metadata: authors: 0: author: Bastos,Paulo S. R.
1: author: Dias,Daniel
2: author: Timoshenko,Olga A.
count: World
docna: 0: docna: Learning, Prices, and firm dynamics
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Construction Industry,Textiles, Apparel & Leather Industry,Business Cycles and Stabilization Policies,General Manufacturing,Common Carriers Industry,Food & Beverage Industry,Plastics & Rubber Industry,Pulp & Paper Industry,Trade and Services,Transport Services,National Governance,Social Analysis,Government Policies,Youth and Governance,Quality of Life & Leisure
teratopic: Macroeconomics and Economic Growth,Social Development,Governance,Industry,Public Sector Development,International Economics and Trade,Transport
abstracts: cdata!: This paper documents new facts about the
            joint evolution of firm performance and prices in
            international markets and proposes a theory of firm dynamics
            emphasizing the interaction between learning about demand
            and quality choice to explain the observed patterns. Using
            data from the Portuguese manufacturing sector, the paper
            documents that: (1) within narrow product categories, firms
            with longer spells of activity in export destinations tend
            to ship larger quantities at similar prices, thus obtaining
            larger export revenue; (2) older exporters tend to import
            more expensive inputs; and (3) revenue growth within
            destinations (conditional on initial size) tends to decline
            with market experience. The authors develop a model of
            endogenous input and output quality choices in a learning
            environment that is able to quantitatively account for these
            patterns. Counterfactual simulations reveal that minimum
            quality standards on exports reduce welfare by lowering
            entry in export markets and reallocating resources from old
            and large toward young and small firms.
repnme: repnme: Learning, Prices, and firm dynamics
display_title: Learning, Prices, and firm dynamics
listing_relative_url: /research/2016/05/26363172/learning-prices-firm-dynamics
topicv3: Political Economy of Reform m1326263 836,Manufacturing Sectors m1326521 1281,Transport m1326661 135,Trade m1326924 698,Trade in Services m1326928 780
publishtoextweb_dt: 2016-05-10T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Social Development,Governance,Industry,Public Sector Development,International Economics and Trade,Transport
no_of_pages: 56
author_keys: 0: author_key: 1210378
1: author_key: 1001852
model_extractions: WPS7667 Policy Research Working Paper 7667 Learning, Prices, and Firm Dynamics _Paulo Bastos Daniel A. Dias Olga A. Timoshenko_ Development Research Group Trade and International Integration Team May 2016
Policy Research Working Paper 7667

# **Abstract**

This paper documents new facts about the joint evolution of firm performance and prices in international markets and proposes a theory of firm dynamics emphasizing the interaction between learning about demand and quality choice to explain the observed patterns. Using data from the Portuguese manufacturing sector, the paper documents that: (1) within narrow product categories, firms with longer spells of activity in export destinations tend to ship larger quantities at similar prices, thus obtaining larger export revenue; (2) older exporters tend to import more expensive inputs; and (3) revenue growth within destinations (conditional on initial size) tends to decline with market experience. The authors develop a model of endogenous input and output quality choices in a learning environment that is able to quantitatively account for these patterns. Counterfactual simulations reveal that minimum quality standards on exports reduce welfare by lowering entry in export markets and reallocating resources from old and large toward young and small firms.

This paper is a product of the Trade and International Integration Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at pbastos@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Learning, Prices, and Firm Dynamics<sup>_∗_</sup>

Paulo Bastos<sup>_†_</sup> Daniel A. Dias<sup>_‡_</sup> Olga A. Timoshenko<sup>_§_</sup> _Keywords_ : Learning about demand, prices, product quality, firm dynamics, quality standards.

_JEL_ : F12; F14; L11; O14.

> _∗_ We are grateful to Logan Lewis and participants at several conferences and seminars for helpful comments. Research for this paper was supported in part by the World Bank’s Multidonor Trust Fund for Trade and Development and through the Strategic Research Program on Economic Development. This work was also supported in part by the facilities and staff of the George Washington University Colonial One High Performance Computing Initiative. The views expressed herein are those of the authors only and not of the Board of Governors of the Federal Reserve System or of any person associated with the Federal Reserve System. We remain responsible for any errors.

> _†_ Development Research Group, The World Bank, 1818 18th Street NW, Washington DC, United States. E-mail: pbastos@worldbank.org.

> _‡_ Board of Governors of the Federal Reserve System, International Finance Division, Washington DC, United States and CEMAPRE, Portugal. E-mail: daniel.dias@frb.gov

> _§_ The George Washington University, Department of Economics and The Elliott School of International Affairs, 2115 G St., NW, Washington DC, 20052, United States. E-mail: timoshenko@gwu.edu

1
# **1 Introduction**

A small proportion of firms generate the bulk of export revenue in each nation (Bernard et al., 2007; Mayer and Ottaviano, 2007). Richer countries tend to have more and larger exporters, with greater concentration in the top 5% (Fernandes, Freund, and Pierola, 2015). These large exporters help define specialization patterns and play a key role in shaping the impact of trade liberalization on macroeconomic volatility (Freund and Pierola, 2015; di Giovanni and Levchenko, 2012). To understand how and why (some) firms eventually become successful exporters, the heterogeneous-firm trade literature is paying growing attention to dynamics. While the increased availability of customs records has made it possible to study firms’ export behavior over time, we still have a limited understanding of the mechanisms underlying the evolution of export performance over the firm life cycle.

In this paper, we use rich micro data to document new facts about the joint evolution of firm performance and prices over the life cycle, and develop a theory of firm dynamics emphasizing the interaction between learning about demand and quality choice to explain the observed patterns. Drawing on transactions-trade and firm-level census data from the Portuguese manufacturing sector, we document that: (1) within narrow product categories, firms with longer spells of activity in export destinations tend to ship larger quantities at similar prices, thus obtaining larger export revenue; and (2) older or more experienced exporters tend to import more expensive inputs. In line with prior research, we also find that the positive relationship between export revenue and market experience reflects growth, not just market selection based on initial size; and that revenue growth within destinations (conditional on initial size) tends to decline with the length of activity there (Eaton et al., 2008; Berthou and Vicard, 2013; Ruhl and Willis, 2014).

To account for the joint observation of these patterns in the data, we introduce quality choice of outputs and inputs (Verhoogen, 2008; Kugler and Verhoogen, 2012) and learning about demand (Jovanovic, 1982; Arkolakis, Papageorgiou, and Timoshenko, 2015) into a Melitz (2003) model of monopolistic competition and firm heterogeneity. In the model, firms supply products of varying quality based on their beliefs about idiosyncratic expected demand. Through the life-cycle, an average surviving firm updates its demand expectations upwards, grows, and, as a result, finds it optimal to upgrade the quality of outputs, which requires using higher quality inputs. Since inputs of higher quality are more expensive, average input prices rise with export experience. The evolution of output prices is less clear-cut. On the one hand, quality upgrading leads to a higher price. On the other hand, an increase in demand expectations increases profitability and causes a price reduction. Hence the model is able to rationalize the varying behavior of input and output prices over the firm life cycle observed in the data.

We explore the quantitative implications of our theory by calibrating it to match crosssectional and dynamic moments of the distributions of sales, exports and prices observed in the Portuguese data. Calibrated to match the observed age-dependence of exports growth 2
and input prices, the model accounts for about a third of the (conditional) size-dependence of growth rates that emerges from the data, and correctly predicts that the quantity of inputs increases with export-age.

Armed with the calibrated model, we assess the implications of regulations imposing minimum product quality standards on exports. We find that this policy reduces welfare through two distinct channels. First, it reduces firm entry in export markets, and hence lowers the number of export varieties available to consumers. Second, it distorts an intensive margin of adjustment. To participate in the export market, marginal exporters are forced to comply with the standard by choosing higher-quality inputs. This choice leads to a reallocation of productive resources from large and old towards small and young firms, which causes a further decline in welfare.

We contribute to several strands of existing research. A recent body of literature on firm dynamics offers variants of Melitz (2003) in which firms experience idiosyncratic shocks to their productivity, including Luttmer (2007), Impullitti, Irarrazabal, and Opromolla (2013), and Arkolakis (2015). If modified to allow for quality choice (as in Kugler and Verhoogen (2012)), this class of models would generate a positive relationship between input prices and export experience: as entrepreneurs become more capable (for exogenous reasons), firms grow and find it optimal to upgrade the quality of outputs and inputs. However, as emphasized by Arkolakis, Papageorgiou, and Timoshenko (2015) this class of models is unable to explain the age-dependence of growth rates (conditional on size) observed in the data.

A related class of models links firm dynamics in export markets to learning about unobserved demand (Albornoz et al., 2012; Chaney, 2014; Eaton et al., 2014; Ruhl and Willis, 2014; Timoshenko, 2015a,b; Arkolakis, Papageorgiou, and Timoshenko, 2015). While the microfoundations of the learning process vary across models, this body of work makes it possible to rationalize the age-dependence of export growth (conditional on size) observed in the data. Existing learning models are not well-suited, however, to explain the observed increase in wages and material input prices with export experience.<sup>1</sup> Our findings also contribute, therefore, to the literature on product quality and trade at the firm-level. We borrow from Verhoogen (2008) and Kugler and Verhoogen (2012) the theoretical ideas that in order to produce higher-quality outputs firms need to use higher-quality inputs; and that all else equal more capable entrepreneurs will choose to produce higher quality products. These hypotheses have found considerable support in the data. Using detailed firm-product records from the Colombian manufacturing sector,

> 1We also build on Cabral and Mata (2003) who show that the firm size distribution is significantly right-skewed and evolves over time toward a lognormal distribution largely because of firm growth (as opposed to selection based on initial size). A related body of evidence reveals that firm growth (in terms of employment, sales or export revenue) declines with age, conditional on initial size (Evans, 1987; Sutton, 1997; Haltiwanger, Jarmin, and Miranda, 2013; Arkolakis, 2015; Timoshenko, 2015a,b). While confirming that these patterns also hold in our data, we depart from previous work by examining the joint evolution of export performance and prices over the firm life cycle; and by providing theory and evidence that the interaction between learning about demand and quality choice is an important driver of firm dynamics.

3
Kugler and Verhoogen (2012) find that larger plants tend to charge more for outputs and pay higher prices for material inputs. In Portuguese data, Bastos, Silva, and Verhoogen (2014) find that firms experiencing an exogenous increase in the share of sales to richer export destinations (where consumers have higher willingness to pay for quality) tend to pay more for material inputs.<sup>2</sup> Our paper contributes to this this literature by shedding light on the dynamic interaction between learning about demand and quality choice in shaping the evolution of firm performance and prices over the life cycle.<sup>3</sup> Finally, our paper contributes to the theoretical literature on minimum quality standards and trade, including Das and Donnenfeld (1989), Fischer and Serra (2000) and Baltzer (2011). A common approach in this literature has been to examine the welfare impacts of quality standards in partial equilibrium models of oligopoly featuring a small (exogenously given) number of producers in each country. By revisiting this question in the context of a quantitative general equilibrium model of firm dynamics, we are able to identify several important new channels by which quality standards influence social welfare. In particular, we find that quality standards reduce welfare by lowering entry in export markets and reallocating resources from large and old towards young and small<sup>4</sup> The paper proceeds as follows. Section 2 describes the data employed. Section 3 presents stylized facts about the evolution of firm performance and prices. Section 4 develops a theory of firm dynamics featuring learning about demand, firm heterogeneity and quality choice of inputs and outputs. Section 5 explores the quantitative implications of the model by calibrating it to the Portuguese data and develops counterfactual simulations on the effects of imposing minimum quality standards in export markets. The last section concludes the paper.

# **2 Data description**

We link and examine data from the _Foreign Trade Statistics_ (FTS) and the _Enterprise Integrated Accounts System_ (EIAS) of Portugal. The FTS are the country’s official infor-

> 2Other recent papers provide several additional pieces of evidence on the relationship between output prices, input prices and firm characteristics. In cross-sectional data, Bastos and Silva (2010) find that more productive Portuguese firms ship larger volumes at higher prices to a given destination, and that exporters tend to charge higher prices in richer destinations. Manova and Zhang (2012) show that Chinese firms that export more, serve more markets and charge higher prices for exports tend to pay more for their imported inputs. Examining data for manufacturing plants in India, the US, Chile, and Colombia, Hallak and Sivadasan (2013) document that, conditional on size, exporting firms charge higher prices, pay higher wages, use capital more intensively, and purchase more expensive material inputs.

> 3Our paper is also related to the literature on product quality and trade at the product-country level, including influential contributions by Schott (2004), Hummels and Klenow (2005), Hallak (2006), Khandelwal (2010) and Hallak and Schott (2011).

> 4Our model is also able to account for recent empirical evidence on the effects of product standards on exporting behavior. Using detailed firm-product-destination data for France, Fontagn ́e et al. (2015) find that standards reduce entry in export markets and lead to an increase in export prices, especially among small exporters.

4
mation source on international trade statistics, gathering export and import transactions (values and physical quantities) of firms located in Portugal by product category (CN classification, 8-digit) and destination or source market. These data are collected in two different ways. Data on trade with countries outside the EU (external trade) are collected via the customs clearance system, which covers the universe of external trade transactions. Information on the transactions with other EU member States (internal trade) are obtained via the Intrastat system, where the information providers are companies engaged in internal trade and registered in the VAT system whose value of annual shipments exceeds a legally binding threshold. Trade transactions in these data are _free on board_ , hence excluding any duties or shipping charges. Despite the above-mentioned constraint, the export and import transactions included in the FTS data aggregate to nearly the total value of merchandise exports and imports reported in the official national accounts.

The EIAS is a census of firms operating in Portugal run by the National Statistics Institute since 2005. Among other variables, it contains information on total employment, sales, wage bill, capital stock, value added, date of constitution, industry code and location. Using unique firm identifiers, we have linked the FTS and EIAS data sets for the years 2005 to 2009.<sup>5</sup> We have further used FTS data spanning the period 1990-2009 to compute exportage and export-destination-age. In each year, these variables are defined, respectively, as the number of consecutive years the firm has been an exporter in any market or an exporter in a particular export destination.<sup>6</sup> As is customary in the empirical trade literature, we restrict the analysis to firms whose main activity is in the manufacturing sector excluding the Petroleum industry. We impose these restrictions using the firm’s selfreported industry code in the EIAS data set, where sectors are defined by the Revision 2.1 of the National Classification of Economic Activities (CAE).<sup>7</sup> All nominal variables are expressed in 2005 euros, using the GDP deflator of Portugal.

Table A1 in the Appendix reports summary statistics. In line with evidence for several other countries (Bernard et al., 2007), we observe that exporters tend to be larger, older, more productive, more capital intensive and pay higher wages than non-exporters. The average exporter in the period 2005-2009 obtained 3.45 million euros of export proceeds, served 5.4 destinations and exported in 8.4 different product categories. Exporting firms sourced on average 2.23 million euros from other nations, distributed by a mean of 14.2 product categories and 3.5 different countries. The average exporter in the sample has 8.3

> 5In both the FTS and EIAS, firms are uniquely identified by their tax identification number (NPC). For statistical confidentiality reasons, the data made available to researchers contains anonymized unique identifiers (a transformation of the real NPC that has a one-to-one mapping to the real one). Hence the mapping of the two data sets was straightforward.

> 6 Since our measures of export experience are computed from trade-transactions data spanning the period 1990-2009, they are truncated at the difference between the reference year and 1990 (and hence are bounded by the upper limit of 20 years).

> 7Firms reporting their main activity to be in the manufacturing sector account for about 82.4% of total exports in the FTS data set for 2005-2009.

5
years of experience in external markets (4.9 years of experienced by individual destination).

# **3 Stylized facts**

In this section we provide a comprehensive analysis of the evolution of firm performance over the life cycle. While the key novel stylized facts we document refer to the joint evolution of performance and prices in international markets, we place these patterns in the context of broader evidence on the dynamics of firm size. This makes it possible to compare key patterns in our data with those reported in the existing empirical literature, and thereby provide an integrated analysis of firm dynamics in both the domestic and external markets.

## **3.1 Firm performance across cohorts**

We begin by examining the relationship between firm performance and age in the crosssection. When examining measures of firm size, we consider the age of the firm. When analyzing export revenue, we consider export-age, defined as the number of consecutive years the firm has been an exporter.

Figure 1 depicts the firm size and export revenue distributions of various cohorts of firms and exporters, based on data for 2005.<sup>8</sup> As in Cabral and Mata (2003) and Angelini and Generale (2008), we use nonparametric estimation methods, notably a kernel density smoother. These methods offer a convenient way of estimating the density of the distribution without imposing much structure on the data.<sup>9</sup> The patterns displayed in the top and middle panels of Figure 1 are well in line with those reported by Cabral and Mata (2003): as firms get older, the size distribution shifts progressively to the right. The diagram reported in the lower panel of this figure focuses solely on exporting firms, and shows that the distribution of export revenue by export-age. As we look at more experienced exporters, the distribution of export revenue shifts systematically to the right.

Inspection of Figure 1 points to a clear relationship between firm performance and age, and between export revenue and export-age. We examine this issue further by estimating an equation of the form: where _yit_ is a measure of size or export performance of firm _i_ in year _t_ , _ageit_ is either the number of years passed since birth of the firm or the number of consecutive years the firm has been an exporter in year _t_ , _λkt_ is an industry-year fixed-effect, _ηr_ is a region

> 8A cohort is defined as the group of firms for which the corresponding age measure in 2005 lied between between 1-5 years, 6-10 years, and so on. Results for each of the other years in the sample are similar, and are available upon request.

> 9As in Angelini and Generale (2008) we use a bandwidth of 0.7. Estimation with alternative bandwidths leads to qualitatively similar results.

6
fixed-effect, and _εikrt_ a random term. Industry-year and region dummies are included to account for possible systematic relationships between firm age and industry affiliation or region.

Table 1 reports the corresponding results. The point estimates clearly corroborate the visual evidence. The estimates in columns (1)-(2) reveal that, among all manufacturing firms, a 10% increase in firm age is associated with a rise of 4.5% in total employment and 5.8% in total sales. Columns (3)-(4) show that these relationships remain fairly similar when restricting the focus to exporters. Finally, the estimates in columns (5)-(7) reveal that export revenue increases systematically with the length of activity in export markets: the estimates in column (5) indicate that when export-age increases by 10%, export revenue increases by 15.9%, on average; those in column (7) reveal that if export-destination-age increases by 10%, export revenue in that market rises by 11.3% on average in that same destination.

# **3.2 Prices, quantities and export experience**

To gain insight about the mechanisms underlying the evolution of export performance over the life cycle, we proceed by examining heterogeneity of prices and physical quantities of exported goods and imported inputs, within narrow product categories, across cohorts of exporters. We run regressions of the form: where _zipjt_ is the export price charged (or physical quantity sold) by firm _i_ in the productdestination pair _pj_ in year _t_ . We run similar regressions where the dependent variable is the import price paid (or physical quantity purchased) by firm _i_ in the product-source pair _pj_ in year _t_ . Finally, we run regressions with average labor earnings at the firm-level, where subscript _pj_ is not relevant.

We use two different measures of age in export markets. Our preferred measure, log export-destination-age, is the log of the number of consecutive years the firm has been serving market _j_ in year _t_ . We also report results using the number of consecutive years the firm has been an exporter (in any market) in year _t_ , log export-age. The terms _ψpjt_ , _λk_ and _ηr_ are fixed-effects by product-destination-year (product-source-year), industry and region, respectively.

Table 2 reports the point estimates from (2), for both prices and quantities of exported products within narrow product categories. The estimates reported in columns (1) and (2) reveal that the relationship between export prices charged by firms and the export experience in that market is positive but not statistically significant. The estimates in columns (3) and (4) show that export volumes increase systematically with export-experience. Figure 2 complements this evidence with a visual representation of these relationships for the various points of the distribution of residuals of the corresponding regressions, using a 7
local polynomial smoother. An inspection of these diagrams confirms that the point estimates yielded by the regression analysis provide a good representation of the relationship observed along the corresponding distributions.

We proceed by examining the behavior of inputs prices, in particular average wages and imported input prices, across cohorts of exporters. The results in column (1) of Table 3 confirm the well-known result that older manufacturing firms tend to pay higher wages on average (Brown and Medoff, 2003). Interestingly, the results in columns (2) and (3) show that a similar relationship holds among exporters: firms with longer spells of export activity tend to pay higher wages, on average.

In Table 4 we examine the relationship between export-age and imported inputs prices and quantities. The results in this table reveal that more experienced exporters tend to purchase larger quantities of inputs at higher prices. Like for export prices, Figure 3 provides a visual representation of these relationships, which confirm the conclusions from the regressions.

For robustness, in Appendix D we examine the extent to which our price and quantity results are sensitive to the choice of the sample period. As we noted above, the EIAS data are only available for the period 2005-2009, whereas the FTS data are available since 1990. In the main analysis, we chose to restrict the focus to the period for which we have complete information, using the the 1990-2004 data only to compute measures of export experience. Tables A2 and A3 in the Appendix report similar results using FTS price and quantity data for 1996-2009, leaving a shorter time interval (1990-1995) solely to compute measures of export experience. Reassuringly, the results reported in these tables reveal that our results are quite robust. The only qualitative difference is that the positive association between export experience and export prices is now more precisely estimated.<sup>10</sup>

# **3.3 Growth versus selection on initial size**

In the analysis above, we characterized the evolution of firm size and export performance over the life cycle using cross-sectional data. A potential explanation for the observed heterogeneity in performance across cohorts is selection on initial conditions. If firms that are initially larger or obtain more revenue when they start serving foreign markets are more likely to survive, older firms and more experienced exporters will naturally be larger and have stronger export performance even in the absence of systematic growth patterns over the life cycle.

Following Cabral and Mata (2003) we first evaluate the empirical relevance of this mechanism by identifying the universe of entrants in 2005 and tracking their performance until 2009. We then perform a similar exercise for the universe of new exporters in 2005 and following them in export markets until 2009.

> 10We have used other time periods and found similar qualitative results.

8
From the 1,268 manufacturing firms that were born in 2005, 948 were still operating in 2009. The upper and middle panel of Figure 4 depicts the distributions of log employment and log sales of these two sets of firms in 2005, as well the 2009 distributions for survivors. Inspection of this figure reveals that the distribution of survivors in 2009 is clearly to the right of that of the universe of entrants in 2005. If selection based on initial size (exit of initially smaller firms) were to explain this evolution, the firm size distribution (FSD) of survivors in 2005 would be expected to be shifted to the right compared to the overall distribution of entrants in 2005. By contrast, if differential growth of initially similar firms were to explain this evolution, the initial FSD of survivors would be expected to resemble that of the universe of entrants in 2005. Inspection of Figure 4 shows that firm growth, as opposed to selection based on initial size, is the main driver of the evolution of performance over the life cycle.

The lower panel of Figure 4 depicts similar distributions, but now focusing on the export revenue of all new exporters in 2005. From the 1,115 manufacturing firms that started exporting in 2005, 224 were still exporting in 2009. It is clear that the distribution of firms that continued exporting until 2009 is clearly to the right of the universe of new exporters in 2005. Hence, this evolution reflects both growth of export revenue among survivors and selection based on initial size: while firms that survived in export markets until 2009 were already larger exporters in 2005, their export revenue grew considerably (in real terms) between 2005 and 2009.<sup>11</sup>

# **3.4 Growth, size and age**

We further characterize the growth process described above by examining the relationship between firm growth and age. We first examine if and how firm growth is systematically related with age, even when controlling for size. Following the literature (Evans, 1987; Sutton, 1997; Haltiwanger, Jarmin, and Miranda, 2013) we estimate a regression of the form: where _yit_ denotes employment or sales by firm _i_ in year _t_ , _yit−_ 1 represents the same variable in the previous year, and age denotes the age of the firm in _t −_ 1. The results in Table 5 confirm the well-known result that firm growth declines with age, even when controlling for size. This finding holds irrespective of whether firm size is measured by employment or sales.

We then perform a similar analysis for growth of export revenue, both overall and within individual destinations. In this case we use export-age or export-destination-age as the measure of experience in export markets:

> 11In the end of the sample period, firm growth in domestic and export markets was likely affected by the international financial crisis. We have verified that our results remain qualitatively similar when excluding 2009 or 2008-09 from the sample.

9
log _yijt −_ log _yijt−_ 1 = _α_ log _yijt−_ 1 + _β_ log _ageijt−_ 1 + _λjt_ + _λk_ + _ηr_ + _εijkrt._ (4) The results are reported in Table 6 and suggest once again that export growth declines with export experience. This relationship holds both for total exports and exports in individual destinations, and prevail when controlling for initial export size. As emphasized by Arkolakis, Papageorgiou, and Timoshenko (2015) this feature of the data cannot be explained by models of random productivity evolution, but can be matched by models of learning about unobserved demand.<sup>12</sup>

# **4 The model**

In this section we develop a learning model with quality choice to jointly explain the evolution of firm growth rates, and input and output prices over the firm life cycle. To capture the conditional age-dependence of growth rates documented in section 3.4 we consider a model of learning by Arkolakis, Papageorgiou, and Timoshenko (2015). To explain the pricing patterns documented in section 3.2, we introduce input and output quality choice as in Kugler and Verhoogen (2012).

## **4.1 Set-up**

Time is discrete and is denoted by _t_ . There are _N_ countries. Each country _j_ is populated by _Lj_ identical infinitely-lived consumers. There are two sectors in each economy: a finalgoods sector and an intermediate-inputs sector. The final-goods sector is populated by a mass of monopolistically competitive firms. Those firms supply horizontally differentiated varieties of various qualities. The intermediate-inputs sector is perfectly competitive and uses a constant-returns-to-scale production technology. Every period there exists an exogenous mass of entrants _Jj_ . There are no sunk costs of entry.

## **4.2 Consumers**

Consumer preferences in country _j_ over the consumption of the composite final good are described by the expected utility function _Uj_ given by

> 12For robustness, in Table A4 we show that similar results are obtained for the period 1996-2009.

10
where _β_ is the discount factor and _Qjt_ is the consumption of the composite final good. _Qjt_ is given by where _qjt_ ( _ω_ ) is the consumption of variety _ω_ in the final-goods sector, Ω _ijt_ is the total set of varieties in the final-goods sector sold in country _j_ originating from country _i_ , and _σ_ is the elasticity of substitution across varieties.

Each variety _ω_ is subject to two sources of demand heterogeneity. First, as in Kugler and Verhoogen (2012), _λjt_ ( _ω_ ) is the quality of variety _ω_ in country _j_ at time _t_ . _λjt_ ( _ω_ ) captures characteristics of variety _ω_ which are chosen by a firm. If chosen, those characteristics increase the utility of a consumer. _λjt_ ( _ω_ ) is known to both consumers and Second, as in Arkolakis, Papageorgiou, and Timoshenko (2015), _ajt_ ( _ω_ ) is the demand shock for variety _ω_ in country _j_ at time _t_ . The demand shock captures inherent variation in preferences across varieties irrespective of the varieties’ quality. The demand shock is given by where _θ_ is the time-invariant component of the shock, a product “appeal” index. The appeal index is subject to the transient preference shocks _εjt_ ( _ω_ ) which are i.i.d. _N ∼_ (0 _, σ_<sup>2</sup> _ε_<sup>).Incontrasttoquality,thedemand shock isknowntoconsumers,butnottofirms.</sup> Each consumer is endowed with a unit of labor which he inelastically supplies to the market, and owns a share of profits of domestic monopolistically-competitive firms. Given their income, consumers minimize the cost of acquiring the aggregate consumption bundle yielding the demand for variety _ω_ given by where _pjt_ ( _ω_ ) is the price of variety _ω_ , _Pjt_ is the aggregate price index, and _Yjt_ is the aggregate spending level in country _j_ at time _t_ . The aggregate price index is given by

# **4.3 Intermediate inputs sector**

The intermediate inputs sector is characterized by perfect competition and a constantreturn-to-scale production technology. The sector uses labor _l_ to produce intermediate 11
inputs of varying quality _c_ : production of _x_ units of an intermediate input of quality _c_ requires _cx_ units of labor. Notice that such production technology implies that production of higher-quality inputs requires more labor resources. The profit of a firm producing an intermediate input of quality _c_ is given by where _wjt_ is the wage rate and _p_<sup>_c_</sup> _jt_<sup>(</sup><sup>_c_)isthepriceofanintermediateinputofquality</sup><sup>_c_in</sup> country _j_ at time _t_ . Perfect competition leads to zero profit yielding to the price of an intermediate input equal to its marginal cost:

# **4.4 Final goods sector**

The final goods sector consists of a continuum of monopolistically competitive firms.

## **Production technology**

Each firm produces one good which it can supply to multiple markets in varying qualities. The production of _q_ physical units of the final good requires _x_ = _φ_<sup>_<u>q</u>_unitsofan</sup> intermediate input, where _φ_ is the productivity level of the firm.

The productivity parameter _φ_ is drawn from a Pareto distribution with the shape parameter _ξ_ and the scale parameter _φ_ min and is known to the firm since entry.<sup>13</sup> In this set-up, the productivity parameter _φ_ measures the efficiency with which the firm can convert units of an intermediate input into units of the final good. A more productive firm can produce the same quantity of output with less units of an input, irrespective of the quality of the intermediate input used.

The quality of an intermediate input, however, is intimately linked to the quality of the final good: an intermediate input of quality _c_ delivers the final good of quality _λ_ = _c_<sup>_γ_</sup> . In addition to the quality of an intermediate input, the production of _λ_ units of quality <u>1</u> of the final good requires incurring _f_<sup>_λ_</sup> = _λ α_ quality-upgrading costs (measured in the units of labor), where _α ≥_ 0. The quality-upgrading costs _f_<sup>_λ_</sup> can be interpreted as an investment in R&D or product design necessary to deliver outputs of higher quality. With this interpretation, _α_ measures the effectiveness of such spending: an increase in _α_ requires incurring less costs to deliver the same level of output quality.<sup>14</sup>

> 13 The probability density of Pareto distribution is given by _ξφ_<sup>_ξ_</sup> min _/φ_<sup>_ξ_+1</sup> . � �

> 14The assumed production technology for the quality of the final good corresponds to the Kugler and Verhoogen (2012) fixed-cost-of-upgrading Leontief production function which can equivalently be written as _λ_ = min _{_ ( _f_<sup>_λ_</sup> )<sup>_α_</sup> _, c_<sup>_γ_</sup> _}_ . The parameter _α_ can therefore be interpreted as the scope for quality differentiation. If the value of _α_ is low, it would be expensive for firms to upgrade quality, and hence the equilibrium will exhibit little variation in the quality of intermediate and final foods. By contrast, if the value of _α_ is high, quality upgrading is relatively inexpensive and the equilibrium will exhibit large heterogeneity in product quality.

12
Finally, selling to market _j_ from market _i_ requires incurring a fixed overhead production cost _fij_ and an iceberg transportation cost _τ ij_ , all measured in units of labor.

## **Belief updating**

The profitability of a firm in market _j_ depends on the firm’s appeal index _θj_ . The firm never observes its product-appeal index in a given market and must make all of its decisions based on beliefs about _θ_ . _j_ The prior belief about _θj_ is given by the initial distribution from which the appeal index is drawn, _N_ (<sup> ̄</sup> _θ, σ_<sup>2</sup> _θ_<sup>).Theposteriorbeliefisgivenbythenormaldistributionwith</sup> mean _μnj_ ( ̄ _aj, n_ ) and variance _υ_<sup>2</sup> _n_<sup>, where</sup><sup>_n_is the number of demand shocks</sup><sup>_ajt_(</sup><sup>_θj_) that the</sup> firm has observed prior to making a current decision and _a_ ̄ _j_ is the mean of those observed demand shocks.<sup>15</sup> We assume that a firm observes one shock per period, hence we also interpret _n_ as a firm’s age. In the limit, as _n →∞_ , the posterior distribution converges to a degenerate distribution centered at _θj_ .

## **The static problem of a firm**

At the start of each period, a firm from country _i_ decides on whether to sell to market _j_ or not, and, conditional on selling to market _j_ , the firm chooses the quantity _qijt_ and the quality _λijt_ of its final good to be sold to market _j_ , and the quantity _xijt_ and the quality _cijt_ of its intermediate input to maximize per-period expected profit. The problem of the firm is given by subject to the following five constraints We close the model in a standard way as described in Timoshenko (2015b) and Arkolakis, Papageorgiou, and Timoshenko (2015). The details are outlined in Appendix E.

# **4.5 Properties of the solution**

In this section we examine properties of the stationary equilibrium and demonstrate how learning about demand affects the quality choice of inputs, the quality of the final good, 13
and the evolution of prices and quantities of inputs and outputs.

From the static problem of a firm (8), the optimal quality of an intermediate input _cij_ is given by _ajt_ where _bj_ ( ̄ _aj, n_ ) = _Eajt|a_ ̄ _j ,n_ � _e σ_ � is the expected demand level.<sup>16</sup> Proposition 1 establishes four properties of the input quality choice.

**Proposition 1** _Properties of the quality of intermediate inputs._

_<u>γ</u> Provided α <_ ( _γ−_ 1)( _σ−_ 1)<sup>_,γ>_1</sup><sup>_andallelseequal_</sup> _(a) cij is increasing in Yj;_ _(b) cij is increasing in φ;_ _(c) cij is increasing in bj; (d) cij is increasing in n if a_ ̄ _j >_<sup> ̄</sup> _θ_ + 2<sup>_σ_</sup> _σθ_<sup>2</sup><sup>_,andisdeclininginnotherwise._</sup> The proofs to all Propositions are included in Appendix G. Proposition 1 states that, provided the investment in quality upgrading is sufficiently effective, i.e. _α_ is low enough, firms will chose higher quality of intermediate inputs and thus supply final goods of higher quality (by equation (13)) to larger markets. Similarly, by part (b) of Proposition 1, more productive firms will chose higher quality of an intermediate input and thus the final output.

While parts (a) and (b) of Proposition 1 are known from Kugler and Verhoogen (2012), parts (c) and (d) are novel to the literature and describe how quality choice varies within firms over time. Part (c) states that quality choice is intimately related to a firm’s idiosyncratic expected demand level. Conditional on the aggregate market size _Yj_ , firms with higher expected demand _bj_ will choose higher quality inputs and thus will supply higher-quality outputs.

More important, however, is that a firm’s expected demand varies over time. As firms learn, they update their beliefs. Thus, firms will upgrade product quality if expected demand is growing, and downgrade quality if expected demand is shrinking, potentially leading to an exit from a market.

As stated in part (d) of Proposition 1, provided that the expected true appeal index ̄ _aj_ is high enough, the quality of intermediate inputs will rise with a firm’s age _n_ . The intuition is straightforward. Every firm starts with the same prior<sup> ̄</sup> _θ_ regarding its true appeal index. If the realized posterior _a_ ̄ _j_ is greater than the prior (more specifically greater than<sup> ̄</sup> _θ_ + _σ_<sup>2</sup> _θ_<sup>_/_(2</sup><sup>_σ_)),afirmwillgrowinitsexpecteddemand</sup><sup>_bj_.Thisgrowthwill</sup>

> 16The complete solution to the firm’s maximization problem is presented in Appendix F.

14
lead to the improvement in the good’s quality and ultimately to an increase in sales.<sup>17</sup> In contrast, firms which overestimated their demand and discover that their true appeal index is below the prior, _a_ ̄ _j <_<sup> ̄</sup> _θ_ + _σ_<sup>2</sup> _θ_<sup>_/_(2</sup><sup>_σ_) to be precise,gradually adjust their expected demand</sup> downwards and shrink in size. Hence, the quality of intermediate inputs of shrinking firms will decline over time.

The data available to us are not sufficient to explicitly measure product quality or demand and test predictions in Proposition 1. We can however examine the model’s implications for the behavior of input and output prices. From equation (10) we see that the price of an intermediate input _p_<sup>_c_</sup> _it_<sup>faced by a final-goods producer is linear in the quality</sup> of an intermediate input. By part (d) of Proposition 1, over time firms tend to increase the quality of intermediate inputs used. Hence firms will also face increasing prices for the intermediate inputs, consistently with the data presented in Table 4 and Figure 3. The price of the final good charged by a firm is given by Proposition 2 below establishes properties of the final-goods prices.

Proposition 2 below establishes properties of the final-goods prices.

**Proposition 2** _Properties of the final-goods prices._

_<u>γ</u> Provided α <_ ( _γ−_ 1)( _σ−_ 1)<sup>_,γ>_1</sup><sup>_andallelseequal_</sup> _(a) pijt is increasing in φ if α > σ−_ <u>1</u> 1<sup>_,andisdeclininginφotherwise;_</sup> _(b) pijt is increasing in bj if α > σ_ +( _γ−γ_ 1)( _σ−_ 1)<sup>_,andisdeclininginbjotherwise;_</sup> _<u>γ θ</u> (c) for α > σ_ +( _γ−_ 1)( _σ−_ 1)<sup>_,pijtisincreasinginnifa_ ̄</sup><sup>_j>_ ̄</sup><sup>_θ_+</sup> 2<sup>_σ_</sup> _σ_<sup>2</sup><sup>_,andisdeclininginn_</sup> _otherwise._ _<u>γ θ</u> (d) for α < σ_ +( _γ−_ 1)( _σ−_ 1)<sup>_,pijtisdeclininginnifa_ ̄</sup><sup>_j>_ ̄</sup><sup>_θ_+</sup> 2<sup>_σ_</sup> _σ_<sup>2</sup><sup>_,andisincreasinginn_</sup> _otherwise._ Similarly to Kugler and Verhoogen (2012), parts (a) and (b) of Proposition 2 state that more profitable firms (as measured by either high productivity or high demand expectations) charge higher prices for their outputs if the scope for quality differentiation is high enough.<sup>18</sup> Parts (c) and (d) of Proposition 2 indicate that, in contrast with input prices, the behavior of output prices depends on parameter configuration. Part (c) of Proposition

> 17This mechanism is intuitive and supported by anecdotal evidence. Consider, for example, the production of the iPhone by Apple. As the firm learns about the growing popularity of its product, it continues to invest in R&D and systematically releases new and upgraded versions of the product.

> 18A similar relation between output prices and productivity holds in the model of Antoniades (2015) who introduces quality choice in the model of Melitz and Ottaviano (2008).

15
2 states that if _α_ is high enough, _α > σ_ +( _γ−γ_ 1)( _σ−_ 1)<sup>tobeprecise,outputpriceswill</sup> increase with age for growing firms. As discussed above, a growing firm is the firm which underestimated its true appeal index and learned that the mean of the observed demand shocks ̄ _aj_ is greater than the prior. Similarly, shrinking firms, i.e when ̄ _aj <_<sup> ̄</sup> _θ_ + 2<sup>_σ_</sup> _σθ_<sup>2, output</sup> prices will decline with age. In contrast, part (d) of Proposition 2 states that when _α_ is below the threshold value of _σ_ +( _γ−γ_ 1)( _σ−_ 1)<sup>,outputpriceswilldeclinewithageforgrowing</sup> firms, and increase with age for shrinking firms.

Another way to understand the intuition behind the ambiguity in the final goods pricing behavior is to consider the trade-off between the effect of quality upgrading versus the increase in profitability on prices. In the context of equation (16), suppose that a firm keeps the quality of an intermediate input unchanged. In this case, the price dynamics are solely driven by changes in demand beliefs, _bj_ . Since demand beliefs enter multiplicatively with productivity into prices, revenues, and profits, the effect of an increase in beliefs is equivalent to an increase in productivity, or an increase in profitability, or a decline in marginal cost. Since price is a mark-up over marginal cost, more profitable firms (either due to falling costs or rising expected demand) will charge lower prices over time. The quality of an intermediate input (hence output) either does not vary or increases by an amount which is insufficient to compensate for falling marginal cost. In the model, the extent of quality adjustment is governed by _α_ . For low values of _α_ , high fixed costs of quality adjustment _f_<sup>_λ_</sup> deter firms from varying the quality of intermediate inputs. As a result, prices decline over time as firms age.

When quality upgrading is cheap ( _α_ is high), an increase in demand beliefs is accompanied by a corresponding increase in the quality of an intermediate input (equation (14)). If the quality of an intermediate input increases by more than one-to-one with respect to beliefs, the price of the final good increases. This occurs exactly when _α > γ/_ ( _σ_ + ( _γ −_ 1)( _σ −_ 1)).

In line with the behavior of quantities as a function of a firm’s age depicted in Figure 2, Proposition 3 establishes the behavior of the optimal quantity of the final good given by

**Proposition 3** _Property of the final-goods quantities._

_<u>γ θ</u> Provided α <_ ( _γ−_ 1)( _σ−_ 1)<sup>_,γ>_1</sup><sup>_andallelseequal,fora_ ̄</sup><sup>_j>_ ̄</sup><sup>_θ_+</sup> 2<sup>_σ_</sup> _σ_<sup>2</sup><sup>_,qijtisincreasingin_</sup> _n if α < γ, and is declining in n otherwise._ From equation (11), the quantity of an intermediate input _xijt_ is linear in the quantity of the final good. Hence, consistently with the data presented in Table 4 and Figure 3, the model also delivers input quantities increasing with the export age of a firm. Notice that, as discussed in Appendix F, the solution to a firm’s problem only exists when _α <_ ( _γ−_ 1)( _<u>γ</u> σ−_ 1)<sup>.</sup> Hence, the model always delivers optimal quantity increasing with age as suggested by 16
Figure 2, as long as ( _γ −_ 1) ( _σ −_ 1) _>_ 1. In the next section, we turn to the quantitative analysis of the model and show that the calibrated parameter values satisfy this restriction. Hence, the quantitative exercise will demonstrate that the model is able to deliver the behavior of input prices and quantities suggested by the data.

# **5 Quantitative analysis**

In this section we calibrate a symmetric two-country model to match the average domestic and export behavior of Portuguese firms over the period 2005-2009, and next explore the quantitative ability of the model to predict the data.

## **5.1 Parameter**

Three parameters of the model can be pinned down independently. The discount factor _β_ is taken to be 0.9606 which corresponds to a quarterly interest rate of 1 percent. As estimated by Amador and Soares (2014) in the context of the Portuguese economy, the elasticity of substitution _σ_ is taken to be 6.16. The exogenous death rate _δ_ is taken to be 2.98%, which corresponds to the average death rate of Portuguese firms in the top 5 percent of the export revenue distribution.<sup>19</sup> Following the argument in Arkolakis, Papageorgiou, and Timoshenko (2015), the standard deviation of the transient preference shocks, _σθ_ , is identified by the extent of the conditional age dependence of firms’ growth rates. Specifically, we target the age coefficient in a regression of the log of export revenue growth on export-age and size, as reported in Table 6, column (6). All else equal, the larger is the standard deviation, the more dispersion there is in the observed distribution of export revenue. The magnitude of _σε_ relative to the standard deviation of the “appeal” index draw, _σθ_ , determines the rate at which firms update their beliefs, and thus the rate at which firms grow. The higher is the variance of the appeal relative to the variance of the shock, the more weight firms attribute towards updating their beliefs in favor of the posterior mean of the observed demand shocks, the faster they grow. Thus, _σε_ is pinned down by the average growth rate of exporter-entrants.

The two parameters governing the quality production function, _α_ and _γ_ , are pinned down by the export-age coefficient in the input price regression in Table 4, and the share of sales from export entrants. From equation (33), parameter _α_ directly governs the extent of the age dependence of the quality of intermediate inputs, hence prices of intermediate inputs. From equation (13), parameter _γ_ governs the rate at which the quality of intermediate inputs translates into the quality of the final good and thus total sales. Given the selection of incumbents based on higher productivity or expected demand (hence quality),

> 19The identifying assumption is that the largest firms in an economy are likely to exit due to exogenous reasons.

17
the size of an export-entrant relative to an average firm declines in _γ_ , and hence the share of export sales accounted for by entrants declines.

Finally, the shape parameter of the Pareto distribution of productivity draws, _ξ_ , is identified by the tail index of the export revenue distribution of exporting firms, and the fixed cost of selling in the export market, _fx_ , is identified by the average revenue of exporters. All else equal, the higher are the fixed costs, the higher is the productivity entry threshold. As a result, more productive exporting firms earn larger revenues yielding higher average sales of exporters. The six parameters, _σε_ , _σθ_ , _α_ , _γ_ , _ξ_ , and _fx_ are jointly calibrated to minimize the sum of the squared deviations of the simulated versus the data moments.

Having calibrated these parameters, the variable trade cost _τ_ is computed to yield the proportion of exporters in the Portuguese data (16.7%). The fixed cost of selling in the domestic market, _fd_ , is computed to yield the ratio of average domestic sales of firms to average export sales of exporters, which is equal to 0.35.

# **5.2 Calibration results**

Table 7 displays the simulated and data moments and Table 8 reports the corresponding calibrated parameter values. As can be seen from Table 7, the moments identify parameters fairly well with the criterion equal to 0.00004.

Figure 5 replicates the results in Figure 3 using simulated data, and depicts estimates of a local polynomial smoother relating the log of export-age and the log of import price (Panel A) or the log of import quantity (Panel B). As expected, import prices tend to increase with export-age, since this relation was a targeted moment in the calibration. In contrast, the calibration did not target the relationship between import quantity and export-age. As can be seen from Panel B of Figure 5, the model delivers a quantity behavior that is also consistent with the data.

The model is calibrated to match the conditional age-dependence of growth rates and input prices. Table 9 reports the growth regression results based on the simulated data. Comparison of the size coefficients in Tables 6 and 9 reveals that the model slightly overpredicts the extent of the conditional size dependence of growth rates. The less strong size-dependence of growth observed in the data may arise due to alternative mechanisms considered in the literature such as financial constraints (Cooley and Quadrini, 2001) or random productivity evolution (Arkolakis, 2015).

# **5.3 Counterfactual experiments**

In this section we use the calibrated two-country model to explore the implications of imposing minimum quality standards on exported goods. Due to the quality standard, any exporting firm in each country must choose the quality of intermediate inputs above 18
̄ a given threshold _c_ .<sup>20</sup> The corresponding problem of the firm is described in Appendix H, and Figure 6 describes the effect on the general equilibrium variables. In all panels of Figure 6, the horizontal axis measures the percent improvement in the average quality of exported goods that results from the imposition of a given minimum quality requirement. All depicted values on the vertical axis are normalized by their corresponding values in the calibrated non-constrained equilibrium.<sup>21</sup> As is evident from Panel A of Figure 6, a quality standard is not welfare improving. For example, a minimum standard leading to 25 percent improvement in the average quality of exported goods reduces real consumption by 2 percent. The intuition for the result is as follows. As can be seen from Panel C, the export-quality standard increases the productivity threshold for entry in the export market and thus reduces the number of exporters (Panel D). The decline in the number of exporters reduces the degree of competition in the domestic market, leading to a higher equilibrium price level (Panel B). Furthermore, the decline in foreign competition leads to entry of less efficient firms in the domestic market: as can be observed in Panels C and D, the domestic entry threshold declines and the mass of domestic varieties rises. At the extensive margin, therefore, the effect of the minimum quality standard on exports is qualitatively equivalent to an increase in the iceberg transportation cost _τ_ , which also leads to a reduction in the number of exporters, an increase in the number of domestic varieties, and an increase in the price level (Melitz, 2003). Our model is therefore able to match recent evidence indicating that standards reduce entry in export markets and lead to an increase in product prices, especially among small exporters (Fontagn ́e et al., 2015).

The quality standard additionally distorts the intensive margin of firm adjustment. For the firms located close to the entry threshold, i.e. either small or young firms, the quality constraint binds. Hence, in order to export, these firms are forced to comply with the standard and, as a result, choose higher quality intermediate inputs. The production of higher quality intermediate inputs requires more labor. Hence, the imposition of the minimum quality standard leads to the reallocation of resources among exporters towards young and small firms. This effect is demonstrated in Figure 7. Panel A and B depict the proportion of labor employed in the production of exports allocated between the bottom 10 and top 10 percent of exporters in the export-sales distribution (including the units of labor embodied in the intermediate inputs purchased by these firms). In Panel A, we observe that as the minimum quality standard increases, the proportion of labor accounted

> 20Bown and Crowley (forthcoming) provide several examples of product standards imposed in practice, and note that it is typical for foreign suppliers to allege that such standards are either too restrictive or applied in way that discriminates against foreign relative to domestic production, potentially forcing them to undertake additional costly investments to meet compliance requirements. Fontagn ́e et al. (2015) offer a detailed empirical treatment of restrictive Sanitary and Phyto-Sanitary (SPS) standards on imports, and note that such standards may require exporting firms to upgrade their products or substitute more costly inputs from those previously used.

> 21Naturally, a stronger improvement in the average quality of exported goods corresponds to a higher minimum quality constraint on intermediate inputs embodied in exports.

19
for by the bottom 10 percent of exporters rises from about 0.8 to 1.2 percent. In contrast, the share of labor among top 10 percent of exporters declines from around 63 to 60 percent. In a similar way, Panels C and D show that there is a reallocation of labor units from old to young exporters.

Finally, as can be seen in Panel E of Figure 6, while the policy raises export quality it leads at best to a small improvement in the overall quality of goods available to consumers. For example, a standard leading to an increase in the quality of exported goods by about 8 percent raises the overall quality of goods available to consumers by less than one percent. Thus, consumers face higher prices and experience almost no difference in the quality of goods available to them. This effect is primarily driven by the rapid decline in the number of exporters relative to domestic firms. Although export quality rises, the proportion of exporting firms declines much faster (as seen in Panel D) yielding a small contribution of higher export quality to the overall quality of goods available to consumers. The latter effect may even dominate: a standard leading to a relatively large improvement in the average quality of exported goods (over 16 percent) leads to a decline in the overall quality of goods available to consumers.

# **6 Conclusion**

We used detailed micro data from the Portuguese manufacturing sector to document new facts about the joint evolution of firm performance and prices over the life cycle: (1) within narrow product categories, firms with longer spells of activity in a destination tend to export larger quantities at similar prices to that market; and (2) older or more experienced exporters tend to import more expensive inputs. In line with previous research, we also reported evidence that the positive relationship between export revenue and market experience reflects growth, not just market selection based on initial size; and that revenue growth within destinations (conditional on initial size) tends to decline with export-age.

To account for the joint observation of these patterns in the data, we developed a theory of endogenous input and output quality choices in a learning environment. In the model, firms supply products of varying quality based on their beliefs about idiosyncratic expected demand. Through the life-cycle, an average surviving firm updates its demand expectations upwards, grows, and, as a result, finds it optimal to upgrade the quality of outputs, which requires using higher quality inputs. Because higher quality inputs are more expensive, average input prices increase with export experience. The evolution of output prices is less clear-cut. On the one hand, quality upgrading leads to a higher price. On the other hand, an increase in demand expectations increases profitability and causes a price reduction. Hence the model is able to rationalize the varying behavior of input and output prices over the firm life cycle observed in the data.

Calibrated to match the observed age-dependence of export growth and input prices, our model slightly over predicts the conditional size-dependence of growth rates that 20
emerges from the data, and correctly predicts that the quantity of inputs increases with export-age. Using the calibrated model, we examined the implications of regulations imposing minimum product quality standards on exports. We found that the imposition of these standards reduces welfare through two distinct channels. First, it lowers entry in export markets and therefore the number of export varieties available to consumers. Second, it distorts an intensive margin of adjustment. To participate in the export market, marginal exporters are forced to comply with the minimum standard by choosing intermediate inputs of higher quality. This choice leads to a reallocation of productive resources from large and old towards small and young firms, leading to a further decline in welfare.

21
# **References**

- Albornoz, Facundo, Gregory Corcos, Emanuel Ornelas, and Hector F. Calvo Pardo. 2012. “Sequential exporting.” _Journal of International Economics_ 88 (1):17–31.

- Amador, Joao and Ana Cristina Soares. 2014. “Competition in the Portuguese economy: Estimated price-cost margins under imperfect labour markets.” ECB Working Papers 1751.

- Angelini, Paolo and Andrea Generale. 2008. “On the evolution of firm size distributions.” _American Economic Review_ 98 (1):426–438.

- Antoniades, Alexis. 2015. “Heterogeneous firms, quality, and trade.” _Journal of International Economics_ 95 (2):263–273.

- Arkolakis, Costas. 2015. “A unified theory of firm selection and growth.” _Quarterly Journal of Economics,_ forthcoming.

- Arkolakis, Costas, Theodore Papageorgiou, and Olga A. Timoshenko. 2015. “Firm learning and growth.” Unpublished manuscript.

- Baltzer, Kenneth. 2011. “Minimum quality standards and international trade.” _Review of International Economics_ 19 (5):936–949.

- Bastos, Paulo and Joana Silva. 2010. “The quality of a firm’s exports: Where you export to matters.” _Journal of International Economics_ 82 (2):99–111.

- Bastos, Paulo, Joana Silva, and Eric Verhoogen. 2014. “Export destinations and input prices.” NBER Working Papers 20143.

- Bernard, Andrew B., Bradford J. Jensen, Stephen J. Redding, and Peter K. Schott. 2007. “Firms in international trade.” _Journal of Economic Perspectives_ 21 (3):105–130.

- Berthou, Antoine and Vincent Vicard. 2013. “Firms’ export dynamics: Experience vs. size.” ECB Working Papers 1616.

- Bown, Chad P. and Meredith A. Crowley. forthcoming. “The empirical landscape of trade policy.” In _Handbook of Commercial Policy_ , edited by Kyle Bagwell and Robert W. Staiger. Elsevier.

- Brown, Charles and James L. Medoff. 2003. “Firm age and wages.” _Journal of Labor Economics_ 21 (3):677–698.

- Cabral, Luis and Jose Mata. 2003. “On the evolution of the firm size distribution: Facts and theory.” _American Economic Review_ 93 (4):1075–1090.

22
- Chaney, Thomas. 2014. “The network structure of international trade.” _American Economic Review_ 104 (11):3600–3634.

- Cooley, Thomas F. and Vincenzo Quadrini. 2001. “Financial markets and firm dynamics.” _American Economic Review_ 91 (5):1286–1310.

- Das, Satya P. and Shabtai Donnenfeld. 1989. “Oligopolistic competition and International trade: Quantity and quality restrictions.” _Journal of International Economics_ 27 (34):299–318.

- DeGroot, Morris. 2004. _Optimal statistical decisions_ . Wiley Classics Library. Hoboken, N.J.: Wiley-Interscience.

- di Giovanni, Julian and Andrei Levchenko. 2012. “Country size, international trade, and aggregate fluctuations in granular economies.” _Journal of Political Economy_ 120 (6):1083–1132.

- Eaton, Jonathan, Marcela Eslava, David Jinkins, Cornell J. Krizan, and James Tybout. 2014. “A search and learning model of export dynamics.” Unpublished manuscript.

- Eaton, Jonathan, Marcela Eslava, Maurice Kugler, and James Tybout. 2008. “The margins of entry into export markets: Evidence from Colombia.” In _Globalization and the organization of firms and markets_ , edited by Elhanan Helpman, Dalia Marina, and Thieery Verdier. Massachusetts: Harvard University Press.

- Evans, David S. 1987. “Tests of alternative theories of firm growth.” _Journal of Political Economy_ 95 (4):657–674.

- Fernandes, Ana, Caroline Freund, and Martha Denisse Pierola. 2015. “Exporter Behavior, country size and stage of development: Evidence from the exporter dynamics database.” _Journal of Development Economics_ forthcoming.

- Fischer, Ronald and Pablo Serra. 2000. “Standards and protection.” _Journal of International Economics_ 52 (2):377–400.

- Fontagn ́e, Lionel, Gianluca Orefice, Roberta Piermartini, and Nadia Rocha. 2015. “Product standards and margins of trade: Firm-level evidence.” _Journal of International Economics_ 97 (1):29–44.

- Freund, Caroline and Martha Denisse Pierola. 2015. “Export superstars.” _Review of Economics and Statistics,_ 97 (5):1023–1032.

- Gabaix, Xavier and Rustam Ibragimov. 2011. “Rank-1/2: A simple way to improve the OLS Estimation of tail exponents.” _Journal of Business and Economic Statistics_ 29 (1):24–29.

23
- Hallak, Juan Carlos. 2006. “Product quality and the direction of trade.” _Journal of International Economics_ 68 (1):238–265.

- Hallak, Juan Carlos and Peter Schott. 2011. “Estimating cross-country differences in product quality.” _Quarterly Journal of Economics_ 126 (1):417–474.

- Hallak, Juan Carlos and Jagadeesh Sivadasan. 2013. “Product and process productivity: Implications for quality choice and conditional exporter premia.” _Journal of International Economics_ 91 (1):53–67.

- Haltiwanger, John, Ron Jarmin, and Javier Miranda. 2013. “Who creates jobs? Small vs. large vs. young.” _Review of Economics and Statistics_ 95 (2):347–361.

- Hummels, David and Pete Klenow. 2005. “The variety and quality of a nation’s exports.” _American Economic Review_ 95 (3):704–723.

- Impullitti, Giammario, Alfonso A. Irarrazabal, and Luca David Opromolla. 2013. “A theory of entry into and exit from export markets.” _Journal of International Economics_ 90 (1):75–90.

- Jovanovic, Boyan. 1982. “Selection and the evolution of industry.” _Econometrica_ 50 (3):649–670.

- Khandelwal, Amit. 2010. “The long and short (of) quality ladders.” _Review of Economic Studies_ 77 (4):1450–1476.

- Kugler, Maurice and Eric Verhoogen. 2012. “Prices, plant size, and product quality.” _Review of Economic Studies_ 79 (1):307–339.

- Luttmer, Erzo. 2007. “Selection, Growth, and the Size Distribution of Firms.” _Quarterly Journal of Economics_ 122:1103–1144.

- Manova, Kalina and Zhiwei Zhang. 2012. “Export prices across firms and destinations.” _Quarterly Journal of Economics_ 127 (1):379–436.

- Mayer, Thierry and Gianmarco Ottaviano. 2007. “The happy few: new facts on the internationalisation of European firms.” Bruegel-CEPR EFIM2007 Report, Bruegel Blueprint Series.

- Melitz, Marc and Gianmarco Ottaviano. 2008. “Market Size, trade, and productivity.” _Review of Economic Studies_ 75 (1):295–316.

- Melitz, Marc J. 2003. “The impact of trade on intra-industry reallocations and aggregate industry productivity.” _Econometrica_ 71 (6):1695–1725.

- Ruhl, Kim J. and Jonathan Willis. 2014. “New exporter dynamics.” Federal Reserve Bank of Kansas City, RWP 14-10.

24
- Schott, Peter. 2004. “Across-product versus within-product specialization in international trade.” _Quarterly Journal of Economics_ 119 (2):647–678.

- Sutton, John. 1997. “Gibrat’s legacy.” _Journal of Economic Literature_ 35 (1):40–59.

- Timoshenko, Olga A. 2015a. “Learning versus sunk costs explanations of export persistence.” _European Economic Review_ 79:113–128.

- ———. 2015b. “Product switching in a model of learning.” _Journal of International Economics_ 95:233–249.

- Verhoogen, Eric. 2008. “Trade, quality upgrading and wage inequality in the Mexican manufacturing sector.” _Quarterly Journal of Economics_ 123 (2):489–530.

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|log exp-dest<br>(7)|1.125***<br>[0.008]<br>155,002<br>0.387<br>Y<br>Y<br>Y|n columns (3)-(7)|ent variable is the|of export revenue||
|---|---|---|---|---|---|
|rs<br>log exp-dest<br>(6)|0.468***<br>[0.012]<br>155,002<br>0.244<br>Y<br>Y<br>Y|od 2005-2009. I|n (5) the depend|riable is the log|*10% level.|
|exporte<br>log exp<br>(5)|1.593***<br>[0.013]<br>29,798<br>0.479<br>Y<br>Y|ms in the peri|09. In colum|dependent va|l, **5% level,|
|log sales<br>(4)|0.613***<br>[0.020]<br>29,798<br>0.254<br>Y<br>Y|ufacturing fr|eriod 2005-20|) and (7) the|r. ***1% leve|
|log empl<br>(3)|0.571***<br>[0.011]<br>29,798<br>0.264<br>Y<br>Y|d of all man|rters in the p|columns (6|by frm-yea|
|rms<br>log sales<br>(2)|0.577***<br>[0.004]<br>178,674<br>0.216<br>Y<br>Y|le is compose|acturing expo|stinations. In|kets, clustered|
|all f<br>log empl<br>(1)|0.454***<br>[0.003]<br>178,674<br>0.225<br>Y<br>Y|imation samp|d of all manuf|frm in all de|errors in brac|
|le:|-age<br>-destination-age<br>ear efects<br>cts<br>n-year efects<br>fects|umns (1)-(2) the est|n sample is compose|port revenue of the|n. Robust standard|
|iab|rt<br>rt<br><br>ed<br>-y<br>fe<br>io<br> e|col|io|ex|io|
|ar|e<br>po<br>po<br>s.)<br>ar<br>try<br> e<br>at<br>try|n|mat|tal|nat|
|Dep.v|log ag<br>log ex<br>log ex<br>N (ob<br>R-squ<br>indus<br>region<br>destin<br>indus|Notes: I|the esti|log of to|by desti|

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Table 2: Export <u>prices</u> and <u>quantities</u> across cohorts, 2005-2009

|Dep. variable:|log expo<br>(1)|rt price<br>(2)|log expor<br>(3)|t quantity<br>(4)|
|---|---|---|---|---|
|log export-destination-age|0.003<br>[0.005]||0.375***<br>[0.007]||
|log export-age||0.005<br>[0.013]||0.145***<br>[0.016]|
|N (obs.)|556,870|556,870|556,870|556,870|
|R-squared|0.831|0.831|0.721|0.716|
|product-destination-year efects|Y|Y|Y|Y|
|industry efects|Y|Y|Y|Y|
|region efects|Y|Y|Y|Y|

Notes: In columns (1) and (2) the dependent variable is the log of export unit values by firm-product-destination. In columns (3) and (4) the dependent variable is the log of export quantities by firm-product-destination. Robust standard errors in brackets, clustered by firm-year. ***1% level, **5% level, *10% level.

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Table 3: Average wages across cohorts, 2005-2009

|all frms|exp|orters|
|---|---|---|
|(1)|(2)|(3)|
|log age<br>0.153***<br>[0.002]|||
|log export-age|0.085***<br>[0.002]||
|log mean export-destination-age||0.080***<br>[0.003]|
|N (obs.)<br>178,674|29,798|29,798|
|R-squared<br>0.173|0.284|0.271|
|industry-year efects<br>Y|Y|Y|
|region efects<br>Y|Y|Y|
|Notes:<br>Mean export-destination-age is defned as|the averag|e of export-|
|destination-age across destinations within frm-year cell|s. Robust st|andard errors|
|in brackets, clustered by frm-year. ***1% level, **5%|level, *10%|level.|

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Table 4: Import <u>prices</u> and <u>quantities</u> across cohorts, 2005-2009

|Dep. variable:|log imp<br>(1)|ort price<br>(2)|log impor<br>(3)|t quantity<br>(4)|
|---|---|---|---|---|
|log export-age|0.025***<br>[0.006]||0.100***<br>[0.013]||
|log mean export-destination-age||0.020***<br>[0.007]||0.124***<br>[0.015]|
|N (obs.)|641,916|641,916|641,916|641,916|
|R-squared|0.730|0.730|0.650|0.650|
|product-source-year efects|Y|Y|Y|Y|
|industry efects|Y|Y|Y|Y|
|region efects|Y|Y|Y|Y|

Notes: In columns (1) and (2) the dependent variable is the log of import unit values by firmproduct-source country. In columns (3) and (4) the dependent variable is the log of import quantities by firm-product-destination. Mean export-destination-age is defined as the average of export-destination-age across destinations within firm-year cells. Robust standard errors in brackets, clustered by firm-year. ***1% level, **5% level, *10% level.

29
|age, 2005-2009<br>log sales_t_-log sales_t−_1<br>(4)<br>(5)<br>(6)|-0.071***<br>-0.072***<br>[0.001]<br>[0.001]<br>-0.013***<br>0.001<br>[0.001]<br>[0.001]<br>122,684<br>122,684<br>122,684|0.071<br>0.041<br>0.071|Y<br>Y<br>Y|Y<br>Y<br>Y|rms in the period 2005-2009. Robust standard|10% level.|
|---|---|---|---|---|---|---|
|h, size and <br>pl_t−_1<br>(3)|-0.037***<br>[0.001]<br>-0.015***<br>[0.001]<br>122,684|0.034|Y|Y|ufacturing f|**5% level, *|
|Firm growt<br>mpl_t_-log em<br>(2)|-0.026***<br>[0.001]<br>122,684|0.023|Y|Y|sed of all man|***1% level,|
|Table 5: <br>log e<br>(1)|-0.044***<br>[0.001]<br>122,684|0.031|Y|Y|ple is compo|by frm-year.|
|Dep variable:|log age_t−_1<br>log empl_t−_1<br>log sales_t−_1<br>N (obs.)|R-squared|industry-year efects|region efects|Notes: The estimation sam|errors in brackets, clustered|

30
|exports-dest_t−_1<br>(6)|-0.033***<br>[0.003]<br>-0.042***<br>[0.001]|75,134<br>0.052|Y<br>Y<br>Y|standard||
|---|---|---|---|---|---|
|s-dest_t_–log <br>(5)|-0.048***<br>[0.001]|75,134<br>0.050|Y<br>Y<br>Y|2009. Robust||
|log export<br>(4)|-0.068***<br>[0.003]|75,134<br>0.039|Y<br>Y<br>Y|e period 2005-||
|orts_t−_1<br>(3)|-0.023***<br>[0.006]<br>-0.021***<br>[0.003]|16,677<br>0.066<br>Y|Y|porters in th|*10% level.|
|log exports_t_–log exp<br>(1)<br>(2)|-0.049***<br>[0.006]<br>-0.026***<br>[0.002]|16,677<br>16,677<br>0.061<br>0.065<br>Y<br>Y|Y<br>Y|posed of all manufacturing ex|year. ***1% level, **5% level,|
|e:|ge_t−_1<br>_−_1<br>ge-destination_t−_1<br>dest_t−_1|ar efects|ts<br>year efects<br>ects|mation sample is com|ts, clustered by frm-|
|l|a<br>s_t_<br>a<br>s-|e|c<br>-<br>f|ti|ke|
|b|t-<br>t<br>t-<br>t|d<br>y|e<br>n<br>e|s|c|
|ria|or<br>or<br>or<br>or|)<br>re<br>y-|f<br>tio<br>y-|e e|ra|
|a|p<br>p<br>p<br>p|.<br>a<br>r|e<br>a<br>r|h|b|
|Dep v|log ex<br>log ex<br>log ex<br>log ex|N (obs<br>R-squ<br>indust|region <br>destin<br>indust|Notes: T|errors in|

31
Table 7: Data and simulation moments, 2005-2009

||Calibration moments|data<br>(1)|simulation<br>(2)|
|---|---|---|---|
|1.|The mean of the logarithm of export sales|11.96|11.96|
|2.|The growth rate of export entrants|31.08%|30.99%|
|3.|The share of sales from export entrants|1.42%|1.42%|
|4.|The age coefcient in the input price regression<sup>_a_</sup>|0.025|0.025|
|5.|The age coefcient in the exports growth regression<sup>_b_</sup>|-0.023|-0.023|
|6.|The tail index of the export sales distribution<sup>_c_</sup>|-1.238|-1.243|
||_Criterion_||_0.00004_|

Notes: Moments correspond to the average export behavior of Portuguese manufacturing firms over the period 2005-2009. _a_ Source: The age coefficient in Table 4, column (1). _b_ Source: The age coefficient in Table 6, column (3). _c_ Source: The empirical estimate of the tail index is presented in Appendix I.

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<u>Table 8: Parameter values</u>

|Parameter|Value|
|---|---|
|_β_|0.9606|
|_σ_|6.160|
|_δ_|0.0298|
|_σθ_|1.46|
|_σε_|2.51|
|_α_|0.06|
|_γ_|1.77|
|_ξ_|7.59|
|_fx_|12,167.23|
|_fd_|4,297.82|
|_τ_|1.05|

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Table 9: Export growth, revenue, and experience in the <u>simulated data</u>

|Dep. variable:|log exports_t_-log exports_t−_1|
|---|---|
|log export-age_t−_1|-0.023***<br>[0.001]|
|log exports_t−_1|-0.032***<br>[0.001]|
|N (obs.)|184,243|
|R-squared|0.01|
|sample|age_≤_20|

Notes: The table reports OLS regressions based on the simulated firm-level sample. Robust standard errors in brackets. ***1% level, **5% level, *10% level.

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Figure 1: Firm performance across cohorts, 2005 <!-- Start of picture text --> age 1−5<br>age 6−10<br>age 11−20<br>age 21−30<br>age >30<br>0 2 4 6 8 10<br>log employment<br>age 1−5<br>age 6−10<br>age 11−20<br>age 21−30<br>age >30<br>0 5 10 15 20<br>log sales<br>export−age 1−5<br>export−age 6−10<br>export−age >10<br>0 5 10 15 20<br>log export revenue<br>.4<br>.3<br>.2<br>density<br>.1<br>0<br>.3<br>.2<br>density<br>.1<br>0<br>.2<br>.15<br>.1<br>density<br>.05<br>0<br><!-- End of picture text --> Notes: The figure depicts non-parametric estimates from a kernel density smoother with bandwidth 0.7, using data from 2005. Age is the number of years since birth of the firm. Export-age is the number of consecutive years the firm has recorded positive export revenue.

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Figure 2: Export prices (quantities) and export-destination-age, residuals 2005-2009 <!-- Start of picture text --> export prices export quantities<br>−2 −1 0 1 2 −2 −1 0 1 2<br>residuals of log export−age in destination residuals of log export−age in destination<br>kernel = epanechnikov, degree = 0, bandwidth = .5, pwidth = .5 kernel = epanechnikov, degree = 0, bandwidth = .5, pwidth = .5<br>.01 .4<br>.005 .2<br>0<br>0<br>residuals of log export price<br>residuals of log export quantity<br>−.005 −.2<br>−.4<br>−.01<br><!-- End of picture text --> Notes: The graph in left of the figure report estimates of a local polynomial smoother relating the residuals from: (1) a regression of the log of export prices by firm-product-destination on product-destination-year, industry and region fixed-effects; and (2) a regression of log export-destination-age on the same set of fixed-effects. The graph in the right panel of the figure reports estimates of a local polynomial smoother relating the residuals from: (1) a regression of the log of export quantities by firm-product-destination on product-destination-year, industry and region fixed-effects; and (2) a regression of log export-destinationage on the same set of fixed-effects. To reduce the influence of outliers in the estimation of the local polynomial, the distributions of the residuals were trimmed by 1% on both tails.

36
Figure 3: Import prices (quantities) and export-age, residuals 2005-2009 <!-- Start of picture text --> import prices import quantities<br>−2 −1 0 1 −2 −1 0 1<br>residuals of log export−age residuals of log export−age<br>kernel = epanechnikov, degree = 0, bandwidth = .5, pwidth = .5 kernel = epanechnikov, degree = 0, bandwidth = .5, pwidth = .5<br>.02<br>.05<br>0<br>0<br>−.02<br>−.05<br>residuals of log import price residuals of import quantity<br>−.04 −.1<br>−.06 −.15<br><!-- End of picture text --> Notes: The graph in the left panel of this figure reports estimates of a local polynomial smoother relating the residuals from: (1) a regression of the log of import prices by firm-product-source country on productsource-year, industry and region fixed-effects; and (2) a regression of log export-age on the same set of fixed-effects. The graph in the right panel of this figure reports estimates of a local polynomial smoother relating the residuals from: (1) a regression of the log of import quantities by firm-product-source country on source-year, industry and region fixed-effects; and (2) a regression of log export-age on the same set of fixed-effects. To reduce the influence of outliers in the estimation of the local polynomial, the distributions of the residuals were trimmed by 1% on both tails.

37
Figure 4: Growth versus selection on initial size, 2005-2009 <!-- Start of picture text --> all entrants, empl. 2005<br>survived through 2009, empl. 2005<br>survived through 2009, empl. 2009<br>0 2 4 6<br>log employment<br>all entrants, sales 2005<br>survived through 2009, sales 2005<br>survived through 2009, sales 2009<br>0 5 10 15 20<br>log sales<br>all new exporters, exports 2005<br>survived through 2009, exports 2005<br>survived through 2009, exports 2009<br>0 5 10 15 20<br>log exports<br>.4<br>.3<br>.2<br>density<br>.1<br>0<br>.3<br>.2<br>density<br>.1<br>0<br>.2<br>.15<br>.1<br>density<br>.05<br>0<br><!-- End of picture text --> Notes: The figure depicts non-parametric estimates from a kernel density smoother with bandwidth 0.7, using data from 2005 and 2009.

38
Figure 5: Input prices (quantities) and export-age, simulated data <!-- Start of picture text --> Panel A Panel B<br>0 1 2 3 0 1 2 3<br>log export−age log export−age<br>kernel = epanechnikov, degree = 0, bandwidth = .19, pwidth = .29 kernel = epanechnikov, degree = 0, bandwidth = .19, pwidth = .29<br>.3 12<br>.28 11.5<br>.26 11<br>log input price<br>log input quantity<br>.24 10.5<br>.22 10<br><!-- End of picture text --> Notes: Panel A display estimates of a local polynomial smoother relating log input prices and log exportage using simulated data. Panel B depicts estimates of a local polynomial smoother relating log input quantity and log export-age using simulated data. The shaded areas corresponds to the 95% confidence interval.

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Figure 6: Effects of minimum quality standards <!-- Start of picture text --> Panel A Panel B<br>1.04<br>1<br>1.02<br>0.98<br>1<br>0.96 0.98<br>0 10 20 30 0 10 20 30<br>Percent Improvement in the Percent Improvement in the<br>Average Export Quality Average Export Quality<br>Panel C Panel D<br>2 1.5<br>Export<br>1.5 Domestic 1<br>Export<br>Domestic<br>1 0.5<br>0.5 0<br>0 10 20 30 0 10 20 30<br>Percent Improvement in the Percent Improvement in the<br>Average Export Quality Average Export Quality<br>Panel E<br>1.01<br>1<br>0.99<br>0 10 20 30<br>Percent Improvement in the<br>Average Export Quality<br>Price Level<br>Real Consumption<br>Entry Thresholds Mass of Varieties<br>Quality of All Goods<br><!-- End of picture text --> Notes: All depicted values on the vertical axis are normalized by their corresponding values in the calibrated non-constrained equilibrium. Authors calculations on model simulation.

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Figure 7: Labor reallocation caused by minimum quality standards <!-- Start of picture text --> Panel A Panel B<br>Share of Labor by Bottom 10 percent Share of Labor by Top 10 percent<br>1.5 64<br>62<br>1<br>60<br>0.5 58<br>0 10 20 30 0 10 20 30<br>Percent Improvement in the Percent Improvement in the<br>Average Export Quality Average Export Quality<br>Panel C Panel D<br>Share of Labor by Young (Age 1−5) Share of Labor by Old (Age ≥ 15)<br>11 71<br>10.5 70.5<br>10 70<br>9.5 69.5<br>0 10 20 30 0 10 20 30<br>Percent Improvement in the Percent Improvement in the<br>Average Export Quality Average Export Quality<br>Percent Percent<br>Percent Percent<br><!-- End of picture text --> Notes: Authors calculations on model simulation.

41