Triplets, quads and quints: Estimating disaggregate trade elasticities with different odds ratios

A.1 Description of data

Trade and tariff data is from COMTRADE and UNCTAD TRAINS respectively. Both data sources are combined and downloaded via WITS (World Integrated Trade Solution^[8]). The tariff is effective applied rates, weighted average, which is most similar to the aggregated AHS tariffs by Caliendo and Parro (2015). It is reported as a tariff equivalent and transformed in the usual way ( 1 + z / 100) before calculations are performed. The trade data from COMTRADE is reported as import value in 1000 USD, as reported by the country, in cif (cost-insurance-freight).

The countries were selected to match the full sample in Caliendo and Parro (2015) as depicted in Table 5 (EU25 in WITS was renamed to “918”/“EUR” for ease of computation).

The selected year is 1993. For the imputation of tariffs: WITS download facility searches available data in neighbouring years, earlier years winning ties. We verify there is no data beyond the imputation range by Caliendo and Parro (2015): 1990–1995.

Caliendo and Parro (2015) use data at the four digit level and aggregate to the two digit level. Here we differ by using the two digit level data provided by WITS.

A.2 Structural gravity trade elasticities

This appendix aims at briefly comparing trade elasticities obtained from the gravity coefficient approach to those obtained from the odds ratio approach by Caliendo and Parro (2015).

The following two fixed effects gravity regressions are run on data for the two digit level of ISIC Rev.3 of the 20 commodities in Caliendo and Parro (2015).

The following table summarises results from these two regressions and compares them to the original results from Caliendo and Parro (2015) and to our own estimates T3 and T4.

Equation (9) depicts the regression for FE16 and FE15. Equation (10) depicts the regression for FE15g, which also includes data from the CEPII gravity dataset.^[9] FE16 includes the 16 countries used above. Because the CEPII dataset has no data on the European Union, it was dropped for FE15g. Results from FE15 are reported for comparison, using the 15 countries in FE15g without further gravity trade cost variables.

Table 6 reports trade elasticities from the following: the three different fixed effects regressions FE16, FE15 and FE15g and our own T3 and T4 estimates. In order to compare the results more easily, the trade elasticities are depicted in Figure 3 (commodities 10 and 23 are dropped for a better presentation). Different colours and shades of grey are used to distinguish the different setups: fixed effects trade elasticities (FE) from the different setups (15), (15g), and (16) are red, brown, and green, framed with increasingly bright shades of grey; our own estimates T3 and T4 are blue and purple, framed by the brightest shades of grey. Additionally, the results are shifted so that FE15 is at the bottom, FE15g and FE16 above it followed by T3, T4 at the top. The trade elasticities are depicted as a thick line, the crossbars represent the 95 percent confidence intervals for each elasticity. The large grey area on the right side of the figure highlights theoretically inconsistent (positive) values.

Figure 3

Trade elasticities from fixed effects gravity and odds ratio triplets and quads.

Estimates for the elasticities from FE15 and FE15g differ but are generally robust. They do not differ significantly because of overlapping confidence intervals, but this can at least partially be attributed to the width of these intervals. FE15 and FE15g are based on identical trade and tariff data and differ only by the inclusion of further trade cost variables that do not differ on the commodity level. The fact that the elasticities are not identical can be interpreted as evidence of some sensitivity of the gravity method to the assumption on the trade cost function – as noted by Anderson and Van Wincoop (2004).

Overall, all elasticities do not appear very different, i. e. most confidence intervals overlap. However, it is striking that most fixed effects elasticities have wider confidence intervals than those from T3 and T4. This allows to draw the conclusion that the odds ratio approach is able to deliver more reliable estimates for trade elasticities than the fixed effects gravity method for the sample used here.