Unequal Welfare Gains from Trade across Countries: The Role of Aggregation and Income Elasticities
One sentence summary: Equal percentage changes in home expenditure shares result in unequal gains across countries depending on their elasticity measures.
The corresponding academic paper by Hakan Yilmazkuday has been accepted for publication at International Economic Journal.
The working paper version is available here.
The working paper version is available here.
Abstract
Sectoral heterogeneity has been shown to affect country-level welfare gains from trade that can be calculated by sector-specific trade elasticities and home expenditure shares. However, empirical analyses of multi-sector models are restricted to a limited number of countries and sectors, mostly due to the lack of data on sector-specific home expenditure shares. This paper first proposes a solution to this limitation by changing the way that foreign products are aggregated at the destination country, where "unbiased" multi-sector welfare gains can be captured by using country-specific trade elasticity measures. Second, the restrictive assumption of unitary importer-income elasticity is relaxed, and it is shown that the trade elasticity in the calculation of welfare gains is replaced by the newly-introduced welfare elasticity, a function of trade and income elasticities. Empirical evidence suggests that equal percentage changes in home expenditure shares result in unequal gains across countries depending on their elasticity measures.
Non-technical Summary
Welfare gains from trade (measured as costs of autarky) can be captured by two key parameters, namely the trade elasticity and home expenditure share in a one-sector environment for a variety of models. Nevertheless, such a convenient calculation may be biased, since one-sector models ignore the interaction among sectors. It is implied that sectoral heterogeneity is accepted as a key ingredient in welfare calculations. However, when the one-sector environment is extended to a multi-sector one, due to the way that sectors are aggregated at the destination country (i.e., an upper-tier aggregation of utility across sectors), the two key parameters are required at the sector level in order to calculate welfare gains from trade; moreover, an additional/third parameter is required at the sector-level to capture sector shares. Although the trade elasticity can be estimated for pretty much any sector and any country by using the corresponding trade and price/tariff data, sector shares and sector-specific home expenditure shares are available only for certain aggregation of sectors in certain countries. Accordingly, in order to calculate welfare gains in a multi-sector environment, several studies focusing on the estimation of both parameters (at the sectoral level) have been restricted to a limited number of countries and a limited number of sectors. Moreover, when the number of countries is limited, the estimated elasticity parameters (especially those that are common across countries) simply cannot represent global trade patterns, which would lead into biased welfare calculations.
In order to address these issues, this paper changes the way that foreign products are aggregated at the destination country so that the trade elasticity and aggregate home expenditure share are enough to calculate welfare gains from trade in a multi-sector framework. This is achieved for each destination country by having an upper-tier aggregation across source countries, and a middle-tier aggregation across sectors. To ensure that the sectoral heterogeneity will still be captured after this change in the order of aggregation, we borrow the concept of "unbiased" welfare gains from the literature and consider country-specific trade elasticity measures. When this proposal is empirically tested, it is shown by the following figure that country-specific trade elasticity measures can in fact be used to obtain "unbiased" multi-sector welfare gains.
Another bias in the calculation of welfare gains may arise due to restrictive assumption of unitary importer-income elasticity. In particular, studies in the literature have shown due to source-specific importer-income elasticity measures that higher importer income results in unequal welfare gains across source countries depending on the average type of product (inferior or luxury) exported by the source country. It is implied that measuring "unbiased" welfare gains also requires the consideration of source-specific importer-income elasticity measures.
Based on this motivation, this paper considers source-specific importer-income elasticity measures by using implicitly additively separable nonhomothetic constant elasticity of substitution (CES) preferences across source countries at the upper-tier aggregation of destination utility. Such an approach is useful to separately capture the source-country-specific importer-income effects in the utility function of destination countries, without giving away the standard features of having CES preferences, so that one can easily distinguish between income and substitution effects.
Based on the discussion so far, this paper considers an upper-tier aggregation across source countries by using implicitly additively separable nonhomothetic CES preferences, a middle-tier aggregation across sectors by a Cobb-Douglas function, and a lower tier aggregation across firm-level goods by CES preferences. The implications of the model regarding trade is estimated at the bilateral country level by using UN Comtrade data between 1995-2015. Since the lower tier aggregation of individual utility is achieved across firm-level goods in the model, firm-level productivity differences are carefully connected to the data on unit prices and the corresponding estimation; therefore, although firm-level data are not utilized, firm-level productivity differences are still taken into account at the aggregated level, without making any assumptions on their distribution. Due to the tiers of aggregation introduced so far, this corresponds to having a weighted average of sectoral log unit prices (measured at the six-digit Harmonized System in UN Comtrade) in the bilateral aggregate trade estimation, where the weights are simply the expenditure weights of sectors. Nevertheless, since firm-level productivity measures are carried over to the bilateral aggregate trade estimation as residuals, aggregated log unit prices become endogenous. By using the implications of the model, bilateral trade costs measured by standard gravity variables are shown to be potential instruments for aggregated unit prices in a Two-Stage Least Squares (TSLS) estimation. In this bilateral aggregate trade estimation, the coefficient in front of aggregated unit prices represents the destination-specific trade elasticity (i.e., one minus the elasticity of substitution), while the coefficient in front of log real total consumption (due to having non-unitary income elasticity) represents the source-specific income elasticity; these estimates are further used to construct country-specific welfare elasticity estimates.
Welfare gains from trade (measured as costs of autarky) can be captured by two key parameters, namely the trade elasticity and home expenditure share in a one-sector environment for a variety of models. Nevertheless, such a convenient calculation may be biased, since one-sector models ignore the interaction among sectors. It is implied that sectoral heterogeneity is accepted as a key ingredient in welfare calculations. However, when the one-sector environment is extended to a multi-sector one, due to the way that sectors are aggregated at the destination country (i.e., an upper-tier aggregation of utility across sectors), the two key parameters are required at the sector level in order to calculate welfare gains from trade; moreover, an additional/third parameter is required at the sector-level to capture sector shares. Although the trade elasticity can be estimated for pretty much any sector and any country by using the corresponding trade and price/tariff data, sector shares and sector-specific home expenditure shares are available only for certain aggregation of sectors in certain countries. Accordingly, in order to calculate welfare gains in a multi-sector environment, several studies focusing on the estimation of both parameters (at the sectoral level) have been restricted to a limited number of countries and a limited number of sectors. Moreover, when the number of countries is limited, the estimated elasticity parameters (especially those that are common across countries) simply cannot represent global trade patterns, which would lead into biased welfare calculations.
In order to address these issues, this paper changes the way that foreign products are aggregated at the destination country so that the trade elasticity and aggregate home expenditure share are enough to calculate welfare gains from trade in a multi-sector framework. This is achieved for each destination country by having an upper-tier aggregation across source countries, and a middle-tier aggregation across sectors. To ensure that the sectoral heterogeneity will still be captured after this change in the order of aggregation, we borrow the concept of "unbiased" welfare gains from the literature and consider country-specific trade elasticity measures. When this proposal is empirically tested, it is shown by the following figure that country-specific trade elasticity measures can in fact be used to obtain "unbiased" multi-sector welfare gains.
Another bias in the calculation of welfare gains may arise due to restrictive assumption of unitary importer-income elasticity. In particular, studies in the literature have shown due to source-specific importer-income elasticity measures that higher importer income results in unequal welfare gains across source countries depending on the average type of product (inferior or luxury) exported by the source country. It is implied that measuring "unbiased" welfare gains also requires the consideration of source-specific importer-income elasticity measures.
Based on this motivation, this paper considers source-specific importer-income elasticity measures by using implicitly additively separable nonhomothetic constant elasticity of substitution (CES) preferences across source countries at the upper-tier aggregation of destination utility. Such an approach is useful to separately capture the source-country-specific importer-income effects in the utility function of destination countries, without giving away the standard features of having CES preferences, so that one can easily distinguish between income and substitution effects.
Based on the discussion so far, this paper considers an upper-tier aggregation across source countries by using implicitly additively separable nonhomothetic CES preferences, a middle-tier aggregation across sectors by a Cobb-Douglas function, and a lower tier aggregation across firm-level goods by CES preferences. The implications of the model regarding trade is estimated at the bilateral country level by using UN Comtrade data between 1995-2015. Since the lower tier aggregation of individual utility is achieved across firm-level goods in the model, firm-level productivity differences are carefully connected to the data on unit prices and the corresponding estimation; therefore, although firm-level data are not utilized, firm-level productivity differences are still taken into account at the aggregated level, without making any assumptions on their distribution. Due to the tiers of aggregation introduced so far, this corresponds to having a weighted average of sectoral log unit prices (measured at the six-digit Harmonized System in UN Comtrade) in the bilateral aggregate trade estimation, where the weights are simply the expenditure weights of sectors. Nevertheless, since firm-level productivity measures are carried over to the bilateral aggregate trade estimation as residuals, aggregated log unit prices become endogenous. By using the implications of the model, bilateral trade costs measured by standard gravity variables are shown to be potential instruments for aggregated unit prices in a Two-Stage Least Squares (TSLS) estimation. In this bilateral aggregate trade estimation, the coefficient in front of aggregated unit prices represents the destination-specific trade elasticity (i.e., one minus the elasticity of substitution), while the coefficient in front of log real total consumption (due to having non-unitary income elasticity) represents the source-specific income elasticity; these estimates are further used to construct country-specific welfare elasticity estimates.
The corresponding welfare elasticity estimates have an average value
of -5.40 across countries with a range between -7.33 and -2.99. In
order to show the contribution of this paper in a clear way, the
obtained welfare elasticity estimates are further compared to the common
(across countries) trade elasticity estimate of about -4.95 that is
obtained by the very same data set. With respect to the welfare gains
obtained by the welfare elasticity, the welfare gains obtained by the
common trade elasticity are underestimated by up to about 14% for
highly-trading or high-income countries such as Ireland, Switzerland,
and Germany, while they are overestimated by up to about 9% for
less-trading or low-income countries such as Congo, Aruba and Guyana.
When we search for a systematic explanation for the heterogeneity of
these biases across countries by using the implications of our model, we
show that it is not only connected to per capita income of countries
but also connected to the total trade of source countries. This
heterogeneity across countries is also reflected in the calculation of
global welfare gains, where they range between 6.70% and 8.38% when
heterogeneity is ignored and considered, respectively.
The corresponding academic paper by Hakan Yilmazkuday has been accepted for publication at International Economic Journal.
The working paper version is available here.
The working paper version is available here.