Estimating household consumption insurance

This paper performs a Monte Carlo study on efficient method of moments (EMM), generalized method of moments (GMM), quasi-maximum likelihood estimation (QMLE) and maximum likelihood estimation (MLE) for a continuous-time square-root model under two challenging scenarios – high persistence in mean and strong conditional volatility – that are commonly found in estimating the interest rate process. MLE turns out to be the most efficient of the four methods, but its finite sample inference and convergence rate suffer severely from approximating the likelihood function, especially in the scenario of highly persistent mean. QMLE comes second in terms of estimation efficiency, but it is the most reliable in generating inferences. GMM with lag-augmented moments has, overall, the lowest estimation efficiency, possibly due to the ad hoc choice of moment conditions. EMM shows an accelerated convergence rate in the high-volatility scenario, while its over-rejection bias in the mean persistence scenario is unacceptably large. Finally, under a stylized alternative model of the US interest rates, the overidentification test of EMM obtains the ultimate power for detecting misspecification, while the GMM J-test is increasingly biased downwards in finite samples.

GMM estimation of spatial autoregressive models with moving average disturbances

In this paper, we study the class of first order Periodic Generalized Autoregressive Conditional heteroscedasticity processes ( PGARCH ⁢ ( 1 , 1 ) {\mathrm{PGARCH}(1,1)} for short) in which the parameters in the volatility process are allowed to switch between different regimes. First, we establish necessary and sufficient conditions for a PGARCH ⁢ ( 1 , 1 ) {\mathrm{PGARCH}(1,1)} process to have a unique stationary solution (in periodic sense) and for the existence of moments of any order. Next, we are able to estimate the unknown parameters involved in model via the so-called generalized method of moments (GMM). We construct an estimator and establish its asymptotic properties. Specifically, we demonstrate its consistency and asymptotic normality. The GMM estimator in some cases can be more efficient than the least squares estimator (LSE) and the quasi maximum likelihood estimator (QMLE). Some simulation studies are also performed to highlight the impact of our theoretical results.

Two competitive analytical approaches, namely, the generalized method of moments (GMM) and quasi-maximum likelihood (QML) are widely used in statistics and econometrics literature for inferences in stochastic volatility models (SVMs). Alternative numerical approaches such as monte carlo markov chain (MCMC), simulated maximum likelihood (SML) and Bayesian approaches are also available. All these later approaches are, however, based on simulations. In this paper, we revisit the analytical estimation approaches and briefly demonstrate that the existing GMM approach is unnecessarily complicated. Also, the asymptotic properties of the likelihood approximation based QML approach are unknown and the finite sample based QML estimators can be inefficient. We then develop a precise set of moment estimating equations and demonstrate that the proposed method of moments (MM) estimators are easy to compute and they perform well in estimating the parameters of the SVMs in both small and large time series set up. A ‘working’ generalized quasi-likelihood (WGQL) estimation approach is also considered. Estimation methods are illustrated by reanalyzing a part of the Swiss-Franc and U.S. dollar exchange rates data.

A neural network demand system with heteroskedastic errors

Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators

Few estimation methods were discussed to handle the missing data problem in the panel data models. However, in the panel vector autoregressive (PVAR) model, there is no estimator to handle this problem. The traditional treatment in the case of incomplete data is to use the generalized method of moment (GMM) estimation based on only available data without imputation of the missing data. Therefore, this paper introduces a new GMM estimation for the PVAR model in case of incomplete data based on the mean imputation. Moreover, we make a Monte Carlo simulation study to study the efficiency of the proposed estimator. We compare between two GMM estimators based on the mean squared error (MSE) and relative bias (RB) criteria. The first is the GMM estimation based on the list-wise (LW) and the second is the GMM estimation using the mean imputation (MI) at multi-missing levels. The results showed that the MI estimator provides more efficiency than the LW estimator.

The method of moments is based on a relation Eθ0(h(Xt, θ)) = 0, from which an estimator of θ is deduced. In many econometric models, the moment restrictions can not be evaluated numerically due to, for instance, the presence of a latent variable. Monte Carlo simulations method make possible the evaluation of the generalized method of moments (GMM) criterion. This is the basis for the simulated method of moments. Another approach involves defining an auxiliary model and finding the value of the parameters that minimizes a criterion based either on the pseudoscore (efficient method of moments) or the difference between the pseudotrue value and the quasi-maximum likelihood estimator (indirect inference). If the auxiliary model is sufficiently rich to encompass the true model, then these two methods deliver an estimator that is asymptotically as efficient as the maximum likelihood estimator.

Assessing GMM Estimates of the Federal Reserve Reaction Function

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.

The choice of initial weighting matrix and the problem of instruments proliferation are crucial issues in generalized method of moments (GMM) estimators of dynamic panel models. In this study, we propose alternative system GMM estimators that utilize suboptimal initial weighting matrices together with reduced instruments set (specifically lag-limited and partially collapsed instruments). Comparison of the performance of the proposed estimators against the conventional estimator was undertaken in terms of bias, root mean squared error (RMSE) and coverage probabilities through Monte Carlo simulations. Our simulation results revealed that sub-optimally weighted system GMM estimator adopting partially collapsed instruments outperforms the standard GMM estimator in terms of both bias and RMSE for large T and large variance ratios as the coefficient of the lagged dependent variable gets close to zero. Under these scenarios, the system GMM estimators based on reduced instruments were also found to perform well in terms of coverage probabilities. As the process approaches a random walk, however, there is no considerable gain from the use of suboptimal initial weights matrix and reduced instruments in general.

Quasi Maximum Likelihood Estimation of Value at Risk and Expected Shortfall

We develop a class of ARCH models for series sampled at unequal time intervals set by trade orquote arrivals. Our approach combines insights from the temporal aggregation for GARCH models discussed byDrost and Nijman (1993) and Drost and Werker (1996), and the autoregressive conditional duration model ofEngle and Russell (1996) proposed to model the spacing between consecutive financial transactions.The class of models introduced here will be called ACD-GARCH. It can be described as a random coefficientGARCH, or doubly stochastic GARCH, where the durations between transactions determine the parameterdynamics. The ACD-GARCH model becomes genuinely bivariate when past asset-return volatilities are allowedto affect transaction durations, and vice versa. Otherwise, the spacings between trades are consideredexogenous to the volatility dynamics. This assumption is required in a two-step estimation procedure. Thebivariate setup enables us to test for Granger causality between volatility and intratrade durations. Undergeneral conditions, we propose several Generalized Method of Moments (GMM) estimation procedures, somehaving a Quasi Maximum Likelihood Estimation (QMLE) interpretation. As illustration, we present anempirical study of the IBM 1993 tick-by-tick data. We find some evidence that volatility of IBM stock pricesGranger-causes intratrade durations. We also find that the persistence in GARCH drops dramatically onceintratrade durations are taken into account.

This study examines the endogeneity effect on autoregressive linear models of AR (1) in small samples, making use of the Ordinary Least Square (OLS) estimator, Two-Stage Least Squares (2SLS) estimator, and Generalized Method of Moment (GMM) estimator, based on the sensitivity analysis of sample size and specification errors in estimator determination in linear regression model through the use of Monte Carlo simulation and application to real-life data. The simulation indicates that 2SLS and GMM estimators show the smallest biases when the sample size is varied from n = 10, 25, 50 to 100. The estimator that performs best when sample size n = 10 across autocorrelation (ρ) and significant correlation (α) at all levels of replication of 10,000 is GMM. In the real-life data, OLS and 2SLS exhibit higher endogeneity characteristics from the dataset used. The empirical analysis base on MSE criteria GMM is the best estimator for dealing with external shock factors to inflations embedded with endogeneity in the linear model. When endogeneity and autocorrelation are bedeviled in a linear AR (1) model, in small samples, using the GMM estimator will provide the best results in small samples than using 2SLS and OLS.

In this study, we introduce a novel approach, called the quasi maximum likelihood estimation (Q-MLE), for estimating large-dimensional matrix factor models. In contrast to the principal component analysis based approach, Q-MLE considers the heteroscedasticity of the idiosyncratic error term, the heteroscedasticity of which is simultaneously estimated with other parameters. Interestingly, under the homoscedasticity assumption of the idiosyncratic error, the Q-MLE estimator encompassed the projected estimator (PE) as a special case. We provide the convergence rates and asymptotic distributions of the Q-MLE estimators under mild conditions. Extensive numerical experiments demonstrate that the Q-MLE method performs better, especially when heteroscedasticity exists. Furthermore, two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincide with financial, economic, or geographical interpretations.