A Comparison of Alternative Methods to Model Endogeneity in Count Models. An Application to the Demand for Health Care and Health Insurance Choice.

Several estimators have been suggested to tackle the problem of endogenous regressors and selectivity in count regression models. They differ in the structure and the degree of parametrization of the underlying models. The estimation of health services utilization conditional on the choice of different forms of health insurance provides a classical example of such problems. In Switzerland, basic health insurance is mandatory and each individual is insured separately. The insurance premium varies by region of residence but is independent of income and risk. The insured face a minimal annual deductible for ambulatory health services. Annually, they are given a choice of higher deductibles to reduce their insurance premium by a regulated percentage. The choice of a higher deductible sets incentives for a more cautious utilization of health services. Clearly, the choice is made based on expected health service utilization. The effect of the choice of a higher than the minimal deductible on the number of physician visits is analyzed. A matching estimator, a GMM estimator, two-stage method of moments estimators which account for selectivity and endogenous switching count regression models are applied to data from the 1997 Swiss Health Survey. Incentive-induced behavioral changes are disentangled from selection effects. The main finding is that most of the observed lower utilization for individuals with a high insurance deductible is caused by self- selection of individuals into the respective insurance contracts which either differ in their preferences or are healthier in unobserved aspects of their health status.demand for health care and insurance, count models, endogenous regressors

Semi-nonparametric count data estimation with an endogenous binary variable

This paper proposes a semi-nonparametric Poisson model with an endogenous binary variable, which generalizes bivariate correlated unobserved heterogeneity using Hermite polynomials, and compares this model with a parametric one. The National Health Interview Survey (NHIS) data from 1990 shows the difference between the endogenous binary variable's coefficients of the semi-nonparametric and parametric models.Endogenous switching

COUNTS WITH AN ENDOGENOUS BINARY REGRESSOR: A SERIES EXPANSION APPROACH

We propose an estimator for count data regression models where a binary regressor is endogenously determined. This estimator departs from previous approaches by using a flexible form for the conditional probability function of the counts. Using a Monte Carlo experiment we show that our estimator improves the fit and provides a more reliable estimate of the impact of regressors on the count when compared to alternatives which do restrict the mean to be linear-exponential. In an application to the number of trips by households in the US, we find that the estimate of the treatment effect obtained is considerably different from the one obtained under a linear-exponential mean specification.Count data, Polynominal Poisson Expansions, Flexible Functional Form.

Extracting information from S-curves of language change

It is well accepted that adoption of innovations are described by S-curves (slow start, accelerating period, and slow end). In this paper, we analyze how much information on the dynamics of innovation spreading can be obtained from a quantitative description of S-curves. We focus on the adoption of linguistic innovations for which detailed databases of written texts from the last 200 years allow for an unprecedented statistical precision. Combining data analysis with simulations of simple models (e.g., the Bass dynamics on complex networks) we identify signatures of endogenous and exogenous factors in the S-curves of adoption. We propose a measure to quantify the strength of these factors and three different methods to estimate it from S-curves. We obtain cases in which the exogenous factors are dominant (in the adoption of German orthographic reforms and of one irregular verb) and cases in which endogenous factors are dominant (in the adoption of conventions for romanization of Russian names and in the regularization of most studied verbs). These results show that the shape of S-curve is not universal and contains information on the adoption mechanism. (published at "J. R. Soc. Interface, vol. 11, no. 101, (2014) 1044"; DOI: http://dx.doi.org/10.1098/rsif.2014.1044)Comment: 9 pages, 5 figures, Supplementary Material is available at http://dx.doi.org/10.6084/m9.figshare.122178

Testing exogeneity of multinomial regressors in count data models: does two stage residual inclusion work?

We study a simple exogeneity test in count data models with possibly endogenous multinomial treatment. The test is based on Two Stage Residual Inclusion (2SRI). Results from a broad Monte Carlo study provide novel evidence on important features of this approach in nonlinear settings. We find differences in the finite sample performance of various likelihood-based tests under correct specification and when the outcome equation is misspecified due to neglected over-dispersion or non-linearity. We compare alternative 2SRI procedures and uncover that standardizing the variance of the first stage residuals leads to higher power of the test and reduces the bias of the treatment coefficients. An original application in health economics corroborates our findings

Estimating average partial effects under conditional moment independence assumptions

I show how to identify and estimate the average partial effect of explanatory variables in a model where unobserved heterogeneity interacts with the explanatory variables and may be unconditionally correlated with the explanatory variables. To identify the populationaveraged effects, I use extensions of ignorability assumptions that are used for estimating linear models with additive heterogeneity and for estimating average treatment effects. New stimators are obtained for estimating the unconditional average partial effect as well as the average partial effect conditional on functions of observed covariates.

Count Data Models with Unobserved Heterogeneity: An Empirical Likelihood Approach

As previously argued, the correlation between included and omitted regressors generally causes inconsistency of standard estimators for count data models. Using a specific residual function and suitable instruments, a consistent generalized method of moments estimator can be obtained under conditional moment restrictions. This approach is extended here by fully exploiting the model assumptions and thereby improving efficiency of the resulting estimator. Empirical likelihood estimation in particular has favorable properties in this setting compared to the two-step GMM procedure, which is demonstrated in a Monte Carlo experiment. The proposed method is applied to the estimation of a cigarette demand function.nonparametric likelihood, poisson model, nonlinear instrumental variables, optimal instruments, approximating functions, semiparametric efficiency

Consistent estimation of zero-inflated count models

Applications of zero-inflated count data models have proliferated in health economics. However, zero-inflated Poisson or zero-inflated negative binomial maximum likelihood estimators are not robust to misspecification. This paper proposes Poisson quasi-likelihood estimators as an alternative. These estimators are consistent in the presence of excess zeros without having to specify the full distribution. The advantages of the Poisson quasi-likelihood approach are illustrated in a series of Monte Carlo simulations and in an application to the demand for health services.Excess zeros, Poisson, logit, unobserved heterogeneity, misspecification

Coherency and regularity of demand systems with equality and inequality constraints

Consumption Function