Thursday, December 22, 2016

Unifying Macro Elasticities in International Economics


Unifying Macro Elasticities in International Economics


One sentence summary: International elasticity puzzle is solved when expenditure shares are taken into account while calculating price elasticities of demand; moreover, international trade and finance literature imply the very same welfare gains from trade when international finance studies have unitary (Armington) elasticity of substitution between home and foreign products or unitary terms of trade.

The corresponding SSRN working paper by Hakan Yilmazkuday is available here.

The Dallas-Fed Globalization Institute working paper version is available here.
 

Abstract
International trade studies have higher macro (Armington) elasticity measures compared to international finance studies. This observation has evoked not only mixed policy implications regarding tariffs and exchange rates but also mixed welfare gains from trade. Regarding the policy implications, this so-called international elasticity puzzle is solved in this paper by distinguishing between elasticities of substitution and price elasticities of demand that are connected to each other through expenditure shares. It is shown theoretically and confirmed empirically that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the elasticity of substitution across products of foreign countries. It is implied that one can always find an elasticity of substitution across foreign countries that would be consistent with different macro elasticities in the two literatures; therefore, the puzzle is something artificial due to the way that the foreign products are aggregated at destination countries. Regarding the welfare gains from trade, the two literatures are shown to have the very same implications when international finance studies have a unitary macro elasticity of substitution between home and foreign products or unitary terms of trade. As opposed to the existing literature that has offered many supply-side solutions to the puzzle, the results in this paper are independent of the supply side and thus are consistent with any production structure.


Non-technical Summary
International trade studies have higher macro (Armington) elasticity measures compared to international finance studies. Since price changes are converted into quantity changes and thus real effects through these elasticities, this observation has evoked mixed policy implications regarding tariffs and exchange rates in the two literatures (e.g., see Ruhl (2008)). Moreover, since welfare gains from trade are directly connected to these macro elasticity measures (as in Arkolakis, Costinot, and Rodríguez-Clare (2012)), this observation has also evoked mixed welfare gains between the two literatures. Due these mixed implications, this observation has been called the international elasticity puzzle.

In order to have a better idea about the magnitude of this puzzle, we would like to consider the elasticity measures used in the literature. Although elasticity measures differ across studies, international finance studies mostly follow Backus, Kehoe, and Kydland (1994) with a macro elasticity value of about 1.5, while international trade studies mostly follow Anderson and Van Wincoop (2004) or recently Simonovska and Waugh (2014a) and Simonovska and Waugh (2014b) with a macro elasticity value of about 5. It is implied that if we directly employ these numbers in a policy analysis, say, in order to investigate the effects of a foreign price change due to tariffs or exchange rates, international trade studies imply quantity changes that are at least three times the international finance studies. Similarly, if we use the formula for the welfare gains from trade as introduced by Arkolakis, Costinot, and Rodríguez-Clare (2012), which is a function of home expenditure share and the macro elasticity, international finance studies imply welfare gains (in percentage terms) that are about eight times the international trade studies (for any given home expenditure share).

This paper unifies these macro elasticities that lead into mixed results in the two literatures. Since the upper-tier aggregation is achieved across source countries (including home country) in international trade studies, and it is achieved across home and foreign products in international finance studies, the two literatures are connected to each other by an additional tier of aggregation across different foreign countries in international finance. Although such an additional tier is missing in international finance studies, it is well understood to exist in the background.

Within this framework, we show that there is no connection between the macro elasticities of the two literatures when expenditure shares are negligible in the calculation of price elasticities. The tables turn when such expenditure shares are taken into account in this paper, which results in having price elasticities of demand connected to elasticities of substitution through such expenditure shares. We show that such a strategy helps us understand several differences across studies in the literature regarding the elasticity measures such as the differences due to simulating versus estimating, differences due to the level of disaggregation (e.g., having different digits of data), and differences between long-run and short-run elasticity measures. More importantly, such a strategy also allows us connect macro elasticities in the two literatures through the elasticity of substitution across different foreign countries in international finance that is newly introduced in this paper. In particular, when expenditure shares are considered, we show that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the elasticity of substitution across products of foreign countries. It is implied that one can always find an elasticity of substitution across foreign countries that would be consistent with different macro elasticities in the two literatures; therefore, the puzzle is solved theoretically. Then, how can one make sense of the mixed policy implications and mixed welfare gains from trade implied by the two literatures? We focus on this question next.

From a researcher’s or a policy maker’s perspective, since policy implications for any individual good coming from an individual foreign country should not depend on how foreign goods are artificially aggregated at the destination country, we equalize the micro price elasticities of demand (depending on expenditure shares) between the two literatures to show theoretically and confirm empirically that the elasticity of substitution across different foreign countries plays an important role in the determination of the puzzle. Therefore, the policy implications at the individual foreign good level are automatically equalized, although the artificially created upper-level elasticities are allowed to change between the two literatures; this inductive approach is different from the deductive approach followed by the existing literature, where the upper-level variables (e.g., utility) are taken as given, while lower-level variables are allowed to change. Since policy implications are equalized between the two literatures for each and every foreign good, the international elasticity puzzle disappears at the disaggregated micro level. It is implied that the policy analysis should be first achieved at the disaggregated micro level and then aggregated up to obtain macro implications; such a strategy has also been used by Imbs and Mejean (2015) who have calibrated macro elasticities using a weighted average of sector elasticities.

After solving the puzzle due to its policy implications at the micro level, we continue with focusing on different implications by the two literatures regarding the welfare gains from trade at the macro level (which also correspond to the macro-level effects of a foreign shock in home country). Rather than using the simplified version of the formula given by Arkolakis, Costinot, and Rodríguez-Clare (2012), we consider the full definition of welfare gains (measured by the costs of autarky) in order to have a comparison between the two literatures by searching for aggregate price indices that would have to adjust to keep the consumer utility the same between the current openness to trade and a hypothetical autarky, for any given expenditure. We show that the two literatures have the very same welfare gains from trade when there is unitary macro elasticity of substitution between home and foreign products or when there is unitary terms of trade in international finance. Hence, there is no international elasticity puzzle from the perspective of welfare gains from trade as long as there is unitary macro elasticity or unitary terms of trade in international finance and as long as we do not make any simplifying assumptions regarding the implications of our models for welfare gains from trade; we should rather derive our model-specific formulas.

The theoretical framework in this paper is closest to the study by Feenstra, Luck, Obstfeld, and Russ (2014) who have three tiers of aggregation in their CES framework; the disaggregation is across goods in the upper-tier, across home and foreign products in the middle-tier, and across foreign sources in the lower tier. They call their middle-tier elasticity (across home and foreign products) as the "macro" elasticity, while they call their lower-tier elasticity (across foreign source countries) as the "micro" elasticity. They consider these "macro" and "micro" elasticities as the elasticities used in international finance and international trade studies, respectively, which they estimate at the good level and show that their "macro" elasticity is higher than their "micro" elasticity only for half of the goods investigated; hence, they have a good-level investigation while comparing their "macro" and "micro" elasticities. However, this aggregation strategy is not consistent with either international trade or international finance studies, where the former aggregates across source countries in the upper-tier (e.g., see Anderson and Van Wincoop (2003), Anderson and Van Wincoop (2004), Head and Ries (2001), Hummels (2001), or Yilmazkuday (2012), among many others), and the latter aggregates across home and foreign countries in the upper-tier (e.g., see Backus, Kehoe, and Kydland (1994), Blonigen and Wilson (1999), Corsetti, Dedola, and Leduc (2008), Enders, Müller, and Scholl (2011), or Heathcote and Perri (2002), among many others). Since the international elasticity puzzle is about the comparison of these upper-tier macro elasticities in the two literatures (rather than the middle-tier or the lower-tier), the aggregation strategy used by Feenstra, Luck, Obstfeld, and Russ (2014) is useless to address this puzzle. In contrast, our aggregation strategy successfully employs the upper-tier macro elasticities as they are exactly used in the two literatures.

It is important to emphasize that the results in this paper are independent of the supply side and thus are consistent with any production structure in the literature. In contrast, the existing literature has focused on many solutions to the puzzle based on the supply side. For example, Ruhl (2008) has proposed a solution based on firm-level entry costs and uncertainties on future productivities in a Melitz (2003) framework; Fitzgerald and Haller (2014) have both fixed and sunk costs of export participation, where participation in different export markets are considered as independent decisions after conditioning on a common marginal cost of production; Crucini and Davis (2016) consider the speed of adjustment of capital in the distribution sector; Ramanarayanan (2015) considers intermediate inputs in which heterogeneous producers face a plant-level irreversibility in the structure of inputs used in production; Arkolakis, Eaton, and Kortum (2012) consider the difference between the adjustments in extensive and intensive margins of trade in an Eaton and Kortum (2002) framework. Accordingly, it is implied by the demand-side investigation in this paper that we do not need such supply-side complications in order to understand the puzzling difference between macro elasticities of the two literatures. The puzzle is rather something artificial due to the way that the foreign products are aggregated at destination countries.

The corresponding working paper by Hakan Yilmazkuday is available here.


Tuesday, December 20, 2016

Understanding Long-run Price Dispersion


Understanding Long-run Price Dispersion


One sentence summary: At the PPP level, almost all of price dispersion is attributed to unskilled wage dispersion, while at the LOP level, borders and distance contribute about equally to price dispersion that is rising in the distribution share.

The corresponding paper by Mario J. Crucini and Hakan Yilmazkuday has been published at Journal of Monetary Economics.


Abstract
We use a unique panel of retail prices spanning 123 cities in 79 countries from 1990 to 2005, to uncover six novel properties of long-run international price dispersion. First, at the PPP level, virtually all (91.6%) of price dispersion is attributed to service-sector wages, consistent with a dominant role of the retail distribution margin. Second, at the level of individual goods and services, the average contribution of service-sector wages is significantly reduced, one-third as large (31.9%). This reflects the fact that good-specific sources of price dispersion, such as trade costs and good-specific markups, tend to average out across goods. Third, at the LOP level, borders and distance contribute about equally to price dispersion with distance elasticities consistent with the existing trade gravity literature which links trade volumes (rather than relative prices) to borders and distance. Fourth, in the cross-section, price dispersion is rising in the distribution share consistent with the notion that baby-sitting services and haircuts embody local wages to a far greater extent than highly traded manufactured goods. Fifth, we provide the first estimates of distribution margins at the micro-level and show them to be very different across goods and substantial in the aggregate, where they account for about 55% of consumption expenditure. Sixth, these estimates are broadly consistent with more aggregated U.S. NIPA measures currently used in the literature.


Non-technical Summary
The Law-of-One-Price (LOP) is the theoretical proposition that, absent official and natural barriers to trade, international prices are equated in common currency units, and a laborer's purchasing power (i.e., real wage) is determined only by their labor productivity. A stark empirical implication of this proposition is that the cross-country correlation between price levels and wage levels is zero. As is well known, this implication of goods market integration is grossly at odds with the data. The Penn Effect, in recognition of the ambitious work of Heston, Kravis, Lipsey, who developed the Penn World Tables, shows a strong positive correlation between international price levels and per capita income.

The following figure shows the microeconomic counterpart of this fact using the panel data of our study. Microeconomic in this context means the prices of individual goods and services across cities of the world, as opposed to aggregate price levels at the national level. Specifically, each point in the scattterplot is the price of an individual good or service in a particular city plotted against the hourly wage of domestic cleaning help in that particular city. Prices and wages have been averaged over the period 1990 to 2005 to eliminate transitory deviations associated with business cycles and exchange rate fluctuations.


Specifically, there are 300 goods and services (up to missing observations) for each city and there are 123 cities in total. The prices and wages used to construct these time-averages are from the Economist Intelligence Unit (EIU) World Cost of Living Survey which spans 79 countries. As far as we know, this is the first study to use time-averaged data to study long-run deviations from the LOP and Purchasing Power Parity (PPP). The points labeled with an asterisk are price levels computed as expenditure-weighted averages of the individual prices.

In the figure, the estimated line through the scatter of price levels has a slope of 0.52 and an R-squared value of 0.37. The estimation is by geometric mean regression to consider for possible measurement errors in both the price and wage data. A common set of consumption expenditure weights are used for all cities. These consumption expenditure weights are taken from the PWT, averaged across all OECD nations. 

In words: a doubling of wages is associated with a 52 percent higher price level. This finding is typically associated with the seminal works of Harrod (1933), Balassa (1964), and Samuelson (1964); however, the HBS theory assumes that LOP holds for traded goods but not for non-traded goods. According to this view, called the classical dichotomy, there should be a horizontal line traced out by traded goods for which the LOP holds and a line with a slope of unity for non-traded goods. The trivial example is the hourly wage of domestic help itself, which produces a slope of one by recognizing that the market price of this non-traded service is, in fact, the hourly wage for unskilled labor. The figure above, obviously, is not much more sympathetic to the classical dichotomy than it is to complete market integration.

To help resolve this puzzle, this paper estimates distribution and trade cost wedges using a trade model augmented with a retail distribution sector (developed in Crucini and Yilmazkuday, 2009). We have two sets of results, one for relative price levels (PPP) and the other at the level of individual goods (LOP). 

Regarding PPP, the variance of price levels for international city pairs is found to be almost entirely explained by international wage differences, 92% by our estimate. Both the absolute amount of price dispersion and the relative importance of wage differences falls when the sample is restricted to cities in countries at similar stages of development while the role of retail productivity increases. The contribution of cross-city wage differences falls to 8% when the sample is restricted to city pairs within the same country. It is important to keep in mind that the amount of price level dispersion across cities that are located in the same country is a trivial 3-5%; as such, a modest amount of wage or retail productivity variance goes a long way in terms of accounting for the lion's share of the variance. The thrust of the PPP analysis is that when long run price level differences are consequential, the differences are attributable to the level of economic development, not traditional trade frictions.

The table turns dramatically in favor of borders and trade costs and away from wages and retail productivity, as explanatory factors, when the focus is LOP deviations. Pooling all international city pairs, the explanatory power of the HBS theory (wage dispersion) falls by a factor of three, to about 32%. Traditional theories of trade that emphasis distance and borders now account for the lion's share of price disperison, about 41%. City effects account for almost none of the international LOP variation. Essentially, this is because international LOP deviations are both large and idiosyncratic to the good once we condition on the wage level. The remainder is a residual term, which may reflect good and location-specific markups as well as other variables omitted from the model. The following figure shows how this decomposition changes across goods, where the vertical axis shows the deviations from LOP, while the horizontal axis shows the distribution share of goods.








Monday, December 19, 2016

Understanding Interstate Trade Patterns

Understanding Interstate Trade Patterns


One sentence summary: Interstate elasticity measures that are essential for any policy analysis within the U.S. are identified by combining state-level trade and production data.

The corresponding paper by Hakan Yilmazkuday has been published at Journal of International Economics.


Abstract
This paper models and estimates bilateral trade patterns of U.S. states in a CES framework and identifies the elasticity of substitution across goods, the elasticities of substitution across varieties of each good, and the good-specific elasticities of distance by using markup values obtained from the production side. Compared to the international trade literature, the elasticity of substitution estimates are lower across both goods and varieties, while the elasticity of distance estimates are higher. Although home-bias effects at the state level are significant, there is evidence for decreasing effects over time.


Non-technical Summary
The elasticity of substitution and the elasticity of distance are two key parameters used by policy makers to derive quantitative results in international or intranational trade, because the effects of a policy change are evaluated by converting policy changes into price effects through these parameters. Therefore, there is no question that the measurement of these parameters is of fundamental importance in economic modeling where they connect quantities to prices. In empirical trade studies, especially the famous and successful gravity models, usual subproducts of an empirical analysis are some measures of these elasticities; however, in a typical gravity model estimation, one cannot identify the elasticity of substitution (across goods and/or varieties) and the elasticity of distance at the same time. This paper proposes a new approach by considering markups in the production side to estimate the elasticity of substitution across goods, the elasticities of substitution across varieties of each good, and the good-specific elasticities of distance, all identified in the empirical analysis.

A monopolistic-competition model consisting of a finite number of regions and a finite number of goods is employed in a constant elasticity of substitution (CES) framework. Each region consumes all varieties of each good, while it produces only one variety of each good. On the consumer side, as is standard in a CES framework, bilateral trade of a variety of a good across any two regions depends on the relative price of the variety and total demand of the good in the destination (importer) region. Similarly, total imports of a good in a region depends on the relative price of the good and total demand of all goods in the region. On the production side, having market power in the production of a variety of each good results in positive markups in each region. In equilibrium, markups at the good level are connected to the elasticities of substitution across varieties of each good.

We show that the simple CES framework is sufficient to estimate/calculate all structural parameters in the model when trade, distance, and markup measures are known. The estimated parameters correspond to:
  • the elasticity of substitution across varieties of each good; 
  • the elasticity of substitution across goods; 
  • the good-specific elasticities of distance, which govern good-specific trade costs; 
  • the heterogeneity of individual tastes, measuring geographic barriers and the so-called home-bias.

The key innovation is to bring in additional data for markups at the good level and use them to aid in identification of all types of elasticities mentioned above. The chain of logic is as follows:
  1. Elasticities of substitution across varieties of each good are estimated by markup data. 
  2. Elasticities of distance at the good level are identified through combining markups and bilateral trade estimates. 
  3. In each region, source prices of each variety (of each good) are calculated using markup data and source fixed effects obtained by the bilateral trade estimation. 
  4. For each destination, composite price indices and total imports are calculated at the good level. 
  5. The elasticity of substitution across goods is estimated using the calculated composite price indices and total imports.

The empirical results show that
  • the elasticity of substitution across varieties is about 3.01 on average across goods
  • the elasticity of distance is about 0.45 on average across goods
  • the elasticity of substitution across goods is about 1.09

Compared to the existing literature, the elasticity of substitution estimates are lower, and the elasticity of distance measures (thus, trade costs) are higher in this paper. The lower elasticity of substitution and the higher elasticity of distance measures in this paper likely arise through considering information from the production side that the demand-driven gravity models are unable to account for.

Besides providing identification solutions, this paper also investigates home-bias effects and shows that they are significant at the U.S. state level. Considering historical home-bias measures from earlier studies (that use data from 1993 and 1997), it is implied that home-bias effects are decreasing through time. Nevertheless, when home-bias effects are compared across goods and across states, they are significantly dispersed; much remains to be learned from such dispersion.