When are instruments generated from geographic characteristics in bilateral relationships invalid?

Abstract

Summary In their highly influential paper, “Does Trade Cause Growth?,” Frankel and Romer estimate a trade equation to predict bilateral trade shares, which are in turn aggregated to construct an instrument for trade openness in income regressions. The Frankel‐Romer approach has gained widespread popularity as a method to generate instruments for trade and many other outcome variables from estimated bilateral relationships. In this paper, we show analytically and empirically that the Frankel–Romer instrument gives inconsistent estimates for the effect of trade on income when fitted values for zero and missing bilateral shares are omitted from the instrument. This leads to a violation of the exclusion restriction because the instrument captures the endogenous variation in the observed probability that countries engage in bilateral trade, as reflected in the number of observed trading partners. This violation disappears when predicted bilateral shares for all observed and unobserved bilateral trade relationships are included in the instrument for trade openness.

Trade and Economic Growth: Does the Sophistication of Traded Goods Matter?

“…As shown by Deij et al (2021), this gives consistent results regardless of whether the absence of reported trade is due to no trade, misreported data entry, or that the data are not published.…”

“…The robustness checks give no evidence of a violation of the exclusion restrictions. First, the results are robust to the inclusion of out-of-sample bilateral trade predictions that are used to form the instrument, which is shown by Deij et al (2021) to be an important check for exclusion restrictions when the instruments are generated from the gravity model. Second, we show that migration and trade are determined by different geographic characteristics, suggesting that the exclusion restriction is not violated because the geographic instruments capture the income effects of immigration.…”

“…Why is it important to include out-of-sample predictions in the instrument set as a check for the exclusion restrictions? Deij et al (2021) show that a serious violation of the exclusion restriction may occur if only observed bilateral trade relationships are used to form the trade instrument.…”

“…Our theory and empirical methodology builds on a number of earlier studies (Young, 1991;Galor and Weil, 1996;Frankel and Romer, 1999;Yanikkaya, 2003;Galor and Mountford, 2008;Andersen and Dalgaard, 2011;Ortega and Peri, 2014;Pascali, 2017;Feyrer, 2009Feyrer, , 2019Deij et al, 2021). The studies closest to ours are Coe and Helpman (1995), Coe et al (1997), Madsen (2007), Galor and Mountford (2008), Kim and Lin (2009), and .…”

“…They used gravity equations based on geographic characteristics to predict bilateral trade between countries. However, the results based on their identification strategy remain mixed and sensitive to the choice of data, model specification, and the inclusion of confounding factors (Rodriguez and Rodrik, 2000;Irwin and Terviö, 2002;Ortega and Peri, 2014;Deij et al, 2021).…”