Tiemen Woutersen

Dynamic Time Series Binary Choice

This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.

Instrumental Variable Estimation with Heteroskedasticity and Many Instruments

It is common practice in econometrics to correct for heteroskedasticity. This paper corrects instrumental variables estimators with many instruments for heteroskedasticity. We give heteroskedasticity robust versions of the limited information maximum likelihood (LIML) and Fuller (1977, FULL) estimators; as well as heteroskedasticity consistent standard errors thereof. The estimators are based on removing the own observation terms in the numerator of the LIML variance ratio. We derive asymptotic properties of the estimators under many and many weak instruments setups. Based on a series of Monte Carlo experiments, we find that the estimators perform as well as LIML or FULL under homoskedasticity, and have much lower bias and dispersion under heteroskedasticity, in nearly all cases considered.

ASYMPTOTIC DISTRIBUTION OF JIVE IN A HETEROSKEDASTIC IV REGRESSION WITH MANY INSTRUMENTS

This paper derives the limiting distributions of alternative jackknife IV (JIV) estimators and gives formulae for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that \frac{\sqrt{K_{n}}}{n} \to \infty as n \to \infty, where K_n and r_n denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIML, B2SLS, and 2SLS, all of which are inconsistent in the presence of heteroskedasticity, unless \frac{K_n}{r_n}\to 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r_n and K_n.

The singularity of the information matrix of the mixed proportional hazard model

Elbers and Ridder (1982) identify the Mixed Proportional Hazard model by assuming that the heterogeneity has finite mean. Under this assumption, the information matrix of the MPH model may be singular. Moreover, the finite mean assumption cannot be tested. This paper proposes a new identification condition that ensures non-singularity of the information bound. This implies that there can exist estimators that converge at rate root N. As an illustration, we apply our identifying assumption to the Transformation model of Horowitz (1996). In particular, we assume that the baseline hazard is constant near t=0 but make no no parametric assumptions are imposed for other values of t. We then derive an estimator for the scale normalization that converges at rate root N.

Asymptotic Distribution of JIVE in a Heteroskedastic IV Regression with Many Instruments

[enter Abstract Body]This paper derives the limiting distributions of alternative jackknife IV (JIV ) estimators and gives formulae for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005). We show that J IV estimators are asymptotically normal; and that standard errors are consistent provided that √Kn/rn → 0, as n → ∞, where Kn and rn denote, respectively, the number of instruments and the rate of growth of the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIML, B2SLS, and 2SLS, all of which are inconsistent in the presence of heteroskedasticity, unless Kn/rn → 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on strength of the instruments as measured by the relative orders of magnitude of rn and Kn.

Identification and Estimation of Single‐Index Models with Measurement Error and Endogeneity

Economic variables are often measured with an error and may be endogenous. In this paper, we give new identification results for the ratio of partial effects in linear index models with measurement error and endogeneity. The identification restrictions include independence of covariates and error terms, and the derivative of some conditional mean functions being nonzero. We propose a local polynomial regression estimator to estimate the single‐index parameters. We apply these tools to estimate the labour‐supply elasticity and find that the labour‐supply elasticity for married men is positive, while the coefficients for married women are negative for the full sample and positive for the working sample.

The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model

We reconsider the efficiency bound for the semi-parametric Mixed Proportional Hazard (MPH) model with parametric baseline hazard and regression function. This bound was first derived by Hahn (1994). One of his results is that if the baseline hazard is Weibull, the efficiency bound is singular, even if the model is semi-parametrically identified. This implies that neither the Weibull parameter nor the regression coefficients can be estimated at the root N rate. We show that Hahns results are confined to a class of models that is closed under the power transformation. The Weibull model is the most prominent model of this class. We also present a new nonparametric identification result. This identification results allows for infinite mean of the mixing distribution and ensures that the efficiency bound is nonsingular. This implies that root N estimation is possible.

Proportional Hazard Model

The estimation of duration models has been the subject of significant research in econometrics since the late 1970s. Cox (1972) proposed the use of proportional hazard models in biostatistics and they were soon adopted for use in economics. Since Lancaster (1979), it has been recognized among economists that it is important to account for unobserved heterogeneity in models for duration data. Failure to account for unobserved heterogeneity causes the estimated hazard rate to decrease more with the duration than the hazard rate of a randomly selected member of the population. Moreover, the estimated proportional effect of explanatory variables on the population hazard rate is smaller in absolute value than that on the hazard rate of the average population member and decreases with the duration. To account for unobserved heterogeneity Lancaster proposed a parametric mixed proportional hazard (MPH) model, a partial generalization of Cox’s proportional hazard model, that specifies the hazard rate as the product of a regression function that captures the effect of observed explanatory variables, a baseline hazard that captures variation in the hazard over the spell, and a random variable that accounts for the omitted heterogeneity. In particular, Lancaster (1979) introduced the mixed proportional hazard model in which the hazard is a function of a regressor X unobserved heterogeneity v, and a function of time λ(f),

Estimating the long-run impact of microcredit programs on household income and net worth

\theta \left( {t|X,v} \right)=v{{e}^{{X{{\beta }_{0}}}}}\lambda \left( t \right).