Generalized least squares and maximum likelihood estimation of the logistic function for technology diffusion

Given a simple stochastic model of technology adoption, we derive a function for technological diffusion that is logistic in the deterministic part and has an error term based on the binomial distribution. We derive two estimators—a generalized least squares (GLS) estimator and a maximum likelihood (ML) estimator—which should be more efficient than the ordinary least squares (OLS) estimators typically used to estimate technological diffusion functions. We compare the two new estimators with OLS using Monte-Carlo techniques and find that under perfect specification, GLS and ML are equally efficient and both are more efficient than OLS. There was no evidence of bias in any of the estimators. We used the estimators on some example data and found evidence suggesting that under conditions of misspecification, the estimated variance-covariance of the ML estimator is badly biased. We verified the existence of the bias with a second Monte-Carlo experiment performed with a known misspecification. In the second experiment, GLS was the most efficient estimator, followed by ML, and OLS was least efficient. We conclude that the GLS estimator of choice.     

The asymptotic efficiency of semiparametric estimators for censored linear regression models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantite, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model

This paper is concerned with the estimation of the autoregressive parameter in a widely considered spatial autocorrelation model. The typical estimator for this parameter considered in the literature is the (quasi) maximum likelihood estimator corresponding to a normal density. However, as discussed in this paper, the (quasi) maximum likelihood estimator may not be computationally feasible in many cases involving moderate- or large-sized samples. In this paper we suggest a generalized moments estimator that is computationally simple irrespective of the sample size. We provide results concerning the large and small sample properties of this estimator.     

When outcome heterogeneously matters for selection: a generalized selection correction estimator

The classical Heckman (1976, 1979) selection correction estimator (heckit) is misspecified and inconsistent, if an interaction of the outcome variable with an explanatory variable matters for selection. To address this specification problem, a full information maximum likelihood (FIML) estimator and a simple two-step estimator are developed. Monte Carlo (MC) simulations illustrate that the bias of the ordinary heckit estimator is removed by these generalized estimation procedures. Along with OLS and ordinary heckit, we apply these estimators to data from a randomized trial that evaluates the effectiveness of financial incentives for reducing obesity. Estimation results indicate that the choice of the estimation procedure clearly matters.     

Estimation of Discrete Choice Dynamic Programming Models

This study reviews estimation methods for the infinite horizon discrete choice dynamic programming models and conducts Monte Carlo experiments. We consider: the maximum likelihood estimator (MLE), the two‐step conditional choice probabilities estimator, sequential estimators based on policy iterations mapping under finite dependence, and sequential estimators based on value iteration mappings. Our simulation result shows that the estimation performance of the sequential estimators based on policy iterations and value iteration mappings is largely comparable to the MLE, while they achieve substantial computation gains over the MLE by a factor of 100 for a model with a moderately large state space.     

Some simulation studies of nonparametric estimators

This paper constructs a number of Monte Carlo studies to assess the quality of various nonparametric estimators that have been proposed recently for the estimation of nonlinear econometric models. We consider both kernel and Fourier series based methods of estimation, and also examine techniques that have been suggested to improve the bias properties of the kernel estimator. The two models examined are a production function and a model emphasising the effects of risk. The Fourier estimator does very well in estimating the first of these, but not the second, while the kernel estimator shows substantial bias for the first, which is only partially alleviated by the procedures advocated for bias correction, and good results for the second.     

On Calculation of the Extended Gini Coefficient

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.     

The Box-Cox transformation-of-variables in regression

The application of the Box-Cox transformation to the dependent and independent variables is discussed. Maximum likelihood and iterative GLS estimators are used and bootstrapping is carried out to compare the bootstrap sample variability with the finite sample variability (RMSE) and improve RMSE estimation. The biases of parameter estimators were shown to be substantial in small samples. The standard errors obtained from the Hessian matrix were a poor measure of the finite sample variability. Thet-ratios of the linear parameter estimators may not be normally distributed in small samples.The authors acknowledge the helpful comments of two referees.     

Asymptotic Properties Of The Estimator Of The Long-Run Coefficient In A Dynamic Model With Integrated Regressors And Serially Correlated Errors

In this paper we examine the asymptotic properties of the estimator of the long-run coefficient (LRC) in a dynamic regression model with integrated regressors and serially correlated errors. We show that the OLS estimators of the regression coefficients are inconsistent but the OLS-based estimator of the LRC is superconsistent. Furthermore, we propose an alternative consistent estimator of the LRC, compare the two estimators through a Monte Carlo experiment, and find that the proposed estimator is MSE-superior to the OLS-based estimator.     

Bias correcting adjustment coefficients in a cointegrated VAR with known cointegrating vectors

The maximum likelihood estimator of the adjustment coefficient in a cointegrated vector autoregressive model (CVAR) is generally biased. For the case where the cointegrating vector is known in a first-order CVAR with no intercept, we derive a condition for the unbiasedness of the maximum likelihood estimator of the adjustment coefficients, and provide a simple characterization of the bias in case this condition is violated. A feasible bias correction method is shown to virtually eliminate the bias over a large part of the parameter space.     

Robust estimation of the simplified multivariate GARCH model

In this paper, robust M-estimation of multivariate GARCH models are considered. The simplified GARCH model is chosen that involves the estimation of only univariate GARCH models, and hence easy to estimate, and does not put additional constraints on the model. The results of Monte Carlo simulations showed that accurate estimates of conditional correlations can be obtained using these robust estimators when the errors are heavy-tailed. We also investigate the forecasting performance of the class of robust estimators in predicting value-at-risk using various evaluation measures and collect empirical evidences of the better predictive potential of estimators such as LAD and B-estimator over the widely-used quasi-maximum likelihood estimator for the estimation and prediction of multivariate GARCH models. Applications to real data sets are also presented.     

A Comparison of Alternative Non-parametric Estimators of the Short Rate Diffusion Coefficient

In this paper we discuss the estimation of the diffusion coefficient in one-factor models for the short rate via non-parametric methods. We test the estimators proposed by Ait-Sahalia (1996) , Stanton (1997) and Bandi and Phillips (2003) on Monte Carlo simulations of the Vasicek and CIR model. We show that the Ait-Sahalia estimator is not applicable for values of the mean reversion coefficient typically displayed by interest rate data, while the Stanton and Bandi–Phillips estimators perform better. Each of the three estimators depends crucially on the choice of the bandwidth parameter. Our analysis shows that the estimators give different results for both the data set analysed by Ait-Sahalia (1996) and by Stanton (1997) . Finally we show that the data sets used by Ait-Sahalia and Stanton are inherently different and, in particular, that very short-term data exhibit characteristics which are inconsistent with a diffusion.     

On the estimation and forecasting of international migration: how relevant is heterogeneity across countries?

This paper performs a comparative analysis of estimation as well as of out-of-sample forecasting results of more than 20 estimators common in the panel data literature using the data on migration to Germany from 18 source countries in the period 1967–2001. Our results suggest that the choice of an estimation procedure has a substantial impact on the parameter estimates of the migration function. Out-of-sample forecasting results indicate the following: (1) the standard fixed effects estimators clearly outperforms the pooled OLS estimator, (2) both the fixed effects estimators and the hierarchical Bayes estimator exhibit the superior forecast performance, (3) the fixed effects estimators outperform GMM and other instrumental variables estimators, (4) forecasting performance of heterogenous estimators is mediocre in our data set.     

Estimating average economic growth in time series data with persistency

This paper studies estimation of average economic growth in time series models with persistency. In particular, a joint estimation of the trend coefficient and the autoregressive parameter is considered. An analysis on the proposed estimator is provided. Our analysis is also extended to the case with general disturbance distributions. A nonlinear M estimator and a class of partially adaptive M estimators which adapt themselves with respect to a measure of the tailthickness are considered. The joint estimator and its partially adapted version are compared with several conventional estimators. Monte Carlo experiments indicate that the proposed estimators have good finite sample performance. We use the proposed estimation procedure to estimate the growth rates for real GNP and consumer price index in 40 countries.     

Testing of the mean reversion parameter in continuous time models

In this paper we use the approximate bias expressions developed in Yu (2012) and Bao et al. (2013) to improve the testing of the ordinary least squares or quasi-maximum likelihood estimator of the mean reversion parameter in continuous time models. We follow the approach given in Iglesias and Phillips (2005) and Chambers (2013), where if we bias correct the estimated mean reversion parameter, we can improve on the small sample properties of the testing procedure. Simulation results confirm the usefulness of this approach using a t$t$-statistic in this setting in the near unit root situation when the mean reversion parameter is approaching its lower bound. Therefore we always recommend bias correcting when applying a t$t$-statistic in practice in this context.     

Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models

This paper considers estimation of the parameters for the fractionally integrated class of processes known as ARFIMA. We consider the small sample properties of a conditional sum-of-squares estimator that is asymptotically equivalent to MLE. This estimator has the advantage of being relatively simple and can estimate all the parameters, including the mean, simultaneously. The simulation evidence we present indicates that estimation of the mean can make a considerable difference to the small sample bias and MSE of the other parameter estimates.     

A comparison of bias approximations for the two-stage least squares (2SLS) estimator

We consider the bias of the two-stage least squares (2SLS) estimator in linear instrumental variable regression with only one endogenous regressor. By using asymptotic expansion techniques, we approximate the 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.     

State Dependence in Welfare Benefits in a Non-Welfare Context

This study investigates state dependence in social assistance benefits in Turkey, where benefit receipt and persistence rates have significantly increased over the past decade. We estimate state dependence through dynamic random-effects probit models, controlling for observed and unobserved heterogeneity, and endogenous initial conditions. In particular, we employ Wooldridge’s estimator to achieve consistent and correct estimates of state dependence and compare the results with estimates from Heckman’s reduced-form approach as a sensitivity check. Both estimators enable us to disentangle true state dependence from its spurious components and address the potential bias due to the short panel length. Our results suggest that the receipt of benefits in the last year increases the likelihood of benefit receipt in the current year, namely the structural state dependence, by 17.2–19.5 percentage points.