Gravity, Productivity and the Pattern of Production and Trade

The aggregated incidence of bilateral trade costs is derived from the gravity model. Incidence is equivalent to a TFP penalty. Sectoral and national differences in TFP have sharp implications for the equilibrium pattern of production and trade in a specific factors model of production. Unskilled labor is intersectorally mobile. Skilled labor acquires sector specific skills. Productivity shocks cause incidence shock that induce ex post inefficient allocation of skilled labor. Below (above) average TFP sectors produce less and have below (above) average skill premia. Ex ante efficient allocation is lower in sectors with riskier TFP incidence, despite risk neutrality. JEL Classification: F10, D24 ∗I am grateful to Christian Broda for helpful comments on an earlier version at the NBER ITI Summer Institute, 2007. I thank participants in seminars at Drexel University, Brandeis University and Oxford University for comments on an earlier versions. Distribution frictions intuitively drag down productivity, with implications for trade patterns. Total Factor Productivity (TFP) is modeled in this paper as the product of the sectoral incidence of trade frictions and Hicks neutral sectoral productivity frictions. Operational measures of sectoral incidence based on the structural gravity model aggregate the enormous real world complexity of bilateral trade costs. Sharp implications of TFP differences for the global equilibrium pattern of production and trade are drawn using the specific factors model of production. Simple aggregate incidence measures are available under the assumption of trade separability (Anderson and van Wincoop, 2004): the distribution of goods across bilateral pairs is separable from the allocation of resources and expenditures across product lines within countries. It is as if each producing sector in each economy traded with a single world market. Specializing the trade allocation model to a CES structure results in the economic theory of gravity (Anderson, 1979; Anderson and van Wincoop, 2003, 2004). Outward and inward multilateral resistance give respectively the supply side and demand side incidence of trade frictions in conditional general equilibrium for each country and sector. It is not necessary to solve the full general equilibrium to solve for incidence. The allocation of expenditure and resources across sectors within each economy is determined by a vector of world prices margined up by its national sellers’ incidence. Global equilibrium requires that world prices clear world markets. Specializing the resource allocation model to the specific factors model permits sharp predictions. Unskilled labor is intersectorally mobile. The other factor is potentially mobile prior to production as well, but it must take on sector specific attributes to be deployed in production. Call this factor skilled labor to fix ideas. Sector specific skills are acquired, then productivity shocks are realized, prices are realized and the ex post efficient allocation of unskilled labor occurs. Neither factor of production is internationally mobile. The global general equilibrium pattern of production in this model, call it specific gravity, is explained by sector specific factor endowments (a supply shifter), taste parameters (a demand shifter) and the equilibrium incidence of TFP. The monopolistic competition variant of the model endogenizes the taste shifter. Looking across countries, the (multi-) factoral terms of trade and hence wages and real incomes are negatively related to the incidence of TFP. Looking across sectors within a country, the sector specific skill premium is reduced by high incidence of productivity frictions. The efficient ex ante allocation of skilled labor is characterized. Higher sectoral variance lowers ex ante efficient sectoral investment despite risk neutrality. Looking across countries, higher variance of the incidence of productivity shocks lowers ex post production efficiency. It is plausible that the national variance of the incidence rises with the mean, implying that ex post inefficiency is larger for economies with higher average trade costs. The same qualitative properties obtain when the model is extended to include intermediate goods combined with vertical disintegration (outsourcing) using the model of selection into trade of Helpman, Melitz and Rubinstein (2007). The closest related model is that of Eaton and Kortum (2002). They embed gravity in a Ricardian model of trade featuring productivity differences resulting from draws from nationally differing Frechet distributions. In equilibrium the model is observationally equivalent to the one good/many varieties gravity model (see Anderson and van Wincoop, 2004). Costinot and Komunjer (2007) extend the Eaton-Kortum framework to a multi-good setting. The specific gravity model nests the Costinot-Komunjer model as a special case when the efficient allocation of skilled labor is made after the realization of productivity draws. The more general case has two advantages in descriptive power. It allows a role for relative factor endowment differences, and it allows a role for income distribution. Ex post specificity combines with productivity shocks to generate the well documented phenomenon of sectorally heterogeneous returns to otherwise identical skilled labor, positively correlated with export intensity. Another advantage (not exploited here) is that the model links easily to the interest group political economy model of trade policy that endogenizes part of trade frictions. A less closely related recent literature that seeks to explain the pattern of production by international differences in endowments and technology lacks an appropriate general treatment of trade costs. Davis and Weinstein (2001) use the multi-cone Heckscher-Ohlin continuum of products model, but effectively assume that all the incidence of trade costs is on the demand side. Romalis (2004) considers the role of uniform trade costs in resource allocation using the multi-cone Heckscher-Ohlin continuum model, but in a NorthSouth model with M identical countries in each half of the world. Trade costs disappear from his empirical work via a substitution that is valid only using the high degree of uniformity of the model. Trefler’s HOV model (1995) allows for technology differences and home bias in preferences, but the home