Time and causality: A Monte Carlo assessment of the timing-of-events approach

We present new Monte Carlo evidence regarding the feasibility of separating causality from selection within non-experimental duration data, by means of the non-parametric maximum likelihood estimator (NPMLE). Key findings are: (i) the NPMLE is extremely reliable, and it accurately separates the causal effects of treatment and duration dependence from sorting effects, almost regardless of the true unobserved heterogeneity distribution; (ii) the NPMLE is normally distributed, and standard errors can be computed directly from the optimally selected model; and (iii) unjustified restrictions on the heterogeneity distribution, e.g., in terms of a pre-specified number of support points, may cause substantial bias.     

A heteroscedasticity-consistent covariance matrix estimator for time series regressions

This paper provides a covariance matrix estimator for the ordinary least squares coefficients of a linear time series model which is consistent even when the disturbances are heteroscedastic. This estimator does not require a formal model of the heteroscedasticity. One can also obtain a direct test of heteroscedasticity, although Monte Carlo experiments show that it may have low power.     

Shrinkage estimation of semiparametric multiplicative error models

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data or the recently proposed Focused Information Criterion. We illustrate such a methodology using a semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into their dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that, from the forecasting perspective, an appropriate shrinkage strategy can significantly improve on the baseline maximum likelihood estimation.     

Bayesian limited-information analysis of nonlinear simultaneous equations systems

This paper presents a Bayesian limited-information estimation method that can be used to estimate a single nonlinear equation that forms part of a system of simultaneous equations. The method can be looked upon as the Bayesian counterpart of Amemiya's nonlinear limited-information maximum-likelihood estimator as well as a generalization of Drèze's Bayesian limited-information estimator for linear simultaneous equations systems. The method is illustrated by applying it to the problem of estimating a CES-production function which forms part of a complete model of firm behavior.     

Model selection for hazard rate estimation in presence of censoring

This note presents an estimator of the hazard rate function based on right censored data. A collection of estimators is built from a regression-type contrast, in a general collection of linear models. Then, a penalised model selection procedure provides an estimator which satisfies an oracle inequality. In particular, we can prove that it is adaptive in the minimax sense on Hölder spaces.     

Semiparametric Estimation of a Duration Model

Within the framework of the proportional hazard model proposed in Cox (1972), Han and Hausman (1990) consider the logarithm of the integrated baseline hazard function as constant in each time period. We, however, proposed an alternative semiparametric estimator of the parameters of the covariate part. The estimator is considered as semiparametric since no prespecified functional form for the error terms (or certain convolution) is needed. This estimator, proposed in Lewbel (2000) in another context, shows at least four advantages. The distribution of the latent variable error is unknown and may be related to the regressors. It takes into account censored observations, it allows for heterogeneity of unknown form and it is quite easy to implement since the estimator does not require numerical searches. Using the Spanish Labour Force Survey, we compare empirically the results of estimating several alternative models, basically on the estimator proposed in Han and Hausman (1990) and our semiparametric estimator.     

A semiparametric model for binary response and continuous outcomes under index heteroscedasticity

This paper formulates a likelihood‐based estimator for a double‐index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double‐index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the ‘mean response’. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government‐financed school. Copyright © 2009 John Wiley & Sons, Ltd.     

On the Lp error of the Grenander-type estimator in the Cox model

We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for L_p-error of the Grenander-type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the L_p-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.     

Learning in a multilateral bargaining experiment

This paper analyzes data from an investigation of a majoritarian bargaining experiment. A learning model is proposed to account for the evolution of play in this experiment. It is also suggested that an adjustment must be made to account for the panel structure of the data. Such adjustments have been used in other fields and are known to be important as unadjusted standard errors may be severely biased downward. These results indicate that this adjustment also has an important effect in this application. Furthermore, an efficient estimator that takes into account heterogeneity across players is proposed. A unique learning model to account for the paths of play under two different amendment rules cannot be rejected with the standard estimator with adjusted standard errors, however it can be rejected using the efficient estimator. The data and the estimated learning model suggest that after proposing “fair” divisions, subjects adapt and their proposals change rapidly in the treatment where uneven proposals are almost always accepted. Their beliefs in the estimated learning model are influenced by more than just the most recent outcomes.     

A comparison of the Amemiya GLS and the Lee-Maddala-Trost G2SLS in a simultaneous-equations Tobit model

This paper proposes a class of GLS estimators for the structural parameters of a simultaneous-equations Tobit model and shows that this class contains an estimator which is asymptotically more efficient than an alternative estimator proposed by Lee, Maddala and Trost in 1980.     

THE ROLE OF CONDITIONAL HETEROSKEDASTICITY IN IDENTIFYING AND ESTIMATING LINEAR TRIANGULAR SYSTEMS,WITH APPLICATIONS TO ASSET PRICING MODELS THAT INCLUDE A MISMEASURED FACTOR

A new estimator is proposed for linear triangular systems, where identification results from the model errors following a bivariate and diagonal GARCH(1,1) process with potentially time‐varying error covariances. This estimator applies when traditional instruments are unavailable. I demonstrate its usefulness on asset pricing models like the capital asset pricing model and Fama–French three‐factor model. In the context of a standard two‐pass cross‐sectional regression approach, this estimator improves the pricing performance of both models. Set identification bounds and an associated estimator are also provided for cases where the conditions supporting point identification fail. Copyright © 2013 John Wiley & Sons, Ltd.     

Autocorrelation and Bias in Short Time Series: An Alternative Estimator

The conventional first-order autocorrelationcoefficient r₁ generates an empiricalbias when it is applied to short time series.The properties of this estimator have beenexamined with a Monte Carlo simulation studyusing the MATLAB program (version5.2). This study also analyzes the functionof the empirical bias with the polynomicregression and derives a polynomic fittingmodel for different sample sizes. In thisway, a new estimator that has been correctedby the absolute value of the fitting model(r_1') is proposed. Having analyzed thestatistical properties of the estimator r_1',it is shown that the empirical bias generatedby r_1' is less in relationship to r₁ andr₁₊. The results of the study make itpossible to verify that the mean squared errorassociated to the estimator r₁ isless than that of r₁. Thus, the coefficient r_1'is recommended to estimate the lag-oneautocorrelation coefficient in samples under 50observations.     

Optimality of least squares in the seemingly unrelated regression equation model

In this article the authors have investigated the situations in which the single-equation least squares estimator is identical with the generalized least squares estimator in the seemingly unrelated regression model. The condition obtained turned out to be advantageous from an empirical point of view as it permits one to decide whether to go for a single-equation least squares method or Zellner's method with estimated disturbance variance covariance matrix for estimating the coefficients in the model.     

Repeated substitution method: The ratio estimator for the population variance

This paper proposes a new unbiased estimator for the population variance in finite population sample surveys using auxiliary information. This estimator has a smaller mean squared error than the conventional unbiased estimator, the ratio estimator established by Isaki (1983) and it has the same precision than the regression estimator. Furthermore, it is a much more interesting estimator from the computation viewpoint.     

Sampling with probabilities proportional to the variable of interest

To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a good estimator.
The paper places this problem against a theoretical background. Sampling with unequal probabilities is considered in a general context. The special case that the sampling probabilities are a function of the variable under investigation, is discussed in detail. As a better estimator the harmonic mean of the observations is presented. Most properties of this estimator are difficult to derive analytically, but a suitable variance estimator is derived. The behavior of estimator and variance estimator is studied in a number of quite different examples.     

On the relative efficiency of estimators which include the initial observations in the estimation of seemingly unrelated regressions with first-order autoregressive disturbances

The generalized least squares estimator for a seemingly unrelated regressions model with first-order vector autoregressive disturbances is outlined, and its efficiency is compared with that of an approximate generalized least squares estimator which ignores the first observation. A scalar index for the loss of efficiency is developed and applied to a special case where the matrix of autoregressive parameters is diagonal and the regressors are smooth. Also, for a more general model, a Monte Carlo study is used to investigate the relative efficiencies of various estimators. The results suggest that Maeshiro (1980) has overstated the case for the exact generalized least squares estimator, because, in many circumstances, it is only marginally better than the approximate generalized least squares estimator.     

Calibration methods for estimating quantiles

We propose a calibrated estimator of the quantiles of sample survey data and discuss the asymptotic theory behind it. This estimator is defined for any sampling design and uses the information available on J auxiliary variables. A simulation study based on a real population is used to compare the estimator with various methods proposed previously.     

On a two-step estimation of a multivariate logit model

In this article the author studies the properties of the two-step estimation method proposed by Domencich and McFadden (Urban Travel Demand, North-Holland, 1975) for a multivariate logit model and shows that it is consistent but asymptotically less efficient than the maximum likelihood estimator. Its computation, however, can be considerably simpler than that of the maximum likelihood estimator, especially in models involving several dependent variables.     

A finite sample correction for the variance of linear efficient two-step GMM estimators

Monte Carlo studies have shown that estimated asymptotic standard errors of the efficient two-step generalized method of moments (GMM) estimator can be severely downward biased in small samples. The weight matrix used in the calculation of the efficient two-step GMM estimator is based on initial consistent parameter estimates. In this paper it is shown that the extra variation due to the presence of these estimated parameters in the weight matrix accounts for much of the difference between the finite sample and the usual asymptotic variance of the two-step GMM estimator, when the moment conditions used are linear in the parameters. This difference can be estimated, resulting in a finite sample corrected estimate of the variance. In a Monte Carlo study of a panel data model it is shown that the corrected variance estimate approximates the finite sample variance well, leading to more accurate inference.