Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency

This paper considers the estimation of Kumbhakar et al. (J Prod Anal. doi:10.1007/s11123-012-0303-1, 2012) (KLH) four random components stochastic frontier (SF) model using MLE techniques. We derive the log-likelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closed-form expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three different applications.     

A Simple Estimator of Two-Dimensional Copulas,with Applications1

Copulas are distributions with uniform marginals. Non-parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi-spaced grid a natural starting point. However, the mixed-integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non-parametric MLE of B-spline coefficients on possibly non-equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.     

Prediction from ARFIMA models: Comparisons between MLE and semiparametric estimation procedures

This paper considers the effects on multi-step prediction of using semiparametric local Whittle estimators rather than MLE for long memory ARFIMA models. We consider various representations of the minimum MSE predictor with known parameters. We then conduct a detailed simulation study for when the true parameters are replaced with estimates. The predictor based on MLE is found to be superior, in the MSE sense, to the predictor based on the two-step local Whittle estimation. The “optimal” bandwidth local Whittle estimator produces worse predictions than the local Whittle using an agnostic bandwidth of the square root of the sample size.     

A Simple Estimator of Two‐Dimensional Copulas,with Applications1

Copulas are distributions with uniform marginals. Non‐parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi‐spaced grid a natural starting point. However, the mixed‐integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non‐parametric MLE of B‐spline coefficients on possibly non‐equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.     

时变Copula模型的非参数推断

运用Copula模型研究金融变量之间的相关结构,是近年来金融分析中的一个热点,如何估计Copula模型中的时变参数则是一个重点和难点问题。本文从非参数建模思想为切入点,提出经验分布函数—局部极大似然法(ECDF-LML)估计Copula函数中的时变参数,研究了Copula模型参数是否时变的统计假设检验问题。最后通过大量随机模拟研究验证了本文所提出的方法较DCC-MGARCH方法在刻画随机变量动态相关性方面更具优越性且很稳健。     

Growth and convergence in a multi-country empirical stochastic Solow model

The paper considers international per capita output and its growth using a panel of data for 102 countries between 1960 and 1989. It sets out an explicitly stochastic Solow growth model and shows that this has quite different properties from the standard approach where the output equation is obtained by adding an error term to the linearized solution of a deterministic Solow model. It examines the econometric properties of estimates of beta convergence as traditionally defined in the literature and shows that all these estimates are subject to substantial biases. Our empirical estimates clearly reflect the nature and the magnitude of these biases as predicted by econometric theory. Steady state growth rates differ significantly across countries and once this heterogeneity is allowed for the estimates of beta are substantially higher than the consensus in the literature. But they are very imprecisely estimated and difficult to interpret. The paper also discusses the economic implications of these results for sigma convergence. © 1997 John Wiley & Sons, Ltd.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.     

Labour-use efficiency in Swedish social insurance offices

This paper considers the estimation of frontier production functions in panel data models. It proposes a multi-stage method to obtain estimates of (1) the parameters of a flexible input requirement function and (2) technical inefficiency decomposed into time-invariant (firm-specific), time-varying, and the residual components. The proposed method is used to analyse labour-use efficiency of Swedish local social insurance offices on the basis of a large panel of observations during the time period 1974–84. Empirical results show: (1) substantial variations in labour-use efficiency among these offices, with the mean efficiencies declining over time; (2) presence of economies of scale, thereby meaning that most of the offices were of suboptimal size.     

Panel data models with multiple time-varying individual effects

This paper considers a panel data model with time-varying individual effects. The data are assumed to contain a large number of cross-sectional units repeatedly observed over a fixed number of time periods. The model has a feature of the fixed-effects model in that the effects are assumed to be correlated with the regressors. The unobservable individual effects are assumed to have a factor structure. For consistent estimation of the model, it is important to estimate the true number of individual effects. We propose a generalized methods of moments procedure by which both the number of individual effects and the regression coefficients can be consistently estimated. Some important identification issues are also discussed. Our simulation results indicate that the proposed methods produce reliable estimates.     

Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan

This paper provides closed-form likelihood approximations for multivariate jump-diffusion processes widely used in finance. For a fixed order of approximation, the maximum-likelihood estimator (MLE) computed from this approximate likelihood achieves the asymptotic efficiency of the true yet uncomputable MLE as the sampling interval shrinks. This method is used to uncover the realignment probability of the Chinese Yuan. Since February 2002, the market-implied realignment intensity has increased fivefold. The term structure of the forward realignment rate, which completely characterizes future realignment probabilities, is hump-shaped and peaks at mid-2004. The realignment probability responds quickly to economic news releases and government interventions.     

Switching generalized autoregressive score copula models with application to systemic risk

Recent financial disasters have emphasized the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme events strongly relies on their flexibility to account for the highly nonlinear and asymmetric dependence patterns observed in financial time series. In this paper, we develop a new class of flexible copula models where the dependence parameters evolve according to a Markov switching generalized autoregressive score (GAS) dynamics. Maximum likelihood estimation is performed using a two‐step procedure where the second step relies on the expectation–maximization algorithm. The proposed switching GAS copula models are then used to estimate the conditional value at risk and the conditional expected shortfall, measuring the impact on an institution of extreme events affecting another institution or the market. The empirical investigation, conducted on a panel of European regional portfolios, reveals that the proposed model is able to explain and predict the evolution of the systemic risk contributions over the period 1999–2015.     

Consumer Feelings and Equilibrium Product Quality

This paper considers the possibility that a firm can invest not only in the true product quality, but also in activities such as merchandizing and store atmospherics that influence consumer perception of the product quality. Consumers make their purchase decisions based on the signal (perception) of quality they experience, where the signal is influenced by both the true product quality valued by the consumer and the affect of the consumer at the time of the signal formation. In this situation, a firm finds it optimal to invest in both product quality and in variables inducing affect, even though rational consumers, in equilibrium, correctly solve back for the true product quality. We uncover an asymmetry in the effects of the cost of producing quality and the cost of inducing affect. As a firm's cost of quality decreases, the firm will find it optimal to invest more both in the true quality and in the affect inducement, even if it does not have a lower cost of inducing affect. Conversely, if a firm finds it easier to induce affect, then the product quality decreases but affect-inducing activities increase.
Under competition, we find that the firm investing more in quality also invests more in affect creation. An implication of this is that in a competitive environment, consumers can rationally associate an up-lifting store atmosphere, affect inducing merchandizing, or mood-creating communication with high quality products even when the firm has no need to signal their private cost of quality information, and when there is no consumption externality of the affect. We also analyze the case in which firms might have different costs and consumers are uncertain about the costs incurred by a given firm. Here again we show that the perceived quality production is positively correlated with both the true quality and the affect inducing activities.     

A Comparative Analysis of Different IV and GMM Estimators of Dynamic Panel Data Models

It is well known that the usual procedures for estimating panel data models are inconsistent in the dynamic setting. A large number of consistent estimators however, have been proposed in the literature. This paper provides a survey of the majority of mainstream estimators, which tend to consist of IV and GMM ones. It also considers a newly proposed extension to the promising Wansbeek–Bekker estimator (Harris & Mátyás, 2000). To provide guidance to the applied researcher working on micro-datasets, the small sample performance of these estimators is evaluated using a set of Monte Carlo experiments.     

Causal inference,time and observation plans in the social sciences

This paper first discusses the role of time in causal inferences in the social sciences. It then compares in detail how panel and event history observation designs affect causal analysis. It shows that the collection of event history data is an extremely useful approach for uncovering causal relationships or mapping out systems of causal relations. It concludes that event history data provide an optimal basis for a causal understanding of social processes because they allow the social researcher to relate the change in future outcomes to conditions in the past at each point in time.     

一种多资产组合风险度量解决之道：正则藤Copula

为准确地度量包含有多项金融资产的组合的风险,本文提出使用一种新的高维Copula构建方法,正则藤Copula（Canonical Vine Copula）,来对多资产间的非线性相关结构进行建模,该函数呈现为一个以一系列成对Copula函数作为节点的“藤”的层叠结构。本文基于上海、香港和台湾三个股票市场对构建该高维Copula函数时各个节点上成对Copula函数类型的选取进行了讨论,并证实了正则藤Copula函数相比传统的多元Copula函数能够更灵活地描述各市场间尾部相关性的复杂形式。样本外风险预测绩效分析和模拟研究均表明,使用正则藤Copula函数确实能够更为稳健和准确地预测组合VaR。     

Robust and consistent estimation of nonlinear errors-in-variables models

This paper considers the consistent estimation of nonlinear errors-in-variables models. It adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn. This paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors-in-variables model. The identification is established through characteristic functions. The estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage, and at the second stage, a semiparametric nonlinear least-squares estimator is proposed. The consistency of the proposed estimator is also established. Finite sample performance of the estimator is investigated through a Monte Carlo study.     

A cautionary note on methods of comparing programmatic efficiency between two or more groups of DMUs in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann–Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal–Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann–Whitney and Kruskal–Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework.      

Mean squared error of ridge estimators in logistic regression

It is well known that the maximum likelihood estimator (MLE) is inadmissible when estimating the multidimensional Gaussian location parameter. We show that the verdict is much more subtle for the binary location parameter. We consider this problem in a regression framework by considering a ridge logistic regression (RR) with three alternative ways of shrinking the estimates of the event probabilities. While it is shown that all three variants reduce the mean squared error (MSE) of the MLE, there is at the same time, for every amount of shrinkage, a true value of the location parameter for which we are overshrinking, thus implying the minimaxity of the MLE in this family of estimators. Little shrinkage also always reduces the MSE of individual predictions for all three RR estimators; however, only the naive estimator that shrinks toward 1/2 retains this property for any generalized MSE (GMSE). In contrast, for the two RR estimators that shrink toward the common mean probability, there is always a GMSE for which even a minute amount of shrinkage increases the error. These theoretical results are illustrated on a numerical example. The estimators are also applied to a real data set, and practical implications of our results are discussed.     

Farm heterogeneity and technical efficiency: Some results from Swedish dairy farms

This paper introduces farm-heterogeneity in measuring technical efficiency of Swedish dairy farms using farm-level data. In calculating technical efficiency which is allowed to vary over time and across farms, we control for farm-specific effects. This is possible only when panel data is available. Furthermore, we separate technical efficiency from technical change—the presence of which is indicated by a shift in the production function over time,ceteris paribus. We also calculate percentage change in technical efficiency to examine whether farm efficiencies have improved over time. Finally, a comparison of technical efficiency, elasticities of different inputs, and technical change is made across different years and panels. The data includes four panels of dairy farms observed during the period 1976–1988, excluding 1985.We thank two anonymous referees, Anders Klevmarken and Lennart Hjalmarsson for valuable comments. Financial support from SJFR, the Gothenburg Economic School Foundation, Jan Wallender and Tore Browaldh Research Foundations is gratefully acknowledged.     

A count-amount model with endogenous recording of observations

This paper discusses some of the problems which are encountered if an event ? is only recorded if its value satisfies a recording criterion A. It follows that we get an incorrect idea of the frequency of the events and of its true distribution. In order to solve these problems, an econometric model has been constructed by means of which consistent estimation of the true parameters is possible. The model is estimated on consumer purchases, where the number of purchases is assumed to be NEGBIN-distributed and the purchase amounts obey a lognormal distribution. Purchases are only recorded if their value exceeds Dfl. 10. It is shown that ignoring the recording condition will result in biased estimates and invalid predictions. Apart from this, the model is, among others, relevant for insurance problems, marketing surveys and criminological and epidemiological phenomena.