the ASIP and China Custom Data. The matchingcriteria are in the main text of the paper.

Table A.2: Summary Statistics (2006)

Total Exporters

Product ScopeNumber of Firms Export ValueN % of total Value % of total

1 34,879 23.02 26,624.71 6.402 21,728 14.34 23,346.14 5.613 14,860 9.81 21,976.69 5.284 10,870 7.17 18,912.32 4.545 8,496 5.61 15,538.85 3.73

6− 10 22,380 14.77 53,065.52 12.7511− 30 21,391 14.12 79,534.55 19.1031− 50 5,290 3.49 31,152.95 7.4851− 70 2,982 1.97 17,115.56 4.11> 70 8,658 5.71 129,058.06 31.00Total 151,534 100 416,325.3 100

Matched Sample

Product ScopeNumber of Firms Export ValueN % of total Value % of total

1 10,892 21.51 13,197.05 8.742 7,946 15.69 12,402.61 8.213 5,936 11.72 11,797.43 7.814 4,462 8.81 10,838.26 7.185 3,528 6.97 8,911.25 5.90

6− 10 9,186 18.14 29,835.19 19.7511− 30 7,406 14.62 37,467.43 24.8131− 50 934 1.84 10,839.69 7.1851− 70 219 0.43 4,691.00 3.11> 70 139 0.27 11,051.66 7.32Total 50,648 100.00 151,031.57 100.00

Products are defined at HS eight-digit level. Export value is in million ofU.S. dollars.

31

Table A.3: Classification of Industries

Industry Description Range of HS 2-Digit CodeAnimal & Animal Products 01-05Vegetable Products 06-15Foodstuffs 16-24Mineral Products 25-26Chemicals & Allied Industries 28-38Plastics & Rubbers 39-40Raw Hides, Skins, Leather & Furs 41-43Wood & Wood Products 44-49Textile 50-63Footwear & Headgear 64-67Stone & Glass 68-71Metals 72-83Machinery & Electrical 84-85Transportation 86-89Miscellaneous 90-97

Table A.4: Proportion of Exporters by Destination

Destination Probability of being ExporterUnited States 23.90%

Japan 17.78%Hong Kong 16.78%South Korea 15.29%

Germany 13.99%Italy 12.17%

United Kingdom 11.27%India 11.14%

Netherlands 11.12%Taiwan 9.82%Russia 9.75%

United Arab Emirates 9.34%Canada 9.25%Spain 8.99%

Australia 8.71%Singapore 8.40%Indonesia 6.93%

France 6.54%

Matched sample. Probability of being exporter in a destination is the ratioof the number of exporters in that destination relative to the total numberof matched domestic firms in 2006.

32

B Stylized Facts

Exporter Scope across Firms and Destinations

Table B.1: Decomposition of Product Scope

Sample Year Model Fit (R2) dj af2000 0.30 0.01 0.292001 0.31 0.01 0.302002 0.32 0.01 0.312003 0.34 0.01 0.322004 0.35 0.01 0.342005 0.36 0.01 0.352006 0.37 0.01 0.36

All Chinese Exporters. R2 from regression (1).

Sale and Scope Disconnect

Figures B.1 and B.2 replicate the stylized fact without demeaning sales and scope by the num-ber of products. Figure B.3 displays the relationship between log scope and log sales, which arenormalized with industry average. Figure B.4 shows the relationship between log scope and our es-timated productivity. Figure B.5 displays the relationship between product scope and value addedper worker. We exclude the single-product firms from our sample, and re-plot the relationshipbetween sale and scope in Figure B.6 and B.7. The pattern remain similar to our baseline.

Figure B.1: Product Scope and Sales of Exporters in the U.S. (2006)

(a) All Sample (b) Matched Sample

33

Figure B.2: Product Scope and Productivity of Exporters in the U.S. (2006)

Figure B.3: Demeaned Log Scope and Log Sales

(a) All Sample (b) Matched Sample

Figure B.4: Demeaned Log Scope and Estimated Productivity

34

Figure B.5: Demeaned Scope and Value Added per Worker

(a) Levels (b) Normalized by Industry Averages

Figure B.6: Excluding Single-Product Firm: Scope and Sales

(a) All Sample (b) Matched Sample

Figure B.7: Excluding Single-Product Firm: Scope and Estimated Productivity

35

Local Polynomial Smoothing Fitting

Instead of fitting the scope-sale relationship using linear function, we adopt a non-parametricmethod using LOWESS (locally weighted scatter-plot smoothing).The fitted curves display thesimilar pattern to the baseline figures.

Figure B.8: LOWESS: Scope and Sales

(a) All Sample (b) Matched Sample

Figure B.9: LOWESS: Scope and Estimated Productivity

36

Disconnect by Industry

37

38

39

40

41

42

43

Disconnect by Destination

We replicate the stylized facts by destination for Germany (Figure B.10), United Kingdom (FigureB.11), India (Figure B.12), Italy (Figure B.13), Japan (Figure B.14), and South Korea (FigureB.15). In each figure, Panel (a) display the disconnect between sales and scope, and Panel (b)display the product scope distribution by quartile of sales.

Figure B.10: Germany

(a) Sales, Productivity and Scope (b) Scope Distribution

44

Figure B.11: United Kingdom

(a) Sales, Productivity and Scope (b) Scope Distribution

Figure B.12: India

(a) Sales, Productivity and Scope (b) Scope Distribution

45

Figure B.13: Italy

(a) Sales, Productivity and Scope (b) Scope Distribution

Figure B.14: Japan

(a) Sales, Productivity and Scope(b) Scope Distribution

46

Figure B.15: South Korea

(a) Sales, Productivity and Scope(b) Scope Distribution

Alternative Classifications of Goods

Figure B.16 and B.17 display the sales-scope disconnect, when we define a product as a HS six-digitgood or as a HS four-digit good. Figure B.18 displays the disconnect between productivity andscope using the same classifications. Finally, we divide firms into those that produce homogeneousgoods and those that produce differentiated goods following the definition by Rauch (1999).

Figure B.16: HS six-digit: Scope and Sales

(a) All Sample (b) Matched Sample

47

Figure B.17: HS four-digit: Scope and Sales

(a) All Sample (b) Matched Sample

Figure B.18: Scope and Estimated Productivity

(a) HS six-digit (b) HS four-digit

48

49

Alternative Years

B.1 What Explains the Disconnect?

Table B.2 reports univariate regression of product scope (conditional on sales) on a variety offirm characteristics. We use the logarithmic form for both dependent and independent variables.Firm controls include capital, employment, capital intensity, total asset, total liability, value addedper worker, R&D investment, advertisement investment, firm age, state-equity share, and foreign-equity share. Table B.3 reports pooling regression of product scope (conditional on sales) on avariety of firm characteristics.

Table B.2: Correlation Between Scope (Conditional on Sales) and Firm Characteristics (Univariate Regression)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)Animal & Chemicals Footwear Machinery Mineral Plastics Leather Stone Vegetable Wood

Char. \Ind Products Allied Foodstuffs Headgear Electrical Metals Products Others Rubbers Furs Glass Textile Transport Products Products

Capital (K) -0.01 0.01*** -0.01*** 0.03*** 0.01*** -0.01*** -0.02*** 0.03*** 0.02*** 0.01*** 0.00*** -0.03*** 0.01*** -0.01 0.01***(0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Employment -0.01 0.01*** 0.02*** 0.05*** 0.03*** -0.01*** -0.02** 0.06*** 0.03*** 0.02*** -0.00 0.05*** 0.03*** 0.00 0.03***(0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00)

K-Intensity 0.06 -0.03*** -0.12*** -0.24*** -0.08*** 0.00 -0.07*** -0.03* 0.01 -0.09* 0.01 -0.45*** -0.05 -0.06* 0.02*(0.07) (0.01) (0.02) (0.09) (0.01) (0.01) (0.02) (0.02) (0.01) (0.05) (0.01) (0.02) (0.03) (0.04) (0.01)

Asset -0.01** 0.02*** -0.00 0.05*** 0.02*** -0.01*** -0.03*** 0.04*** 0.03*** 0.01** 0.01*** -0.03*** 0.03*** -0.01 0.01***(0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00)

Liability -0.01** 0.02*** -0.00 0.03*** 0.02*** -0.02*** -0.03*** 0.03*** 0.02*** 0.01** 0.00** -0.03*** 0.03*** -0.01 0.01***(0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00)

VA per Worker -0.00 0.02*** -0.03*** -0.01** 0.02*** -0.02*** -0.04*** -0.00** 0.01*** -0.03*** 0.02*** -0.09*** 0.07*** -0.01 -0.03***(0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.01) (0.00)

R&D 0.01 0.01*** -0.00 0.02*** 0.01*** 0.00 -0.02 0.02*** 0.01*** 0.00 0.01** -0.01** 0.02*** 0.03*** 0.02***(0.02) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.01) (0.00)

Ads. -0.01 0.02*** 0.01** 0.02*** 0.02*** -0.00 -0.02** 0.03*** 0.02*** 0.01** 0.02*** 0.00 0.05*** -0.01* -0.01***(0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00)

Firm Age -0.01 0.02*** 0.01** 0.04*** 0.01*** 0.00 -0.02 0.03*** 0.01*** 0.02*** 0.01*** 0.00 -0.02*** -0.00 0.03***(0.01) (0.00) (0.01) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.01) (0.00) (0.00) (0.01) (0.01) (0.00)

State Share -0.05 -0.04*** -0.05** -0.13*** -0.04*** -0.04*** 0.03 0.06*** -0.09*** 0.22*** 0.03** -0.09*** 0.11*** -0.02 0.01(0.05) (0.01) (0.02) (0.02) (0.01) (0.01) (0.04) (0.01) (0.02) (0.05) (0.01) (0.02) (0.02) (0.05) (0.02)

Foreign Share 0.13*** 0.04*** 0.02 0.08*** -0.02*** 0.04*** 0.03 0.01 0.04*** 0.08*** 0.05*** 0.18*** -0.17*** 0.08*** 0.04***(0.03) (0.01) (0.01) (0.01) (0.00) (0.01) (0.03) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01)

Table B.3: Correlation Between Scope (Conditional on Sales) and Firm Characteristics (Pooling Regression)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)Animal & Chemicals Footwear Machinery Mineral Plastics Leather Stone Vegetable Wood

Char. \Ind Products Allied Foodstuffs Headgear Electrical Metals Products Others Rubbers Furs Glass Textile Transport Products Products

Capital (K) 0.06 -0.02** -0.09*** -0.00 -0.02*** 0.03*** 0.24** -0.03*** 0.07*** -0.03 -0.02 -0.11*** -0.09*** 0.06 -0.02(0.08) (0.01) (0.03) (0.03) (0.01) (0.01) (0.10) (0.01) (0.01) (0.04) (0.01) (0.02) (0.02) (0.08) (0.03)

Employment 0.00 -0.06*** 0.04 -0.06 -0.00 -0.01 0.15 0.09*** -0.06*** -0.19*** -0.01 0.11*** 0.03 0.04 0.01(0.10) (0.01) (0.03) (0.04) (0.01) (0.01) (0.14) (0.01) (0.01) (0.06) (0.02) (0.02) (0.02) (0.08) (0.03)

K-Intensity -0.59 -0.12*** 0.01 -2.14*** -0.14*** 0.06*** -0.57 0.01 -0.29*** 1.52 0.31*** -0.35*** -0.03 -0.47 0.04(0.61) (0.03) (0.10) (0.67) (0.04) (0.01) (0.56) (0.05) (0.04) (1.50) (0.07) (0.08) (0.13) (0.47) (0.05)

Asset -0.21 0.10*** 0.07* 0.19*** 0.04*** 0.01 -0.51*** 0.03* 0.07*** 0.37*** -0.00 0.24*** 0.09** 0.04 -0.01(0.22) (0.02) (0.04) (0.04) (0.01) (0.02) (0.17) (0.01) (0.02) (0.09) (0.03) (0.03) (0.04) (0.09) (0.05)

Liability 0.11 -0.02* 0.01 -0.06** 0.01 -0.07*** 0.14* -0.03*** -0.02 -0.20*** 0.03* -0.18*** 0.00 -0.07 0.04(0.15) (0.01) (0.03) (0.03) (0.01) (0.01) (0.08) (0.01) (0.01) (0.05) (0.01) (0.02) (0.02) (0.06) (0.03)

VA per Worker 0.10* -0.02** -0.01 0.12*** -0.01 -0.03*** 0.22* -0.01 -0.05*** -0.33*** 0.03* 0.00 0.05*** -0.02 -0.01(0.05) (0.01) (0.02) (0.03) (0.01) (0.01) (0.12) (0.01) (0.01) (0.06) (0.01) (0.02) (0.01) (0.04) (0.02)

R&D 0.06** 0.01*** 0.00 -0.02*** 0.01*** 0.01*** -0.01 0.01*** -0.01*** 0.05*** -0.00 -0.01** 0.00 0.00 0.01(0.03) (0.00) (0.01) (0.01) (0.00) (0.00) (0.02) (0.00) (0.00) (0.02) (0.01) (0.01) (0.01) (0.02) (0.01)

Ads. -0.09** 0.00* -0.00 0.02*** 0.00 0.00 -0.07** 0.01*** 0.02*** 0.02** 0.01** 0.02*** 0.04*** 0.02 -0.01(0.04) (0.00) (0.01) (0.01) (0.00) (0.00) (0.03) (0.00) (0.00) (0.01) (0.00) (0.01) (0.00) (0.03) (0.01)

Firm Age 0.16** -0.01* 0.04* -0.03 -0.02*** 0.03*** 0.08 0.05*** -0.02* -0.03 0.06*** 0.01 -0.02 -0.02 0.04*(0.07) (0.01) (0.02) (0.02) (0.00) (0.01) (0.07) (0.01) (0.01) (0.03) (0.01) (0.01) (0.01) (0.05) (0.02)

State Share -0.09 -0.01 -0.20*** -0.13 -0.11*** 0.01 0.62** 0.07*** -0.26*** -0.87** 0.05 -0.11** 0.12*** -0.35** 0.08(0.19) (0.02) (0.05) (0.09) (0.02) (0.03) (0.24) (0.03) (0.04) (0.36) (0.04) (0.04) (0.04) (0.16) (0.07)

Foreign Share 0.33** -0.00 -0.05 0.13*** -0.01 0.08*** 0.21* 0.11*** 0.06*** 0.05 0.02 0.21*** -0.22*** 0.10 0.00(0.15) (0.02) (0.04) (0.04) (0.01) (0.02) (0.11) (0.02) (0.02) (0.09) (0.03) (0.04) (0.03) (0.10) (0.05)

Obs 118 8,853 852 1,062 21,397 4,155 57 6,611 2,800 335 2,271 4,417 3,237 220 706R-squared 0.23 0.01 0.04 0.11 0.01 0.04 0.44 0.06 0.10 0.19 0.06 0.08 0.11 0.10 0.04

Table B.2: each point estimate is obtained by univariate regression, in which the dependent variable is the log of the scope conditional on sales and the independent variable is thelog of the firm characteristic. Table B.3: all independent variables are pooled together. *** p<0.01, ** p<0.05, * p<0.1.

C Estimation of Productivity

We use Levinsohn and Petrin (2003) method to estimate firm productivity. This method is appliedto our dataset of Chinese firms in ASIP as follows. Let yit denotes the value added of firm i inyear t, and the production function is

yt =β0 + βllit + βkkit + βmmit + ωit + εit

=βllit + φ(kit,mit) + εit

where φ(kit,mit) ≡ β0 +βkkit+ω(kit,mit). We substitute φ(kit,mit) in equation of yit with a third-order polynomial approximation in kit and mit, after which we are able to obtain the consistentestimation of the value-added equation using OLS as

yit = δ0 + βlit +3∑s=0

3−s∑j=0

δsjksitm

jit + εit

This provides the first stage of estimation, from which we obtain βl and an estimate of φit.Next, we estimate βk, which begins by computing the estimated value of φit:

φit = yit − βllit = δ0 +3∑s=0

3−s∑j=0

δsjksitm

jit − βllit

For any candidate value of β∗k , we compute the prediction for ωit as ωit − φit − β∗kkit. We assume

a consistent (nonparametric) approximation to E(ωit|ωit−1) as

ωit = γ0 + γ1ωt−1 + γ2ω2t−1 + γ3ω

3t−1 + eit

Given β, β∗k and E(ωit|ωit−1), we rewrite the sample residuals as

εit + eit = yit − βllit − β∗kkit − E(ωit|ωit−1)

Finally, we estimate βk as the solution to:

minβ∗k

∑i

∑t

(yit − βllit − β∗kkit − E(ωit|ωit−1)

)2

In practice, we use data of ASIP for 2005 and 2006. We measure value added as outcomevariable yit, employment as the freely chosen variable (lit), total fixed asset as capital (kit), andintermediate input and the sales cost as the proxy variables.17

17The sales cost for a firm is the cost of merchandise in its beginning inventory plus the net cost of merchandisepurchased minus the cost of merchandise in its ending inventory. We try different specifications using differentvariables to measure the mit, and the estimated productivity are highly positively correlated.

52

D Theory Appendix

D.1 Model’s Derivation

This section shows how to derive the closed-form expression of our parametrized model. Letθ = θ(σ − 1). Using h(ω) = exp(θω) into (10) yields:

h(δij(c, β))σ−1 =

(β∗ij(c)

β

)exp(θδij(c, β)) =

(β∗ij(c)

β

)(23)

δij(c, β) =1

θ

[ln β∗ij(c)− ln β

](24)

Using (23), the firm’s cost aggregator H(δij(c, β)) is given by:

H(δij(c, β)) =

[∫ δij(c,β)

0

h(ω)1−σdω

] 11−σ

=

[1

θ− exp(−θδij(c, β))

θ

] 11−σ

=

[1

θ− β

β∗ij(c)θ

] 11−σ

(25)

Our sales and scope disconnect (12) becomes:(h(δij(c, β))

H(δij(c, β))

)σ−1

=Rij(c, β)

σfijβ

Rij(c, β)

exp(θδij(c, β))− 1=σfijβ

θ(26)

The revenues of a variety ω of firm with cost draw c and fixed cost draw β is given by:

r(ω, c, β) = σfijβ∗ij(c)h(ω)1−σ = σfijβ

∗ij(c) exp(−θω) (27)

Integrating (27) across the varieties exported to a destination, and using (25) yields firm’s aggregaterevenues in destination j:

Rij(c, β) = σfijβ∗ij(c)H(δij(c, β))1−σ =

σfij

θ

[β∗ij(c)− β

](28)

Using our parametrized distribution for the fixed cost shock, the expected revenues over the possiblerealizations of β, conditional on c, are given by:

E[Rij(c)] =

(β∗ij(c)

βmcα

)γ ∫ β∗ij(c)

0

Rij(c, β)γβγ−1

(β∗ij(c))γ

=σfij

θ(γ + 1)

(β∗ij(c))γ+1

(βmcα)γ(29)

53

Using (26), (28) and (24), profits of a firm with cost draw c and fixed cost shock β are:

Πij(c, β) = fijβ

[(h(δij(c, β))

H(δij(c, β))

)σ−1

− δij(c, β)

]= fijβ

[Rij(c, β)

σfijβ− δij(c, β)

]=

= fijβ

[1

βθ

[β∗ij(c)− β

]− δij(c, β)

]= fijβ

[1

βθ

[β∗ij(c)− β

]− 1

θ

[ln β∗ij(c)− ln β

]]=

=fij

θ

[β∗ij(c)− β − β ln β∗ij(c) + β ln β

]Expected profits over the possible realizations of β are given by:

E[Πij(c)] =fij

θ(γ + 1)2

(β∗ij(c))γ+1

(βmcα)γ(30)

Let γ = (σ − 1)(γ + 1). Setting the expected profits (30) equal to the fixed cost of entry to adestination Fij, and using the definition of β∗ij(c) yield the cost cutoff c∗ij:

fij

θ(γ + 1)2

(β∗ij(c∗ij))

γ+1

(βm(c∗ij)α)γ

= Fij (31)[1

fij(σ − 1)

[Ajσ − 1

σ

]σ(τijwic

∗ij)−(σ−1)

]γ+1fij

θ(γ + 1)2

1

(βm(c∗ij)α)γ

= Fij[1

σ − 1

[Ajσ − 1

σ

]σ]γ+1 (τijwic∗ij)−γf−γij F

−1ij

θ(γ + 1)2

1

(βm(c∗ij)α)γ

= 1[1

σ − 1

[Ajσ − 1

σ

]σ]γ+1 (τijwi)−γf−γij F

−1ij

βγmθ(γ + 1)2= (c∗ij)

αγ+γ

Thus, the cost cutoff c∗ij equals:

c∗ij = (τijwi)− γαγ+γ f

− γαγ+γ

ij F− 1αγ+γ

ij

[[1

σ − 1

[Ajσ − 1

σ

]σ]γ+11

θ(γ + 1)2βγm

] 1αγ+γ

(32)

The higher the variable or fixed costs of exporting, the lower the cutoff: a firm must have a lowdraw of c to decide to pay Fij to reach a destination with high trade costs. Conveniently, c∗ij canbe written as a function of the domestic cost cutoff c∗jj:

c∗ij = c∗jj

(τijwiτjjwj

)− γαγ+γ

(fijfjj

)− γαγ+γ

(FijFjj

)− 1αγ+γ

(33)

Moreover, taking the ratio between β∗ij(c) and β∗ij(c∗ij) yields:

β∗ij(c) = β∗ij(c∗ij)

(c

c∗ij

)−(σ−1)

(34)

54

By (31),

β∗ij(c∗ij) =

[βγmFij θ(γ + 1)2

fij

] 1γ+1

(c∗ij)αγγ+1 (35)

Using (34) and (35) in (30) and (29), the expected profits and revenues can be writte as a functionof c and c∗ij:

E[Πij(c)] =fij

θ(γ + 1)2

(β∗ij(c∗ij))

γ+1

(βmcα)γ

(c

c∗ij

)−γ− Fij = Fij

[(c

c∗ij

)−γ−αγ− 1

](36)

E[Rij(c)] = σ(γ + 1)Fij

(c

c∗ij

)−γ−αγ(37)

Conditional on entry in a destination j, average profits and revenues are given by:

πij =

∫ c∗ij

0

E[Πij(c)]κcκ−1

(c∗ij)κdc =

Fij(αγ + γ)

κ− αγ − γ(38)

Rij =Fijκσ(γ + 1)

κ− αγ − γ(39)

Expected profits are then given by:

πei =∑j

(c∗ijci

)κπij =

(αγ + γ)

κ− αγ − γ∑j

Fij

(c∗ijci

)κSetting the expected profits equal to the fixed cost of entry wifE yields:

(αγ + γ)

κ− αγ − γ∑j

Fij

(c∗ijci

)κ= wifE (40)

Total revenues from i to j are given by:

Tij = Ni

(c∗ijci

)κRij = Ni

(c∗ijci

)κFijκσ(γ + 1)

κ− αγ − γ(41)

Thus, market clearing and trade balance imply that:∑j

Tij = wiLi

Niκσ(γ + 1)

κ− αγ + γ

∑j

Fij

(c∗ijci

)κ= wiLi (42)

Dividing (42) by (40) yields the mass of entrants Ni:

Ni =Li(αγ + γ)

fEκσ(γ + 1)(43)

55

Revenues from i to j are then given by:

Tij =αγ + γ

fE(κ− αγ − γ)LiFij c

−κi c∗κij (44)

Using (33), the trade share becomes:

λij =Tij∑v Tvj

=Lic−κi (τijwi)

− κγαγ+γ f

− κγαγ+γ

ij F1− κ

αγ+γ

ij∑v Lv c

−κv (τvjwv)

− κγαγ+γ f

− κγαγ+γ

vj F1− κ

αγ+γ

vj

(45)

By market clearing, Tij = λijwjLj. Thus, using (44), the cost cutoff c∗ij is given by:

c∗ij = ci

(λijLjwjLiFij

) 1κ[fE(κ− αγ − γ)

αγ − γ

] 1κ

(46)

Hence, using (34), (35) and (46), the fixed cost cutoff for a firm with cost draw c is given by:

β∗ij(c) = β∗ij(c∗ij)

(c

c∗ij

)−(σ−1)

=

[βγmFij θ(γ + 1)2

fij

] 1γ+1

(c∗ij)αγγ+1

(c

c∗ij

)−(σ−1)

=

=

[βγmFij θ(γ + 1)2

fij

] 1γ+1

(c∗ij)αγ+γγ+1 c−(σ−1) =

=

[βγmFij θ(γ + 1)2

fij

] 1γ+1[ci

(λijLjwjLiFij

) 1κ[fE(κ− αγ − γ)

αγ − γ

] 1κ

]αγ+γγ+1

c−(σ−1) =

=[βγmθ(γ + 1)2

] 1γ+1

[fE(κ− αγ − γ)

αγ − γ

] αγ+γκ(γ+1)

︸ ︷︷ ︸= B

(Fijfij

) 1γ+1

cαγ+γγ+1

i

(λijLjwjLiFij

) αγ+γκ(γ+1)

c−(σ−1)

= B

(Fijfij

) 1γ+1

cαγ+γγ+1

i

(λijLjwjLiFij

) αγ+γκ(γ+1)

c−(σ−1) (47)

Using (47) into (24) yields:

δij(c, β) =1

θ

[ln β∗ij(c)− ln β

]=

=ln B

θ+

αγ + γ

θ(γ + 1)ln ci +

1

θ(γ + 1)

[ln

(Fijfij

)+αγ + γ

κln

(λijLjwjLiFij

)]− 1

θln c− 1

θln β

(48)

Assuming that Fij = wjF , we obtain the expression outlined in the paper:

δij(c, β) = δ +αγ + γ

θ(γ + 1)ln ci −

1

θ(γ + 1)ln

(fijwj

)+

αγ + γ

κθ(γ + 1)ln

(λijLjLi

)− 1

θln c− 1

θln β

where δ = ln Bθ

+ κ−αγ−γκθ(γ+1)

lnF .

56

D.2 Effects of a Reduction in Trade Costs

Let us consider the effects of a change in either variable trade costs τij or fixed cost per varietyfij on total exports from i to j . Taking the total derivative of (19), keeping the mass of entrantsconstant, yields the following decomposition of the change in total exports:

dTij = Ni

[∫ β∗ij(c∗ij)

0

Rij(c∗ij, β)bc(β)gi(c

∗ij)dβ

]dc∗ij+ Change in Entrants

+Ni

[∫ c∗ij

0

Rij(c, β∗ij(c))bc(β

∗ij(c))gi(c)dc

]dβ∗ij(c)+ Change in Active Firms

+Ni

∫ c∗ij

0

∫ β∗ij(c)

0

dRij(c, β)bc(β)gi(c)dβdc Intensive Margin

Let us discuss each component with the help of Figure D.1. First, a change in trade costsmodifies the cost cutoff that pins down the mass of entrants in each destination j. Thus, a changein c∗ij affects total exports by the level of sales of firms at the cost cutoff. Secondly, a change intrade costs affects the set of active firms, by shifting the β∗ij(c) curve. However, the contributionof this margin for a small variation in trade costs is zero. In fact, firms with β equal to the cutoffhave zero revenues. As a result, a small change in the cutoff β∗ij(c) does not affect aggregate tradeflows.

Figure D.1: Trade Margins𝛽

𝑐𝑐𝑖𝑗∗

Δ Entrants

No Production

𝛽𝑖𝑗∗ (𝑐)

𝛽𝑖𝑗′∗(𝑐)

𝑐𝑖𝑗′∗

Δ Active Firms

The last term of the decomposition is the intensive margin: the change in the sales of eachfirm. This margin can be further decomposed into the change in the firm’s sales from existingproducts - the within-firm intensive margin - and the change in the firm’s number of products- the within-firm extensive margin. Let εH(δ) = −d lnH(δ)

δ> 0 and εh(δ) = d lnh(δ)

δ> 0 be the

elasticity of the firm’s average productivity, and marginal costs with respect to the scope. The

57

within-firm trade margins can be written as:

−d lnRij(c, β)

d ln fij= 0︸︷︷︸

Intensive

+εH(δ(c, β))

εh(δ(c, β))︸ ︷︷ ︸Extensive

−d lnRij(c, β)

d ln τij= σ − 1︸ ︷︷ ︸

Intensive

+ (σ − 1)εH(δ(c, β))

εh(δ(c, β))︸ ︷︷ ︸Extensive

A reduction in the fixed cost per variety and destination fij only affects the extensive marginof trade while a variation in τij both affect the intensive and the extensive margin. Using our

functional forms, εH(δ(c,β))εh(δ(c,β))

=(

exp(θδij(c, β))− 1)−1

and, thus, it decreases with firm’s scope. The

result arises because the scope of firms with wide-scope responds less to trade shock. Moreover,the contribution to total sales of additional varieties is smaller the farther away they are from thecore. Hence, the wider the current scope the smaller their contribution to the firm’s sales.

Using our parametrized gravity equation (45), letting the fixed cost to enter a destination beexpressed as Fij = wjFj, we obtain:

λij =Lic

κi (τijwi)

− κγαγ+γ f

− κγαγ+γ

ij∑Iv=1 Lv c

κv(τvjwv)

− κγαγ+γ f

− κγαγ+γ

vj

(49)

The trade elasticity is a constant that depends on the shape parameter κ of the distribution ofproductivities, the shape parameter γ of the distribution of fixed cost shocks, the parameter αthat controls the correlation between the two distributions, and the elasticity of substitution σ:

−d ln

(λijλjj

)d ln τij

=κγ

αγ + γ− γ︸ ︷︷ ︸

Extensive

+ γ︸︷︷︸Intensive

=κγ

αγ + γ

−d ln

(λijλjj

)d ln fij

=κγ

αγ + γ− γ︸ ︷︷ ︸

Extensive

+ γ︸︷︷︸Intensive

=κγ

αγ + γ

Let us consider the trade elasticity with respect to variable trade costs τij. If α = 0, the elasticitybecomes κ, and is identical to that arising from “single attribute” models of single- or multi-product firms (Chaney, 2008; Bernard et al., 2011). The reason for this result lies in the fact thataggregate trade flows are not affected by a change in the number of active firms, because firmswith β = β∗ij(c) have zero revenues. Moreover, since the intensive margin is offset by an equalchange in the extensive margin, the only adjustment mechanism that affects total export is thechange in the number of entrants (change in c∗ij).

If α > 0, productivity and flexibility are positively related and the trade elasticity is smallerthan κ. For higher levels of α, less productive firms expect lower profits, and, therefore, theirentry in a destination is dampened. A positive α magnifies the productivity differences acrossfirms, which could be achieved in a standard model with a smaller κ. On the contrary, when α isnegative, the trade elasticity is larger than the standard one.

The effect of γ depends on whether α is positive or negative. If α > 0, the trade elasticity

58

with respect to variable trade costs declines with γ while it increases with γ for α < 0. Whenflexibility and productivity are positively related, entry is further dampened by higher values of γthat reduce expected profits. In contrast, when flexibility and productivity are negatively related,less productive firms are likely more flexible and they benefit from less disperse fixed cost shock(higher γ).

On the other hand, for α = 0 the elasticity with respect to fixed trade cost depends on γ aswell. In particular, it is increasing in γ and approaches the standard case (Bernard et al., 2011)when γ → ∞. Hence, the elasticity is smaller than “single attribute” model: heterogeneity inflexibility reduces the responsiveness of trade to changes in fij. This arises because a fixed costshock only affects the expected profits of firms that are active, conditional on drawing a β belowthe cost cutoff.

D.3 Quality and Disconnect between Sales and Scope

The main results of the paper hinge on the fact that the disconnect between sales of firms and theirscope can only be rationalized with a firm-destination specific shock to the within-firm extensivemargin. Two firms with the same scope can have different sales if they are subject to heterogeneousshocks to their extensive margins. This section illustrates how a shock to the intensive marginfails to account for such a disconnect.

Shocks to the intensive margin, in addition to productivity, are usually represented by demandshifters, which are interpreted as quality or product appeal (Hottman et al., 2016). We followthis line of research and consider extensions to the baseline model in which firms or products areheterogeneous in quality and quality is subject to shocks. In particular, we consider the firm’sproblem under two types of shocks. First, we examine a firm-destination specific shock to thequality of all firm’s products. Second, we consider the product-firm-destination specific shocks ofthe models of Bernard et al. (2011) and Arkolakis et al. (2015).

Shocks to the quality of the entire product range

Consider an extension to the baseline model, in which firms differ in terms of the marginal costof their core variety c and in their quality, or product appeal z. We model quality as a demandshifter which is common for all the varieties produced by a firm. The demand for product ω isgiven by:

pij(z, ω) = Ajzσ−1σ xij(ω)−

1σ

Let us consider the problem of a firm in a destination j, after having discovered its quality drawz in that destination. Firm’s profits are given by:

Πij(c, z) =

∫ δij(c,z)

0

[(pij(z, ω)− τijwich(ω))xij(ω)− fij]dω

Profit maximization yields the standard pricing equation of the baseline model:

pij(ω, c) =σ

σ − 1τijwich(ω)

59

It is convenient to re-write the profits of a variety ω as follows:

πij(ω, c, z) =1

σ − 1zσ−1

[Ajσ − 1

σ

]σ(τijwich(ω))1−σ − fij

Firm’s introduce varieties until the profits of the last one δij(c, z) are equal to zero: πij(δij(c, z), c, z) =0. The optimal scope is implicitly defined as:

h(δij(c, z))σ−1 =

1

fij(σ − 1)zσ−1

[Ajσ − 1

σ

]σ(τijwic)

1−σ

Firm’s revenues on a variety ω are given by:

rij(ω, c, z) =σ

σ − 1zσ−1

[Ajσ − 1

σ

]σ(τijwich(ω))1−σ = σfij

(h(ω)

h(δij(c, z))

)1−σ

Integrating the revenues per variety over the scope of the firm yields:

Rij(c, z) = σfij

(h(δij(c, z))

H(δij(c, z))

)σ−1

Take two firms with different levels of quality and productivity that have the same scope. Inthis model, the two firms also have the same revenues. The reason for this result is that thequality shock is isomorphic to the productivity shock. A positive shock to quality increases, by thesame proportion, scope and sales, because it makes discontinued varieties profitable once again.As a result, quality and productivity heterogeneity cannot rationalize the documented disconnectbetween sales and scope.

Product specific shocks

Let us now consider the case in which each variety produced by a firm faces a quality shock in adestination. In particular, let the demand for variety ω be subject to a random demand shifterz(ω):

pij(z, ω) = Ajz(ω)σ−1σ xij(ω)−

1σ

Profit maximization yields the same pricing equation as before. It is convenient to re-write theprofits of a variety ω as follows:

πij(ω, c, z) =1

σ − 1

[Ajσ − 1

σ

]σ(τijwic)

1−σ(z(ω)

h(ω)

)σ−1

− fij

The demand shock z(ω) enters the profit function in the same way as the inverse of h(ω).

If we make a deterministic assumption and let z(ω)h(ω)

= exp(θω) we are back to our baselinemodel. Namely, our baseline model nests a model in which there are quality differences across theproducts of the same firm. The parameter θ has a slightly different interpretation from the baselinecase. In this scenario, θ would capture how fast revenues fall as the firm introduces product furtherfrom its core, because of a reduction in quality weighted by the marginal costs.

Let us consider the Bernard et al. (2011) model, in which there are no cost differences acrossthe varieties within a firm, namely h(ω) = 1 ∀ ω. Each firm has a unit mass of potential varieties,

60

and in each destination a firm draws the variety-specific shock z from a distribution with CDFG(z) and pdf g(z), which is common across firms. There exists a firm-quality cutoff z∗(c), suchthat a firm only introduces variety with a quality level higher than z∗(c). Setting profits to zeroyields the quality cutoff:

(z∗(c))1−σ =1

fij(σ − 1)

[Ajσ − 1

σ

]σ(τijwic)

1−σ

The derivation follows straightforwardly from the previous ones. For details see Bernard et al.(2011). Firm’s revenues on a variety with quality z are given by:

rij(z, c) = σfij

(z

z∗(c)

)σ−1

Aggregate firm’s revenues are given by:

Rij(c) = σfij

∫ ∞z∗(c)

(z

z∗(c)

)σ−1

g(z)dz

while the scope is given by:δij(c) = 1−G(z∗(c))

Both revenues and the scope only depend on the realization of the marginal cost c. The varietyspecific shocks do not affect the expected total revenues or the scope of the firm. The varietyspecific shocks only affect which of the potential varieties is sold, but not their total number.18

Given our analysis of trade margins, we argue that in order to understand how firms react to tradeshock the sufficient statistics is the scope and not which products are sold.

Heterogeneous distributions of quality

The result from the Bernard et al. (2011) model relies on the assumption that quality is drawnfrom the same distribution G(z) across firms and destinations. To rationalize our first and secondstylized fact in the Bernard et al. (2011) model, we would need shocks to this distribution whichare firm-destination specific. In other words, each firm in each destination would have to drawquality from different distributions. However, the differences in distribution have to generateheterogeneity in the extensive margin rather than the intensive margin. To gather some intuition,let us assume that G(z) is an unbounded Pareto distribution with shift parameter m and shapeparameter a > σ − 1. Scope and revenues are given by:

Rij(c) = σfija

a− σ + 1

ma

z∗(c)a

δij(c) =ma

z∗(c)a

18The same logic applies to the model of Arkolakis et al. (2015), when considering only the shocks to productappeal. In their case, however, firms produce a discrete number of products. Thus, two firms with the same revenuesmight have scope that differs by one unit, depending on the realization of the shocks.

61

and, thus,

Rij(c) = σfija

a− σ + 1δij(c)

If firms differ in terms of the shift parameter m, the disconnect between sales and scope cannotbe explained. In other words, if the average quality differs across firms, firms with the same scopewill have the same sales. The only reason for the presence of a disconnect between sales and scopeis a firm-destination specific shock to the shape parameter a. This parameter is similar in spiritto our θ, the parameter that captures how fast marginal costs rise as firms move away from theircore.19

Heterogeneity in θ could rationalize the sale and scope disconnect at a the cost of tractability.Moreover, we argue that heterogeneity in θ still captures the concept of flexibility that is centralto this paper. In fact, we define flexibility as the ability to introduce new products at low costs.Whether the low cost comes from the fixed cost or a different slope in the marginal cost schedule,the effects are analytically different but the intuition is analogous.

E Simulated Method of Moments Algorithm and Moments

This section describes in detail the Simulated Method of Moments (SMM) procedure we follow toestimate the set of parameters Θ = [θ, σ, γ, α, βm, κ]. First, we describe the simulation algorithm,which, for a given set of candidate parameters, generates the behavior of Chinese firms. Second,we list the moments we target. Third, we minimize the deviations of the simulated moments fromthe moments from the data to estimate the set of parameters Θ.

E.1 Derivations

We assume that the fixed costs Fij and fij are expressed in destination labor units. Before wedescribe the algorithm, let us derive a few equations that will be used. First, let us consider themass of firms Mij exporting to a destination j :

Mij = Ni

∫ c∗ij

0

∫ β∗ij(c)

0

gc(β)g(c)dβdc = Ni

∫ c∗ij

0

∫ β∗ij(c)

0

κγ

βγmcκβγ−1cκ−αγ−1dβdc =

= Ni

∫ c∗ij

0

κ

βγmcκ(β∗ij(c))

γcκ−αγ−1dc =

= Ni

∫ c∗ij

0

κ

βγmcκ(β∗ij(c

∗ij))

γcκ−αγ−γ(σ−1)−1(c∗ij)γ(σ−1)dc =

= Ni

∫ c∗ij

0

κ

βγmcκ(β∗ij(c

∗ij))

γcκ−αγ−γ(σ−1)−1(c∗ij)γ(σ−1)dc =

= Niκ

(κ− αγ − γ(σ − 1))βγmcκ(β∗ij(c

∗ij))

γ(c∗ij)κ−αγ =

= Niκ

(κ− αγ − γ(σ − 1))βγmcκ

[βγmFij θ(γ + 1)2

fij

] γγ+1

(c∗ij)κ− αγ

γ+1

19A similar argument applies to σ.

62

We can compute the ratio of firms exporting to a destination j from i relative the mass of firmsexporting to a reference country r:

Mij

Mir

=

[c∗ijc∗ir

]κ− αγγ+1

(50)

Let Dij = (β∗ij(c∗ij))(c

∗ij)

σ−1. Then, we can re-write the expression for the firm’s scope as:

exp(θδij(c, β)) = Dijc−(σ−1)β−1

Let φ = c−(σ−1)β−1 denote the entry-adjusted measure of productivity, a variable that describesthe combination of c and β of a firm in a destination. The entry-adjusted productivity cutoff,which is the combination of c and β such that a firm will not produce in a destination, equals:

φ∗ij = D−1ij

Hence, the scope of a firm with entry-adjusted productivity φ equals:

exp(θδij(φ)) =φ

φ∗ij

The relationship between entry-adjusted productivity cutoff and marginal cost cutoff is:

φ∗ijφ∗ir

=Dir

Dij

=(β∗ir(c

∗ir))(c

∗ir)

σ−1

(β∗ij(c∗ij))(c

∗ij)

σ−1=

[c∗irc∗ij

] αγγ+1

+σ−1

(51)

E.2 Simulation Algorithm

Given the candidate parameters Θ, the algorithm simulates the revenues and scope of Jsim =1, 000, 000 hypothetical Chinese firms, for each destination they serve j = 1, ..., D. Given thatour model features a continuum of firms, we choose a large value for Jsim to approximate such acontinuum. We set D = 18 and consider the most popular destinations for Chinese exporters -which constitute 70% of total exports. The list of eighteen destinations is provided in Table A.4.Table A.3 provides the industry coverage for the whole sample. We refine our samples to firmswhose exporting scope is less than 100. The refined sample constitutes 99.5% of the total firmnumber and 92.75% of the total exports to the 18 countries.

Prior to the simulation, we independently draw Jsim realizations of the firms’ marginal costpercentiles uc from the standard uniform distribution. To maximize the number of observations weuse for the simulation, we condition our sample to contain only firms that enter a given referencedestination r. We use r = China, namely firms that sell in the domestic economy and r = US,namely the firms that export to the US. Any iteration of the algorithm begins with the computationof the marginal cost draws of firms. Given the marginal cost percentile uc, we recover the marginalcost of firms as:

c = (uc)1κ c∗ir

In other words, we condition our sample only to contain the firms that are productive enough toenter the domestic economy. In practice, we normalize c∗ir to one. We back out the marginal costcutoff for all other destinations using the ratio of the number of firms selling to a destination j

63

relative to the number of firms selling to r using (50):

c∗ij =

[Mij

Mir

] 1κ− αγ

γ+1c∗ir

For each destination j and each firm c, such that c ≤ c∗ij we draw the firm-destination specificflexibility shock percentile uβ(c)j. The fixed-cost draw of a firm is then computed as:

β(c)j = βmcα(uβ(c)j)

1γ

We obtain the entry-adjusted productivity measure (51) as:

φ∗ij =

[c∗irc∗ij

] αγγ+1

+σ−1

φ∗ir

We normalize φ∗ir to one, thus, simulating the behavior of the firms that, with the same entry-adjusted productivity, would be active in the reference destination. We compute φ = c−(σ−1)β−1,which is the entry-adjusted measure of productivity. A firm is active in a destination, if φ ≥ φ∗ij.The exporter scope of a firm in a destination is then given by:

δij(φ) =1

θ

[lnφ− lnφ∗ij

]For some moments we derive later, it is useful to discretize the scope of firms as follows:

δij(φ)int = 1 + int(δij(φ))

where int denotes the integer part of the continuous form of the scope.We generate this firm’s ω-th ranked product in destination j (with scope δij(φ)int) as20

rωij = exp

[θ

(δij(φ)int − (int(ω) + 1)︸ ︷︷ ︸

discretize the product index

)]× β

where θ = θ(σ − 1). The above expression on product revenue rωij omits the destination-specificshifters. Both shifters are common across exporters at the same destination and firm invariantin our simulation as we normalize the relevant moments by the corresponding destination-specificmedian or extreme. The revenues of the firm are given by:

Rij(φ, β) = β[exp(θδij(φ))− 1]

or

Rij(φ, β) =

δij(φ)int∑ω=1

rωij

where we neglect the multiplicative componentσfij

θ, given the normalizations we introduce in the

20The full expression should be rωij = σfChina,j exp

[θ(δij(φ)int−ω

)]×β. Since we will neutralize the destination

specific term by normalizations, it does not matter if we include the term σfChina,j or not.

64

following section.

E.3 Moments

In this section, we define the moments used in the simulated method of moments algorithm. Toseparately identify the parameters relevant for the stochastic components (productivity and fixedcost distribution) and the parameters that govern firm’s production function, we use the momentsso that they are comparable across destinations by neutralizing the destination-specific shifters.

M1: Within-destination and within-firm product sales concentration

The first set of moments compares the sales of a firm’s top-selling product and other products’sales of the same firm. Consider a firm with marginal and fixed cost draw (c, β) in a destinationj. Let r1ij(c, β) denote the revenues of the top selling product of the firm (in our model, ω = 0)in a destination j, and rωij(c, β) denote the total revenues generated by the products in group ωfor a firm in a destination j. The log sales ratio between the sales of products in ω and the coreproduct equals:

ln(r1ωij(c, β)) = ln

(rωij(c, β)

r1ij(c, β)

)= −θω (52)

We focus on the multi-product firms who export more than one product. We compute ln(r1ωij(c, β))for these firms, and pool the log sales ratio ln(r1ωij(c, β)) by product group ω ∈ 2, ..., 7,8, ...31, 32, ...127, 128, ... across firms and destination. For instance, consider ω ∈= 2, ..., 7.This set contains the log sales ratio ln(r1ωij(c, β)) for ω ∈ 2, ..., 7 across all destinations j andall firms (c, β).

For each product group we rank order the sales ratio ln(r1ωij(c, β)) from the highest to the low-est. This gives us a collection of ordered sequence for each product group ln(r1ω(100)), ..., ln(r1ω(0)).Then for any selected percentiles p, we obtain our moment conditions:

M1ωp = ln(r1ω(p)), ω ∈ 2, ..., 3, 4, ...7, 8, ...15, 16, ...p ∈ 90, 80, 70, 60, 50, 40, 30, 20

The above procedures generate 4× 8 moment conditions which is our first set of moments usedin SMM algorithm.

M2: Within-destination sales of the core products

Our second set of moments compares the sales of core products across firms within the samedestination. We divide firms into five groups by their (discrete) scope in a destination δij(c, β)int ∈1, 2, ..., 7, 8, ...15, 16, ...31, 32, .... We label the product subgroups with superscript δ.The revenues of the core product (ω = 0) of a firm with marginal and fixed cost draws (c, β), andscope group δ in a destination j are given by:

r(0, (c, β))δij = σfijβ∗ij(c∗ij)

(c

c∗ij

)−(σ−1)

(53)

Let (cm, βm) denote the firm with the median level of core-product sales in a destination j andproduct group δ. To neutralize the destination specific shifter, we normalize the sales (53), by the

65

median sales:

r(0, (c, β))δij =r(0, (c, β))δij

r(0, (cm, βm))δij=( c

cm

)−(σ−1)

(54)

Next, we pool over these ratios across destinations and firms by product group δ, and rankorder the ratios from the highest to the lowest. This gives us a collection of ordered sequencer(0)δ(100), ..., r(0)δ(0). Consider, for instance, δ = 1. The sequence contains the sales of the single-product exporter in a destination, normalized by the median sales of single-product firms in thesame destination, pooled over destinations and firms. From the sequence we pick the observationsat the select percentile P (ω) = p.

M2δp = ln(r(0)δ(p)), δ ∈ 1, 2, 3, 4, ..., 7, 8, ...15, 16, ...p ∈ 95, 90, 85, 80, 70, 60, 40, 30, 20

The above procedures generate 4× 9 moment conditions.

M3: Within-destination exporter scope distribution

The third set of moments captures the exporter scope distribution by destinations. We computethe share S δij of firms with scope at least as large as δ in a destination j as the percentage of thetotal number of exporters in the same destination:

S δij =

∑φ>φ∗ij

I(δij(φ) ≥ δ)∑φ>φ∗ij

I(δij(φ) ≥ 0)(55)

Next, we take the arithmetic means across destinations and this gives us the third set of momentconditions:

M3δ =1

D

D∑j=1

S δij, δ ∈ 2, 4, 8, 16, 32

This procedure would provide us with 5 moment conditions.

M4: Within-destination firm sales distribution

Our fourth set of moment conditions reflects sales distribution by destinations and scope groups.We label the product subgroups with superscript δ. For each destination j and scope groupδij(φ) ∈ 1, 2, ..., 7, 8, ...15, 16, ...31, 32, ..., we normalize the sales with the median sales

within each destination product scope group, i.e., Rδij(φ, β)/Rmδ

ij (φm, βm):

Rδij(φ, β)

Rmδij (φm, βm)

=β[exp(θδij(φ))− 1]

βm[exp(θδij(φm))− 1]

For each scope group δ, we pool over all the destination countries and firms and rank ordernormalized sales from the highest to the lowest. This gives us a collection of ordered sequence

66

(Rδ

Rmδ

)(100)

, ...,(

Rδ

Rmδ

)(0)

. For any select percentiles P (ω) = p, we obtain the moment conditions:

M4δp = ln

(Rδ

Rmδ

)(p)

, δ ∈ 1, 2, 3, 4, ..., 7, 8, ...15, 16, ...

p ∈ 95, 90, 85, 80, 70, 60, 40, 30, 20

The above procedures generate 4× 9 moment conditions.

M5: Within-firm exporter scope distribution

Our fifth set of moment conditions compares the export scopes within firms across destinationsby double normalizing the export scope. To begin with, we only focus on the subset of firms thatat least export to the U.S. market. For each firm, we first calculate the firm-destination specificrelative21 exporter scope (relative to the scope in the U.S.) and denote it as bij(c):

bij(c) = δij(c, β(c)j)− δiUS(c, β(c)US) =1

θ[ln β(c)US − ln β(c)j + lnφ∗iUS − lnφ∗ij] (56)

For each destination, we rank order the relative scope bij(c) of all firms in that destinationand further normalize bij(c) with the median level within the destination22 to obtain bij(c) =bij(c)−med(bij(c)):

bij(c) = bij(c)−med(bij(c)) =1

θ[ln β(c)US − ln β(c)j − ln β(cm)US + ln β(cm)j] (57)

Next, we pool over all firms selling in the different destinations, and rank over the double-normalized scope difference from the highest to the lowest, and we denote this new sequence asb(100), ..., b(0). For any select percentiles p, we obtain the moment conditions:

M5p = b(p), p ∈ 90, 85, 80, 75, 60, 55, 45, 40, 25

The above procedures generate 9 moment conditions.

E.4 Statistical Inference

To estimate the key parameters Θ, we first take the differences between observed and simulatedmoments ∆M(Θ) = Mdata −Msim. There are 118 moment conditions as implied by above. The

true parameter Θ0 will satisfy E[∆M(Θ0)] = 0. So we search for the optimal Θ to minimizethe weighted sum of squares, i.e., ∆M(Θ)′W∆M(Θ). Ideally, W is the positive semi-definiteweighting matrix which is chosen at W = V−1, where V is the variance-covariance matrix of themoments ∆M(Θ). However, the true variance-covariance matrix is unobserved, and we use itsempirical estimates:

21Normalizing a firm’s scope with its U.S. scope eliminates the firm specific shifter.22The second normalization removes the destination specific shifter.

67

V =1

NBstrp

NBstrp∑i=1

(Mdata −MBstrpi ) (Mdata −MBstrp

i )′ (58)

where Mdata is moment conditions from the data, and MBstrpi denotes the moments generated from

a random sample (sample i) that is drawn with replacement from the original firms by destinationin the dataset. NBstrp is the number of Bootstrap samples. Due to the large dimensions, wecannot invert V. Instead, we calculate the Moore-Penrose pseudo-inverse. Next, we calculate thestandard deviation of Θ via bootstrapping. Specifically, we repeat the estimation process 30 times,using ∆MBstrp(Θ) = MBstrp −Msim where we replace Mdata in ∆M(Θ) with MBstrp, to generatestandard errors. This method is also used in Arkolakis et al. (2015), which allows for samplingand simulation errors.

E.5 Model Fit

Figure E.1 displayed the model fit for the simulated moments and the counterpart in data. FigureE.2 provides the estimation performance by each set of moments. The overall estimation is quiteaccurate according to the high R2. In each set of moments, the scatter plots also indicate thatthere is no systematic difference between the simulated moments and their counterpart in data.

Figure E.1: Estimation Performance: Moments Comparison Overall

68

Figure E.2: Estimation Performance: Moments Comparison by Moment

69

E.6 Simulated Stylized Facts

Figure E.3: Counterfactural Stylized Facts: Pooled Sample

(a) Product Scope and Sales (b) Product Scope and Productivity

(c) Distribution of Product Scope (d) Distribution of Product Scope By Quartile

(e) Distribution of Sales

Figure E.3 displays the simulated stylized facts, which are generated with the parameters calibratedusing the pooled sample and the United States as reference country. Figure E.3a and E.3b presentthe relationship between product scope and firm sales and productivity for the overall sample.

70

Consistent with the evidence as found in data, conditional on each firm productivity/sale, weobserve dispersion in number of products. The disconnect is also robust to the normalizationwith sample mean, as displayed in Figure E.4. Figure E.3c to Figure E.3e display product scopeand sales distribution, as well as product distribution by sales quartile. All these moments areconsistent with the findings in the data.

Figure E.4: Counterfactural Stylized Facts: Scope and Sales Disconnect

In Figure E.5, we show the simulated stylized facts when productivity and flexibility are inde-pendent. We set α as zero while keeping other parameters the same as their calibrated value. Asdisplayed by Figure E.5a and E.5b, the disconnect between sales and scope is weaker, as after acertain level of sales there are no more single product firms or firms with narrow scope. We alsoobserve from Figure E.5d, the independence between flexibility and productivity fails to accountfor the scope distributions by sales quartile.

In Figure E.7, we repeat the stylized facts using the same calibrated parameters except thatwe choose γ to be two times as big as its original level. Similarly, in Figure E.6 we choose γ to behalf of our calibrated level. A higher value of γ implies the less likelihood to have bigger fixed costfor a firm, and, in turn, the product scope is also wider in this case.

71

Figure E.5: Counterfactural Stylized Facts: α = 0

(a) Product Scope and Sales (b) Product Scope and Productivity

(c) Distribution of Product Scope (d) Distribution of Product Scope By Quartile

(e) Distribution of Sales

72

Figure E.6: Counterfactural Stylized Facts: Low γ

(a) Product Scope and Sales (b) Product Scope and Productivity

(c) Distribution of Product Scope (d) Distribution of Product Scope By Quartile

(e) Distribution of Sales

73

Figure E.7: Counterfactural Stylized Facts: High γ

(a) Product Scope and Sales (b) Product Scope and Productivity

(c) Distribution of Product Scope (d) Distribution of Product Scope By Quartile

(e) Distribution of Sales

74