A Monte Carlo comparison of traditional and Stein-rule estimators under squared error loss

This paper reports the results of using an orthonormal regression model, a squared error loss measure and Monte Carlo procedures, to compare the risk functions of traditional and Stein-rule pre-test estimators under a variety of conditions. The results of the sampling experiment indicate that the Stein-rule estimators not only dominate the sampling theory estimators used in applied econometric work but that in contrast to conventional wisdom thegains from using members of the Stein-rule family may be quite significant over a large range of the parameter space.     

Asymptotic properties of Monte Carlo estimators of diffusion processes

This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed of convergence of the Euler scheme. We also study estimators of conditional expectations of diffusions. After characterizing expected approximation errors, we construct second-order bias-corrected estimators. We also derive new convergence results for the Mihlstein scheme. Illustrations of the results are provided in the context of simulation-based estimation of diffusion processes.     

Discriminating between autoregressive forms: A Monte Carlo comparison of Bayesian and ad hoc methods

The paper considers the problem of discriminating between the autoregressive forms of a Koyck distributed lag model and a regression model with autocorrelated distrubances. Several interpretations of an ad hoc rule-of-thumb suggested by Griliches are compared with Bayesian posterior odds analysis in a Monte Carlo experiment. The Bayesian analysis is generally superior to the rules-of-thumb, the latter exhibiting large probabilities of type I error, and low power. The rules-of-thumb excessively favour the distributed lag model, while the Bayesian method is free from such bias. All methods improve with increased sample size.     

Measuring the costs of children: parametric and semiparametric estimators1

How much additional income does a family with four children need to attain the same welfare level as a family with two children? And how much does a single person need compared to a childless couple? These questions are important in applied micro-economics and underlie public policy on, for example, social benefits and child allowances. In microeconomics, this is known as the problem of measuring equivalence scales. We estimate these scales using two types of subjective survey information. First, we use answers to survey questions on the income required to attain a given utility level. We compare the results for the usual linear model with semiparametric estimates, in which the functional form of the relationship between required income and family size and actual income is left unspecified. Second, we use answers to the question: how satisfied are you with actual household income? We present parametric and semiparametric estimates for ordered response models explaining this discrete variable. We find that according to the second type of information, costs of children are much larger than according to the first.     

Edgeworth approximations for semiparametric instrumental variable estimators and test statistics

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable estimator considered in Newey (Econometrica 58 (1990) 809) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and (a version of) nearest neighbor estimates as special cases. Our expansions are valid to order n^−2ε for some 0<ε<1/2, where ε depends on the smoothness and dimensionality of the data distribution and on the order of the polynomial chosen by the practitioner. We use the expansions to define optimal bandwidth selection methods for both estimation and testing problems and apply our methods to simulated data.     

A Monte Carlo permutation test for co-occurrence data

Researchers commonly use co-occurrence counts to assess the similarity of objects. This paper illustrates how traditional association measures can lead to misguided significance tests of co-occurrence in settings where the usual multinomial sampling assumptions do not hold. I propose a Monte Carlo permutation test that preserves the original distributions of the co-occurrence data. I illustrate the test on a dataset of organizational categorization, in which I investigate the relations between organizational categories (such as “Argentine restaurants” and “Steakhouses”).     

A classified bibliography of Monte Carlo studies in econometrics

The Monte Carlo method of exploring the properties of econometric estimators and significance tests has yielded a considerable amount of information that has practical value in guiding choice of technique in applied research. This paper presents a bibliography of such Monte Carlo studies over the period 1948–1972. About 150 citations are listed alphabetically by author, and also under a detailed subject-matter classification scheme.     

Advanced Multilevel Monte Carlo Methods

This article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law. The MLMC approach works with a hierarchy of biassed approximations, which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider some Markov chain Monte Carlo and sequential Monte Carlo methods, which have been introduced in the literature, and we describe different strategies that facilitate the application of MLMC within these methods.     

面板数据协整关系检验的一个简明蒙特卡洛实验框架

体现处于考察中的面板数据之问的样本关联性,本文设计出一个简明蒙特卡洛实验框架以生成单一方程式面板数据之间协整关系检验统计值之有限样本密度分布及对应临界值。本文的蒙特卡洛实验框架提供了一个简明的可操作平台,可以运用于涉及面板数据协整关系检验的相关实证研究。为检测所发展的计量分析方法的可操作性与适用性,本文给出了相关应用实例。     

面板数据单位根检验的一个简明蒙特卡洛实验框架

本文考虑到构成面板数据之横截面时间序列扰动项之间的关联性和异质性，设计出一个简明的蒙特卡洛实验框架以生成面板数据单位根检验统计值之有限样本密度分布和对应临界值。我们设计的蒙特卡洛框架提供了一个简明的可操作平台，可以运用于涉及到面板数据单位根检验的相关实证研究。     

A Monte Carlo study of autoregressive integrated moving average processes

Six of the simpler ARMA type models are examined with respect to properties of a variety of proposed estimators of unknown parameters. The findings suggest that if only one estimation method were available to a researcher the choice should probably be maximum likelihood. Stationarity- and invertibility-restricted estimation would appear appropriate when parameters are thought to be within 5 percent of constraint boundaries.     

On consistency of the weighted least squares estimators in a semiparametric regression model

This paper is concerned with the semiparametric regression model \(y_i=x_i\beta +g(t_i)+\sigma _ie_i,~~i=1,2,\ldots ,n,\) where \(\sigma _i^2=f(u_i)\), \((x_i,t_i,u_i)\) are known fixed design points, \(\beta \) is an unknown parameter to be estimated, \(g(\cdot )\) and \(f(\cdot )\) are unknown functions, random errors \(e_i\) are widely orthant dependent random variables. The p-th (\(p>0\)) mean consistency and strong consistency for least squares estimators and weighted least squares estimators of \(\beta \) and g under some more mild conditions are investigated. A simulation study is also undertaken to assess the finite sample performance of the results that we established. The results obtained in the paper generalize and improve some corresponding ones of negatively associated random variables.     

Optimal forecasting with heterogeneous panels: A Monte Carlo study

We contrast the forecasting performance of alternative panel estimators, divided into three main groups: homogeneous, heterogeneous and shrinkage/Bayesian. Via a series of Monte Carlo simulations, the comparison is performed using different levels of heterogeneity and cross sectional dependence, alternative panel structures in terms of T and N and the specification of the dynamics of the error term. To assess the predictive performance, we use traditional measures of forecast accuracy (Theil’s U statistics, RMSE and MAE), the Diebold–Mariano test, and Pesaran and Timmerman’s statistic on the capability of forecasting turning points. The main finding of our analysis is that when the level of heterogeneity is high, shrinkage/Bayesian estimators are preferred, whilst when there is low or mild heterogeneity, homogeneous estimators have the best forecast accuracy.     

A Monte Carlo study of ranked efficiency estimates from frontier models

Parametric stochastic frontier models yield firm-level conditional distributions of inefficiency that are truncated normal. Given these distributions, how should one assess and rank firm-level efficiency? This study compares the techniques of estimating (a) the conditional mean of inefficiency and (b) probabilities that firms are most or least efficient. Monte Carlo experiments suggest that the efficiency probabilities are easier to estimate (less noisy) in terms of mean absolute percent error when inefficiency has large variation across firms. Along the way we tackle some interesting problems associated with simulating and assessing estimator performance in the stochastic frontier model.     

Homogeneity tests in meta-analysis: a Monte Carlo comparison of statistical power and Type I error

The statistical power and Type I error rate of several homogeneity tests, usually applied in meta-analysis, are compared using Monte Carlo simulation: (1) The chi-square test applied to standardized mean differences, correlation coefficients, and Fisher's r-to-Z transformations, and (2) S&H-75 (and 90 percent) procedure applied to standardized mean differences and correlation coefficients. Chi-square tests adjusted correctly Type I error rates to the nominal significance level while the S&H procedures showed higher rates; consequently, the S&H procedures presented greater statistical power. In all conditions, the statistical power was very low, particularly when the sample had few studies, small sample sizes, and presented short differences between the parametric effect sizes. Finally, the criteria for selecting homogeneity tests are discussed.     

A Monte Carlo evaluation of the power of some tests for heteroscedasticity

Szroeter's asymptotically normal test outperforms the Goldfeld-Qu2ndt test, the Breusch-Pagan Lagrange multiplier test and BAMSET, when it is possible to order the observations according to increasing variance. With no prior information on variance ordering, BAMSET is best. Some observations concerning degree of heteroscedasticity and model specification are made.