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We discuss a class of copula-based ordered probit models with endogenous switching. Such models can be useful for the analysis of self-selection in subjective well-being equations in general, and job satisfaction in particular, where assignment of regressors may be endogenous rather than random, resulting from individual maximization of well-being. In an application to public and private sector job satisfaction, and using data on male workers from the German Socio-Economic Panel for 2004, and using two alternative copula functions for dependence, we find consistent evidence for endogenous sector selection.

We propose a quasi–maximum likelihood estimator for the location parameters of a linear regression model with bounded and symmetrically distributed errors. The error outcomes are restated as the convex combination of the bounds, and we use the method of maximum entropy to derive the quasi–log likelihood function. Under the stated model assumptions, we show that the proposed estimator is unbiased, consistent, and asymptotically normal. We then conduct a series of Monte Carlo exercises designed to illustrate the sampling properties of the quasi–maximum likelihood estimator relative to the least squares estimator. Although the least squares estimator has smaller quadratic risk under normal and skewed error processes, the proposed QML estimator dominates least squares for the bounded and symmetric error distribution considered in this paper.

In this chapter, we use the minimum cross-entropy method to derive an approximate joint probability model for a multivariate economic process based on limited information about the marginal quasi-density functions and the joint moment conditions. The modeling approach is related to joint probability models derived from copula functions, but we note that the entropy approach has some practical advantages over copula-based models. Under suitable regularity conditions, the quasi-maximum likelihood estimator (QMLE) of the model parameters is consistent and asymptotically normal. We demonstrate the procedure with an application to the joint probability model of trading volume and price variability for the Chicago Board of Trade soybean futures contract.

The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and misspecification-robust alternative to the quasi-maximum likelihood estimator (QMLE). In this paper we investigate the asymptotic behavior of the VTE when the stationary distribution of the GARCH process has infinite fourth moment. Existing studies of historical asset returns indicate that this may be a case of empirical relevance. Under suitable technical conditions, we establish a stable limit theory for the VTE, with the rate of convergence determined by the tails of the stationary distribution. This rate is slower than that achieved by the QMLE. The limit distribution of the VTE is nondegenerate but singular. We investigate the use of subsampling techniques for inference, but find that finite sample performance is poor in empirically relevant scenarios.

The authors consider the quasi maximum likelihood (MLE) estimation of dynamic panel models with interactive effects based on the Ahn et al. (2001, 2013) quasi-differencing methods to remove the interactive effects. The authors show that the quasi-difference MLE (QDMLE) over time is inconsistent when N→∞ whether T is fixed or goes to infinity. On the other hand, the QDMLE is consistent and asymptotically unbiased if the difference is taken over individuals when T is large whether N is fixed or large. Monte Carlo studies are conducted to compare the performance of the QDMLE using different quasi-difference methods.

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

In this chapter, the authors contribute toward building a better understanding of farmers’ responses to behavioral drivers of land-use decision by establishing an alternative analytical procedure, which can overcome various drawbacks suffered by methods currently used in existing studies. Firstly, our procedure makes use of spatially high-resolution data, so that idiosyncratic effects of physical environment drivers, e.g., soil textures, can be explicitly modeled. Secondly, we address the well-known censored data problem, which often hinders a successful analysis of land-use shares. Thirdly, we incorporate spatial error dependence (SED) and heterogeneity in order to obtain efficiency gain and a more accurate formulation of variances for the parameter estimates. Finally, the authors reduce the computational burden and improve estimation accuracy by introducing an alternative generalized method of moments (GMM)–quasi maximum likelihood (QML) hybrid estimation procedure. The authors apply the newly proposed procedure to spatially high-resolution data in England and found that, by taking these features into consideration, the authors are able to formulate conclusions about causal effects of climatic and physical environment, and environmental policy on land-use shares that differ significantly from those made based on methods that are currently used in the literature. Moreover, the authors show that our method enables derivation of a more effective predictor of the land-use shares, which is utterly useful from the policy-making point of view.

This chapter proposes M-estimators of a fractional response model with an endogenous count variable under the presence of time-constant unobserved heterogeneity. To address the endogeneity of the right-hand-side count variable, I use instrumental variables and a two-step procedure estimation approach. Two methods of estimation are employed: quasi-maximum likelihood (QML) and nonlinear least squares (NLS). Using these methods, I estimate the average partial effects, which are shown to be comparable across linear and nonlinear models. Monte Carlo simulations verify that the QML and NLS estimators perform better than other standard estimators. For illustration, these estimators are used in a model of female labor supply with an endogenous number of children. The results show that the marginal reduction in women's working hours per week is less as women have one additional kid. In addition, the effect of the number of children on the fraction of hours that a woman spends working per week is statistically significant and more significant than the estimates in all other linear and nonlinear models considered in the chapter.

It is shown in Chou (2005). Journal of Money, Credit and Banking, 37, 561–582that the range can be used as a measure of volatility and the conditional autoregressive range (CARR) model performs better than generalized auto regressive conditional heteroskedasticity (GARCH) in forecasting volatilities of S&P 500 stock index. In this paper, we allow separate dynamic structures for the upward and downward ranges of asset prices to account for asymmetric behaviors in the financial market. The types of asymmetry include the trending behavior, weekday seasonality, interaction of the first two conditional moments via leverage effects, risk premiums, and volatility feedbacks. The return of the open to the max of the period is used as a measure of the upward and the downward range is defined likewise. We use the quasi-maximum likelihood estimation (QMLE) for parameter estimation. Empirical results using S&P 500 daily and weekly frequencies provide consistent evidences supporting the asymmetry in the US stock market over the period 1962/01/01–2000/08/25. The asymmetric range model also provides sharper volatility forecasts than the symmetric range model.