International Trade Gravity Model Yiqing Xie School of Economics Fudan University Dec. 20, 2013 Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 1 / 23
Outline Chaney (2008) Helpman, Melitz and Rubinstein (2008) Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 2 / 23
Macro Implications of Firm Heterogeneity By introducing firm-level heterogeneity, Melitz (2003) was able to explain micro-level facts inconsistent with previous theories. Question: Does the introduction of firm heterogeneity have further implications at the macro-level? Next models provide positive answers by showing that: Selection of heterogeneous firms into exports matters for trade volumes: Chaney (2008), HMR (2008). Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 3 / 23
Chaney (2008): Contribution Gravity equation in the Melitz framework with many countries and asymmetric trade costs Decomposition of trade volumes into intensive and extensive margins The impact of elasticity of substitution on trade margins Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 4 / 23
Chaney (2008): Contribution In Krugman (1980), exports from i to j satisfy gravity: Exports ij = Cst Y i Y j (TradeBarriers ij ) σ 1 If goods are less substitutable (lower σ), consumers are willing to buy foreign varieties even at a higher costs. Trade barriers have little impact on bilateral trade volumes. Key assumptions: firms are identical and there are only variable trade costs. Every firm exports to every country in the world. We have the above gravity equation. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 5 / 23
Chaney (2008): Contribution In a (version of) Melitz (2003) with Pareto distributed productivities, Chaney (2008) shows that exports satisfy Exports ij = Cst Y i Y j (TradeBarriers ij ) ε(σ) with ε (σ) < 0 Firm heterogeneity plus fixed costs of exporting creates A new margin of trade: Extensive margin (the number of firms that export to a certain destination) Main finding: A higher elasticity makes the intensive margin (exports per firm) more sensitive to changes in trade barriers, whereas it makes the extensive margin less sensitive. The effect from the extensive margin dominates. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 6 / 23
Chaney (2008): Model N asymmetric countries with population L n The only factor of production is labor. There are H + 1 sectors and sector 0 provides a single homogenous good. The other H sectors are made of continuum of differentiated products. The utility function is given by where U = q µ 0 0 µ 0 + H ( h=1 Ω h q(ω) ) ( ) σ h σ h 1 µ σ h 1 h σ h dω H µ h = 1 and σ h > 1. h=1 Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 7 / 23
Chaney (2008): Model The homogenous good is freely traded and used as the numeraire: the price of this good is unity! CRS: one unit of labor produces w n units of the product in country n. Therefore, wage in country n is equal to w n (exogenous). Each country differs in L n (population size) and w n (wage level). There are two types of trade barriers: τ h ij : iceberg trade costs from i to j in industry h f h ij : fixed costs of exporting Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 8 / 23
Chaney (2008): Model Each firm in sector h draws a random unit labor productivity ϕ. The underlying productivity distribution G(ϕ) is assumed to be Pareto, so that G h (ϕ) = 1 ϕ γ h with γ > 2 and γ > σ h 1, where γ h is an inverse measure of the heterogeneity in sector h. The total mass of potential entrants in country n in each differentiated sector is proportional to w n L n. There is no free entry. Therefore, total profits are not equal to zero and have to be distributed. Workers worldwide hold a diversified portfolio of all firms in the world and the homogenous good is the vehicle to repatriate dividends. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 9 / 23
Chaney (2008): Intensive Margin Export revenue at the firm level is given by x ij (ϕ) = { ( ) Yj (σ 1)/γ ( ) θj σ 1 λ 3 Y w i τ ij ϕ σ 1 if ϕ ϕ ij 0 otherwise where λ 3 is a constant and θ j is a remoteness index for country j. Notice that as in the Krugman (1980) model, variable trade costs affect export sales with an elasticity of (σ 1). Hence, conditional on positive exports, the higher the elasticity of substitution, the larger the response of trade flows to transport costs. The impact of variable trade costs on revenues per firm Intensive margin: x ij (ϕ) Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 10 / 23
Chaney (2008): Extensive Margin With firm-heterogeneity, the impact of trade barriers reflects the impact of both variable and fixed trade costs on revenues per firm as well as total number of firms. Extensive margin: ϕ ij Aggregate exports from i to j (Gravity Equation) X ij = µ Y iy j Y ( ) wi τ γ ij (f ij) [γ(σ 1) 1] θ j In a Krugman model with homogenous firms, we would instead obtain: X K ij = µ Y iy j Y ( w i τ ij θ K j ) (σ 1) The extensive margin amplifies the impact of variable trade costs. The extensive margin also works through fixed exporting costs. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 11 / 23
Chaney(2008): Trade Margins and Trade Costs The Impact of Variable Trade Costs The elasticity of X ij with respect to τ ij can be decomposed into ζ d ln X ij = (σ 1) + (γ (σ 1)) = γ d ln τ ij }{{}}{{} Intensive Extensive The elasticity of X ij with respect to τ ij is now higher than in the case with homogeneous firms, since γ > σ 1. The same elasticity is now independent of σ. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 12 / 23
Chaney(2008): Trade Margins and Trade Costs The Impact of Variable Trade Costs A reduction of variable trade barriers implies that each existing exporter exports more. This is the intensive margin. It is more sensitive when the elasticity of substitution is high. (Krugman story) At the same time, higher potential profits attract new entrants. This is the extensive margin. When goods are more substitutable (large σ), each new export entrant could only capture a very small amount of market share. The effect of extensive margin is small when σ is large. When firms are more homogeneous (large γ), the size of new entrant will be larger. The effect of extensive margin is large when γ is large. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 13 / 23
Chaney(2008): Trade Margins and Trade Costs The Impact of Fixed Exporting Costs Similarly, the elasticity of X ij with respect to f ij can be decomposed into ξ d ln X ( ) ij γ = 0 d ln f ij }{{} + (σ 1) 1 γ = (σ 1) 1 Intensive }{{} Extensive The elasticity of X ij with respect to f ij is decreasing in the elasticity of substitution σ. When goods are more substitutable (large σ), the number of new entrants is smaller. The elasticity of X ij with respect to f ij is increasing in γ, and thus higher in more homogenous sectors. When firms are more homogeneous (large γ), the number of new entrant will be larger. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 14 / 23
Chaney (2008): Summary Introducing firm heterogeneity preserves the gravity structure of bilateral trade volumes. The impact of trade barriers on trade flows is dampened by the elasticity of substitution (and not magnified as in Krugman). Two trade margins: intensive and extensive. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 15 / 23
Chaney (2008) Aside: connection with Eaton and Kortum (2002) Eaton and Kortum (2002) have developed a Ricardian model also leading to a gravity equation. In both models, average revenues per variety are independent of variable trade costs. As a result, elasticity of bilateral exports with respect to variable trade costs only is a function of productivity parameters (ie not of σ). But in both models, this feature (that changes in bilateral trade flows only reflects changes in number of varieties exported) relies heavily on functional form assumption: Pareto and Frechet, respectively. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 16 / 23
HMR (2008): Motivation HMR start from the observation that many countries do not trade with each other: close to half of all country pairs do not export to each other and a small fraction exports in one direction only. Standard estimates of the gravity equation discard the zero trade flows: HMR argue that zeros contain useful information. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 17 / 23
HMR (2008): Summary Like Chaney (2008), Helpman, Melitz, and Rubinstein (2008) start from a Melitz (2003) model with asymmetric countries, but in order to explain zeros in the data they consider truncated Pareto distributions. Under these assumptions, they show that standard estimates of the elasticity of firm s revenues with respect to distance will be biased: Omitted variable bias Sample selection bias Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 18 / 23
HMR (2008): Summary Omitted Variable Bias can be understood as follows: Changes in bilateral trade flows also reflect changes in number of exporting firms. Since number of exporting firms is negatively correlated with trade costs, this induces upward bias. This is related to Chaney?s observation that elasticity of trade?flows with respect to variable trade costs is not equal to the elasticity of substitution, but the shape parameter of the Pareto γ > σ 1. Sample Selection Bias can be understood as follows: Sample of non-zero trade?flows is not a random sample of trade?flows. In this sample, unobserved component of trade costs tends to be lower for countries further away, which induces downward bias. Contribution: Show how to correct for two sources of biases using a two-stage estimation procedure. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 19 / 23
HMR (2008): Two-Stage Procedure In the first stage, a Probit selection equation is derived from the model (1 when exports, 0 otherwise). With the predicted values of the Probit equation we can compute the estimated latent variable and the control variable for the fraction of firms that export. correct the omitted variable bias We will also include the standard Heckman-correction term (the inverse Mills ratio). correct the sample selection bias For the procedure to work, one needs a variable that enters the first stage (affects through the fixed costs), but not the second stage. the cost of creating a business Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 20 / 23
HMR (2008): Two-Stage Procedure Benchmark Estimates Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 21 / 23
HMR (2008): Two-Stage Procedure Bias Decomposition Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 22 / 23
HMR (2008): Results Standard gravity estimates overestimate the effect of distance on trade flows (distance coefficient falls by about 1/3) since they ascribe to the intensive margin an effect that really works through selection into exporting. The bias stemming from firm-level heterogeneity is more important than the Heckman selection bias. Yiqing Xie (Fudan University) Int l Trade - Gravity (Chaney and HMR) Dec. 20, 2013 23 / 23