Product Quality Differentiation and the Impact of International Trade Antoine Gervais University of Notre Dame

Jeff Thurk University of Notre Dame

April 2011 PRELIMINARY - PLEASE DO NOT CITE COMMENTS ARE WELCOME

Abstract We ask whether incorporating product quality differentiation has real effects on trade flows and welfare. We develop and estimate a general equilibrium model of international trade that includes endogenous product quality differentiation amongst heterogeneous firms. Including both transportation and ad valorem trade costs as in Hummels and Skiba (2004) is crucial to creating a channel for product quality to have real effects. The model provides a framework to quantify the effects of quality differentiation on trade flows and welfare in response to a trade liberalization vis-a-vis a workhorse model similar to Melitz (2003). We find that allowing firms to choose their product quality increases the welfare gains from trade liberalization significantly.

Keywords: Firm heterogeneity, International trade, Quality, R&D Welfare. JEL Classification Numbers: F12

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1

Introduction

A new and rapidly expanding literature suggests that product quality differentiation plays a crucial role in explaining important features of international trade patterns. Within narrowly defined product categories exporting firms charge higher prices than firms producing exclusively for the domestic market (Kugler and Verhoogen (2010), Hallak and Sivadasan (2009) and Gervais (2010)). This suggests that more productive firms produce goods of higher quality. Moreover, when developed and developing countries export in the same product category, high per capita countries export high price varieties (Schott (2004) and Hummels and Klenow (2005)). This suggests that rich countries have a comparative advantage in the production of high quality products. Finally, the average export price is higher when countries sell to richer more distant countries (e.g. Baldwin and Harrigan (2010) and Manova and Zhang(2010)). This implies that product differentiation has important implication for the impact of trade liberalization. One of the main difficulty in this line of research is that product quality is unobservable in general. Most studies use average unit value to make inference on quality (citation). However, as explained in Gervais (2010), price variation may not capture the full extend of quality variation. Moreover, many factors other than quality can lead to price dispersion. Motivated by these observations we develop a structural model of international trade with endogenous product quality to answer the following question: What are the welfare and trade flow effects, if any, of incorporating product quality differentiation into workhorse trade models such as Melitz (2003)? In section 2, we incorporate endogenous product quality into a Melitz-style model of international trade, where quality is an unobserved demand shifter. We allow heterogeneous firms to invest in R&D to upgrade their product quality, thereby increasing profits. Firms can also choose to trade internationally but face fixed and variable trade costs, where the latter are split into per unit transportation and ad valorem variable costs as in Hummels and Skiba (2004). We show that these transportation costs affect the productivity-quality mix of traded goods, hence have real effects on trade flows and welfare. Without them, matching export price moments is really just an issue of relabeling as noted in Kugler and Verhoogen (2010) and therefore, there are no real effects. In sections 3 and 4, we jointly-estimate key parameters of both the full model with product quality differentiation and a Melitz-style model with only heterogeneity in firm productivity. Not surprisingly, we find that product quality plays an important role in explaining export prices differences around the world. We also find that firms in developed countries tend to produce higher quality goods by leveraging their access to large markets via low trade costs

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and their comparative advantage in producing high quality goods via lower costs of quality upgrading. In section 5, we use our estimated models to evaluate the impacts of trade liberalization on trade flows and welfare. We find that the model with quality differentiation generates about 60% more welfare gains than the Melitz-style model. The gain is not uniform, however, as countries with relatively low import shares tend to experience larger welfare gains. This suggests a concave relationship between welfare and trade costs. We also find that that the change in export revenue is smaller in the quality model, as firms use the increased market access (via decreased trade costs) to increase their product quality. Production quantity is then smaller (relative to the Melitz model) leading to the smaller relative effect on exports. We summarize the results and present conclusions in section 6. Additional information on the data, computational algorithms, and main theoretical results are available in appendices.

2

Model

The model is similar to Melitz (2003). Firms are heterogeneous in their level of productivity and quality, where the latter is an endogenous choice. Firm profit is increasing in productivity level, quality level, and competitor prices. Firms also make trade decisions which are subject to fixed, unit, and ad valorem transportation costs.

2.1

Households

Time is discrete and the horizon is infinite. There are N countries indexed by i = 1, . . . , N . Each country is populated by a mass of identical consumers Li . Each consumer is endowed with a unit of time and supplies labor inelastically. Agents in all countries and time period have identical Cobb-Douglas preferences over two types of goods. To simplify notation we omit time and country subscripts. U = M 1−α

Z

a(z)q(z)ρ dz

 αρ (1)

z∈Z

The first good, M , is homogeneous and produced with a constant returns production technology that uses one unit of labor input per unit of output. The good can be traded at no cost between countries. It will serve as the numeraire. Since the good is freely-traded, factorprice equalization implies the wage rate is equal to unity in all countries. The second good is a composite produced with a set of differentiated inputs. Define z as the product variety and Z is the set of all product varieties available for consumption. The term a(z) corresponds

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to what we call “quality” of variety z. In essence, quality captures differences in demand.1 We assume that the quality of each variety is perfectly observable to consumers and lies in the compact set A. The parameter α ∈ (0, 1) pins down the share of composite good while ρ ∈ (0, 1) governs substitutability between the differentiated goods. Both parameters are common to all countries. This set-up implies that the demand for variety z is: q(z) = αY P

−1



p(z) a(z)

− ,

with  =

1 >1 1−ρ

(2)

where αY is aggregate spending on differentiated goods,  is the price elasticity of demand, R  1 and P is the price index defined as: P = z∈Z (p(z)/a(z))1− dz 1−

2.2

Firms

Firms produce goods using only labor. Each consumer is endowed with one unit of labor which is supplied inelastically at the market rate – normalized to unity. Firms are heterogeneous in their quality a and productivity x, which lies in the compact set X. A firm with productivity-quality pair (x, a) faces the following cost function:  q λ a , Γi (x, a, q) = fiqual + x and λ reflects increasing/ decreasing production costs associated with higher quality. Firms from country i can sell their products in country j but face three types of trade costs: a fixed per-period trade cost φij ≥ 0, an ad valorem iceberg trade cost τij ≥ 1, and a per unit trade cost tij ≥ 0. The fixed export cost captures the expense required to set up an export relationship (e.g., management overhead), while the latter variable costs capture all costs related to tariffs and transporting goods from country i to country j, respectively. Hummels and Skiba (2004) document the existence of these different variable costs and their relative effects on international trade flows. As we’ll show below, these trade costs will be essential for quality differentiation to drive real effects which a productivity-only model cannot generate. Arkolakis (2008) shows the prevalence of small exporters (measured in revenue or employment) in the data. To match this fact, we assume that firms draw idiosyncratic fixed export costs φ each period before profits are realized and that these draws are uncorrelated over time. In particular, a firm from country i wishing to sell goods in country j draws φij from a distribution Fij . 1

As in Johnson(2010), Kugler and Verhoogen (2011) and Gervais (2010), conditional on price, the demand will be higher for high quality goods.

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Firms choose to trade if profits are greater than this the realized export cost. Define the trade indicator variable: ( 1 πij (x, a) ≥ φij Iij (x, a, φ) = (3) 0 otherwise. where πij are the variable profits from selling in country j and φ is the vector of idiosyncratic export draws for the firm in that period.

2.3

Spot Markets

We assume competition in the country j differentiated good sector occurs in a spot market at the beginning of each period. Hence, a firm with differentiated good z from country i with productivity x and quality a solves the following static pricing problem: N X

max

a,{pij ,Iij }N j=1

   τij aλ α Iij pij − tij − qij − φij − fiqual aλ x j=1

(4)

where fiqual aλ is the country-specific cost of quality a. We assume that firms are sufficiently ∂P small such that ∂pijj = 0. Optimal pricing is then only a function of the firm marginal production costs, determined by the productivity level and product quality, and bilateral trade costs. The optimal pricing rule can be written: 1 pij (z) = ρ



τij aλ tij + x

 (5)

where ρ is the constant mark-up applied by all differentiated goods firms. Since firms enter symmetrically into the utility function, defined in (1), and are differentiated only by their level of productivity and quality, it is convenient to refer to variety z by its productivity-quality pair (x, a). Henceforth we will refer to “variety (x, a)” rather than “variety z.” Define µi (x, a) as the mass of country i firms with productivity x and quality a. Define µi (x, a) as the mass of country i firms with productivity x and quality a, then µ = [µ1 , ..., µN ] ∈ M is the vector of firm distributions across the world. We can then rewrite the price index in country j as: " Pj (µ) =

N Z Z X i=1

φ

x∈X

Z

1 # 1−

Iijexp (x, a, φ; µ)a pij (x, a)1− µi (x, a)dFij (φ)

a∈A

We can now describe the spot market equilibrium.

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Equilibrium Definition: Given state µ, a spot market equilibrium in country i is a set of demand functions qij (x, a; µ), pricing rules pij (x, a; µ), profit functions πij (x, a; µ), and trade decisions Iijexp (x, a; µ) such that aggregate spending equals aggregate income: Yi = Li + Πi , where Πi is total firm profit in country i. Implicit in the last equation is the assumption that agents hold diversified stock portfolios in the differentiated good firms.

2.4

Endogenous Product Quality

We assume that productivity is fixed over time but that firms can choose their quality level by conducting R&D. We assume that firms make their quality decision prior to drawing their fixed export costs. Firms that decide to pay high fixed production costs are able to produce goods of higher quality. In the current setup, the optimal choice of quality depends on the characteristics of the domestic market and the export decisions of the firms. This happens because, all else equal, access to a larger market increases the profitability of quality investment. The optimal quality is given by: ai (x; µ) = argmax α (1 − ρ)ρ−1 a

N Z X j=1

" Iij

φ

#   λ 1− τa Yj Pj−1 a t + − φij dFij (φ) − fiqual aλ x

(6) Since the export decision rules and optimal quality depend on each other in a complex way, we cannot obtain close form solutions. However, as can be seen from the last equation, the optimal quality depends on the firm’s market access. A decrease in trade costs or an increases in market size will increase market access, thereby increasing the optimal quality. Also note that all firms with productivity x in country i choose the same quality a, so that firm quality outcomes depend only on aggregate effects.

2.5

Incumbent Firm Profits

An incumbent firm in country i with productivity x and aggregate state µ has discounted profits conditional on the law of motion for the aggregate state (Υ : M → M). Recursively, the value of the incumbent firm is Vi (x, φ; µ) =

N X

Iijexp (x, a; µ)[πij (x, a; µ)

j=1

s.t.

µ0 = Υ(µ)

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 − φij ] +

1−δ 1+r



E{Fij } {Vi (x, φ0 ; µ0 )}

(7)

Where a is the quality decision rule defined in equation 6, r is the rate of return, and δ is the exogenous exit rate common to firms in all countries.

2.6

Entry

Outside firms may choose to enter the industry by employing fie units of labor. Prospective firms enter if, and only if, the expected discounted value of entry is greater than fie . Entering firms in country i draw their initial productivity and quality levels from a time-invariant cdf Gi . The distribution of productivity and quality is allowed to vary across countries. Conditional on aggregate state the (µ) and the law of motion (Υ), a prospective firm in country i chooses entry if and only if 1 · E[Vi (x0 , µ0 )|Gi ] ≥ fie 1+r s.t. µ0 = Υ(µ)

(8)

Define the function ei (µ) as the firm entry rate in country i, then Υi for country i is 0

Z

0

µi (x , a ) = (1 − δ)

1{a0 =a(x;µ)} [µi (x, a) + Gi (x0 )ei (µ)]

(9)

a∈A

2.7

Feasibility

R P exp R I exp (x, a; µ)µi (x, a) as total labor spent on export costs in Define Lexp = N i j=1 fij x∈X a∈A ij country i. The labor feasibility constraint in country i is then Li ≥

LM i

+

fie ei (µ)

+

Lexp i

Z

Z

+

li (x, a; µ)µi (x, a) + x∈X

a∈A

fiqual

Z x∈X

Z

aλ µi (x, a) (10)

a∈A

e where LM i denotes total employment in production of the homogeneous good M, fi ei is the R R labor employed by entering firms, x∈X a∈A li (x, a; µ)µi (x, a) is the total labor employed in R R the production of differentiated goods, and fiqual x∈X a∈A aλ µi (x, a) is total labor employed in quality-upgrading.

Equilibrium Definition: For every µ = [µ1 , µ2 , ..., µN ], an open economy equilibrium are firm spot market functions {qij , pij , Iijexp , πij }, aggregate prices {Pi }, decision rules {ai , ei }, and law of motion Υ = {Υi } where: i. Static firm maximization generates the spot market functions {qij , pij , Iijexp , πij } and aggregate price index Pi ∀ i, j

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ii. the firm quality decision rule ai solves the incumbent firm’s investment problem (equation 6) ∀i iii. the mass of entering firms ei implies expected discounted profits are zero (equation 8) ∀i iv. the law of motion Υ : M → M satisfies equation 9 ∀i v. the freely-traded homogeneous good equalizes wage rates around the world such that wi = 1 ∀i = 1, ..., N vi. the labor feasibility constraint binds (equation 10) ∀i

2.8

Why Quality Matters

The model differs from the benchmark Melitz model in two important ways. First, firms are allowed to choose the quality of their output, a. The main implication is that fixed costs of production are increasing in quality and endogenous in our model. Essentially firms decide on how much to invest in their technology in order to maximize their profit. Because of that endogenous investment it is not possible to rewrite the model in terms of qualityadjusted productivity to obtain the benchmark Melitz model. In a sense, our setup is similar to the recent model developed by Atkeson and Burstein (2010) where firms invest in their productivity. However, we interpret change in efficiency as quality variation and use price moments to discipline the model. The second difference is the presence of per unit transport costs. Importantly, in the presence of transportations costs, changes in quality (a) and efficiency (x) that keep domestic revenue constant will have different impact on export behavior. This happens because an increase in quality raises domestic price thereby reducing the percentage increase in price associated with the per unit transport cost whereas efficiency has the opposite impact. Therefore, changes in quality and efficiency that leave domestic revenue unchanged have different impacts on firm selection into exporting. Consider two exporting firms with the same domestic revenue but different quality and efficiency. The interaction between quality and transport cost leads to higher export profit for the high quality firm. Hence, conditional on domestic sales, the probability that a firm export is greater if they produce higher quality products.

3

Structural Estimation

In this section, we discuss how we solve the model and fit it to key moments from the data. The model represents a complex and nonlinear function from the parameter to the moment

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space. Consequently, we don’t have closed-form solutions for moments as a function of the parameters, and instead choose to solve the model using Simulated Method of Moments (SMM).

3.1

Model Specification

The model presented depends on a selection of countries N, specifications for firm entry e N N distributions {Gi }N i=1 , market entry cost {fi }i=1 , bilateral unit trade costs {tij }i,j=1 , bilateral N tariff rates {τij }N i,j=1 , the distributions for bilateral fixed trade costs {Fij }i,j=1 , the elasticity of substitution , the spending share of traded goods α, the firm exit rate δ, cost parameters for quality upgrading λ, fiqual , the time preference parameter β, and the discount factor r. We pin-down some of these by making the following assumptions. To choose the country sample, we computed aggregate exports for each country for the period 1985-1995 and chose the 20 countries with the highest shares of international exports. These countries together accounted for about 92% of all world exports.2 These The firm productivity distributions Gi are assumed Pareto with the shape parameter κ, hence the firm productivity distributions are the same for all countries. The spending share of traded goods is 13% consistent with Eaton and Kortum (2002) and Ramondo (2009). The elasticity of substitution  is 2.7, which is the median value estimated by Broda and Weinstein (2006) for SITC5 products. We use data on firm entry rates from around the world and pin-down the entry cost {fie } using the free-entry condition.3 We chose β using the long run return on US bonds during the period (i.e., r = 7%). We allow firms in highly educated countries a comparative advantage in quality upgrading via our choice of quality cost function. Namely, we assume these costs take the following form fiqual = f qual × (1 − Hi )

(11)

where Hi is the percent of adults in country i with at least a secondary education from Barro and Lee (2000). 3.1.1

Trade Costs

Trade is dependent upon the specification of unit transportation costs {tij }, ad valorem tariffs {τij }, and the distributions of fixed export costs {Fij }. Following Fieler (2010), we approximate the transportation costs {tij } using the following function 2

3

Austria, Belgium, Canada, China, Denmark, Finland, France, Germany, Italy, Japan, Korea, Mexico, Netherlands, Sweden, Singapore, Spain, Switzerland, Taiwan, United Kingdom, and the United States See section 5 for further detail on recovering {fie }.

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tij = δ d distij × (δ b )bordij

(12)

where tii = 1, distij is the log distance between country i and j capitals, and bordij is a common border dummy. For the remaining cost parameters, we set the ad valorem tariff rates to 10% and assume the fixed export costs for a firm from country i interested in trading in country j are drawn from exponential distribution with mean fijexp taking the following form: fijexp = γ × tij , γ > 0 Hence, transportation and fixed export costs are positively correlated.

3.2

Estimation Technique

We jointly estimate Θ = {κ, δ d , δ b , γ, f qual , λ} using a combination of moments from the US Compustat manufacturing database, bilateral trade flows from Feenstra, Lipsey, Deng, Ma, and Mo (2005), as well as price moments from the literature. We chose a sample period of 1985-1995 so as to be consistent with the literature. Despite this broad sample period, there still exists a lot of noise in the Compustat data which may skew the estimation exercise. Similar to Akcigit (2009) and Gervais (2010), we removed industry and year effects using the following procedure. First, compute the median values for moments of interest. Second, remove industry (4 digit SIC) and time effects. Third, recover the deviations and add them back to the medians. The result are firm moments centered around the medians but purged of industry and time effects. Our estimation procedure consists of minimizing the weighted squared distance between the J moments generated by the model and those observed in the data. ˆ = argmin[MΘ0 W MΘ ] Θ

(13)

Θ

where   MΘ =  

M1d − MKd −

1 Ns

1 Ns

PS



.. . PS

  

m ˆ s=1 M1 (Θ)

s=1

ˆ MKm (Θ)

W is the positive, semi-definite optimal weight matrix which guarantees the existence of a minimal value. We compute W using a 2-step procedure where we first solve equation 13 using an identity matrix. After a minimal value is found, we simulate the model 1000 times, collect relavent moments, and construct the covariance matrix B. The “optimal” weight

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matrix is then W = B −1 .

3.3

Identification

We chose a subset of the large set of moments available to identify Θ. The quality upgrading cost parameters λ and f qual are identified by a collection of US and international moments during the period 1985-1995. We use moments on US firm R&D intensity (R&D expense/ revenue) observed in the Compustat data, since quality-upgrading in the model represents a form of R&D. We also use average standardized log price charged by US exporters and non-exporters as reported in Hallak and Sivadasan (2009). Matching these latter moments is appealing methodologically since it connects the model to the motivating stylized pricing facts noted in section 1. Recall that the model generates endogenous firm revenue distributions which are a function of the Pareto shape parameter κ and the endogenous quality choices by firms. Define κ ˜ as the Pareto parameter consistent with the observed (or generated) firm revenue distribution. Consequently, matching the κ ˜ observed in the US Compustat data and the model provides identification for κ. The final parameters are related to trade costs. We identify γ using the share of US manufacturing spending on imports, where we calculate import share similar to Eaton and Kortum (2002). We identify the unit transport cost parameters δ d , δ b using a technique similar to Simonovska and Waugh (2011) where use the equilibrium trade flows to estimate the following simple gravity model ln(Tij ) = δ˜0 + δ˜d distij + δ˜b bordij + uij where ln(Tij ) is logged trade from country i to country j. It is important to note that while this equation carries the usual coefficient inerpretations (e.g., trade decreases in the distance between countries), the model does not generate this equation so the estimated coefficients are likely different than the unit trade cost parameters δ d and δ b . That said, the coefficients do provide useful information. A positive value for δ d , for example, implies increased unit trade costs leading to a decrease in trade flows between countries i,j and a negative value for δ˜d .

4

Results

Recall that the objective of this paper is to assess the quantitative implications of product quality differentiation. We answer this question via the framework provided by the model

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which we refer to as the “Full” model. A nice aspect of this model is that it nests a simpler model where firms are heterogeneous only productivity. We’ll refer to this model as the “Melitz” model, though there are differences between this model and Melitz (2003). This model will provide a nice benchmark to assess the contribution of product quality differentiation with respect to trade flows and welfare.

4.1

Estimating the Full Model

Since the objective function (13) is non-linear and likely discontinuous, we solve for θˆ using a simulated annealing algorithm. Standard errors are computed using a numerical approximation to the Jacobian at the given point estimates. Table 1 presents the results.4 Table 1: Estimation Results Variable Estimate κ 4.78 γ 5,934.58 δd 0.01 b δ 0.75 λ 1.57 qual f 7.71

(Quality) SE 1.9930 3.4670 0.0036 0.0363 0.0890 0.6572

All parameters are significant, suggesting strong identification with the targeted moments. Tables 2 and 3 present the targeted and untargeted moments. Table 2: Targeted Moments (Quality) Data Model Average price charged: - US exporters (pex ) 0.050 0.202 nex - US non-exporters (p ) -0.020 -0.231

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US revenue dist. (˜ κ) Avg research intensity (US) Import share (US)

0.100 0.080 0.099

0.092 0.016 0.259

OLS gravity coefficients: - distance - common border

-0.377 1.277

0.057 1.221

The computational algorithm is detailed in the appendix.

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Table 3: Untargeted Moments (Quality) Data Model Median research intensity 0.050 0.016 Large to small firms (US): - Revenue - Net income - Margin - Research intensity

19.472 8.944 1.115 0.498

2.763 2.460 0.921 1.054

Price correlations: - real GDP per capita - export status (std) - export status

0.100 0.080 0.030

0.081 0.433 0.107

The model replicates the targeted moments well by construction. Since the model is over-identified, though over-identification implies that the fit will not be perfect. The most notable deviation pertains to the US import share. The model seems to trade-off weaker fit in the import share, in favor of matching the other moments which are generally strongly correlated with trade volume. The model does a surprisingly poor job matching the OLS gravity coefficient for distance not only in value but also in sign. This is likely due to the small sample of countries and the relatively simple way we’re modeling the fixed trade costs. The targeted price moments are from Hallak and Sivadasan (2009) and correspond to the average log standardized prices charged by US exporters and non-exporters, respectively. 5 The model correctly generates higher prices amongst exporting firms, though the spread between exporter and non-exporter prices are greater than observed in the data. The untargeted moments provide a useful test of the model. Median research intensity for US firms is lower than observed in the data and is close to the average research intensity. We also break the US Compustat data into “large” and “small” firms where large (small) firms are those above (below) median revenue. The ratio of large firm to small firm revenue is significantly smaller than the value observed in the data, as the ratio of net income. It is important to note that net income includes R&D expense (i.e., money spent on quality upgrading) and money spent on fixed export costs, so the net income margin may not be constant across firms. These results suggest the model generates too little dispersion. The last bucket of moments relates to price correlations. Schott (2004) documents a positive correlation between exporters’ per capita real GDP and the prices they charge. 5

We compute the moments by first standardized the log prices using the entire sample. We then compute the average log prices for exporters and non-exporters.

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Hallak and Sivadasan (2009) also show that both standardized and non-standardized US prices are increasing with export status, which are similar to the targeted moments discussed above. Recall that firm quality decisions depend on domestic market size and the firm’s proximity to foreign markets, as well as the country-specific cost of quality upgrading. These sources of heterogeneity generate firm quality distributions that vary around the world. Table 4 provides further insight into the quality choices made by firms in each country. Table 4: Firm Statistics in Each Country (Quality Model) Country GDP/firm Hi (%) AUT 7076.92 55.37 BEL 1264.37 31.88 CAN 597.33 36.79 CHE 1758.62 48.24 CHN 1212.24 24.87 DEU 3374.07 54.70 DNK 955.07 43.71 ESP 633.68 15.16 FIN 1637.50 31.56 FRA 1577.78 33.37 GBR 503.82 34.41 ITA 2204.55 26.72 JPN 3038.28 40.88 KOR 1270.27 40.65 MEX 270.87 12.37 NLD 483.43 44.62 SGP 345.16 22.18 SWE 1432.43 40.34 TWN 1274.60 27.98 USA 1463.21 51.96 Average 1618.71 35.89 ? normalized by USA.

Avg Quality? 1.07 0.93 0.93 1.01 0.85 1.11 0.97 0.82 0.93 0.90 0.93 0.89 0.94 0.94 0.79 1.03 0.77 0.97 0.89 1.00 0.93

Avg Price? 1.13 0.88 0.88 1.03 0.77 1.16 0.97 0.74 0.86 0.87 0.88 0.83 0.88 0.91 0.69 1.02 0.69 0.94 0.82 1.00 0.90

Avg Profit? 0.55 0.50 0.48 0.55 0.65 0.86 0.46 0.49 0.38 0.72 0.54 0.72 0.96 0.49 0.38 0.52 0.27 0.46 0.40 1.00 0.57

% of Firms Export 92.31 81.61 60.69 79.31 57.93 71.48 75.36 65.68 65.62 74.07 67.80 75.76 53.59 55.86 58.44 83.70 45.16 67.57 61.90 51.92 67.29

The model indicates that firms from developed countries generally produce higher quality goods, while developing countries tend to produce low quality goods. This reflects large market access via high real GDP per firm, low trade costs, and a comparative advantage (disadvantage) in producing high quality goods via lower costs of quality upgrading (f q uali ). German firms produce the highest quality goods in equilibrium (11% higher quality than the average US firm) by leveraging their close proximity to other large markets in Europe (via the large number of exporting firms) and low quality upgrading costs (via high education).

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Firms from Mexico and China, on the other hand, have relatively higher quality upgrading costs and are more isolated from large markets. Firms in the US produce goods of higher quality than average despite having below average GDP per firm and a low likelihood of export. The fact that the average US firm generates profit almost twice the average firm in the ROW suggests that US exporting firms enter markets such as Mexico where they can lever their quality advantage. Table 5: Prices Charged by Domestic Firms (Quality Model) Country Average Std Min Max AUT 0.98 0.31 0.81 1.85 BEL 0.77 0.29 0.61 2.62 CAN 0.77 0.29 0.61 2.82 CHE 0.90 0.24 0.74 1.88 CHN 0.68 0.27 0.53 2.84 DEU 1.01 0.39 0.80 3.57 DNK 0.84 0.25 0.68 1.57 ESP 0.64 0.22 0.51 1.95 FIN 0.75 0.37 0.58 2.57 FRA 0.76 0.22 0.62 1.93 GBR 0.77 0.32 0.61 4.88 ITA 0.72 0.28 0.57 2.78 JPN 0.77 0.41 0.61 5.93 KOR 0.79 0.26 0.64 2.58 MEX 0.60 0.23 0.48 3.15 NLD 0.89 0.34 0.70 3.39 SGP 0.60 0.23 0.50 1.86 SWE 0.82 0.24 0.64 1.68 TWN 0.71 0.29 0.55 2.46 USA 0.87 0.30 0.71 4.20 Average 0.78 0.29 0.63 2.82 Recall that prices are a function of both productivity and the endogenous quality choice, but that the distribution of firm productivity is fixed across countries. Consequently, equilibrium prices should reflect similar trends as discussed above and Table 5 confirms that developed countries charge higher prices than developing countries due to their quality upgrading advantage. Table 5 also provides key moments for the simulated price distribution in each country. The firm price distribution in Japan has the highest variance in the sample, though the average price charged by Japanese firms is only about average. Mexican firms, on the other hand, not only charge prices well below average, but also prices that are much more uniform.

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4.2

Estimating the Melitz Model

Table 6 presents the results for our Melitz-style model. Table 6: Estimation Results (Melitz) Variable Estimate SE κ 2.56 0.0412 γ 703.81 804.0344 δd 0.09 0.0306 b δ 0.81 0.0191 The unit transport cost parameters are both significant and similar to the parameter estimates from the Full model. The parameters κ and γ, however, are significantly different from the earlier parameter estimates. The γ point estimate result is puzzling because it’s neither close to the one estimated in the Full model, nor is it significantly different than zero. This could potentially be due to the low country sample size and the relatively simple way we model the fixed export costs. Presumably allowing firms to quality upgrade adds an additional level of heterogeneity that provides further identification. The differences in parameter estimates for κ reflect the ability of firms to differentiate themselves via quality upgrading in the Full model. Recall that the κ is largely identified by fitting a Pareto distribution to the revenue distribution of US firms and that Pareto distributions are first-order stochastically decreasing in their shape parameter. Quality upgrading enables, potentially low productivity, firms to produce high-quality products and generate high revenue. Hence it amplifies the mapping between firm productivity and revenue. Therefore firms can draw from a first-order stochastically inferior productivity distribution (i.e., high κ) and still generate a κ ˜ consistent with the data. These Most of the variables are significant, with Only γ, which regulates the bilateral fixed export cost, Tables 7 and 8 present the targeted and untargeted moments. Table 7: Targeted Moments (Melitz) Data Model US revenue dist. (˜ κ) -0.407 -0.670 Import share (US) 0.099 0.100 OLS gravity coefficients: - distance - common border

-0.377 1.277

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-0.306 1.355

Table 8: Untargeted Moments (Melitz) Data Model Average price charged: - US exporters (pex ) 0.050 -0.184 nex - US non-exporters (p ) -0.020 0.114 Avg research intensity (US) 0.080 0.000 Median research intensity 0.050 0.000 Large to small firms (US): - Revenue - Net income - Margin - Research intensity

19.472 8.944 1.115 0.498

3.757 3.718 0.982 0.000

Price correlations: - real GDP per capita - export status (std) - export status

0.100 0.080 0.030

0.005 -0.297 -0.109

The strong fit between moments and parameters allows us to use an estimation procedure which is just-identified leading to a strong fit between targeted data and model moments. As expected, exporters in this model charge lower prices which is inconsistent with the data. The model also does a poor job matching the correlation between prices charged by firms exporting to the US and their home country real GDP per capita.

5

A Counter Factual Experiment

In the following section, we use the models to answer our question and explore the relative importance of quality and productivity as sources of firm heterogeneity. These experiments present an additional computational burden. Recall a country i firm’s entry decision: 1 · E[Vi (x0 , a0 , µ0 )|G, Υ] ≥ fie 1+r

(14)

where equation 14 is fundamentally one equation with two unknowns: the entry level (ei ) and the fixed cost of entry fie . In estimating the benchmark model, we imposed this equilibrium condition by default and used the observed firm entry rates to solve the model. This strategy simplified the computational burden substantially since it allowed us to avoid recalculating the equilibrium entry rate for each set of parameters. Of course, fixing the mass of entering firms in a counterfactual exercise is not appropriate. We alleviate this issue by recovering

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{fie } from the benchmark model and using (14) to solve for the equilibrium entry rate in each exercise. This approach implicitly assumes that {fie } are deep and do not change for a given exercise, which is a strong assumption. We assess the effects of product quality differentiation by looking at the equilibrium effects of a 10% reduction in trade costs (fixed, variable, and ad valorem) in both the full and Melitz models.

Country AUT BEL CAN CHE CHN DEU DNK ESP FIN FRA GBR ITA JPN KOR MEX NLD SGP SWE TWN USA Average Std

Table 9: Evaluating a 10% Reduction in Trade Costs %∆ % ∆ Exports % ∆ Welfare Quality Melitz Full Diff (F-M) Melitz Full Diff (F-M) 5.15 12.17 12.37 0.20 1.72 2.30 0.58 5.63 15.25 13.89 -1.36 1.50 2.00 0.50 6.03 28.33 19.98 -8.35 0.67 1.42 0.75 5.35 12.92 12.41 -0.51 1.56 2.05 0.48 5.20 19.85 16.16 -3.69 0.65 1.53 0.88 4.38 15.70 14.75 -0.95 1.37 1.92 0.55 5.63 13.74 13.52 -0.22 1.44 1.99 0.55 5.83 17.94 15.80 -2.15 0.74 1.47 0.73 6.02 18.47 16.19 -2.28 1.55 2.03 0.49 5.02 15.76 14.33 -1.43 1.15 1.75 0.60 5.50 17.17 14.73 -2.44 0.35 0.98 0.63 5.09 15.17 14.71 -0.47 1.27 1.88 0.61 4.18 21.22 18.08 -3.14 0.99 1.78 0.79 5.53 20.30 15.37 -4.93 1.22 1.93 0.71 6.72 29.11 20.69 -8.42 0.26 0.82 0.55 5.51 13.27 13.13 -0.14 0.88 1.52 0.64 6.58 21.83 17.35 -4.48 0.98 1.83 0.85 5.69 17.26 15.55 -1.71 1.43 2.01 0.58 5.96 21.73 16.37 -5.36 1.34 2.00 0.66 2.56 20.80 12.53 -8.27 0.36 0.95 0.60 5.38 18.40 15.40 -3.00 1.07 1.71 0.64 0.91 4.65 2.32 2.80 0.44 0.41 0.12

Table 9 tells a couple stories. First, the hypothetical trade liberalization led firms in a net increase in market access for firms in all countries and they responded by increasing their level of product quality on average 5.4%. Interestingly, the response by US firms was more subdued presumably due the relative importance of the domestic market over international markets in the benchmark equilibrium. Second, the Full model in which firms can quality upgrade generates welfare gains that are almost double a model with only firm productivity - a significant welfare difference. This indicates that quality upgrading represents a significant channel which amplifies the gains

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from trade. Not all countries have the same experience, however. Countries with relatively low import shares (see appendix) in the benchmark model appear to benefit more than other countries. This suggests that welfare as a function of trade costs is concave reflecting large returns when trade costs are initially high. Third, the change in export revenue for the Melitz-style model is larger than the change in export revenue for the Full model. This result is due to the relative response of trade flows and quality decisions in the two models. For now just consider the Full model where there exists two competitive forces. One force is a competition effect where the substantial increase in welfare between the benchmark and counter-factual equilibria implies a substantial decrease in the price index. This represents tougher competition abroad and reduces export revenue for an individual firm. The firm, of course can fight this increase by choosing to quality upgrade. Indeed, we see that the average firm increases its quality level by 5%. Of course, the competitive effect also exists in the Melitz model. The significant difference in welfare effects between the Melitz and Full model shows that the competition effect in the Full model is larger than in the Melitz model. This, in turn, implies that the average change in exports is lower in the Full model than in the Melitz model. Further, this result appears to be robust to different choices of trade liberalization experiments, though we do not contend this is to be a global result (i.e., true for all parameter values).

6

Conclusion

[TBD]

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References Akcigit, U. (2009): “Firm Size, Innovation Dynamics and Growth,” Mimeo. Arkolakis, C. (2008): “Market Penetration Costs and the New Consumers Margin in International Trade,” . Atkeson, A., and A. Burstein (2010): “Innovation, Firm Dynamics, and International Trade,” manuscript. Barro, R. J., and J.-W. Lee (2000): “International Data on Educational Attainment: Updates and Implications,” NBER Working Paper No. 42. Broda, C., and D. E. Weinstein (2006): “Globalization and the Gains from Variety,” The Quarterly Journal of Economics, 121(2), 541–585. Eaton, J., and S. Kortum (2002): “Technology, Geography, and Trade,” Econometrica, 70(5), 1741–1779. Feenstra, R. C., R. E. Lipsey, H. Deng, A. C. Ma, and H. Mo (2005): “World Trade Flows: 1962-2000,” . Fieler, A. C. (2010): “Non-Homotheticity and Bilateral Trade: Evidence and a Quantitative Explanation,” Mimeo. Gervais, A. (2010): “Product Quality, Firm Heterogeneity, and International Trade,” Mimeo. Hallak, J., and J. Sivadasan (2009): “Firms’s Exporting Behavior under Quality Constraints,” NBER Working Paper No.14928. Helpman, E., M. Melitz, and Y. Rubinstein (2008): “Estimating Trade Flows: Trading Partners and Trading Volumes,” The Quarterly Journal of Economics, 123(2), 441–487. Hummels, D., and P. Klenow (2005): “The variety and quality of a nation’s exports,” American Economic Review, pp. 704–723. Hummels, D., and A. Skiba (2004): “Shipping the Good Apples Out? An Empirical Confirmation of the Alchian-Allen Conjecture,” Journal of Political Economy, 112(6), 1384–1402. Kugler, M., and E. Verhoogen (2010): “Prices, Plant size, and Product Quality,” Review of Economic Studies. Melitz, M. J. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 71(6), 1695–1725. OECD (2008): “STAN Database,” www.oecd.org/sti/stan/. Penn World Table 6.2 (2008): http://pwt.econ.upenn.edu/.

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Ramondo, N. (2009): “Size, Geography, and Multinational Production,” mimeo. Schott, P. (2004): “Across-product versus within-product specialization in international trade,” Quarterly Journal of Economics, 119(2), 647–678. Simonovska, I., and M. E. Waugh (2011): “The Elasticity of Trade: Estimates and Evidence,” . Standard & Poor‘s web.wharton.upenn.edu/wrds/. World Bank Group www.worldbank.org.

(2008):

Compustat

(1954-2007):

“Entrepreneurship

21

Survey

https://wrdsand

Database,”

Appendix A:

Solving the Model

Define the expected long-run firm distribution as µ ˜. Given a set of parameters Θ, solving the model follows these steps: 1. Guess a value for the long-run expected firm distribution. Call this µ ˜0 = [˜ µ01 , ..., µ ˜0N ]. 2. Given µ ˜0 , compute the optimal deviations each country i: (a) Guess the long-run expected firm distribution for country i. Call this µ ˆ0i ˜0 , compute firm profits (b) Given µ ˆ0i and µ (c) Given firm profits, compute equilibrium firm decision rules di (x, a) and value functions Vi (x, a) (d) Given firm decision rules, generate a new guess for the long-run expected firm distribution. Call this µ ˆ1i (e) Stop if k µ ˆ1i − µ ˆ0i k∞ is sufficiently small. Otherwise, set µ ˆ0i = µ ˆ1i and return to (a). ˜1 − µ ˜0 k∞ is sufficiently small. Otherwise, set µ ˜0 = µ ˜1 ˆ0N ]. Stop if k µ 3. Define µ ˜1 = [ˆ µ01 , ..., µ and return to (1).

Appendix B:

Computing Equilibrium Entry Rates

Solving for the new steady-state in a given exercise proceeds along the following steps: 1. Solve the benchmark model using the estimated parameters and recover {fie } 2. Guess equilibrium firm entry rate e0 (a) Compute steady-state equilibrium decision rules, value functions, and firm distribution as discussed in section ?? (b) Compute

1 1+r

· E[V (x0 , µ∗ )|G]

(c) Update the guess for the country i firm entry rate using 1

0

log(e ) = log(e ) + log



 1 0 0 ∗ · E[Vi (x , a , µ )|G] − log(fie ) 1+r

where µ∗ is the steady-state firm productivity distribution (d) Stop if |e1 − e0 | is sufficiently small. Otherwise, set e0 = e1 and return to (2)

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Appendix C:

Data Sources Table 10: Data Sources

Variable Tij distij borderij GDPi Li Hi ei

Description Compustat (1954-2007) Bilateral trade flows Manufacturing spend Distance (capitals) Common borer dummy Real GDP ($US 1990) Population % of Li with at least secondary education Firm entry rates

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Source Standard & Poor‘s Compustat (1954-2007) Feenstra, Lipsey, Deng, Ma, and Mo (2005) OECD (2008) Helpman, Melitz, and Rubinstein (2008) Helpman, Melitz, and Rubinstein (2008) Penn World Table 6.2 (2008) Penn World Table 6.2 (2008) Barro and Lee (2000) World Bank Group (2008)

Appendix D:

Additional Results from the Full Model

Quality Decision Rules byby Country Figure 1: Quality Decision Rules Country

Quality Choice (Normalized to 1)

1

0.8

0.6

0.4

0.2 TWN USA SGP SWE MEX NLD JPN KOR GBR ITA FIN FRA DNK ESP CHN DEU CAN CHE AUT BEL

0 0 0.2 0.4 0.6 0.8 1

Productivty (Normalized to 1)

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Table 11: Estimated Costs (Quality Model) Average Trade Costs Entry Cost? Country i ti,: τi,: fi,: fie AUT 0.04 1.10 223.81 0.55 BEL 0.04 1.10 218.23 0.50 CAN 0.05 1.10 320.97 0.48 CHE 0.04 1.10 216.61 0.55 CHN 0.05 1.10 304.65 0.65 DEU 0.04 1.10 213.11 0.86 DNK 0.04 1.10 225.95 0.46 ESP 0.04 1.10 249.31 0.49 FIN 0.04 1.10 259.47 0.38 FRA 0.04 1.10 221.66 0.72 GBR 0.04 1.10 240.46 0.54 ITA 0.04 1.10 230.25 0.72 JPN 0.05 1.10 317.57 0.96 KOR 0.05 1.10 310.33 0.49 MEX 0.05 1.10 324.40 0.38 NLD 0.04 1.10 219.18 0.52 SGP 0.05 1.10 313.94 0.27 SWE 0.04 1.10 241.83 0.46 TWN 0.05 1.10 309.08 0.40 USA 0.05 1.10 316.28 1.00 ? entry costs normalized by USA.

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Table 12: Import Shares (Quality Model) Country Data (%) Model (%) AUT 33.12 96.96 BEL 45.16 82.08 CAN 27.45 43.78 CHE 36.76 86.47 CHN 2.51 49.32 DEU 17.51 77.58 DNK 29.11 79.93 ESP 14.76 46.39 FIN 19.24 87.95 FRA 21.92 64.57 GBR 33.70 25.20 ITA 13.81 72.81 JPN 2.25 65.68 KOR 15.68 73.95 MEX 20.46 19.35 NLD 84.80 49.16 SGP 73.55 65.24 SWE 27.52 81.40 TWN 24.63 79.73 USA 9.90 25.90

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