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The Review of Economic Studies
, Volume Advance Article – Nov 20, 2017

33 pages

/lp/ou_press/the-role-of-firm-factors-in-demand-cost-and-export-market-selection-ggJ8Mv2AJQ

- Publisher
- Oxford University Press
- Copyright
- © The Author 2017. Published by Oxford University Press on behalf of The Review of Economic Studies Limited.
- ISSN
- 0034-6527
- eISSN
- 1467-937X
- D.O.I.
- 10.1093/restud/rdx066
- Publisher site
- See Article on Publisher Site

Abstract In this article, we use micro data on both trade and production for a sample of large Chinese manufacturing firms in the footwear industry from 2002 to 2006 to estimate an empirical model of export demand, pricing, and market participation by destination market. We use the model to construct indexes of firm-level demand, marginal cost, and fixed cost. The empirical results indicate substantial firm heterogeneity in all three dimension with demand being the most dispersed. The firm-specific demand and marginal cost components account for over 30% of market share variation, 40% of sales variation, and over 50% of price variation among exporters. The fixed cost index is the primary factor explaining differences in the pattern of destination markets across firms. The estimates are used to analyse the supply reallocation following the removal of the quota on Chinese footwear exports to the EU. This led to a rapid restructuring of export supply sources on both the intensive and extensive margins in favour of firms with high demand and low fixed costs indexes, with marginal cost differences not being important. 1. Introduction Firm-level heterogeneity has become a driving factor in theoretical models and empirical studies that analyse firm pricing decisions, destination decisions, and trade patterns in international markets. Theoretical models that embody heterogeneous firms have been developed by Eaton and Kortum (2002), Melitz (2003), and Bernard et al. (2003) and used to analyse aggregate patterns of trade. There are multiple potential sources of firm heterogeneity that can generate differences across firms in their trade decisions. Building on models of industry dynamics by Jovanovic (1982) and Hopenhayn (1992), heterogeneity in production costs has been one, heavily-analysed source of firm differences. In an empirical study using French firm-level data, Eaton et al. (2011) find that accounting for firm heterogeneity in efficiency results in substantial improvements in the ability to predict which firms enter which destination markets and, to a lesser degree, the volume of sales in the destination. A second source of firm heterogeneity reflects differences in the fixed cost of entering new export markets. In addition to firm efficiency, Das et al. (2007), Eaton et al. (2011), and Arkolakis (2010) find that differences in entry costs are important in explaining patterns of dynamic export entry, or the number of markets a firm serves, or the size distribution of exporting firms. More recently, a third source of heterogeneity, reflecting differences in product quality or other demand-side factors that lead to differences in market shares across firms, has been incorporated in trade models. Johnson (2012) and Khandelwal (2010) estimate structural models of demand using product-level data on prices and trade flows between countries and find evidence consistent with quality variation at the country level.1Crozet et al. (2012) exploit firm level data on prices, exports, and direct quality measures for champagne producers and find quality is positively correlated with price, quantity and the number of destination markets the firm sells in. They also show that it is important to correct for the endogenous selection of destination markets when estimating the effect of quality on export variables. In this article, we quantify the importance of three sources of firm heterogeneity, marginal production cost, export fixed cost, and demand, in explaining the export decisions of Chinese footwear manufacturing firms across seven destination markets. Our framework allows us to tie together the pricing, output, and participation decisions with a consistent set of firm-level demand and cost components. Based on their empirical study of French exporting firms, Eaton et al. (2011) conclude that it is important to recognize that firm-level characteristics impact decisions in many markets and conclude that “any theory ignoring features of the firm that are universal across markets misses much”. We focus on these firm-level characteristics that are universal across the firm’s markets. The success of Chinese manufacturing exports is one of the most significant phenomena in world trade in the last two decades, however, debates remain about the underlying causes at the individual producer level. One possibility is that Chinese firms invested in “capability building” to improve their product appeal and demand (See Sutton, 2007; Brandt et al., 2008; Schott, 2008) while a second possibility is that they succeeded primarily because of low labour and input costs that allow them to serve as a manufacturing base for foreign-owned firms (Branstetter and Lardy, 2008). In this article, we study the relative importance of firm-level cost and demand factors in explaining Chinese firm-level export performance by developing an empirical model of demand, cost, and dynamic export participation that can quantify firm heterogeneity in each of these dimensions.2 We estimate the model using micro data on prices and quantities of exported goods and firm costs for a panel of 738 large Chinese exporting firms in the footwear industry from 2002 to 2006. In our data set, the firm-level export price, quantity, and destination patterns indicate a potentially important role for three dimensions of firm heterogeneity that persist across destinations. Firms that export to many destinations also export to more difficult destinations and have higher average export quantities in each destination. This is consistent with either persistent firm-level demand heterogeneity or heterogeneity in marginal cost. These same firms also have higher average export prices which suggests that the demand differences are costly to produce or maintain and is not consistent with low cost being the sole determinant of export success. Furthermore, conditional on the same average sales per destination, some Chinese firms systematically export to more markets, implying lower firm-level export fixed cost. The only way to distinguish the role of cost and demand heterogeneity is to specify a structural model that includes distinct demand, marginal cost and fixed cost components at the firm level. In the econometric model we develop, the measure of firm demand heterogeneity relies on across-firm differences in export market shares, controlling for firm prices, in the destination markets. The measure of cost heterogeneity relies on differences in firm export prices, controlling for observable firm costs and markups, across destinations. Fixed cost heterogeneity relies on differences in market participation patterns, controlling for cost and demand differences. All three factors play a role in determining the firm’s profits in each export market and thus the decision to export. We exploit the fact that, in the export context, we have multiple observations on many of the firms because they export to multiple destination markets and this helps to both identify the distribution of firm-level demand and cost components and control for the endogenous selection of which markets to sell in. The econometric methodology we utilize is a practical application of a Hierarchical Bayesian method that relies on MCMC and Gibbs sampling for implementation. This allows us to both include a large number of unobservables, three for each of our 738 firms, and to incorporate them in non-linear equations, such as the probability of exporting, in a very tractable way. The empirical results indicate that across-firm differences in the number and mix of export destinations is substantially affected by heterogeneity in the fixed cost dimension. Demand heterogeneity also has a small impact on differences in the extensive margin of exports. On the intensive margin, both the demand and marginal cost factors are approximately equally important in explaining export price variation across firms and destinations, but demand differences are more important in explaining variation in export revenue. Finally, we use our firm indexes to study the reallocation of export sales across Chinese producers in response to the removal of the quota on Chinese exports of footwear to the EU. We find that removal of the quota led to a substantial change in the mix of firms that exported to the EU with the shift in composition towards firms with higher demand and lower fixed cost indexes, but no strong correlation with marginal cost differences. The next section of the article develops the theoretical model of export demand, pricing, and market participation. The third section develops the estimation methodology, the fourth section describes the Chinese firm-level data and summary statistics. The fifth section presents the structural parameter estimates and the final section analyses the changes in the composition of exporting firms in response to removal of the EU quota on Chinese footwear imports. 2. Model of a Firm’s Demand, Pricing, and Export Decisions 2.1. Demand We begin with a demand model that can be used to estimate an index of firm demand. Denote $$k$$ as an individual six-digit product produced by a specific firm $$f$$. A firm can produce and export multiple products. An individual importer $$i^{\prime }s$$ utility function from purchasing product $$k$$ from firm $$f$$ is: \begin{equation} U_{ikf}^{dt}=\delta _{kf}^{dt}+\epsilon_{i}. \label{utility2} \end{equation} (1) This specification allows for a variety-specific component $$\delta _{kf}^{dt}$$ that varies by destination market and year and an $$iid$$ transitory component $$\epsilon _{i}$$ that captures all heterogeneity in preferences across importers.3Berry (1994) shows that, if $$\epsilon _{i}$$ is assumed to be a Type I extreme value random variable then we can aggregate over importers and express the market share for product $$kf$$ in market $$dt$$. Define the inclusive value of all varieties in the market as $$V^{dt}=\sum\nolimits_{kf} \exp (\delta _{kf}^{dt})$$. The market share for product $$kf$$ in market $$dt$$ can be written in the logit form $$\tilde{s}_{kf}^{dt}=\exp (\delta _{kf}^{dt})/V^{dt}$$. If we normalize this market share by a single variety where $$\delta _{0}^{dt}=0$$ the normalized logarithmic market share takes the simple form: \begin{equation} ln(\tilde{s}_{kf}^{dt})-ln(s_{0}^{dt})=\delta _{kf}^{dt}. \label{share} \end{equation} (2) We will model the variety-specific term $$\delta _{kf}^{dt}$$ as a combination of firm, product group, destination market, and variety components. Specifically, if product $$k$$ is produced by firm $$f$$, then \begin{equation} \delta _{kf}^{dt}=\xi _{f}+\xi _{k}-\alpha _{d}\ln \tilde{p} _{kf}^{dt}+u_{kf}^{dt}. \label{delta2} \end{equation} (3) This equation says that there is a firm component $$\xi _{f}$$ or “brand-name” effect to the utility derived from this product. This brand-name effect will be unique to each firm and constant across all markets in which it operates and over time. It could reflect differences in the stock of customers that are familiar with firm $$f$$, size of its distribution network, or quality of the firm’s product. Holding price fixed, an increase in $$\xi _{f}$$ will raise the market share for this variety in all markets. Since the $$\xi _{f}$$ captures all firm-level factors that systematically affect the utility that importers receive from this product, we will refer to it as a firm demand component.4 There is also a product group utility shifter $$\xi _{k}$$ that will lead to higher utility for some product groups in all markets, holding price fixed. We will define this at the four-digit product-group level. The utility and market share of the variety will be declining in the price of the variety where $$\tilde{p}_{kf}^{dt}$$ is the price paid by the importers for product $$kf$$ in the destination market. To convert this price into the FOB price, $$p_{kf}^{dt},$$ set by the producing firm, we incorporate ad valorem trade costs between China and each destination market $$\ln \tilde{p}_{kf}^{dt}=\ln p_{kf}^{dt}+\ln (1+\tilde{\tau}_{dt})$$. In this case $$\tilde{\tau}_{dt}$$ captures all exchange rate effects, tariffs, and shipping costs between China and each destination market in each year. The final term $$u_{kf}^{dt}$$ captures market level shocks to the demand for product $$kf$$. Substituting equation (3) and destination-specific price into the normalized market share equation gives the demand equation for product $$kf$$: \begin{equation} ln(s_{kf}^{dt})\equiv ln(\tilde{s}_{kf}^{dt})-ln(s_{0}^{dt})=\xi _{f}+\xi _{k}-\alpha _{d}\ln p_{kf}^{dt}+\tau _{dt}+u_{kf}^{dt}, \label{demand} \end{equation} (4) where $$\tau _{dt}=-\alpha _{d}ln(1+\tilde{\tau}_{dt})$$. The parameter $$\alpha _{d}$$, which captures the market share response to a change in the FOB price, is allowed to vary across destination markets to reflect the country-specific differences in the consumer tastes, income, and the structure of the domestic retail sector. This demand equation can be estimated using data on the market shares of varieties in different destination markets. Overall, the demand model contains a destination-specific price parameter $$\alpha _{d}$$, destination market/year fixed effects $$\tau _{dt}$$, product group effects $$\xi_{k}$$, and a firm-specific demand shifter $$\xi _{f}$$. One goal of the empirical model developed below will be to estimate the parameters of equation (4) including the firm-specific demand factor $$\xi_{f}$$. 2.2. Cost and pricing To incorporate heterogeneity arising from the production side of the firm’s activities we model log marginal cost of product $$kf$$ in market $$dt$$ as: \begin{equation} \ln c_{kf}^{dt}=\tilde{\gamma}_{dt}+\gamma _{k}+\gamma _{w}lnw_{f}^{t}+h(\xi _{f})+\omega _{f}+v_{kf}^{dt}, \label{logmc} \end{equation} (5) where $$\tilde{\gamma}_{dt}$$ and $$\gamma _{k}$$ are destination/year and four-digit product-group cost factors, and $$w_{f}^{t}$$ is a set of observable firm-specific variable input prices and fixed factors. The specification includes two additional sources of firm-level unobservables. The function $$h(\xi _{f})$$ is included to control for the fact that firms that have higher demand or more desirable products will likely have higher costs if the extra demand is the result of higher quality or investments to build a customer base. The second firm-level unobservable $$\omega _{f}$$ is included to capture time-invariant differences in marginal cost across producers. Finally $$v_{kf}^{dt}$$ are cost shocks at the product-firm level and the firm is assumed to observe these prior to setting the price. For estimation purposes, we will combine the firm costs resulting from $$\xi _{f}$$ and $$\omega _{f}$$ into a single firm marginal cost component that we will represent as $$c_{f}=h(\xi _{f})+\omega _{f}$$. Assuming monopolistically competitive markets, a profit-maximizing firm facing the demand curve in equation (4) will charge a price for product $$kf$$ in market $$dt$$ given by:5 \begin{equation} \ln p_{kf}^{dt}=\gamma _{dt}+\gamma _{k}+\gamma _{w}lnw_{f}^{t}+c_{f}+v_{kf}^{dt}, \label{pricing} \end{equation} (6) where $$\gamma _{dt}=\ln (\frac{\alpha _{d}}{\alpha _{d}-1})+\tilde{\gamma}_{dt}$$. This pricing equation shows that the price of product $$kf$$ in market $$dt$$ will depend on the destination-specific demand parameter $$\alpha _{d}$$ and all the marginal cost determinants in equation (5). In particular, this pricing equation shows that $$c_{f}$$ will be a firm-level component of the export price. A second goal of our empirical model is to estimate the parameters of the pricing equation (6) including the firm cost component $$c_{f}$$ while allowing for an unconstrained correlation between $$c_{f}$$ and $$\xi _{f}.$$ The final specification issue for the demand and pricing equation concerns the shocks $$u_{kf}^{dt}$$ and $$v_{kf}^{dt}.$$ We allow them to be both serially and contemporaneously correlated for each product and destination: \begin{eqnarray} u_{kf}^{dt} &=&\rho _{u}u_{kf}^{dt-1}+eu_{kf}^{dt} \label{serialcorr} \\ v_{kf}^{dt} &=&\rho _{\nu }v_{kf}^{dt-1}+ev_{kf}^{dt}, \notag \end{eqnarray} (7) where the two transitory shocks, $$eu$$ and $$ev$$ are distributed: \begin{equation} e=(eu,ev)\sim N(0,\Sigma _{e}). \label{transhock} \end{equation} (8) In the demand and pricing equations we allow for multiple sources of serial correlation through the firm effects $$\xi _{f}$$ and $$c_{f}$$ and the serially-correlated transitory shocks $$u_{kf}^{dt}$$ and $$v_{kf}^{dt}.$$ Conditional on the permanent firm heterogeneity and product and destination dummies, the transitory demand and cost shocks are $$iid$$ across destination and products. The pricing model implies that price in the demand curve, equation (4), is correlated with the firm demand component $$\xi _{f}$$ and the transitory demand shock $$u_{kf}^{dt}$$. In estimation we use the firm-level cost shifters $$lnw_{f}^{t}$$ as exogenous excluded variables. These include the log of the average manufacturing wages in the urban area and surrounding rural area, the log of land price for the city in which firm $$f$$ is located, and the firm’s capital stock. 2.3. Export revenue and profitability Using the demand and pricing equations, (4) and (6), we can express the expected revenue of product $$kf$$ in market $$dt$$. Define the destination specific markup as $$\mu_{d}=\frac{\alpha _{d}}{\alpha _{d}-1}$$ and the aggregate demand shifter in market $$dt$$ as $$M^{dt}/V^{dt}$$ where $$M^{dt}$$ is the total market size. Using these definitions we can express the logarithm of the expected revenue for product $$kf$$ as the sum of three components, one of which depends only on market-level parameters and variables, one which incorporates all product-group variables, and one which incorporates all firm-level variables: \begin{equation} \ln r_{kf}^{dt}=\ln \Omega ^{dt}+\ln r_{k}^{d}+\ln r^{dt}(\xi _{f},c_{f}), \label{revenue} \end{equation} (9) where \begin{eqnarray} \ln \Omega ^{dt} &=&\ln (M^{dt}/V^{dt})+\tau _{dt}+(1-\alpha _{d})(\ln \mu _{d}+\gamma _{dt}) \label{rbar2} \\ \ln r_{k}^{d} &=&\xi _{k}+(1-\alpha _{d})\gamma _{k} \notag \\ \ln r^{dt}(\xi _{f},c_{f}) &=&\xi _{f}+(1-\alpha _{d})\left( \gamma _{w}lnw_{f}^{t}+c_{f}\right) +C_{uv}. \notag \end{eqnarray} (10) In this equation ln$$\Omega ^{dt}$$ captures all market-level factors that affect product revenue, including the market size and overall competition, tariff, exchange rate effects, markup, and destination-specific cost. The second term $$\ln r_{k}^{d}$$ captures all product group effects in both demand and cost. The final term, $$\ln r^{dt}(\xi _{f},c_{f}),$$ combines all the firm-specific factors that affect the export revenue of product $$kf$$ in the market: the firm demand component $$\xi _{f},$$ the firm cost component $$c_{f}$$, and the observable firm-level marginal cost shifters $$\gamma _{w}lnw_{f}^{t}.$$ The expectation over the variety-specific demand and cost shocks $$u_{kf}^{dt}$$ and $$v_{kf}^{dt}$$ is denoted by $$C_{uv}$$ A larger value of $$\xi _{f},$$ reflecting higher demand for the firm’s variety, will imply a larger value of $$\ln r^{dt}(\xi _{f},c_{f})$$. Since the term $$(1-\alpha _{d})$$ is negative, a higher value of $$c_{f}$$ will imply a lower level of export revenue for the firm in this destination market. If variation in $$c_{f}$$ across firms only reflects productivity differences, then high $$c_{f}$$ would imply lower export revenue. However, as explained above, $$c_{f}$$ can also include the cost of producing higher demand, so in this case $${\rm corr}(c_{f},\xi _{f})>0$$ and thus, as we compare across firms, higher-demand firms will have higher export revenue if their larger market share, due to $$\xi _{f},$$ outweighs the increase in cost captured by $$c_{f}.$$ Finally, the firm export revenue will vary by destination market because the marginal cost terms are scaled by $$(1-\alpha _{d})$$ and $$\alpha _{d}$$ is destination specific. In a destination with more elastic demand (larger $$\alpha _{d}$$), the cost differences across firms are more important as a source of export revenue differences. Given the functional form assumptions on demand and marginal cost, we can use the revenue equation for product $$kf,$$ (9), to express the total expected profits that firm $$f$$ will earn in market $$dt.$$ If the firm sells a set of varieties, or product line, denoted by $$K_{f}$$, its profit in destination market $$dt$$ is the sum of revenues over all its varieties scaled by the demand elasticity or, if expressed in logs: \begin{equation} \ln \ \pi ^{dt}(\xi _{f},c_{f};w_{f}^{t},K_{f})=\ln \left[ \frac{1}{\alpha _{d} }\right] +\ln \Omega ^{dt}+\ln \left[ \sum_{k\in K_{f}}r_{k}^{d}\right] +\ln r^{dt}(\xi _{f},c_{f}). \label{profit} \end{equation} (11) As shown by this equation, the firm component of export revenue enters directly into the firm’s profits in the market and will be a useful summary statistic of the role of firm demand and cost factors in generating differences in the profitability of exporting firms in a destination market.6 2.4. Exporting decision This model of demand, cost, and profits also implies a set of destination countries for each firm’s exports. The firm’s decision to export to market $$dt$$ is based on a comparison of the profits earned by supplying the market with the costs of operating in the market. If firm $$f$$ sells in market $$d$$ in the current year $$t$$ we assume that it needs to incur a fixed cost $$\mu_{f}+\varepsilon _{f}^{dt}$$ where $$\mu _{f}$$ is a firm-specific fixed cost and $$\varepsilon_{f}^{dt}$$ is a destination fixed cost shock that is modelled as an independent draw from a $$N(0,1)$$ across all markets and years. By specifying the fixed cost in this way, we are allowing a third source of firm heterogeneity, in addition to $$\xi _{f}$$ and $$c_{f}.$$ We will refer to $$\mu_{f}$$ as the firm fixed cost component. If the firm has not sold in the market in the previous year, then it must also pay a constant entry cost $$\kappa _{s}.$$ Define $$I_{f}^{dt-1}$$ as the discrete export indicator that equals one if the firm exported to market $$d$$ in year $$t-1$$ and zero if it did not. The firm will choose to export to this market if the current plus expected future payoff is greater than the fixed cost it must pay to operate. To describe each firm’s export participation decision, we summarize their individual state variables into $$s_{f}^{t}=\{\xi_{f},c_{f},\mu _{f},K_{f},w_{f}^{t}\}$$ and previous export status $$I_{f}^{dt-1}$$. The input price $$w_{f}^{t}$$ and aggregate state variables $$\Omega ^{dt}$$ are assumed to evolve exogenously and the firm has rational expectation of future values.7 The value function of a firm that is making the choice to export to a particular destination $$dt$$ is: \begin{eqnarray} V^{dt}(s_{f}^{t},\Omega ^{dt},I_{f}^{dt-1},\varepsilon _{f}^{dt})&=&\max_{I_{f}^{dt}\epsilon (0,1)}\left[ \pi ^{dt}(s_{f}^{t},\Omega ^{dt})-(1-I_{f}^{dt-1})\kappa _{s}-(\mu _{f}+\varepsilon _{f}^{dt})\right.\nonumber\\ &&\quad \left.+V_{e}^{dt}(s_{f}^{t},\Omega ^{dt}),V_{n}^{dt}(s_{f}^{t},\Omega ^{dt})\right]. \label{value} \end{eqnarray} (12) The first term in brackets is the payoff to exporting, which is the sum of the current profit, net of the fixed and startup costs, plus the expected future value if they choose to export $$V_{e}^{dt}(s_{f},\Omega ^{dt}).$$ The second term in brackets is the expected future payoff if they choose not to export in period $$t,$$$$V_{n}^{dt}(s_{f},\Omega ^{dt}).$$ These expected future values are defined as: \begin{align} V_{e}^{dt}(s_{f}^{t},\Omega ^{dt})& =\beta E_{\varepsilon_{f}^{^{\prime }},s_{f}^{^{\prime }},\Omega ^{^{\prime }}}V^{dt+1}(s_{f}^{^{\prime}},\Omega ^{^{\prime }}|I_{f}^{dt}=1,s_{f}^{t},\Omega ^{dt}) \notag \\ V_{n}^{dt}(s_{f}^{t},\Omega ^{dt})& =\beta E_{\varepsilon _{f}^{^{\prime }},s_{f}^{^{\prime }},\Omega ^{^{\prime }}}V^{dt+1}(s_{f}^{^{\prime }},\Omega ^{^{\prime }}|I_{f}^{dt}=0,s_{f}^{t},\Omega ^{dt}). \notag \end{align} Since the fixed cost contains the stochastic component $$\varepsilon _{f}^{dt}$$ we can define the probability that the firm exports to a particular market as the probability that this component is less than the net benefits of exporting. Define the latent export payoff variable as the difference in the two choices in equation (12): \begin{equation} Y_{f}^{dt}=\pi ^{dt}(s_{f}^{t},\Omega ^{dt})-(1-I_{f}^{dt-1})\kappa _{s}-\mu _{f}+V_{e}^{dt}(s_{f}^{t},\Omega ^{dt})-V_{n}^{dt}(s_{f}^{t},\Omega ^{dt}). \label{latentprofit} \end{equation} (13) The latent payoff will depend on all three sources of firm heterogeneity and we will combine these into a single component that captures the combined effect of all three sources on the participation decision $$\eta _{f}=\eta (\xi _{f},c_{f},\mu _{f}).$$ We will refer to this as the firm export participation component. We parameterize the latent payoff as a function of the set of observable firm and market variables $$X_{f}^{dt}=(w_{f}^{t},K_{f},\Omega ^{dt})$$ and the firm-specific factor $$\eta _{f}$$. \begin{equation*} Y_{f}^{dt}=X_{f}^{dt}\psi +\delta I_{f}^{dt-1}+\eta _{f} \end{equation*} The discrete export participation variable is defined as: \begin{eqnarray} I_{f}^{dt} &=&1\text{ if }X_{f}^{dt}\psi +\delta I_{f}^{dt-1}+\eta _{f}\geq \varepsilon _{f}^{dt} \notag \\ &=&0\text{ otherwise}. \label{discretpart} \end{eqnarray} (14) The third goal of our empirical model is to estimate the parameters of the firm’s market participation decision $$\psi ,\delta$$ and the firm export participation component $$\eta _{f}$$. Given the assumption that $$\varepsilon$$ is distibuted $$N(0,1)$$, this equation is a probit model with a lagged dependent variable and a firm-specific random component.8 The presence of the lagged dependent variable in equation (14) leads to an initial conditions problem. We adopt Heckman’s (1981) method for correcting for initial conditions. We model the firm’s initial year in each destination, denoted $$t=0$$, as a probit model which depends on the initial year factor prices, product mix and destination dummies $$X_{f}^{d0},$$ and the firm-specific participation component. The latter depends on a parameter $$\rho _{\eta }$$ which allows the firm component in the initial year to be correlated with the component in the subsequent years. \begin{eqnarray} I_{f}^{d0} &=&1\text{ if }X_{f}^{d0}\psi _{0}+\rho _{\eta }\eta _{f}\geq \varepsilon _{f}^{d0} \label{initial} \\ &=&0\text{ otherwise}. \notag \end{eqnarray} (15) This adds the parameter vector $$\psi _{0}$$ and $$\rho _{\eta }$$ to the set of structural parameters to be estimated.9 The final element of the empirical model is the specification of the stochastic relationship between the three sources of firm heterogeneity, $$\xi _{f},c_{f},$$ and $$\eta _{f}.$$ We model the firm variables as: \begin{equation} (\xi _{f},c_{f},\eta _{f})\sim N(0,\Sigma _{f}) \label{firmdist} \end{equation} (16) where $$\Sigma _{f}$$ is an unconstrained covariance matrix among the three components. This covariance matrix will provide estimates of the extent of firm heterogeneity in demand, marginal production cost, and fixed cost and the correlation between them. 3. Estimation The goal of the empirical model is to estimate the structural parameters for demand and pricing, equations (4), (6), (7), and (8), export market participation, equations (14) and (15), and the distribution of the firm-specific components $$\xi _{f},$$$$c_{f}$$, and $$\eta _{f},$$ equation (16). For each firm, our data consist of product mix $$K_{f}$$, a set of cost shifters $$lnw_{f}^{t}$$ for each year, and export market participation dummies $$I_{f}^{dt}$$ for each destination and year. Conditional on exporting to a destination in a year, $$I_{f}^{dt}=1$$, we also observe prices $$lnp_{fk}^{dt}$$ and market shares $$\ln s_{fk}^{dt}$$ for each product sold by firm $$f$$. To simplify the presentation of the likelihood function, we group the data and structural parameters in the following way. Define the full vector of participation dummies for firm $$f$$ over all destination $$d$$ and time $$t$$ observations as $$I_{f}$$ and denote the full vector of prices and market shares for the firm over all destinations, time, and products $$k$$ as $$lnp_{f}$$ and $$\ln s_{f}$$, respectively. Finally, denote the full set of data for firm $$f$$ as $$D_{f}$$ and the full set of data over all firms as $$D$$. The structural parameters are grouped in a way that will facilitate estimation. Denote the set of demand and cost parameters that are common for all firms as $$\Theta _{1}=(\alpha _{d},\tau_{dt},\xi _{k},\gamma _{w},\gamma _{dt},\gamma _{k},\rho _{u},\rho _{\nu },\Sigma _{e})$$ and the participation parameters as $$\Theta _{2}=(\psi ,\delta ,\psi _{0},\rho _{\eta })$$. Denote the firm effects as $$(\xi ,c,\eta )_{f}$$ and let $$g((\xi ,c,\eta )_{f}|\Theta _{3})$$ be the joint distribution of the firm effects which depend on the parameter $$\Theta _{3}=\Sigma _{f}$$. The likelihood function, conditional on $$(\xi ,c,\eta )_{f}$$, for firm $$f$$ can be separated into a participation component which only depends on the parameters $$\Theta _{2}$$ and the firm participation component $$\eta _{f}$$, and the price and quantity components which depend on $$\Theta_{1}$$ and the firm demand and marginal cost terms $$\xi _{f}$$ and $$c_{f}$$. Focusing first on the discrete destination decisions for firm $$f$$, the likelihood function for these data can be expressed using equations (14) and (15) as: \begin{equation} lp(I_{f}|\Theta _{2},\eta _{f})=\prod\limits_{d}[\prod\limits_{t=1}^{T}P(I_{f}^{dt}|\psi ,\delta ,\eta _{f},X_{f}^{dt},I_{f}^{dt-1})]P(I_{f}^{d0}|\psi _{0},\rho _{\eta },\eta _{f},X_{f}^{d0}). \label{lp} \end{equation} (17) sThe last term on the right-hand side of equation (17) represents the contribution of the initial year observations on the firm’s export destinations $$I_{f}^{d0}$$ to the likelihood. The likelihood for the price and quantity observations of firm $$f$$ is: \begin{equation} ld(lnp_{f},\ln s_{f}|\Theta _{1},\xi _{f},c_{f})=\prod\limits_{d,k}[\prod\limits_{t=\tau _{0}+1}^{\tau _{1}}h(u_{kf}^{dt},v_{kf}^{dt}|u_{kf}^{dt-1},v_{kf}^{dt-1},\Theta _{1},\xi _{f},c_{f})]. \label{ld} \end{equation} (18) Since each firm exports to different destinations during different years, the starting year that we observe active price and quantity data $$\tau _{0}$$ and the ending year $$\tau _{1}$$ is firm-destination-product specific.10 Combining the participation, price, and quantity components, the likelihood for firm $$f$$ (conditional on $$(\xi ,c,\eta )_{f})$$ is then: \begin{equation} l(D_{f}|\Theta _{1},\Theta _{2},(\xi ,c,\eta )_{f})=lp(I_{f}|\Theta _{2},\eta _{f})ld(lnp_{f},\ln s_{f}|\Theta _{1},\xi _{f},c_{f}). \label{ldlp} \end{equation} (19) We could estimate the parameters $$\Theta _{1},\Theta _{2},\Theta _{3}$$ by specifying a distributional assumption on $$g((\xi ,c,\eta )_{f}|\Theta _{3})$$ and constructing the full likelihood for $$D_{f}$$ by integrating over $$\xi ,c,\eta .$$ \begin{equation} l(D_{f}|\Theta _{1},\Theta _{2},\Theta _{3})=\int l(D_{f}|\Theta _{1},\Theta _{2},(\xi ,c,\eta ))g((\xi ,c,\eta )|\Theta _{3})d\xi dcd\eta. \label{lfull} \end{equation} (20) However, our primary interest is not to just estimate the common parameter vector $$\Theta_{1},\Theta _{2},\Theta _{3}$$ but to also construct an estimate of $$(\xi ,c,\eta )_{f}$$ for each firm. The Bayesian MCMC methodology is very attractive for this purpose. Instead of integrating $$(\xi ,c,\eta )$$ out, we will sample from the joint posterior distribution over all the parameters, $$\Theta _{1},\Theta _{2},\Theta _{3}$$ and the firm components $$(\xi ,c,\eta)_{f}$$ for all firms.11 The Bayesian approach requires we define a prior distribution on the parameters. Denote the prior on the common structural parameters as $$P(\Theta _{1},\Theta _{2},\Theta _{3}).$$ Assuming that $$(\xi ,c,\eta )_{f}$$ is independent across all firms $$f=1...F$$, the joint posterior distribution is: \begin{eqnarray} &&P(\Theta _{1},\Theta _{2},\Theta _{3},(\xi ,c,\eta )_{1},...,(\xi ,c,\eta )_{F}/D)\nonumber\\ &&\quad\propto \left( \prod\limits_{f}l(D_{f}|\Theta _{1},\Theta _{2},(\xi ,c,\eta )_{f})g((\xi ,c,\eta )_{f}|\Theta _{3}))\right) P(\Theta _{1},\Theta _{2},\Theta _{3}). \label{jtposterior} \end{eqnarray} (21) Our goal is to characterize the posterior distribution, equation (21) numerically. This will allow us to describe the posterior distribution of both the $$\Theta$$ parameters and the demand, marginal cost, and export participation component $$\xi _{f}$$, $$c_{f}$$, and $$\eta _{f}$$ for each firm. We use Markov Chain Monte Carlo (MCMC) simulation to generate a sequence of draws from this posterior distribution. As we detail in the Appendix, the model structure allows us to rely on Gibbs Sampling to simulate these draws sequentially for blocks of parameters. Specifically, for each iteration, we sample the firm heterogeneity components $$\xi _{f},c_{f},\eta _{f}$$ conditional on the data and common parameters $$\Theta _{1},\Theta _{2},\Theta _{3}$$. We then draw $$\Theta_{1}$$, $$\Theta _{2}$$, and $$\Theta _{3}$$ from their respective conditional posterior distributions which depend on the data and firm heterogeneity components $$\xi _{f},c_{f},\eta _{f}$$. $$\Theta_{1}$$ includes the price elasticity parameters in the demand equation, which could potentially be subject to endogeneity bias resulting from correlation in $$\xi _{f}$$ and $$c_{f}$$ and in $$u_{fk}^{dt}$$ and $$v_{fk}^{dt}$$. We rely on an empirical strategy outlined by Rossi et al. (2005) to implement a sub-Gibbs Sampler within the step that draws $$\Theta _{1}$$. This step effectively uses the $$lnw_{f}^{t}$$ as instruments within our Bayesian framework. Details of the sampling strategy and the prior distributions are given in the Appendix. 4. Chinese Firm-Level Production and Trade Data 4.1. Data sources We will use the empirical model developed above to study the determinants of trade by Chinese firms operating in the footwear industry. The data we use in this article are drawn from two large panel data sets of Chinese manufacturing firms. The first is the Chinese Monthly Customs Transactions from 2002 to 2006 which contains the value and quantity of all Chinese footwear exporting transactions at the six-digit product level. This allows us to construct a unit value price of exports for every firm-product-destination combination which makes it feasible to estimate demand models and construct a measure of each firm’s demand component. We supplement the trade data with information on manufacturing firms from the Annual Survey of Manufacturing, an extensive survey of Chinese manufacturing firms conducted each year by the Chinese National Bureau of Statistics. This survey is weighted towards medium and large firms, including all Chinese manufacturing firms that have total annual sales (including both domestic and export sales) of more than 5 million RMB (approximately $${\$}$$600,000). This survey is the primary source used to construct many of the aggregate statistics published in the Chinese Statistical Yearbooks. It provides detailed information on ownership, production, and the balance sheet of the manufacturing firms surveyed. To identify firms that have production facilities, these data are important in our research to provide measures of total firm production and capital stocks. In China, these two data sources are collected by different agencies and do not use a common firm identification number. They do, however, each report the Chinese name, address, phone number, zip code, and some other identifying variables for each firm. We have been engaged in a project to match the firm-level observations across these two data sets using these identifying variables. To create instrumental variables used in our estimation, we further supplement data of rural wage, urban wage, and land transfer price of each city and its surrounding rural areas from the Chinese City Statistical Yearbooks. In this article, we study the export behaviour of firms in the footwear industry. We chose this industry for study because it is a major export industry in China, accounting for more than 70% of the footwear imports in the large markets in North America and Japan, has a large number of exporting firms, more than 2,500 exporters were present in 2002, and was subject to a quota in the countries of the European Union during the first part of our sample period. We will use our estimated model to examine the sorting of firms along demand and cost dimensions both during and after the quota regime. In this industry, there are eighteen distinct six-digit products and they can grouped into three 4-digit product classes: textile footwear, rubber footwear, and leather footwear. In this industry, we are able to identify $$738$$ unique firms in both the custom’s and production data sets. To be included in the sample, each firm must have at least one product/destination/year observation with exports. In the sample, in each destination/year between 20% and 50% of the firms are active. Table 1 reports the number of these firms that are present in each of the sample years. This varies from 490 to 688 firms across years.12 Table 1 Number of firms in the sample Year Number of firms Number of exporting firms Export rate 2002 490 329 0.670 2003 570 448 0.786 2004 688 609 0.885 2005 686 609 0.888 2006 658 541 0.822 Year Number of firms Number of exporting firms Export rate 2002 490 329 0.670 2003 570 448 0.786 2004 688 609 0.885 2005 686 609 0.888 2006 658 541 0.822 Table 1 Number of firms in the sample Year Number of firms Number of exporting firms Export rate 2002 490 329 0.670 2003 570 448 0.786 2004 688 609 0.885 2005 686 609 0.888 2006 658 541 0.822 Year Number of firms Number of exporting firms Export rate 2002 490 329 0.670 2003 570 448 0.786 2004 688 609 0.885 2005 686 609 0.888 2006 658 541 0.822 The key demand variable is the market share of each firm/six-digit product in a destination. The market share of product $$fk$$ in market $$dt$$ is defined as the sales of product $$fk$$ divided by the total imports of footwear from all supplying countries in market $$dt.$$ The market shares for the Chinese firms in our sample are very small, more than 99% of the sample observations are below 0.004 and the maximum market share in any destination-year is 0.039. The fact that there are few observations with large market shares justifies our assumption of monopolistic competition in the firm’s pricing decision.13 4.2. Empirical patterns for export participation and prices In this subsection, we summarize some of the empirical patterns of export market participation and export pricing for Chinese firms that produce footwear and discuss factors in the model that will help capture them. The second and third columns of Table 1 summarize the number and proportion of sample firms that export in each of the years. To be in the sample it is required that a firm export to at least one destination in two consecutive years. The number of exporting firms varies from 329 to 610 and the export rate varies from 0.67 to 0.89 over time. Among the exporting firms, the destination markets vary in popularity. Table 2 reports the fraction of exporting firms in our sample that export to each destination between 2002 and 2006. U.S./Canada is the most popular destination, with approximately half of the exporting firms in our sample exporting to these countries in any year. This is followed by Japan/Korea and Rest of Asia, where approximately 40% of the exporting firms sell. Japan/Korea has fallen slightly over time as a destination. Between 28% and 37% of the exporting firms sell in the Non-EU countries of Europe, Africa, and Latin America. Australia/New Zealand is the least popular destination market, with 19% of the Chinese exporters selling there on average, and a declining export rate over time. These numbers suggest that export profits will vary by destination market. Market size, tariffs, transportation costs, and degree of competition are all country-level factors that could contribute to differences in the profitability of destination markets and result in different export rates. They are captured in the theoretical model through the terms in $$\ln \Omega^{dt}$$ in equation (10) and the participation decision in each market will depend on the interaction of these country-level factors and the firm-level distribution of profitability. Table 2 Proportion of exporting firms by destination Destination 2002 2003 2004 2005 2006 Average U.S./Canada 0.544 0.533 0.495 0.493 0.494 0.512 Japan/Korea 0.410 0.384 0.377 0.380 0.375 0.385 Rest of Asia 0.362 0.413 0.428 0.430 0.410 0.408 Non-EU Europe 0.365 0.359 0.356 0.374 0.390 0.369 Africa 0.234 0.275 0.282 0.351 0.348 0.298 Latin America 0.274 0.263 0.280 0.290 0.298 0.281 Australia/NZ 0.219 0.221 0.177 0.184 0.159 0.192 Destination 2002 2003 2004 2005 2006 Average U.S./Canada 0.544 0.533 0.495 0.493 0.494 0.512 Japan/Korea 0.410 0.384 0.377 0.380 0.375 0.385 Rest of Asia 0.362 0.413 0.428 0.430 0.410 0.408 Non-EU Europe 0.365 0.359 0.356 0.374 0.390 0.369 Africa 0.234 0.275 0.282 0.351 0.348 0.298 Latin America 0.274 0.263 0.280 0.290 0.298 0.281 Australia/NZ 0.219 0.221 0.177 0.184 0.159 0.192 Table 2 Proportion of exporting firms by destination Destination 2002 2003 2004 2005 2006 Average U.S./Canada 0.544 0.533 0.495 0.493 0.494 0.512 Japan/Korea 0.410 0.384 0.377 0.380 0.375 0.385 Rest of Asia 0.362 0.413 0.428 0.430 0.410 0.408 Non-EU Europe 0.365 0.359 0.356 0.374 0.390 0.369 Africa 0.234 0.275 0.282 0.351 0.348 0.298 Latin America 0.274 0.263 0.280 0.290 0.298 0.281 Australia/NZ 0.219 0.221 0.177 0.184 0.159 0.192 Destination 2002 2003 2004 2005 2006 Average U.S./Canada 0.544 0.533 0.495 0.493 0.494 0.512 Japan/Korea 0.410 0.384 0.377 0.380 0.375 0.385 Rest of Asia 0.362 0.413 0.428 0.430 0.410 0.408 Non-EU Europe 0.365 0.359 0.356 0.374 0.390 0.369 Africa 0.234 0.275 0.282 0.351 0.348 0.298 Latin America 0.274 0.263 0.280 0.290 0.298 0.281 Australia/NZ 0.219 0.221 0.177 0.184 0.159 0.192 Table 3 provides evidence that the number of destinations a firm exports to and the popularity of the destination are related. The first column of the table reports the proportion of firms that sell in only one destination market (0.348) through all seven destinations (0.062). Slightly more than one-third of the firms sell in only one market. The fraction of firms selling in multiple markets declines monotonically as the number of markets increases from 18.2% selling in two destinations to 6.2% selling in all seven destinations. The remainder of the table gives the proportion of firms exporting to $$n=1,...7$$ destinations, conditional on exporting to one of the destinations. The destinations are ordered from most to least popular in terms of overall export rate. The table shows a clear correlation between number of destinations and the popularity of the destination. Firms that export to the most popular destinations, U.S./Canada and Japan/Korea, are most likely to export to only one destination. The firms that export to the least popular destinations, Africa, Latin American, and Australia/NZ, are most likely to export to a large number of destinations. Firms that export to the Rest of Asia and non-EU Europe are in the middle, more likely to export to one or two destinations than the Africa, Latin American, Australia/NZ exporters, but less likely than the U.S./Canada and Japan Korea exporters. This pattern is consistent with underlying sources of firm heterogeneity that persist across all the firm’s destination markets. Firms with demand, marginal cost, and fixed cost components that allow them to be profitable in difficult markets, that is ones with low aggregate demand or high transport and entry costs, will also tend to be profitable in more popular markets and export to a larger total number of markets. This pattern is also consistent with evidence in Eaton et al. (2011) who show that French firms export to a hierarchy of countries and conclude that firm-level factors that persist across markets is an important factor that generates the dependence in the set of destination markets. Firm-level demand and cost components play a major role in the empirical model developed here. Table 3 Frequency distribution of total number of destinations Number destinations $$n$$ (overall frequency) Conditional on exporting to: U.S./Can Jap/Kor Rest Asia Non-EU Africa Lat Am Aust/NZ 1 (0.348) 0.209 0.323 0.095 0.123 0.033 0.040 0.063 2 (0.182) 0.159 0.108 0.153 0.136 0.117 0.056 0.143 3 (0.134) 0.130 0.099 0.172 0.136 0.168 0.119 0.080 4 (0.112) 0.123 0.112 0.164 0.158 0.178 0.181 0.134 5 (0.102) 0.143 0.112 0.149 0.184 0.182 0.220 0.170 6 (0.061) 0.113 0.121 0.134 0.114 0.154 0.181 0.116 7 (0.062) 0.123 0.125 0.134 0.149 0.168 0.203 0.295 Number destinations $$n$$ (overall frequency) Conditional on exporting to: U.S./Can Jap/Kor Rest Asia Non-EU Africa Lat Am Aust/NZ 1 (0.348) 0.209 0.323 0.095 0.123 0.033 0.040 0.063 2 (0.182) 0.159 0.108 0.153 0.136 0.117 0.056 0.143 3 (0.134) 0.130 0.099 0.172 0.136 0.168 0.119 0.080 4 (0.112) 0.123 0.112 0.164 0.158 0.178 0.181 0.134 5 (0.102) 0.143 0.112 0.149 0.184 0.182 0.220 0.170 6 (0.061) 0.113 0.121 0.134 0.114 0.154 0.181 0.116 7 (0.062) 0.123 0.125 0.134 0.149 0.168 0.203 0.295 Table 3 Frequency distribution of total number of destinations Number destinations $$n$$ (overall frequency) Conditional on exporting to: U.S./Can Jap/Kor Rest Asia Non-EU Africa Lat Am Aust/NZ 1 (0.348) 0.209 0.323 0.095 0.123 0.033 0.040 0.063 2 (0.182) 0.159 0.108 0.153 0.136 0.117 0.056 0.143 3 (0.134) 0.130 0.099 0.172 0.136 0.168 0.119 0.080 4 (0.112) 0.123 0.112 0.164 0.158 0.178 0.181 0.134 5 (0.102) 0.143 0.112 0.149 0.184 0.182 0.220 0.170 6 (0.061) 0.113 0.121 0.134 0.114 0.154 0.181 0.116 7 (0.062) 0.123 0.125 0.134 0.149 0.168 0.203 0.295 Number destinations $$n$$ (overall frequency) Conditional on exporting to: U.S./Can Jap/Kor Rest Asia Non-EU Africa Lat Am Aust/NZ 1 (0.348) 0.209 0.323 0.095 0.123 0.033 0.040 0.063 2 (0.182) 0.159 0.108 0.153 0.136 0.117 0.056 0.143 3 (0.134) 0.130 0.099 0.172 0.136 0.168 0.119 0.080 4 (0.112) 0.123 0.112 0.164 0.158 0.178 0.181 0.134 5 (0.102) 0.143 0.112 0.149 0.184 0.182 0.220 0.170 6 (0.061) 0.113 0.121 0.134 0.114 0.154 0.181 0.116 7 (0.062) 0.123 0.125 0.134 0.149 0.168 0.203 0.295 While Table 3 provides evidence that firm-level factors help determine the extensive margin of trade, we also find evidence that the intensive margin of trade is affected. Table 4 investigates the individual firm’s price and quantity decision to highlight the important dimension of firm heterogeneity in the data. The table reports the $$\overset{\_}{R}^{2}$$from OLS regressions of log price and log quantity on combinations of product, destination, year, and firm dummies in explaining price and quantity variation. The destination-year combination, which will capture country-specific macro and industry conditions, accounts for just over 1% of the sample variation in prices and just over 5% in quantity. The product dimension accounts for 33.7% of the sample variation in log price and 10.7% in log quantity. Most importantly, the firm dimension accounts for the vast majority of the sample variation: 74.4% of the price variation and 39.8% of the quantity. Combining the firm and product dimensions together generates some additional explanatory power but the improvement is modest. Overall, the table simply illustrates that most of the micro-level price and quantity variation is accounted by across-firm differences, some by differences in the type of product (leather versus rubber versus plastic shoes), and very little by time and destination. This reinforces the focus of our empirical model on characterizing the extent of firm heterogeneity in demand and cost conditions. Table 4 Source of price and quantity variation $$\overset{\_}{R}^{2}$$ from OLS regressions Categories of Controls Log price Log quantity Destination*Year (35 categories) 0.014 0.051 Four-Digit Product (3 categories) 0.337 0.107 Firm (738 firms) 0.744 0.398 Destination*Year, Product 0.344 0.145 Destination*Year, Product, Firm 0.809 0.448 Destination*Year, Product*Firm 0.837 0.493 $$\overset{\_}{R}^{2}$$ from OLS regressions Categories of Controls Log price Log quantity Destination*Year (35 categories) 0.014 0.051 Four-Digit Product (3 categories) 0.337 0.107 Firm (738 firms) 0.744 0.398 Destination*Year, Product 0.344 0.145 Destination*Year, Product, Firm 0.809 0.448 Destination*Year, Product*Firm 0.837 0.493 Table 4 Source of price and quantity variation $$\overset{\_}{R}^{2}$$ from OLS regressions Categories of Controls Log price Log quantity Destination*Year (35 categories) 0.014 0.051 Four-Digit Product (3 categories) 0.337 0.107 Firm (738 firms) 0.744 0.398 Destination*Year, Product 0.344 0.145 Destination*Year, Product, Firm 0.809 0.448 Destination*Year, Product*Firm 0.837 0.493 $$\overset{\_}{R}^{2}$$ from OLS regressions Categories of Controls Log price Log quantity Destination*Year (35 categories) 0.014 0.051 Four-Digit Product (3 categories) 0.337 0.107 Firm (738 firms) 0.744 0.398 Destination*Year, Product 0.344 0.145 Destination*Year, Product, Firm 0.809 0.448 Destination*Year, Product*Firm 0.837 0.493 We also find that the extensive margin and the intensive margin are correlated in a way that is consistent with firm-level heterogeneity that persists across markets. Table 5 reports coefficients from regressions of log price and log quantity on dummy variables for the number of destination markets. All coefficients are relative to firms with only one destination and the regressions include a full set of product, year, destination dummies. The first column of the table shows that firms that export to three to six destinations have prices, on average, that are statistically significantly higher than firms that export to one destination, but prices for firms that export to two or seven destinations are not significantly different. The second column shows that, with the exception of three destinations, the average firm export quantity to each market also rises, although not monotonically, as the number of destinations increases. In these cases, the average quantity of sales in each market are between 11% and 51% higher than the base group. Table 5 Price and quantity versus number of destinations (standard errors) Number of destinations Log price Log quantity 2 0.020 (0.024) 0.109 (0.086) 3 0.133 (0.025) $$-$$0.172 (0.088) 4 0.082 (0.025) 0.173 (0.088) 5 0.107 (0.024) 0.145 (0.084) 6 0.172 (0.025) 0.507 (0.088) 7 0.009 (0.022) 0.281 (0.079) Number of destinations Log price Log quantity 2 0.020 (0.024) 0.109 (0.086) 3 0.133 (0.025) $$-$$0.172 (0.088) 4 0.082 (0.025) 0.173 (0.088) 5 0.107 (0.024) 0.145 (0.084) 6 0.172 (0.025) 0.507 (0.088) 7 0.009 (0.022) 0.281 (0.079) Regressions include a full set of year, product, destination dummies. Table 5 Price and quantity versus number of destinations (standard errors) Number of destinations Log price Log quantity 2 0.020 (0.024) 0.109 (0.086) 3 0.133 (0.025) $$-$$0.172 (0.088) 4 0.082 (0.025) 0.173 (0.088) 5 0.107 (0.024) 0.145 (0.084) 6 0.172 (0.025) 0.507 (0.088) 7 0.009 (0.022) 0.281 (0.079) Number of destinations Log price Log quantity 2 0.020 (0.024) 0.109 (0.086) 3 0.133 (0.025) $$-$$0.172 (0.088) 4 0.082 (0.025) 0.173 (0.088) 5 0.107 (0.024) 0.145 (0.084) 6 0.172 (0.025) 0.507 (0.088) 7 0.009 (0.022) 0.281 (0.079) Regressions include a full set of year, product, destination dummies. Overall, Table 5 shows that the intensive margin, the average quantity of sales in each market, is positively related to the number of destinations the firm exports to, but the pattern is noisy. The complex relationship between the quantity of sales and the extensive margin indicates that there is likely a role for multiple sources of firm-level heterogeneity. Firms with low fixed costs of exporting would sell in more destinations, other things equal, but they would also require higher demand or lower marginal cost to explain the higher quantity of sales. The price is also higher for firms that export to more markets, except for the seven destinations. This is not consistent with low marginal cost and low price being the sole determinant of export participation and price. This is consistent with underlying firm differences in demand: firms with high demand components export to more markets and sell more, but also have higher marginal costs and thus higher prices. Overall, the empirical patterns summarized in Tables 3–5 suggest that firm-level differences in profitability that persist across destination markets is a likely contributor to the export decisions on both the extensive and intensive margins for Chinese footwear exporters, but it is not possible to identify the source of the firm differences from this evidence, so we turn to estimation of an empirical model with distinct firm demand, marginal cost, and fixed cost components. 5. Empirical Results In this section, we report estimates of the system of demand, pricing, and market participation equations using the Bayesian MCMC methodology. We report the posterior means and standard deviations of the parameters that are common across firms, $$\Theta _{1}$$, $$\Theta _{2}$$, and $$\Theta _{3}$$ defined in Section 3, and summarize the role of the three sources of firm heterogeneity in generating price, quantify and export participation differences across firms. 5.1. Demand estimates Table 6 reports estimates of the demand curve parameters, equation (4) which include the destination-specific price parameters $$\alpha _{d}$$ and group demand shifters $$\xi_{k}.$$ The demand elasticity in each market is $$-\alpha _{d}$$ and the markup, the ratio of price to marginal cost, is $$\alpha _{d}/(\alpha _{d}-1)$$. The first three columns of results correspond to the system of equations using the Bayesian MCMC methodology and the entries are the mean and standard deviations of the posterior draws from the Markov chain. Each column uses a different set of instrumental variables to control for the endogeneity of the output price.14 The column labelled IV1 uses the log of the urban wage and the log of the rural wage for manufacturing workers in the city where the firm is located. IV2 adds the log of the local land rental price to the instrument set and IV3 further adds the log of the firm’s capital stock. The IV1 and IV2 instruments vary at the city-year level. The third set of instruments includes one firm-level variable, the capital stock, in the set.15 These system estimates recognize and account for the endogenous selection of the export markets that the firm participates in. For comparison, the final two columns report OLS and IV estimates of just the demand equation, without specifying the endogenous selection of export markets. To be consistent with the model assumption of $$\xi _{f}$$, we use a random effect IV specification, and just report the results for the IV1 set of instruments. Table 6 Demand curve parameter estimates (standard error) Bayesian system of equations Demand equation only Parameter IV1 IV2 IV3 OLS IV1 –$$\alpha _{d}$$ U.S./Canada $$-$$2.720 (0.319) $$-$$2.804 (0.319) $$-$$2.693 (0.348) $$-$$0.657 (0.075) $$-$$1.735 (0.845) –$$\alpha _{d}$$ Japan/Korea $$-$$2.850 (0.326) $$-$$2.932 (0.326) $$-$$2.818 (0.356) $$-$$0.633 (0.096) $$-$$2.140 (1.474) –$$\alpha _{d}$$ Australia/NZ $$-$$2.629 (0.343) $$-$$2.708 (0.342) $$-$$2.589 (0.366) $$-$$0.259 (0.128) $$-$$2.083 (0.909) –$$\alpha _{d}$$ Rest of Asia $$-$$2.943 (0.326) $$-$$3.028 (0.327) $$-$$2.916 (0.356) $$-$$0.973 (0.082) $$-$$2.949 (0.644) –$$\alpha _{d}$$ Non-EU Europe $$-$$2.297 (0.325) $$-$$2.381 (0.325) $$-$$2.264 (0.349) $$-$$0.198 (0.089) $$-$$1.157 (0.699) –$$\alpha _{d}$$ Africa $$-$$3.186 (0.334) $$-$$3.272 (0.334) $$-$$3.156 (0.359) $$-$$1.064 (0.097) $$-$$3.286 (0.687) –$$\alpha _{d}$$ Latin America $$-$$2.889 (0.335) $$-$$2.974 (0.334) $$-$$2.856 (0.360) $$-$$0.800 (0.100) $$-$$2.941 (0.654) $$\xi _{g}$$ leather 0.303 (0.242) 0.356 (0.244) 0.288 (0.254) $$-$$1.032 (0.069) 0.110 (0.384) $$\xi _{g}$$ textile $$-$$0.899(0.162) $$-$$0.908 (0.160) $$-$$0.902 (0.161) $$-$$0.912 (0.069) $$-$$0.826 (0.091) Bayesian system of equations Demand equation only Parameter IV1 IV2 IV3 OLS IV1 –$$\alpha _{d}$$ U.S./Canada $$-$$2.720 (0.319) $$-$$2.804 (0.319) $$-$$2.693 (0.348) $$-$$0.657 (0.075) $$-$$1.735 (0.845) –$$\alpha _{d}$$ Japan/Korea $$-$$2.850 (0.326) $$-$$2.932 (0.326) $$-$$2.818 (0.356) $$-$$0.633 (0.096) $$-$$2.140 (1.474) –$$\alpha _{d}$$ Australia/NZ $$-$$2.629 (0.343) $$-$$2.708 (0.342) $$-$$2.589 (0.366) $$-$$0.259 (0.128) $$-$$2.083 (0.909) –$$\alpha _{d}$$ Rest of Asia $$-$$2.943 (0.326) $$-$$3.028 (0.327) $$-$$2.916 (0.356) $$-$$0.973 (0.082) $$-$$2.949 (0.644) –$$\alpha _{d}$$ Non-EU Europe $$-$$2.297 (0.325) $$-$$2.381 (0.325) $$-$$2.264 (0.349) $$-$$0.198 (0.089) $$-$$1.157 (0.699) –$$\alpha _{d}$$ Africa $$-$$3.186 (0.334) $$-$$3.272 (0.334) $$-$$3.156 (0.359) $$-$$1.064 (0.097) $$-$$3.286 (0.687) –$$\alpha _{d}$$ Latin America $$-$$2.889 (0.335) $$-$$2.974 (0.334) $$-$$2.856 (0.360) $$-$$0.800 (0.100) $$-$$2.941 (0.654) $$\xi _{g}$$ leather 0.303 (0.242) 0.356 (0.244) 0.288 (0.254) $$-$$1.032 (0.069) 0.110 (0.384) $$\xi _{g}$$ textile $$-$$0.899(0.162) $$-$$0.908 (0.160) $$-$$0.902 (0.161) $$-$$0.912 (0.069) $$-$$0.826 (0.091) The models include a full set of destination*year dummies. Table 6 Demand curve parameter estimates (standard error) Bayesian system of equations Demand equation only Parameter IV1 IV2 IV3 OLS IV1 –$$\alpha _{d}$$ U.S./Canada $$-$$2.720 (0.319) $$-$$2.804 (0.319) $$-$$2.693 (0.348) $$-$$0.657 (0.075) $$-$$1.735 (0.845) –$$\alpha _{d}$$ Japan/Korea $$-$$2.850 (0.326) $$-$$2.932 (0.326) $$-$$2.818 (0.356) $$-$$0.633 (0.096) $$-$$2.140 (1.474) –$$\alpha _{d}$$ Australia/NZ $$-$$2.629 (0.343) $$-$$2.708 (0.342) $$-$$2.589 (0.366) $$-$$0.259 (0.128) $$-$$2.083 (0.909) –$$\alpha _{d}$$ Rest of Asia $$-$$2.943 (0.326) $$-$$3.028 (0.327) $$-$$2.916 (0.356) $$-$$0.973 (0.082) $$-$$2.949 (0.644) –$$\alpha _{d}$$ Non-EU Europe $$-$$2.297 (0.325) $$-$$2.381 (0.325) $$-$$2.264 (0.349) $$-$$0.198 (0.089) $$-$$1.157 (0.699) –$$\alpha _{d}$$ Africa $$-$$3.186 (0.334) $$-$$3.272 (0.334) $$-$$3.156 (0.359) $$-$$1.064 (0.097) $$-$$3.286 (0.687) –$$\alpha _{d}$$ Latin America $$-$$2.889 (0.335) $$-$$2.974 (0.334) $$-$$2.856 (0.360) $$-$$0.800 (0.100) $$-$$2.941 (0.654) $$\xi _{g}$$ leather 0.303 (0.242) 0.356 (0.244) 0.288 (0.254) $$-$$1.032 (0.069) 0.110 (0.384) $$\xi _{g}$$ textile $$-$$0.899(0.162) $$-$$0.908 (0.160) $$-$$0.902 (0.161) $$-$$0.912 (0.069) $$-$$0.826 (0.091) Bayesian system of equations Demand equation only Parameter IV1 IV2 IV3 OLS IV1 –$$\alpha _{d}$$ U.S./Canada $$-$$2.720 (0.319) $$-$$2.804 (0.319) $$-$$2.693 (0.348) $$-$$0.657 (0.075) $$-$$1.735 (0.845) –$$\alpha _{d}$$ Japan/Korea $$-$$2.850 (0.326) $$-$$2.932 (0.326) $$-$$2.818 (0.356) $$-$$0.633 (0.096) $$-$$2.140 (1.474) –$$\alpha _{d}$$ Australia/NZ $$-$$2.629 (0.343) $$-$$2.708 (0.342) $$-$$2.589 (0.366) $$-$$0.259 (0.128) $$-$$2.083 (0.909) –$$\alpha _{d}$$ Rest of Asia $$-$$2.943 (0.326) $$-$$3.028 (0.327) $$-$$2.916 (0.356) $$-$$0.973 (0.082) $$-$$2.949 (0.644) –$$\alpha _{d}$$ Non-EU Europe $$-$$2.297 (0.325) $$-$$2.381 (0.325) $$-$$2.264 (0.349) $$-$$0.198 (0.089) $$-$$1.157 (0.699) –$$\alpha _{d}$$ Africa $$-$$3.186 (0.334) $$-$$3.272 (0.334) $$-$$3.156 (0.359) $$-$$1.064 (0.097) $$-$$3.286 (0.687) –$$\alpha _{d}$$ Latin America $$-$$2.889 (0.335) $$-$$2.974 (0.334) $$-$$2.856 (0.360) $$-$$0.800 (0.100) $$-$$2.941 (0.654) $$\xi _{g}$$ leather 0.303 (0.242) 0.356 (0.244) 0.288 (0.254) $$-$$1.032 (0.069) 0.110 (0.384) $$\xi _{g}$$ textile $$-$$0.899(0.162) $$-$$0.908 (0.160) $$-$$0.902 (0.161) $$-$$0.912 (0.069) $$-$$0.826 (0.091) The models include a full set of destination*year dummies. Focusing on the system estimates, we observe that the demand elasticity for each country varies little across the different instrument sets. Using the results for IV2, we see that the demand elasticities $$-\alpha _{d}$$ vary from $$-$$2.381 to $$-$$3.272 across destination countries. They are highest in the low-income destinations, Africa, Latin America, and the Rest of Asia, where they vary between $$-$$2.974 and $$-$$3.272. This implies lower markups in these destinations with the ratio of price to marginal cost varying from 1.440 to 1.506. The higher-income destinations, U.S./Canada, Australia/NZ, Japan/Korea, and non-EU Europe, have demand elasticities that vary between $$-2.381$$ and $$-$$2.932 and markups that all exceed 1.518. Finally, the two product group coefficients imply that consumers get higher utility from leather shoes and lower utility from textile shoes, relative to rubber shoes. In contrast, the OLS estimates of the price elasticity are substantially closer to zero, varying from $$-0.198$$ to $$-1.064$$. This finding of more inelastic demand is consistent with the expected positive bias in the demand elasticity due to the endogeneity of prices when using the OLS estimator. The IV estimator of the simple demand equation does not account for the endogenous selection of export markets. It produces estimates of $$-\alpha_{d}$$ that are more elastic than OLS but, in most cases, are less elastic than the system estimates and have much larger standard errors.16 5.2. Pricing equation estimates Table 7 reports parameter estimates of the pricing equation (6). These include coefficients that shift the marginal cost function including the local wage rate for urban and rural workers, the land rental price, and the firm’s capital stock, as well as product dummy variables. The coefficients on both wage rates are always positive, as expected, and highly significant.17 When the land rental price is added to the marginal cost specificiation (IV2) it is also positive and significant but becomes insignificant when the capital stock is also added as a marginal cost shifter (IV3). The sign of the capital coefficient in the last case is positive, which is not consistent with it being a shifter of the short-run marginal cost function.18 The product dummies indicate that leather footwear prices are, on average 60% higher and textile footwear prices are 5.5% lower than the base group, rubber footwear. Table 7 Pricing equation parameter estimates Bayesian system of equations IV1 IV2 IV3 $$ln(urbanwage)_{ft}$$ 0.200 (0.022) 0.180 (0.024) 0.175 (0.024) $$ln(ruralwage)_{ft}$$ 0.041 (0.010) 0.038 (0.010) 0.039 (0.010) $$ln(landrentalprice)_{ft}$$ 0.014 (0.007) 0.011 (0.007) $$ln(capital)_{ft}$$ 0.005 (0.002) Product Group Dummies $$(\gamma _{k})$$ Leather Shoes 0.597 (0.032) 0.596 (0.031) 0.596 (0.031) Textile Shoes $$-$$0.054 (0.037) $$-$$0.054 (0.036) $$-$$0.055 (0.036) Transitory Shocks ($$\rho _{u},\rho _{v},\Sigma _{e})$$ $$\rho _{u}$$ 0.640 (0.009) 0.640 (0.009) 0.640 (0.009) $$\rho _{v}$$ 0.671 (0.011) 0.669 (0.011) 0.669 (0.011) $$Var(eu)$$ 2.107 (0.114) 2.134 (0.115) 2.096 (0.114) $$Var(ev)$$ 0.084 (0.002) 0.084 (0.002) 0.084 (0.002) $$Cov(eu,ev)$$ 0.169 (0.026) 0.177 (0.026) 0.167 (0.028) Bayesian system of equations IV1 IV2 IV3 $$ln(urbanwage)_{ft}$$ 0.200 (0.022) 0.180 (0.024) 0.175 (0.024) $$ln(ruralwage)_{ft}$$ 0.041 (0.010) 0.038 (0.010) 0.039 (0.010) $$ln(landrentalprice)_{ft}$$ 0.014 (0.007) 0.011 (0.007) $$ln(capital)_{ft}$$ 0.005 (0.002) Product Group Dummies $$(\gamma _{k})$$ Leather Shoes 0.597 (0.032) 0.596 (0.031) 0.596 (0.031) Textile Shoes $$-$$0.054 (0.037) $$-$$0.054 (0.036) $$-$$0.055 (0.036) Transitory Shocks ($$\rho _{u},\rho _{v},\Sigma _{e})$$ $$\rho _{u}$$ 0.640 (0.009) 0.640 (0.009) 0.640 (0.009) $$\rho _{v}$$ 0.671 (0.011) 0.669 (0.011) 0.669 (0.011) $$Var(eu)$$ 2.107 (0.114) 2.134 (0.115) 2.096 (0.114) $$Var(ev)$$ 0.084 (0.002) 0.084 (0.002) 0.084 (0.002) $$Cov(eu,ev)$$ 0.169 (0.026) 0.177 (0.026) 0.167 (0.028) The model includes a full set of destination*year dummies. Table 7 Pricing equation parameter estimates Bayesian system of equations IV1 IV2 IV3 $$ln(urbanwage)_{ft}$$ 0.200 (0.022) 0.180 (0.024) 0.175 (0.024) $$ln(ruralwage)_{ft}$$ 0.041 (0.010) 0.038 (0.010) 0.039 (0.010) $$ln(landrentalprice)_{ft}$$ 0.014 (0.007) 0.011 (0.007) $$ln(capital)_{ft}$$ 0.005 (0.002) Product Group Dummies $$(\gamma _{k})$$ Leather Shoes 0.597 (0.032) 0.596 (0.031) 0.596 (0.031) Textile Shoes $$-$$0.054 (0.037) $$-$$0.054 (0.036) $$-$$0.055 (0.036) Transitory Shocks ($$\rho _{u},\rho _{v},\Sigma _{e})$$ $$\rho _{u}$$ 0.640 (0.009) 0.640 (0.009) 0.640 (0.0