Professor João Santos Silva

Exponential regressions are frequently used when outcomes are non-negative. They are attractive because they are easy to interpret and to estimate, using pseudo maximum likelihood (PML). However, the validity of these methods depends on the correct specification of the conditional expectation, and little is known regarding their properties when the conditional expectation is misspecified. We show that PML estimators of misspecified exponential models provide optimal approximations to the conditional expectation, in a weighted mean squared error sense, and we give conditions under which their Poisson PML estimator identifies average marginal effects.

Gravity equations are an important tool in empirical international trade research. We study to what extent sector-level parameters can be recovered from aggregate gravity equations estimated via Poisson pseudo maximum likelihood. We show that in the leading case where trade cost regressors do not vary at the sector level, estimates obtained with aggregate data have a clear interpretation as a weighted average of sectoral elasticities. Otherwise the estimates are biased but researchers may possibly infer the direction of the bias. We illustrate our results by revisiting Baier and Bergstrand's (2007) influential study of the effects of free trade agreements.

We study the conditions under which it is possible to estimate regression quantiles by estimating conditional means. The advantage of this approach is that it allows the use of methods that are only valid in the estimation of conditional means, while still providing information on how the regressors affect the entire conditional distribution. The methods we propose are not meant to replace the wellestablished quantile regression estimator, but provide an additional tool that can allow the estimation of regression quantiles in settings where otherwise that would be difficult or even impossible. We consider two settings in which our approach can be particularly useful: panel data models with individual effects and models with endogenous explanatory variables. Besides presenting the estimator and establishing the regularity conditions needed for valid inference, we perform a small simulation experiment, present two simple illustrative applications, and discuss possible extensions.

We develop a simple method for the estimation of quantile regressions for corner solutions data (i.e., fully observed non-negative data that have a mixed distribution with a mass-point at zero), focusing particular attention on the case where the domain of the variate of interest is bounded both from below and from above. We use the proposed method to study the determinants of the extensive margin of trade and Önd that most regressors have very di§erent impacts on di§erent parts of the distribution.

We study the semi-parametric estimation of the conditional mode of a random vector that has a continuous conditional joint density with a well-defined global mode. A novel full-system estimator is proposed and its asymptotic properties are studied. We specifically consider the estimation of vector autoregressive conditional mode models and of systems of linear simultaneous equations defined by mode restrictions. The proposed estimator is easy to implement and simulations suggest that it is reasonably behaved in finite samples. An empirical example illustrates the application of the proposed methods, including its use to obtain multi-step forecasts and to construct impulse response functions.

Understanding and quantifying the determinants of the number of sectors or firms exporting in a given country is of relevance for the assessment of trade policies. Estimation of models for the number of exporting sectors, however, poses a challenge because the dependent variable has both a lower and an upper bound, implying that the partial effects of the explanatory variables on the conditional mean of the dependent variable cannot be constant. We argue that ignoring these bounds can lead to erroneous conclusions and propose a flexible specification that accounts for the doubly-bounded nature of the dependent variable. We empirically investigate the problem and the proposed solution, finding significant differences between estimates obtained with the proposed estimator and those obtained with standard approaches

We review the contribution of "The Log of Gravity" (Santos Silva and Tenreyro, 2006), summarize the main results in the ensuing literature, and provide a brief review of the state-of-the-art in the estimation of gravity equations and other constant-elasticity models.

In this note we reappraise the measure of the importance of time-dependent price setting rules suggested by Klenow and Kryvtsov (2005, "State-Dependent or Time-Dependent Pricing: Does It Matter for Recent U.S. Inflation?," Bank of Canada Working Paper 05-4). Furthermore, we propose an alternative way to gauge the significance of this type of price setting behavior, which can be interpreted as an upper bound for the proportion of price trajectories which are compatible with the uniform nonsynchronization hypothesis. The merits of the proposed measure are highlighted in an application using micro-data. Our results suggest that a large proportion of price trajectories may be compatible with simple time-dependent price setting mechanisms, but the strength of this evidence very much depends on the way that is used to evaluate the importance of this type of behavior.