Dear Statalist,
Thanks to Kit Baum, the new Stata command ppml_fe_bias is now available to download from the SSC repository: type "ssc install ppml_fe_bias, replace".
This command corrects for various incidental parameter problems that arise in PPML models with more than one fixed effect, especially in the context of so-called "gravity" models that are often applied to data on international trade, migration, and other types of spatial flows. The correction techniques it uses come from a recent paper by Martin Weidner and myself (Weidner and Zylkin, 2020) on improving inferences in PPML gravity models with "three-way" (origin-time, destination-time, and origin-destination) fixed effects. The biases this command addresses affect both the point estimates as well as the standard errors in these types of models. We also include an option for correcting a related bias that arises in the standard errors of the standard "two-way" (origin-time and destination time fixed effects only) gravity model.
Those who are familiar with the incidental parameter problem may be thrown off by the idea that incidental parameters can pose an issue for PPML models. Usually, when PPML is discussed in this context, it is to remark on how it is unaffected by the incidental parameter problem (Wooldridge, 1999; Fernández-Val and Weidner, 2016). Indeed, even in the complex setting of a three-way fixed effects gravity model, it is noteworthy that PPML estimates are generally consistent, whereas other common alternatives (OLS, Gamma PML), are not.
At the same time, it turns out that the unique way in which the three fixed effects interact in the three-way model induces a bias in PPML estimates when the time dimension is fixed. Because the estimator is consistent, the bias may be small in absolute terms, but the worrying part is that it is always large relative to the standard error, meaning that it always poses an issue for inference even with large samples. One of the main contributions of this command is to provide researchers with a correction for this bias.
The bias is point estimates is not the only bias one should worry about. It also turns out that cluster-robust standard errors typically used for inference are themselves biased, sometimes substantially so. This latter issue is reminiscent of a similar problem that has been documented for the simpler two-way PPML gravity model (see, e.g., Egger and Staub, 2015; Jochmans, 2017; Pfaffermayr, 2019). Thus, the ppml_fe_bias package also includes options for correcting standard errors in both two-way as well as three-way gravity models.
If you are interested in learning more, there is a dedicated github with examples and more details. PPML models with two-way and three-way fixed effects are currently very popular in applied empirical work and actually a frequent topic of conversation on this message board. Thus, I hope that users who visit this site interested in learning about gravity models will find this package useful!
Regards,
Tom
Thanks to Kit Baum, the new Stata command ppml_fe_bias is now available to download from the SSC repository: type "ssc install ppml_fe_bias, replace".
This command corrects for various incidental parameter problems that arise in PPML models with more than one fixed effect, especially in the context of so-called "gravity" models that are often applied to data on international trade, migration, and other types of spatial flows. The correction techniques it uses come from a recent paper by Martin Weidner and myself (Weidner and Zylkin, 2020) on improving inferences in PPML gravity models with "three-way" (origin-time, destination-time, and origin-destination) fixed effects. The biases this command addresses affect both the point estimates as well as the standard errors in these types of models. We also include an option for correcting a related bias that arises in the standard errors of the standard "two-way" (origin-time and destination time fixed effects only) gravity model.
Those who are familiar with the incidental parameter problem may be thrown off by the idea that incidental parameters can pose an issue for PPML models. Usually, when PPML is discussed in this context, it is to remark on how it is unaffected by the incidental parameter problem (Wooldridge, 1999; Fernández-Val and Weidner, 2016). Indeed, even in the complex setting of a three-way fixed effects gravity model, it is noteworthy that PPML estimates are generally consistent, whereas other common alternatives (OLS, Gamma PML), are not.
At the same time, it turns out that the unique way in which the three fixed effects interact in the three-way model induces a bias in PPML estimates when the time dimension is fixed. Because the estimator is consistent, the bias may be small in absolute terms, but the worrying part is that it is always large relative to the standard error, meaning that it always poses an issue for inference even with large samples. One of the main contributions of this command is to provide researchers with a correction for this bias.
The bias is point estimates is not the only bias one should worry about. It also turns out that cluster-robust standard errors typically used for inference are themselves biased, sometimes substantially so. This latter issue is reminiscent of a similar problem that has been documented for the simpler two-way PPML gravity model (see, e.g., Egger and Staub, 2015; Jochmans, 2017; Pfaffermayr, 2019). Thus, the ppml_fe_bias package also includes options for correcting standard errors in both two-way as well as three-way gravity models.
If you are interested in learning more, there is a dedicated github with examples and more details. PPML models with two-way and three-way fixed effects are currently very popular in applied empirical work and actually a frequent topic of conversation on this message board. Thus, I hope that users who visit this site interested in learning about gravity models will find this package useful!
Regards,
Tom
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