Statistical inference of partially linear varying coefficient spatial autoregressive models

This paper proposes a semiparametric partially linear varying coefficient spatial autoregressive model, which is a generalization of standard spatial autoregressive model and partially linear spatial autoregressive model. To estimate the unknown spatial lag parameter, constant coefficients and coefficient functions, a profile quasi-maximum likelihood approach based on the local-linear method is introduced. To test the existence of the spatial effects, a generalized likelihood ratio test statistic is proposed, and a residual-based bootstrap procedure is used to derive the p-value of the test. Some simulations are conducted to examine the performance of our proposed procedures and the results are satisfactory. Furthermore, a real-world example is given to demonstrate the application of the proposed procedures.     

Kernel-based estimation of semiparametric regression in triangular systems

We propose a kernel-based estimator for a partially linear model in triangular systems where endogenous variables appear both in the nonparametric and linear component functions. Our estimator is easy to implement, has an explicit algebraic structure, and exhibits good finite sample performance in a Monte Carlo study.     

Instrumental variables estimation with partially missing instruments

This paper shows that instrumental variables estimators currently in use, require strong but neglected auxiliary assumptions to be consistent in situations with partially missing instruments. We introduce an alternative instrumental variables estimator that does not require auxiliary assumptions.     

Weak exogeneity in partially nonstationary models

This paper is dedicated to analysing the conditions for weak exogeneity in partially nonstationary models. After adopting a particular identification regime which is based on a triangularization of the parameters of the cointegration relations, we show that the conditions for weak exogeneity developed in the literature can be stated in terms of the parameters of the so-called structural form. This alternative presentation of the conditions permits new interpretations and provides fresh insights on how to test the exogeneity hypothesis.     

An MPEC estimator for misclassification models

In this paper, we propose a constrained maximum likelihood estimator for misclassification models, by formulating the estimation as an MPEC (Mathematical Programming with Equilibrium Constraints) problem. Our approach improves the numerical accuracy and avoids the singularity problem. Monte Carlo simulations confirm that the proposed estimator reduces bias and standard deviation of the estimator, especially when the sample is small/medium and/or the dimension of latent variable is large.     

Efficient realized variance, regression coefficient, and correlation coefficient under different sampling frequencies

Efficiency of the realized variance of an asset is improved by taking advantage of another asset whose return is cross-sectionally correlated with that of the asset and is less sensitive to market microstructure noises permitting higher frequency sampling than the original asset.     

Iterative algorithm for non parametric estimation of the instrumental variables quantiles

This paper proposes a simple algorithm for the numerical computation of the non parametric IV quantile estimation. This algorithm is based on the Landweber iterations for solving a nonlinear integral equation. The paper is illustrated by numerical simulations.     

Nonparametric lag selection for nonlinear additive autoregressive models

The lag selection procedure based on the final prediction error (FPE) is investigated when the additive structure is a priori known in the nonparametric autoregression. The consistency of the lag selection is proved, followed by the finite sample simulation results.     

Lagged duration dependence in mixed proportional hazard models

We study the identification of a mixed proportional hazard model with lagged duration dependence when data provide multiple outcomes per stratum. Within strata variation is exploited to non-parametrically identify lagged duration dependence in more general models than in the literature.     

Partial identification in binary response models with nonignorable nonresponses

This study investigates the identification of parameters in semiparametric binary response models of the form y=1(x^′β+v+ε>0)$y=1(x^{\prime }\beta +v+\epsilon >0)$ when there are nonignorable nonresponses. We propose an estimation procedure for the identified set, the set of parameters that are observationally indistinguishable from the true value β$\beta$, based on the special regressor approach of Lewbel (2000). We show that the estimator for the identified set is consistent in the Hausdorff metric.     

An alternative identification of nonlinear dynamic panel data models with unobserved covariates

I provide the nonparametric identification of nonlinear dynamic panel data models. I relax the assumption of covariate evolution in Shiu and Hu (2013) by the results of Hu and Shum (2012). The assumptions include first-order Markov assumptions and a restriction on the evolution of the covariate.     

Semiparametric binary random effects models: Estimating two types of drinking behavior

I propose a new estimator for cross-section semiparametric regressions containing unobserved binary random effects and apply it to alcohol consumption. The random effects (health consciousness) explain a significant proportion of otherwise unexplained variation in alcohol consumption. Education positively correlates with health consciousness.     

Maximum likelihood estimation of search costs

In a recent paper Hong and Shum [2006. Using price distributions to estimate search costs. Rand Journal of Economics 37, 257-275] present a structural method to estimate search cost distributions. We extend their approach to the case of oligopoly and present a new maximum likelihood method to estimate search costs. We apply our method to a data set of online prices for different computer memory chips. The estimates suggest that the consumer population can be roughly split into two groups which either have quite high or quite low search costs. Search frictions confer a significant amount of market power to the firms: Despite more than 20 firms operating in each of the markets, we estimate price-cost margins to be around 25%. The paper also illustrates how the structural method can be employed to simulate the effects of the introduction of a sales tax.     

On modeling heterogeneity in linear models using trend polynomials

The primary aim of the paper is to consider the problems and issues raised when the data exhibit time heterogeneity in the context of linear models. Ignoring time heterogeneity will undermine the reliability of inference and will give rise to untrustworthy evidence. Accounting for it using trend polynomials, however, is non-trivial because it raises several modeling issues. First, when the degree of the polynomial is greater than 4, or so, one needs to deal with the near-multicollinearity problem that arises. The second issue pertains to the type of polynomial that will adequately account for the time heterogeneity. Third, when the trend polynomials are treated as additional regressors, they will give rise to highly misleading statistical results. The paper investigates how different types of polynomials could deal with the near-multicollinearity and the modeling issues they raise, and makes recommendations to practitioners.     

Maximum likelihood estimation of sum-constrained linear models with insufficient observations

A maximum likelihood procedure for estimating sum-constrained linear models is presented, which seems to provide a good balance between excessive observational requirements on the one hand and an unduly restrictive specification of the contemporaneous covariance matrix on the other.     

Are Co-integrated Stock Prices Consistent with the Efficient Market Hypothesis?

This paper responds to the unsatisfactory argument that there is no correspondence between co-integration and the efficient market hypothesis. A law of one co-integrating vector of prices is proposed for the exchange rate and domestic and overseas stock prices. Markets must therefore be efficient in long-run equilibrium because no arbitrage opportunities exist. However, arbitrage activity via the disequilibrium error correction allows above-average (risk-adjusted) returns to be earned in the short run. The elimination of these arbitrage opportunities means that stock market inefficiency in the short run ensures stock market efficiency in the long run.     

A semiparametric estimation of liquidity effects on option pricing

Abstract. This paper proposes a semiparametric option pricing model with liquidity, as proxied by the relative bid-ask spread. A nonparametric volatility function with liquidity costs as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. The SNN estimator is particularly suitable for the characteristics of option data in financial markets. Moreover, we propose a natural extension of the univariate bandwidth parameter optimal estimation to the multivariate case. A statistical design to test competing option pricing models which takes into account the lack of independence between them is also presented. The in-sample performance of the model turns out to be statistically favorable relative to the competing model without liquidity. Also, an additional experiment is performed within sample, but with just a subsample of options not employed in the nonparametric estimation of the implied volatility function being priced. The results are also favorable to our semiparametic theoretical option pricing model with liquidity. However, the out-of-sample performance is quite disappointing regardless of what option pricing model is employed in the estimation. Eva Ferreira and Gonzalo Rubio acknowledge the financial support provided by Dirección Interministerial Científica y Técnica (DGICYT) grants PB98-0149 and PB97-0621 respectively. All three authors aknowledge the financial support provided by Universidad del País Vasco (UPV/EHU) grant UPV 038.321-HA129/99, and the BSI Gamma Foundation. We appreciate the helpful comments of two anonymous referees, ángel León, José M. Campa, Fernando Tusell and Javier Fernández Navas, seminar participants at the Bank of Spain and the European Financial Management Association (Athens), and the computational assistance of Gregorio Serna. We thank Juan Ayuso and MEFF for providing the data used in this article. The contents of this paper are the sole responsability of the authors.     

Consistency and asymptotic normality for equilibrium models with partially observed outcome variables

We derive conditions under which structural econometric models that rely on numerical computation of equilibria produce consistent and asymptotically normal parameter estimates. The conditions are weaker than those required for the application of the implicit function theory.     

Coordination on saddle-path solutions: the eductive viewpoint—linear multivariate models

We examine local strong rationality (LSR) in multivariate models with both forward-looking expectations and predetermined variables. Given hypothetical common knowledge restrictions that the dynamics will be close to those of a specified minimal state variable solution, we obtain eductive stability conditions for the solution to be LSR. In the saddlepoint stable case the saddle-path solution is LSR provided the model is structurally homogeneous across agents. However, the eductive stability conditions are strictly more demanding when heterogeneity is present, as can be expected in multisectoral models. Heterogeneity is thus a potentially important source of instability even in the saddlepoint stable case.     

Testing for normality in linear regression models using regression and scale equivariant estimators

In this paper we provide a general solution to the problem of controlling the probability of a type I error in normality tests for the disturbances in linear regressions when using robust-regression residuals. We show that many classes of well-known robust regression estimators belong to the class of regression and scale equivariant estimators. It is these equivariance properties that are used to reduce the nuisance parameter space under the null, from which we develop Monte Carlo and Maximized Monte Carlo tests for the null of disturbance normality. Finally, we illustrate in a simulation experiment the potential power gains from using robust-regression residuals in testing this null hypothesis.