Rescuing Observed Fixed Effects: Using the Hausman-Taylor Method for Out-of-Sample Trade Projections

Abstract

Abstract In this analysis, we propose the CitationHausman-Taylor (1981) method as an alternative estimation technique for estimating the gravity model of trade. We use an application to highlight the benefits of this technique for panel data estimation in general. Specifically, we compare the Hausman-Taylor method for estimating the unrealized US-Cuban trade potential to the OLS, fixed-effects, and random-effects methods using the out-of-sample approach. The Hausman-Taylor method is ideal because it allows for the inclusion of time-invariant variables in trade projections and circumvents the problem of an ad hoc estimation of the country-specific dummy variable needed for a projection based on the fixed-effects estimator. In addition, it removes the correlation between the error term and included variables which often plagues random-effects estimation. Notes 1See, among others, CitationHelliwell (1998); CitationHelliwell and Verdier (2001); CitationWolf (2000); and CitationAnderson and Wincoop (2003). 2See CitationRose (2000) and CitationPakko and Wall (2001). 3See CitationWang and Winters (1991). 4See CitationPakko and Wall (2001). 5 CitationCornwell and Trumbull (1994) and CitationTrumbull and Wall (1994). 6Since the fixed-effects estimates are consistent whether or not such correlation exists, the random-effects estimates can be compared to the fixed-effects estimates to test whether it is appropriate to use random-effects. This test was developed by CitationHausman and Taylor (1978). Empirically, the random-effects model is almost always rejected. 7See, also, CitationGreene (2003). 8United Nations Economic Commission for Latin America (ECLAC), Economic Survey of Latin America, Citation1963, (New York: United Nations, 1965), p. 273. 9 Economic Impact of U.S. Sanctions with Respect to Cuba: Chapter 3: Overview of the Cuban Economy and the Impact of U.S. Sanctions, U.S. International Trade Commission, February 2001. 10Trade statistics were obtained from Statistics Canada's World Trade Analyzer dataset. 11These data were obtained from the World Bank's Development Indicators Database. 12See, for example, CitationMcPherson, Redfearn, and Tieslau (2000), and CitationThursby and Thursby (1987) for recent support of the Linder hypothesis in the context of the gravity trade model. 13These data were obtained from the Heritage Foundation / Wall Street Journal Index of Economic Freedom. http://www.heritage.org (12/15/04). 14The included agreements are EC, BANG, ASEAN, ECO, GCC, LAIA, SPARTEC, MERCOSU, CEFTA, EFTA, CARICOM, CACM, CIS, BAFTA, NAFTA, PATCRA, CER, EAC, CEMAC, WAEMU, MSG, COMESA, SAPTA, and AFTA. 15See for example, CitationAitken (1973), CitationFidrmuc (1999), CitationFrankel, Stein, and Wei (1995), and CitationYu and Zeitlow (1995). 16These data were obtained from Direct-Line Distances International Edition. 17There is a literature which examines the effect of border on the decision to trade within a country or between bordering countries. In this case, border has been found to have a negative effect on trade. For example, see CitationEngel and Rogers (1996). 18We use an F [9228, 36903] statistic to test if all of the individual effects are equal across groups. The test statistic of 206.44 is far larger than the critical value, and we can conclude that there are indeed individual effects in the data and OLS estimation is not appropriate. 19A test statistic of 37.09 is far larger than the critical value of a chi-squared with 9 degrees of freedom. 20A test statistic of 2.32 (less than the critical value of 16.92) indicates the hypothesis that the individual effects are uncorrelated with the other regressors in the model cannot be rejected. 21 CitationCeglowski (2000), and CitationRose (2004). 22Although the results presented here support the Linder Hypothesis, it should be noted others have found contradictory results when the role of transportation costs are introduced into the model. See, for example, CitationDeardorff (1984). 23A confidence interval is not included for the fixed-effects estimator projection due to the ad hoc estimation procedure.