One sentence summary: The distance puzzle in international trade is solved when non-CES preferences are considered on the demand side.
The corresponding paper by Hakan Yilmazkuday has been published at Review of International Economics.
One channel of welfare-improving globalization is through the increasing integration of trade. Although this is attributed to decreasing effects of distance across countries, the workhorse models of gravity fail to capture it, the so-called the missing globalization or the distance puzzle. This paper shows that this puzzle may be due to the restricting assumption of constant elasticity of substitution (CES) preferences working behind the gravity models. We test the validity of this assumption for different trade intervals and show that it is violated due to the distance elasticity of trade decreasing with the amount of trade. Accordingly, we consider a type of non-CES utility function, namely constant absolute risk version (CARA), and analytically show that the negative relation between trade and distance elasticity of trade is captured by CARA preferences. We estimate the gravity equation implied by CARA preferences, empirically confirm the endogenous relation between trade and distance elasticity of trade, and show that the distance puzzle is solved under CARA preferences. According to the data set used, CARA preferences are also econometrically selected over CES preferences based on their goodness of fit.
The international trade literature characterizes welfare-improving globalization as the increasing integration of trade. This integration is mostly attributed to the decreasing effects of distance over time, due to decreasing freight costs over time as shown in the following figure.
Puzzlingly, however, evidence of long-distance trade integration is nowhere to be found in the estimates of the distance elasticity derived from standard workhorse models of international trade (a.k.a. "gravity" models). As is now well-documented (see, e.g., Disdier and Head, 2008), gravity estimates of the elasticity of trade with respect to distance have continually and regularly been found to be non-decreasing (or even increasing) over time. In other words, despite vast improvements in transportation and communication technologies over the latter half of the twentieth century, standard gravity regressions still find that these innovations have done nothing to make long-distance trade more feasible relative to trade over shorter distances. This has been referred to in the literature as the "missing globalization" puzzle (Coe et al., 2007) or "distance puzzle." Since the estimates of the distance elasticity may also be capturing other unobservable trends in trade costs such as falling costs of long-distance commercial flights (as in Yilmazkuday and Yilmazkuday, 2016), long-distance phone calls or internet (as in Clarke and Wallsten, 2006), and the spread of the English language (as in Ku and Zussman, 2010), the presence of the distance puzzle is even more surprising.
Using a standard data set in the gravity literature in the context of a demand-side model, this paper first confirms that there is a distance puzzle by showing that the distance elasticity of trade (in absolute terms) is increasing over time when constant elasticity of substitution (CES) preferences are considered.
This result is robust to the consideration of different measures of distance (e.g., distance between capital cities, most agglomerated cities, or population weighted measures) as well as the consideration of distance intervals as in Eaton and Kortum (2002). We claim that this result may be due to the structure of CES preferences literally implying a constant elasticity of substitution and a log-linear gravity relation between trade and distance. In particular, if distance elasticity of trade is endogenously determined, this would violate the assumption of CES and thus lead to biased empirical results. We test this hypothesis by differentiating the distance elasticity of trade across different trade intervals (e.g., distance elasticity of trade regarding trade smaller and larger than the median trade) for each year individually. Independent of the number of intervals considered, our results show that the (absolute value of) distance elasticity of trade systematically decreases with the amount of trade for each individual year. Therefore, the assumption of CES is violated for each year in our sample, and this may result in biased estimates of the distance elasticity of trade leading to the distance puzzle. Hence, an alternative modeling approach is required that will lead to endogenously determined distance elasticity of trade that decreases (in absolute value) with respect to the amount of trade.
Accordingly, we introduce a type of non-CES preferences, namely constant absolute risk aversion (CARA), to investigate an alternative structural relation between trade and distance, namely a lin-log gravity-type relationship, which is obtained by endogenously determined elasticity of substitution as the name non-CES literally implies. The key innovation is that under CARA preferences, the distance elasticity of trade is shown to be endogenously determined and decreasing with the quantity traded, which is exactly what we are looking for. We test the lin-log gravity relation implied by CARA preferences using exactly the same data set that we use for CES preferences and show that the distance puzzle is solved under CARA preferences because of the negative effects of distance decreasing over the sample period.
On top of solving the distance puzzle, we also show that CARA preferences are econometrically selected over CES preferences based on their goodness of fit.
The results are further shown to be robust to the consideration of (i) alternative distance measures, (ii) a balanced panel of countries, (iii) zero-trade observations, and (iv) alternative combinations of gravity variables.