A New Procedure For Multiple Testing Of Econometric Models

A significant role for hypothesis testing in econometrics involves diagnostic checking. When checking the adequacy of a chosen model, researchers typically employ a range of diagnostic tests, each of which is designed to detect a particular form of model inadequacy. A major problem is how best to control the overall probability of rejecting the model when it is true and multiple test statistics are used. This paper presents a new multiple testing procedure, which involves checking whether the calculated values of the diagnostic statistics are consistent with the postulated model being true. This is done through a combination of bootstrapping to obtain a multivariate kernel density estimator of the joint density of the test statistics under the null hypothesis and Monte Carlo simulations to obtain a p value using this kernel density. We prove that under some regularity conditions, the estimated p value of our test procedure is a consistent estimate of the true p value. The proposed testing procedure is applied to tests for autocorrelation in an observed time series, for normality, and for model misspecification through the information matrix. We find that our testing procedure has correct or nearly correct sizes and good powers, particular for more complicated testing problems. We believe it is the first good method for calculating the overall p value for a vector of test statistics based on simulation.Bootstrapping, consistency, information matrix test, Markov chain Monte Carlo simulation, multivariate kernel density, normality, serial correlation, test vector

Econometrics in R: Past, Present, and Future

Recently, computational methods and software have been receiving more attention in the econometrics literature, emphasizing that they are integral components of modern econometric research. This has also promoted the development of many new econometrics software packages written in R and made available on the Comprehensive R Archive Network. This special volume on "Econometrics in R" features a selection of these recent activities that includes packages for econometric analysis of cross-section, time series and panel data. This introduction to the special volume highlights the contents of the contributions and embeds them into a brief overview of other past, present, and future projects for econometrics in R.

Some recent developments in microeconometrics: A survey

This paper summarizes some recent developments in rnicroeconometrics with respect to methods for estimation and inference in non-linear models based on cross-section and panel data. In particular we discuss recent progress in estimation with conditional moment restrictions, simulation methods, serniparametric methods, as well as specification tests. We use the binary cross-section and panel probit model to illustrate the application of some of the theoretical results. --

ON THE (INTRADAILY) SEASONALITY AND DYNAMICS OF A FINANCIAL POINT PROCESS: A SEMIPARAMETRIC APPROACH.

A component model for the analysis of financial durations is proposed. The components are the long-run dynamics and the seasonality. The later is left unspecified and the former is assumed to fall within the class of certain family of parametric functions. The joint model is estimated by maximizing a (local) quasi-likelihood function, and the resulting nonparametric estimator of the seasonal curve has an explicit form that turns out to be a transformation of the Nadaraya-Watson estimator. The estimators of the parameters of interest are shown to be root-N consistent and asymptotically efficient. Furthermore, the seasonal curve is also estimated consistently. The methodology is applied to the trade duration process of Bankinter, a medium size Spanish bank traded in Bolsa de Madrid. We show that adjusting data by seasonality produces important misspecifications.

Nonparametric inference of quantile curves for nonstationary time series

The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type I error rates. A wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the asymptotic results. In particular, our results can be used to test the trends of extremes of climate variables, an important problem in understanding climate change. Our methodology is applied to the analysis of the maximum speed of tropical cyclone winds. It was found that an inhomogeneous upward trend for cyclone wind speeds is pronounced at high quantile values. However, there is no trend in the mean lifetime-maximum wind speed. This example shows the effectiveness of the quantile regression technique.Comment: Published in at http://dx.doi.org/10.1214/09-AOS769 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Econometrics in R: Past, Present, and Future

Recently, computational methods and software have been receiving more attention in the econometrics literature, emphasizing that they are integral components of modern econometric research. This has also promoted the development of many new econometrics software packages written in R and made available on the Comprehensive R Archive Network. This special volume on "Econometrics in R" features a selection of these recent activities that includes packages for econometric analysis of cross-section, time series and panel data. This introduction to the special volume highlights the contents of the contributions and embeds them into a brief overview of other past, present, and future projects for econometrics in R

Essays in nonparametric estimation and inference

This thesis consists of three chapters which represent my journey as a researcher during this PhD. The uniting theme is nonparametric estimation and inference in the presence of data problems. The first chapter begins with nonparametric estimation in the presence of a censored dependent variable and endogenous regressors. For Chapters 2 and 3 my attention moves to problems of inference in the presence of mismeasured data. In Chapter 1 we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalise the identification argument put forward in Altonji, Ichimura and Otsu (2012), construct a nonparametric estimator, characterise its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. We show that the estimator is consistent and asymptotically normally distributed. Chapter 2 considers specification testing for regression models with errors-in-variables. In contrast to the method proposed by Hall and Ma (2007), our test allows general nonlinear regression models. Since our test employs the smoothing approach, it complements the nonsmoothing one by Hall and Ma in terms of local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities and develop a bootstrap method to approximate the critical value. We apply the test to the specification of Engel curves in the US. Finally, some simulation results endorse our theoretical findings: our test has advantages in detecting high frequency alternatives and dominates the existing tests under certain specifications. Chapter 3 develops a nonparametric significance test for regression models with measurement error in the regressors. To the best of our knowledge, this is the first test of its kind. We use a ‘semi-smoothing’ approach with nonparametric deconvolution estimators and show that our test is able to overcome the slow rates of convergence associated with such estimators. In particular, our test is able to detect local alternatives at the √n rate. We derive the asymptotic distribution under i.i.d. and weakly dependent data, and provide bootstrap procedures for both data types. We also highlight the finite sample performance of the test through a Monte Carlo study. Finally, we discuss two empirical applications. The first considers the effect of cognitive ability on a range of socio-economic variables. The second uses time series data - and a novel approach to estimate the measurement error without repeated measurements - to investigate whether future inflation expectations are able to stimulate current consumption

Econometric essays on specification and estimation of demand systems

This dissertation focuses on two research themes related to econometric estimation of linear almost ideal demand systems (LAIDS) for U.S. meats. The first theme addresses whether nonstationarity (unit-roots and cointegration) contributes to a dynamic specification of LAIDS models. The results of the effect of nonstationarity are reported in two case studies. The second theme explores the relationship between age and household size with budget shares to specify semiparametric LAIDS model. The results are reported in a third case study that compares parametric and semiparametric models estimates of price and expenditure elasticities. The first case study conducts a comparative analysis of elasticity estimates from static and dynamic LAIDS models. Historical meat consumption data (1975:1-2002:4) for beef, pork and poultry products were used. Hylleberg et al. (1990) seasonal unit roots tests were conducted. Unit roots and cointegration analysis lead to the specification of an ECM of the Engle-Granger type for the LAIDS model. Marshallian and compensated elasticities were generated from the static and dynamic LAIDS models. The study found some model differences in elasticity estimates and rejected homogeneity in the dynamic model. The second case study evaluates the forecasting performance of static and dynamic LAIDS models. Forecast evaluation was based on mean square error (MSE) criteria and recently developed MSE-tests. The study found ECM-LAIDS model performs uniformly better under all forecasting horizons for the beef equation. However, in the case of the pork equation the static model performed better in one-step-ahead and two-step-ahead forecasting horizons while the dynamic model was superior in the three-step-ahead and four-step-ahead forecasting horizons using MSE comparisons. In testing, only the two-steps ahead was superior for pork. The third case study specifies a semiparametric LAIDS model that maintains the linearity assumption of prices and total expenditures and allows nonparametric effects of age and household size. 2003 U.S. Consumer Expenditure Survey data for four meat products (beef, pork, poultry and seafood) were used in the study. Model fit and elasticity estimates revealed negligible differences exist between parametric and semiparametric models

Fitting Truncated Mode Regression Model by Simulated Annealing

Like mean, median, and standard deviation, mode as the value that appears most often in a set of data is an important feature of a distribution. The numerical value of the mode is the same as that of the mean and median in a symmetric distribution but may be very different in a highly skewed distribution. Mode regression, which models the relationship between the mode of a dependent variable and some covariates, was first introduced by Lee in terms of truncated dependent variables. Some modifications of the truncated mode regression have been proposed recently. However, little progress is made on the computation or algorithm of fitting a mode regression due to an NP-hard optimization problem. In this paper we first introduce the popular simulated annealing (SA) to solve the truncated mode regression optimization. Experiments with simulations compare favorably to SA. Then, a mode regression with the proposed algorithm is applied to explore the typical income structure of China. We also compare the income returns to gender, education, experience, job sector, and district between the majority of workers with typical income and the workers with mean, middle income via comparison between mode regression, mean regression, and median regression