Identification issues in models for underreported counts

In this note we study the conditions under which leading models for underreported counts are identified. In particular, we highlight a peculiar identification problem that afflicts two of the most popular models in this class.

Currency Unions in Prospect and Retrospect

We critically review the recent literature on currency unions, and discuss the methodological challenges posed by the empirical assessment of their costs and benefits. In the process, we provide evidence on the economic effects of the euro. In particular, and in contrast with estimates of the trade effect of other currency unions, we find that the impact of the euro on trade has been close to zero. After reviewing the costs and benefits, we conclude with some open questions on normative and positive aspects of the theory of currency unions, emphasizing the need for a unified welfare-based framework to weigh their costs and gains.Currency union, Integration, Exchange Rage, Trade

Quantiles for Counts

This paper studies the estimation of conditional quantiles of counts. Given the discreteness of the data, some smoothness has to be artificially imposed on the problem. The methods currently available to estimate quantiles of count data either assume that the counts result from the discretization of a continuous process, or are based on a smoothed objective function. However, these methods have several drawbacks. We show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques. The performance and implementation of the estimator are illustrated by simulations and an application.Asymmetric maximum likelihood, Jittering, Maximum score estimator, Quantile regression, Smoothing.

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

Helpman, Melitz, and Rubinstein (2008)-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. This note seeks to clarify some econometric aspects of the estimation approach used by HMR and explore the consequences of possible departures from the maintained distributional assumptions.Gravity equation, Heteroskedasticity, Jensens inequality

On the Existence of the Maximum Likelihood Estimates for Poisson Regression

We note that the existence of the maximum likelihood estimates for Poisson regression depends on the data configuration. Because standard software does not check for this problem, the practitioner may be surprised to find that in some applications estimation of the Poisson regression is unusually difficult or even impossible. More seriously, the estimation algorithm may lead to spurious maximum likelihood estimates. We identify the signs of the non-existence of the maximum likelihood estimates and propose a simple empirical strategy to single out the regressors causing this type of identification failure.Poisson estimation, gravity equation

Quantiles for Fractions and Other Mixed Data

This paper studies the estimation of quantile regression for fractional data, focusing on the case where there are mass-points at zero or/and one. More generally, we propose a simple strategy for the estimation of the conditional quantiles of data from mixed distributions, which combines standard results on the estimation of censored and Box-Cox quantile regressions. The implementation of the proposed method is illustrated using a well-known dataset.

Is it different for zeros? Discriminating between models for non-negative data with many zeros

In many economic applications, the variate of interest is non-negative and its distribution is characterized by a mass-point at zero and a long right-tail. Many regression strategies have been proposed to deal with data of this type. Although there has been a long debate in the literature on the appropriateness of different models, formal statistical tests to choose between the competing specifications, or to assess the validity of the preferred model, are not often used in practice. In this paper we propose a novel and simple regression-based specification test that can be used to test these models against each other.

Estimation of count data models with endogenous regressors; an application to demand for health care

The generalized method of moments (GMM) estimation technique is discussed for count data models with endogenous regressors. Count data models can be specified with additive or multiplicative errors. It is shown that, in general, a set of instruments is not orthogonal to both error types. Simultaneous equations with a dependent count variable often do not have a reduced form which is a simple function of the instruments. However, a simultaneous model with a count and a binary variable can only be logically consistent when the system is recursive. The GMM estimator is used in the estimation of a model explaining the number of visits to doctors, with as a possible endogenous regressor a self-reported binary health index. Further, a model is estimated, in stages, that includes latent health instead of the binary health index