GMM estimation of panel data models with time-varying slope coefficients

A difference/system generalized method of moments (GMM) model that imposes time-constant coefficients is common in empirical studies using panel data. However, a rejection by the Sargan–Hansen test is sometimes a serious concern for researchers. We highlight the fact that the Sargan–Hansen test for GMM estimators applied to panel data is a joint test of valid orthogonality conditions and coefficient stability over time. A possible reason for a rejection is therefore that the slope coefficients vary over time. One solution is to estimate an empirical model in which the coefficients are time specific. We apply this solution to the system GMM estimator of simple nondynamic Cobb–Douglas production functions for a selection of Swedish industries and find that relaxing the assumption of constant slope coefficients results in more satisfactory outcomes of the Sargan–Hansen test.     

Efficient parameter estimation for independent and INAR(1) negative binomial samples

We consider moment based estimation methods for estimating parameters of the negative binomial distribution that are almost as efficient as maximum likelihood estimation and far superior to the celebrated zero term method and the standard method of moments estimator. Maximum likelihood estimators are difficult to compute for dependent samples such as samples generated from the negative binomial first-order autoregressive integer-valued processes. The power method of estimation is suggested as an alternative to maximum likelihood estimation for such samples and a comparison is made of the asymptotic normalized variance between the power method, method of moments and zero term method estimators.     

Hedge fund return higher moments over the business cycle

We investigate how macroeconomic and financial uncertainty impacts the behavior of hedge fund strategy higher moments—i.e., co-skewness and co-kurtosis—and their respective cross-sectional dispersions. Consistent with theoretical models, we find that strategy managers trade off these two higher moments when building optimal portfolios. Moreover, these trade-offs depend on the kind of strategy. Our experiments show that the VIX and its conditional variance are the most important factors affecting higher moment risk in the hedge fund industry. They also reveal that the behavior of hedge fund strategies is very asymmetric depending on the phase of the business cycle. In contrast to studies which rely on the mean-variance setting, we find that systemic risk—as measured by the cross-sectional dispersions of higher moments—tends to decrease in the low regime. The indicators of market volatility play a decisive role to explain this decline in systemic risk.     

A Simulation Approach to Nonparametric Empirical Bayes Analysis

We deal with general mixture of hierarchical models of the form m(x) = f_øf(x |θ) g (θ)dθ , where g(θ) and m(x) are called mixing and mixed or compound densities respectively, and θ is called the mixing parameter. The usual statistical application of these models emerges when we have data x_i, i = 1,…,n with densities f(x_i|θ_i) for given θ_i, and the θ₁ are independent with common density g(θ) . For a certain well known class of densities f(x |θ) , we present a sample-based approach to reconstruct g(θ) . We first provide theoretical results and then we use, in an empirical Bayes spirit, the first four moments of the data to estimate the first four moments of g(θ) . By using sampling techniques we proceed in a fully Bayesian fashion to obtain any posterior summaries of interest. Simulations which investigate the operating characteristics of our proposed methodology are presented. We illustrate our approach using data from mixed Poisson and mixed exponential densities.     

Constructing Fama–French Factors from Style Indices: Evidence from the Islamic Equity Market

This study has contributed to the analysis of the Fama–French three-factor model by proving the validity of model using the newly constructed Fama–French factors from Malaysian Islamic stock market. With generalized method of moments and robustness tests, our results compliment earlier studies by comparing the results over two sub-periods, before and after the financial crises and the fall of Lehman Bros. The results of the analysis suggest that the reversal of size effects exists after periods of financial crisis. This is the first attempt to create FF factors and test the model from Islamic equity style indices.     

On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

In this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo is considered. We study a generalization of the Gerber–Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin; and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure, where the claim severities follow a combination of exponentials, is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.     

Covariance of discounted compound renewal sums with a stochastic interest rate

Formulas have been obtained for the moments of the discounted aggregate claims process, for a constant instantaneous interest rate, and for a claims number process that is an ordinary or a delayed renewal process. In this paper, we present explicit formulas on the first two moments and the joint moment of this risk process, for a non-trivial extension to a stochastic instantaneous interest rate. Examples are given for Erlang claims number processes, and for the Ho–Lee–Merton and the Vasicek interest rate models.     

Nonparametric estimation of variance, skewness and kurtosis of the distribution of a statistic by jackknife and bootstrap techniques

While jackknife and bootstrap estimates of the variance of a statistic are well–known, the author extends these nonparametric maximum likelihood techniques to the estimation of skewness and kurtosis. In addition to the usual negative jackknife also a positive jackknife as proposed by BERAN (1984) receives interest in this work. The performance of the methods is investigated by a Monte Carlo study for Kendall's tau in various situations likely to occur in practice. Possible applications of these developments are discussed.     

On the strong uniform consistency of a new kernel density estimator

Summary A new multivariate kernel probability density estimator is introduced and its strong uniform consistency is proved under certain regularity conditions. This result is then applied particularly to a kernel estimator whose mean vector and covariance matrix areμ _n andV _n, respectively, whereμ _n is an unspecified estimator of the mean vector andV _n, up to a multiplicative constant, the sample covariance matrix of the probability density to be estimated, respectively. Work supported by the Natural Sciences and Engineering Research Council of Canada and by the Fonds F.C.A.R. of the Province of Quebec.