J.M.C. Santos Silva

The Log of Gravity

Although economists have long been aware of Jensens inequality, many econometric applications have neglected an important implication of it: under heteroskedasticity, the parameters of log-linearized models estimated by OLS lead to biased estimates of the true elasticities. We explain why this problem arises and propose an appropriate estimator. Our criticism of conventional practices and the proposed solution extend to a broad range of applications where log-linearized equations are estimated. We develop the argument using one particular illustration, the gravity equation for trade. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method.

Taste Variation in Discrete Choice Models

This paper develops an extension of the classical multinomial logit model which approximates a class of models obtained when there is uncontrolled taste variation across agents and choices in addition to the stochastic noise inherent in the logit model. Unlike semiparametric and parametric alternatives, the extended logit model is easy to estimate even when there are many potential choices. Unlike parametric alternatives, it does not require the specification of a distribution of varying tastes. The extended logit model can give a quick indication of the impact of taste variation on estimates and it generates estimates of the covariances of the taste shifters. It can be used as an exploratory device en route to the construction of a model incorporating a particular form of random taste variation and it can be used to determine whether such effort is required at all. When the amount of taste variation is not excessive the approximate model can be adequate itself. The model nests the conventional logit model which leads to a misspecification diagnostic. A method for estimating the model using conventional logit model software is proposed, asymptotic properties of estimators are derived and an application is presented.

Trading Partners and Trading Volumes:Implementing the Helpman-Melitz-Rubinstein Model Empirically

Helpman, Melitz and Rubinstein [Quarterly Journal of Economics (2008) Vol. 123, pp. 441–487] (HMR) present a rich theoretical model to study the determinants of bilateral trade flows across countries. The model is then empirically implemented through a two-stage estimation procedure. We argue that this estimation procedure is only valid under the strong distributional assumptions maintained in the article. Statistical tests using the HMR sample, however, clearly reject such assumptions. Moreover, we perform numerical experiments which show that the HMR two-stage estimator is very sensitive to departures from the assumption of homoskedasticity. These findings cast doubts on any inference drawn from the empirical implementation of the HMR model.

The Chow-Lin method using dynamic models

Abstract This paper presents a simple way of applying the Chow and Lin (Chow, G., Lin, A., 1971. Best linear unbiased interpolation, distribution, and extrapolation of time series by related series. Rev. Econ. Stat. 53, 372–375) method for disaggregation of time series using dynamic models. This extension adds considerable flexibility to the basic approach and is particularly adequate when the series used are stationary or cointegrated. An example is used to illustrate the potential usefulness of the proposed technique.

Glejser's test revisited

Godfrey (1996, Journal of Econometrics 72, 275–299) has shown that the Glejser test for heteroskedasticity is valid only under conditional symmetry. Here, modifications of the Glejser test are suggested. The proposed test statistics are asymptotically valid even when the disturbances are not symmetrically distributed and can be used to test for heteroskedasticity when conditional location functions other than the conditional mean are estimated.

Gravity-defying trade

Heteroskedasticity and the existence of zero values in bilateral-trade data lead to significant biases in standard estimations of the gravity equation. We propose a new estimation technique that addresses these problems, and provide novel estimates of the gravity equation. Three results stand out. First, contrary to general belief, income elasticities are significantly smaller than 1, suggesting modifications to standard trade models. Second, simple estimators of the gravity equation greatly exaggerate the roles of distance and colonial links. Finally, bilateral trade between countries that have signed a free-trade agreement is 30 percent larger than that between other countries, a magnitude remarkably different from that predicted by conventional methods (above 100 percent).

Simulation-based tests for heteroskedasticity in linear regression models: Some further results

Journal of Econometrics 122 Dufour, Khalaf, Bernard and GenestAs shown by the results of Dufour, Khalaf, Bernard and Genest (2004, Journal of Econometrics 122, 317-347), exact tests for heteroskedasticity in linear regression models can be obtained, by using Monte Carlo (MC) techniques, if either (i) it is assumed that the true form of the error distribution under homoskedasticity is known, or (ii) the null hypothesis specifies both homoskedasticity and the form of the error distribution. Non-parametric bootstrap tests of homoskedasticity alone are only asymptotically valid, but do not require specification of the error law. Since information about the precise form of the error distribution is not often available to applied workers, two questions merit attention. First, if the primary purpose is to check for heteroskedasticity, how sensitive are MC tests to incorrect assumptions/claims about the error distribution? Second, what can be said about the relative merits of MC tests and non-parametric bootstrap tests? Theoretical results relevant to these two questions are derived using asymptotic analysis and evidence is provided from simulation experiments.

Generalized Poisson regression for positive count data

This paper suggests a flexible parametrization of the generalized Poisson regression, which is likely to be particularly useful when the sample is truncated at zero. Suitable specification tests for this case are also studied. The use of the models and tests suggested is illustrated with an application to the number of recreational fishing trips taken by households in Alaska

Estimation of default probabilities using incomplete contracts data

This paper develops a count data model for credit scoring which allows the estimation of default probabilities using incomplete contracts data. The main advantage of the proposed approach is that it permits a more efficient use of the data, including that for the most recent clients. Moreover, because the probability of default is specified as a function of the age of the contract, the model provides some information on the timing of the defaults. The model is based on the beta-binomial distribution, which is found to be particularly adequate for this purpose. A well-known dataset on personal loans is used to illustrate the application of the proposed model.

A Note on the Estimation of Mixture Models Under Endogenous Sampling

The main purpose of this paper is to highlight that, in the estimation of mixture models under endogenous sampling, the distribution of the unobservables can be specified either in the actual population or in the artificial population induced by the sampling method. Which of the two approaches is correct depends crucially on the population of interest. The importance of making the correct decision is illustrated with a simple application.