Gains from Trade: Does Sectoral Heterogeneity Matter?
One sentence summary: Sectoral heterogeneity does not always lead to an increase in the gains from trade, which is consistent with the theory.
The corresponding paper by Rahul Giri, Kei-Mu Yi and Hakan Yilmazkuday has been accepted for publication at Journal of International Economics.
The NBER working paper version is available here.
Abstract
This paper assesses the quantitative importance of including sectoral heterogeneity in computing the gains from trade. Our theoretical framework has sectoral heterogeneity along five dimensions, including the elasticity of trade to trade costs. We estimate the sectoral trade elasticity with the simulated method of moments estimator and micro price data. Our estimates range from 2.97 to 8.94. Our benchmark model is calibrated to 21 OECD countries and 20 sectors. We remove one or two sources of sectoral heterogeneity at a time and compare the gains from trade to the benchmark model. We also compare an aggregate model with a single elasticity to the benchmark model. Our main result from these counterfactual exercises is that sectoral heterogeneity does not always lead to an increase in the gains from trade, which is consistent with the theory.
Non-technical Summary
Estimating the gains from international trade is one of the oldest and most important issues in economics. In recent years, owing to the development of easily accessible sectoral, bilateral trade and output data, as well as input-output tables, on the one hand, and tractable multi-sector, multi-country general equilibrium trade models on the other hand, there has been a surge in research quantifying the gains from trade. In many of these studies, there is a presumption that increased sectoral heterogeneity leads to higher gains from trade. This presumption is natural; in a simple multi-sector model in which the only source of heterogeneity across sectors is the initial sectoral trade shares, the multi-sector setting will always yield greater gains from trade, owing to Jensen's inequality, than the aggregate version of this model (with the same parameters).
Abstract
This paper assesses the quantitative importance of including sectoral heterogeneity in computing the gains from trade. Our theoretical framework has sectoral heterogeneity along five dimensions, including the elasticity of trade to trade costs. We estimate the sectoral trade elasticity with the simulated method of moments estimator and micro price data. Our estimates range from 2.97 to 8.94. Our benchmark model is calibrated to 21 OECD countries and 20 sectors. We remove one or two sources of sectoral heterogeneity at a time and compare the gains from trade to the benchmark model. We also compare an aggregate model with a single elasticity to the benchmark model. Our main result from these counterfactual exercises is that sectoral heterogeneity does not always lead to an increase in the gains from trade, which is consistent with the theory.
Estimating the gains from international trade is one of the oldest and most important issues in economics. In recent years, owing to the development of easily accessible sectoral, bilateral trade and output data, as well as input-output tables, on the one hand, and tractable multi-sector, multi-country general equilibrium trade models on the other hand, there has been a surge in research quantifying the gains from trade. In many of these studies, there is a presumption that increased sectoral heterogeneity leads to higher gains from trade. This presumption is natural; in a simple multi-sector model in which the only source of heterogeneity across sectors is the initial sectoral trade shares, the multi-sector setting will always yield greater gains from trade, owing to Jensen's inequality, than the aggregate version of this model (with the same parameters).
However, there are many sources of sectoral heterogeneity in a typical multi-sector trade model. Trade elasticities, value-added shares of gross output, input-output linkages, and final demand shares, in addition to initial trade shares (driven by fundamental productivity and trade costs) can all vary across sectors. The gains from trade are a non-linear function of these parameters and variables; ultimately, whether sectoral heterogeneity yields greater gains depends on whether, for example, sectors with high initial trade shares are also sectors with low value-added shares of gross output. The goal of this paper is to quantitatively evaluate how sectoral heterogeneity affects the gains from trade in a systematic, comprehensive, and structurally consistent way.
We employ a model that embodies these forms of sectoral heterogeneity. Our calibrated model has 20 sectors and 21 countries, and we estimate and calibrate the parameters to match key features of the sectoral production, trade, expenditure and micro-price data. One of the main contributions of our paper is that we estimate the elasticity of trade with respect to trade costs for each of 19 traded sectors using the simulated method of moments (SMM). This methodology builds on the method-of-moments estimation methodology with micro price-level data, by correcting the bias from a small sample of price observations. To our knowledge, this is the first application of the SMM estimator to estimate the trade elasticity at the sector level. We use the Eurostat surveys of retail prices, which covers 12 OECD countries and 19 three-digit ISIC traded good sectors for 1990.
Our sectoral trade elasticity estimates range from 2.97 to 8.94; the median is 4.38. We also estimate the sectoral trade elasticities with the original method-of-moments method and the minimum, maximum, and median elasticities are 4.26, 35.55, and 10.29. So, our SMM estimates are clearly lower, as earlier studies have shown in their papers incorporating a one-sector framework. In addition, the “bias” is larger the smaller the sample size. For example, ISIC 352, Other chemicals, has a sample size of 4, while ISIC 311, Food products, has a sample size of 343. Our SMM estimates are similar across these two industries, 3.75 and 3.57, respectively, but the method-of-moments estimates are 11.93 and 4.28, respectively. These estimates are used in our calibrated model.
We calibrate the other parameters to match their data counterparts and/or to be consistent with sectoral outputs and trade flows. With our calibrated model, we compute the gains from trade by comparing the welfare in our benchmark equilibrium relative to welfare in a counterfactual autarky equilibrium. Our benchmark calibrated model delivers gains from trade ranging from 0.40 percent in Japan to 8.33 percent in Ireland. The median gain in going from autarky to the calibrated equilibrium is 3.96 percent (Mexico). We also decompose the gains into the trade effect and sectoral linkage effect and find that the former is considerably larger than the latter.
We then conduct two sets of counterfactual exercises to assess the role of sectoral heterogeneity. We focus on five sources of heterogeneity in the gains from trade equation: sectoral trade elasticities, value-added gross output ratios, final demand shares, input-output linkages, and initial trade shares. In the first set of exercises, which we think of as “inspect the mechanism” exercises, we eliminate one or two sources of sectoral heterogeneity at a time. For each source of sectoral heterogeneity, we substitute a parameter (or variable) that is common across all sectors. For example, we replace the estimated sectoral trade elasticities with a single elasticity common to all sectors. We compute the gains from trade and compare these gains to those from the benchmark model.
When we eliminate one source of heterogeneity at a time, we find that in all cases the gains from trade are little or moderately changed relative to the benchmark model. That is, when we replace our estimated sectoral trade elasticities with the median estimate (4.38), the sectoral value-added shares with the average value-added share, the sectoral final demand share with the average final demand share, the sectoral intermediate use requirements with an average intermediate use requirements, or the initial sectoral trade shares with a common average initial share, the median gains from trade are within 10 or 20 percent of the benchmark gains. Our results for removing two sources of heterogeneity are similar, as for the most part, the difference in the gains from removing two sources of heterogeneity (relative to the benchmark model) is a sum of each difference in gain from removing one source of heterogeneity. In one final exercise, we remove all heterogeneity associated with intermediate goods and sectoral linkages by considering a value-added only model. We find, as other research has shown, that the gains from a value-added only model are less than one half that of the benchmark model. Overall, we find that most sources of sectoral heterogeneity lead to slight or moderate additional gains from trade, and some sources lead to less.
We employ a model that embodies these forms of sectoral heterogeneity. Our calibrated model has 20 sectors and 21 countries, and we estimate and calibrate the parameters to match key features of the sectoral production, trade, expenditure and micro-price data. One of the main contributions of our paper is that we estimate the elasticity of trade with respect to trade costs for each of 19 traded sectors using the simulated method of moments (SMM). This methodology builds on the method-of-moments estimation methodology with micro price-level data, by correcting the bias from a small sample of price observations. To our knowledge, this is the first application of the SMM estimator to estimate the trade elasticity at the sector level. We use the Eurostat surveys of retail prices, which covers 12 OECD countries and 19 three-digit ISIC traded good sectors for 1990.
Our sectoral trade elasticity estimates range from 2.97 to 8.94; the median is 4.38. We also estimate the sectoral trade elasticities with the original method-of-moments method and the minimum, maximum, and median elasticities are 4.26, 35.55, and 10.29. So, our SMM estimates are clearly lower, as earlier studies have shown in their papers incorporating a one-sector framework. In addition, the “bias” is larger the smaller the sample size. For example, ISIC 352, Other chemicals, has a sample size of 4, while ISIC 311, Food products, has a sample size of 343. Our SMM estimates are similar across these two industries, 3.75 and 3.57, respectively, but the method-of-moments estimates are 11.93 and 4.28, respectively. These estimates are used in our calibrated model.
We calibrate the other parameters to match their data counterparts and/or to be consistent with sectoral outputs and trade flows. With our calibrated model, we compute the gains from trade by comparing the welfare in our benchmark equilibrium relative to welfare in a counterfactual autarky equilibrium. Our benchmark calibrated model delivers gains from trade ranging from 0.40 percent in Japan to 8.33 percent in Ireland. The median gain in going from autarky to the calibrated equilibrium is 3.96 percent (Mexico). We also decompose the gains into the trade effect and sectoral linkage effect and find that the former is considerably larger than the latter.
When we eliminate one source of heterogeneity at a time, we find that in all cases the gains from trade are little or moderately changed relative to the benchmark model. That is, when we replace our estimated sectoral trade elasticities with the median estimate (4.38), the sectoral value-added shares with the average value-added share, the sectoral final demand share with the average final demand share, the sectoral intermediate use requirements with an average intermediate use requirements, or the initial sectoral trade shares with a common average initial share, the median gains from trade are within 10 or 20 percent of the benchmark gains. Our results for removing two sources of heterogeneity are similar, as for the most part, the difference in the gains from removing two sources of heterogeneity (relative to the benchmark model) is a sum of each difference in gain from removing one source of heterogeneity. In one final exercise, we remove all heterogeneity associated with intermediate goods and sectoral linkages by considering a value-added only model. We find, as other research has shown, that the gains from a value-added only model are less than one half that of the benchmark model. Overall, we find that most sources of sectoral heterogeneity lead to slight or moderate additional gains from trade, and some sources lead to less.
In the second set of exercises, we compare the welfare gains in our
benchmark model to our aggregate model. The aggregate model has just one
tradable sector; all heterogeneity across tradable sectors is
eliminated. We also estimate the aggregate trade elasticity with the SMM
methodology; we obtain a value of 2.37. Owing in part to this low
estimate, we find that the gains from trade in the aggregate model are
moderately (about one-third) larger than in the benchmark model. That
is, when we compare our benchmark model with its estimated sectoral
trade elasticities and sectoral heterogeneity on several other
dimensions to our aggregate model with its estimated aggregate trade
elasticity and no sectoral heterogeneity across tradable sectors, it is
the aggregate model with greater gains from trade. Further investigation
shows that the low estimated aggregate elasticity plays a key role. It
is important to reiterate that both sets of elasticities are estimated
in a model-consistent way.
To understand better all of our results, we conduct a Monte Carlo-type exercise in which we simulate prices and trade shares from our calibrated benchmark model. We then aggregate across sectors, and ask: “suppose this data were generated from an aggregate model. What would be the implied aggregate trade elasticity?” We find that the estimated aggregate elasticity from this exercise is about 2.65, which is only slightly larger than our actual estimated aggregate elasticity. In other words, our benchmark model generates data that would be consistent with a low aggregate elasticity in an aggregate model.
Overall, we conclude from our “inspect the mechanism” counterfactual, our benchmark vs. aggregate model counterfactuals, and our Monte Carlo exercise that increased sectoral heterogeneity does not necessarily imply larger gains from trade. This should not be a surprise, because it is just as the theory implies. The formula for the gains from trade shows clearly that whether sectoral heterogeneity per se leads to greater gains depends on two sets of interactions. One is the interaction of the sectoral trade elasticity, initial trade share, final demand share, and value-added share of gross output. The second is the input-output linkages along with the relative prices of inputs. Our results also show that overall, the interactions “cancel” to a large degree. A second conclusion is that model-consistent elasticity estimates should be used no matter the level of aggregation.
The main difference between our results and the previous research is that we use model- consistent trade elasticity estimates of both our benchmark model and our aggregate model. By contrast, much of the previous research uses an average of the sectoral elasticities as a stand-in for the aggregate elasticity. As our work, and previous research, have shown, an appropriate estimated aggregate elasticity is likely to be less than an average of sectoral elasticities. With a lower elasticity, all else equal, there will be greater gains from trade.
Overall, we conclude from our “inspect the mechanism” counterfactual, our benchmark vs. aggregate model counterfactuals, and our Monte Carlo exercise that increased sectoral heterogeneity does not necessarily imply larger gains from trade. This should not be a surprise, because it is just as the theory implies. The formula for the gains from trade shows clearly that whether sectoral heterogeneity per se leads to greater gains depends on two sets of interactions. One is the interaction of the sectoral trade elasticity, initial trade share, final demand share, and value-added share of gross output. The second is the input-output linkages along with the relative prices of inputs. Our results also show that overall, the interactions “cancel” to a large degree. A second conclusion is that model-consistent elasticity estimates should be used no matter the level of aggregation.
The main difference between our results and the previous research is that we use model- consistent trade elasticity estimates of both our benchmark model and our aggregate model. By contrast, much of the previous research uses an average of the sectoral elasticities as a stand-in for the aggregate elasticity. As our work, and previous research, have shown, an appropriate estimated aggregate elasticity is likely to be less than an average of sectoral elasticities. With a lower elasticity, all else equal, there will be greater gains from trade.
The corresponding paper by Rahul Giri, Kei-Mu Yi and Hakan Yilmazkuday has been accepted for publication at Journal of International Economics.
The NBER working paper version is available here.