Unobserved time effects confound the identification of climate change impacts

The FKO PNAS panel for yield statistic: corn in Table 1 displays our regression results for a model with corn yield that excludes the time effect. The results replicate almost exactly the results in the work by Feng et al. (1), which according to that paper, were for a model that included the time effect. The very minor discrepancies are likely because the data in Datasets S1 and S2 were rounded for display. We also note that the R² reported in the work by Feng et al. (1) is most likely the overall R² instead of the adjusted R² as stated. As reported in the work by Feng et al. (1), results in Table 1, columns 3–5, indicate that corn yield has a highly significant, negative effect on migration.

The corrected model for yield statistic: corn in Table 1 is for a model that includes the time effect. The corrected results show that, when the time effect is included, none of the coefficients on corn yield are statistically different from zero, even at the 10% level. The overall fit improves significantly, and the point estimates, although still negative, are significantly smaller in magnitude.

Yield statistic: corn plus wheat in Table 1 shows the results for corn plus wheat. The consequences of including the time effect are the same. The coefficient on yield is no longer statistically different from zero, and the point estimate is substantially closer to zero.

After the model in the work by Feng et al. (1) is correctly estimated using their data, the statistical evidence suggesting a causal relationship between weather-driven crop yields and emigration from Mexico to the United States disappears. The statistical evidence in the work by Feng et al. (1) is based on an incompletely controlled before-and-after comparison of emigration rates and crop yields across states. Any omitted factor positively (negatively) correlated with yields and negatively (positively) correlated with emigration rates over time affecting all states confounds this estimated effect. The results in the work by Feng et al. (1), therefore, cannot be given a causal interpretation, because a variety of factors changed during this period. According to the work by Feng et al. (1), these factors included “the effect of NAFTA, the Peso crisis, and changes in US border controls such as increased border enforcement after 2001” (ref. 1, p. 14258); regarding the second factor, after 1994, “the Peso depreciated considerably against the US dollar, doubling the real wage rate earned by emigrants” (1). The work by Feng et al. (1) also points to the “reform of the land tenure system and the opening of Mexico’s economy through liberalized trade and deregulation of markets” (1), which further impoverished small farmers and rural landholders. These factors would confound a pure before/after comparison, and therefore, they make it absolutely essential to control for them through time effects. Results from correct estimation of the model suggest that, for the sample used in the work by Feng et al. (1), these factors, and not weather, were responsible for the change in emigration rates between the two periods.

We thank Kavi Kumar for helpful discussions.