Beta trigonometric distributions

Beta distributions are popular models for economic data. In this paper, six new distributions are introduced which generalize the standard beta distribution. These distributions involve the trigonometric functions, sine and cosine. Expressions are derived for their analytical shapes, nth moments, method of moments estimators, maximum likelihood estimators and the associated Fisher information matrices. These calculations involve several special functions. A numerical study is performed to show the flexility of these distributions as compared to the standard beta distribution. An application to consumer expenditure data is illustrated to show that the proposed distributions are better models to economic data than one based on the standard beta distribution. Possible ways of extending the models are also discussed.     

Estimating average economic growth in time series data with persistency

This paper studies estimation of average economic growth in time series models with persistency. In particular, a joint estimation of the trend coefficient and the autoregressive parameter is considered. An analysis on the proposed estimator is provided. Our analysis is also extended to the case with general disturbance distributions. A nonlinear M estimator and a class of partially adaptive M estimators which adapt themselves with respect to a measure of the tailthickness are considered. The joint estimator and its partially adapted version are compared with several conventional estimators. Monte Carlo experiments indicate that the proposed estimators have good finite sample performance. We use the proposed estimation procedure to estimate the growth rates for real GNP and consumer price index in 40 countries.     

Estimation of Dynamic Panel Data Sample Selection Models

This paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule, when the latent equations contain strictly exogenous variables, lags of the dependent variables, and unobserved individual effects. We derive a set of conditional moment restrictions which are then exploited to construct two-step GMM-type estimators for the parameters of the main equation. In the first step, the unknown parameters of the selection equation are consistently estimated. In the second step, these estimates are used to construct kernel weights in a manner such that the weight that any two-period individual observation receives in the estimation varies inversely with the relative magnitude of the sample selection effect in the two periods. Under appropriate assumptions, these "kernel-weighted" GMM estimators are consistent and asymptotically normal. The finite sample properties of the proposed estimators are investigated in a small Monte-Carlo study.     

Seemingly unrelated regressions with spatial error components

This article considers various estimators using panel data seemingly unrelated regressions (SUR) with spatial error correlation. The true data generating process (DGP) is assumed to be SUR with spatial error of the autoregressive or moving average type. Moreover, the remainder term of the spatial process is assumed to follow an error component structure. Both maximum likelihood (ML) and generalized moments (GM) methods of estimation are used. Using Monte Carlo experiments, we check the performance of these estimators and their forecasts under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous versus homogeneous panel data models.     

A systematic approach to identify core service technologies

In spite of the importance of service technologies in the service industry, they have not been analysed systematically. In response, this study proposes a new approach to identify core service technologies. At first, the technological interrelationship matrices from the perspectives of intensity, relatedness, and cross-impact are constructed with support, lift, and confidence values calculated by conducting an association rule mining on the co-classification information of business method patent data. The analytic network process is applied to the constructed technological interrelationship matrices in order to produce the importance values of service technologies from each perspective, considering their direct and indirect interrelationships. Data envelopment analysis is then employed to the derived importance values in order to identify core service technologies, putting three perspectives together. The proposed approach can be utilised for both firms’ planning of service technologies and service innovation policy-making of governments.     

Asymptotic Variance–Covariance Matrices of Two-Stage Estimators in the Presence of Continuous and Binary Dependent Variables with an Empirical Application

Journal of Quantitative Economics - We develop a general procedure to derive the asymptotic variance–covariance matrices of several two-stage estimators that can be used to estimate...     

A latent dynamic factor approach to forecasting multivariate stock market volatility

This paper proposes a latent dynamic factor model for high-dimensional realized covariance matrices of stock returns. The approach is based on the matrix logarithm and combines common latent factors driven by HAR processes and idiosyncratic autoregressive dynamics. The model accounts for positive definiteness of covariance matrices without imposing parametric restrictions. Simulated Bayesian parameter estimates are obtained using basic Markov chain Monte Carlo methods. An empirical application to 5-dimensional and 30-dimensional realized covariance matrices shows remarkably good forecasting results, in-sample and out-of-sample.     

Modelling of scale change, periodicity and conditional heteroskedasticity in return volatility

This paper extends the GARCH model to a wide class of nonstationary processes by proposing a semiparametric GARCH model for simultaneous modelling of conditional heteroskedasticity, slow scale change and periodicity in the volatility of high-frequency financial returns. A data-driven algorithm is developed for estimating the model. An approximate significance test of daily periodicity and the use of Monte Carlo confidence bounds for the scale function are proposed. The practical performance of the proposal is investigated in detail using some German stock price returns. It is shown that the various volatility components are all significant. Asymptotic properties of the proposed estimators are investigated.     

Forecasting the Consumer Confidence Index with tree-based MIDAS regressions

The macroeconomic literature has recently uncovered the importance of the consumer confidence variations at driving business cycles. However, it remains a challenge to predict changes in agents'confidence by exploiting the information from ultra high-frequency sentiment data extracted from social media. Based on the mixed data sampling (MIDAS) literature, we propose a new MIDAS method that introduces regression tree-based algorithms into the MIDAS framework. Our method is more flexible at sampling high-frequency lagged regressors compared to existing MIDAS models with tightly parametrized functions of lags. In an out-of-sample forecasting exercise for the Consumer Confidence Index, our results reveal that (i) the proposed procedure exploits more fully the information from historical sentiment data and (ii) our method substantially improves the forecast accuracy and confirms the role of social media at affecting the consumer confidence.     

The bias of some estimators for panel data models with measurement errors

The paper deals with the (asymptotic) bias in the estimation of regression slope coefficients from panel data observed with error. Unobserved individual and time specific heterogeneity is also assumed. The estimators considered include: the standard ‘within’ and ‘between’ estimators, and estimators based on differences over time. It is shown that in terms of bias, there may be a trade-off between the effect of heterogeneity and of measurement errors. The paper also shows that in situations where the number of observations of each individual is finite (and in practice often small), changes in the correlograms of the measurement error and of the latent exogenous variable may substantially affect the relative bias of the different estimators of the slope coefficient.     

An empirical estimation for mean-reverting coal prices with long memory

In this paper we discuss the calibration issues of power models built on mean-reverting processes combined with long memory. The unknown parameters of fractional mean-reversion processes are estimated by a hybrid estimation method, which is built upon the marriage of the quadratic variation and the least squares. We perform a simulation study to test the efficiency of these estimators and to compare with the approach proposed by Høg (1999). Moreover, we apply our estimation procedure to some sample series of Chinese coal spot prices in real life situations. These results support the use of fractional mean-reversion processes in modeling Chinese coal prices.     

Estimating SUR system with random coefficients: the unbalanced panel data case

A system of regression equations for analyzing panel data with random heterogeneity in intercepts and coefficients, and unbalanced panel data is considered. A maximum likelihood (ML) procedure for joint estimation of all parameters is described. Since its implementation for numerical computation is complicated, simplified procedures are presented. The simplifications essentially concern the estimation of the covariance matrices of the random coefficients. The application and ‘anatomy’ of the proposed algorithm for modified ML estimation are illustrated by using panel data for output, inputs and costs for 111 manufacturing firms observed up to 22 years.     

A note on the inefficiency of non-linear estimators

An upper bound on the inefficiency of non-optimally weighted method of moments estimators is reported, along with a necessary and sufficient condition for the equivalence of non-optimally and optimally weighted estimators. An example is considered in which a precise expression for the inefficiency bound is attainable.     

An asymptotic variance inequality for instrumental variable estimators signaling proportional bias increases

An asymptotic variance inequality for instrumental variable (IV) estimators is proposed, which suggests a critical variance that signals proportional increases in the bias of IV estimators through the augmentation of a set of instruments.     

Poverty analysis with missing data: alternative estimators compared

Poverty models are generally estimated by using sample surveys affected by missing data problems. Most methods proposed to take account of missing data problems consider point estimators which typically impose restrictive assumptions. However, it is possible to identify a range of logically possible values for the poverty probability, an identification interval, without imposing any assumption. It is then of interest to check whether the point estimates lie within the identification interval. This is a way to check the validity of the assumptions imposed by point estimators. Using the ECHP we perform this check to assess different estimation methods.     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

On the use of better measured proxies in regression analysis

Improving the measurement of mismeasured regressors may cause the inconsistency in least-square coefficient estimators to rise. An explanation for this result is provided and a more comprehensive summary of the data that is free of this problem is proposed.     

OPTIMAL FORECAST COMBINATION UNDER REGIME SWITCHING*

This article proposes a new forecast combination method that lets the combination weights be driven by regime switching in a latent state variable. An empirical application that combines forecasts from survey data and time series models finds that the proposed regime switching combination scheme performs well for a variety of macroeconomic variables. Monte Carlo simulations shed light on the type of data‐generating processes for which the proposed combination method can be expected to perform better than a range of alternative combination schemes. Finally, we show how time variations in the combination weights arise when the target variable and the predictors share a common factor structure driven by a hidden Markov process.     

Small Sample Properties Of Existing And New Estimators Of The Autocorrelation Coefficient And Regression Coefficients In The Context Of Ar(1) Errors

This study systematically and comprehensively investigates the small sample properties of the existing and some new estimators of the autocorrelation coefficient and of the regression coefficients in a linear regression model when errors follow an autoregressive process of order one. The new estimators of autocorrelation coefficient proposed here are based on the jackknife procedure. The jackknife procedure is applied in two alternative ways: first to the regression itself, and second to the residuals of the regression model. Next, the performance of the existing and new estimators of autocorrelation coefficient (thirty-three in total) is investigated in terms of bias and the root mean squared errors. Finally, we have systematically compared all of the estimators of the regression coefficients (again thirty-three) in terms of efficiency and their performance in hypothesis testing. We observe that the performance of the autocorrelation coefficient estimators is dependent upon the degree of autocorrelation and whether the autocorrelation is positive or negative. We do not observe a direct link between the bias and efficiency of an estimator. The performance of the estimators of the regression coefficients also depends upon the degree of autocorrelation. If the efficiency of regression estimator is of concern, then the iterative Prais-Winsten estimator should be used since it is most efficient for the widest range of independent variables and values of the autocorrelation coefficient. If testing of the hypothesis is of concern, then the estimators based on jackknife technique are certainly superior and are highly recommended. However, for negative values of the autocorrelation coefficient, the estimators based on Quenouille procedure and iterative Prais-Winsten estimator are comparable. But, for computational ease iterative Prais-Winsten estimator is recommended.

     

Nonparametric methods for estimating and testing for constant betas in asset pricing models

In this article, we study the performance of a smoothing spline method in estimating and testing for constant betas in two well-known asset pricing models, the usual market model and the three-factor model. The spline estimator is computed taking into account the conditional heteroscedasticity of the errors. Using the right model and estimation procedure for the variance term plays a crucial role in gaining efficiency in beta estimators. A simulation study shows the good performance of our method; in all the scenarios simulated, it outperforms the benchmark rolling estimator. The method enables users to obtain confidence intervals and to test for the significance and constancy of betas. Finally, the method is applied to US data, comprising 25 portfolios formed based on size and the ratio of book equity to market equity. The results show that the time-variability of the betas plays an important role, mainly when sensitivity to the HML factor is considered.