Adjusting for measurement error in the value added model: evidence from Portugal

The multilevel value added approach to measuring school effectiveness is now widely used. We propose a method to adjust for measurement error to investigate the extent to which this changes school effect estimates. It is applied to longitudinal data collected in the region of Cova da Beira (NUT III) for 1st, 3rd, 5th, 7th and 8th grades. Three different variance component models are considered, depending on the predictor variables included. Assuming measurement error occurs in explanatory and/or response variables, corrections are made for different values of the coefficient of reliability. Moreover, models are fitted under the assumption of either independent or correlated measurement errors.     

A simple estimator for nonlinear error in variable models

We propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data, such as validation data or double measurements, are available. We assume that the marginal distributions of the measurement errors are Laplace (double exponential) with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other. Under these assumptions, we derive simple revised moment conditions in terms of the observed variables. They are used to make inference about the model parameters and the variance of the measurement error. The results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest. Our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute. Our estimation method is particularly useful in situations where no additional data are available, which is the case in many economic data sets. Simulation study demonstrates good finite sample properties of our proposed estimator. We also examine the performance of the estimator in the case where the error distribution is misspecified.     

Errors-in-variables in demand systems

The rejection of symmetry and other restrictions in demand systems may be due to measurement errors in the exogenous variables. It is shown that symmetry conditions can be used to identify and consistently estimate a linear model's parameters when measurement error exists. Several identification rules are derived and estimation of identified models is considered. Results are applied to estimation of the Almost Ideal Demand System for the United Kingdom.     

Estimation methods for male labor supply functions How to take account of nonlinear taxes

Nonlinear taxes create econometric difficulties when estimating labor supply functions. One estimation method that tackles these problems accounts for the complete form of the budget constraint and uses the maximum likelihood method to estimate parameters. Another method linearizes budget constraints and uses instrumental variables techniques. Using Monte Carlo simulations I investigate the small-sample properties of these estimation methods and how they are affected by measurement errors in independent variables. No estimator is uniquely best. Hence, in actual estimation the choice of estimator should depend on the sample size and type of measurement errors in the data. Complementing actual estimates with a Monte Carlo study of the estimator used, given the type of measurement errors that characterize the data, would often help interpreting the estimates. This paper shows how such a study can be performed.     

ERRORS IN VARIABLES IN ECONOMETRICS: NEW DEVELOPMENTS AND RECURRENT THEMES*

The paper reviews some old and new approaches to the analysis of linear models with errors in variables. The emphasis is on the identification problems that usually arise in errors–in–variables models and on the various types of additional information that econometricians have invoked to be able to estimate parameters consistently. The approaches discussed include instrumental variables, grouping, simultaneous equations, multiple equations and bounds on measurement error variances.     

Simple,Efficient and Distribution-free Approach to Interaction Effects in Complex Structural Equation Models

Structural equation models with mean structure and non-linear constraints are the most frequent choice for estimating interaction effects when measurement errors are present. This article proposes eliminating the mean structure and all the constraints but one, which leads to a more easily handled model that is more robust to non-normality and more general as it can accommodate endogenous interactions and thus indirect effects. Our approach is compared to other approaches found in the literature with a Monte Carlo simulation and is found to be equally efficient under normality and less biased under non-normality. An empirical illustration is included.     

On B-robust instrumental variable estimation of the linear model with panel data

The aim of this paper is to demonstrate how to acquire robust consistent estimates of the linear model when the fundamental orthogonality condition is not fulfilled. With this end in view, we develop two estimation procedures: Two stage generalized M (2SGM) and robust generalized method of moments (RGMM). Both estimators are B-robust, i.e. their associated influence function is bounded, consistent and asymptotic normally distributed. Our simulation results indicate that the relatively efficient RGMM estimator (in regressions with heteroskedastic and/or autocorrelated errors) provides accurate parameter estimates of a panel data model with all variables subject to measurement errors, even if a substantial portion of the data is contaminated with aberrant observations. The traditional estimation techniques such as 2SLS and GMM break down when outliers corrupt the data.     

Sequential estimation in generalized linear models when covariates are subject to errors

Sequential methods have been used for many applications; especially, when fixed sample procedures are not possible and/or when “early stopping” of sampling is beneficial for applications. At the same time, the issue of how to make correct inferences when measurement errors are present has drawn considerable attention from statisticians. In this paper, the problems of sequential estimation of generalized linear models when there are measurement errors in both adaptive and fixed design cases are studied. The proposed sequential procedure is proved to be asymptotically consistent and efficient in the sense of Chow and Robbins [Ann Math Stat 36(2):457–462, 1965] when measurement errors decay gradually as the number of sequentially selected design points increases. This assumption is useful in sequentially designed experiments, and can also be fulfilled in the case when replicate measurements are available. Some numerical studies based on a Rasch model and a logistic regression model are conducted to evaluate the performance of the proposed procedure.     

Mismeasured Household Size and its Implications for the Identification of Economies of Scale*

We consider the possibility that demographic variables are measured with errors which arise because household surveys measure demographic structures at a point‐in‐time, whereas household composition evolves throughout the survey period. We construct and estimate sharp bounds on household size and find that the degree of these measurement errors is non‐trivial. These errors have the potential to resolve the Deaton–Paxson paradox, but fail to do so.     

影响国际旅游服务ⅡT的基本因素研究

全球经济一体化以及区域经济一体化进程的深入使国际旅游服务贸易得到了蓬勃发展。文中首次将产业内贸易(Intra-Industry Trade,IIT)理论引入国际旅游服务贸易研究当中,以产业内贸易的视角来观察双向对流的国际旅游服务贸易(即旅游服务IIT)。以东盟为例,探讨了国际旅游服务IIT的发展现象,进而结合旅游学相关理论分析了影响双向对流旅游服务贸易的基本因素。对影响国际旅游服务IIT基本因素的研究可以为提高国际旅游服务IIT的程度,实现贸易多方的"共赢"提供决策依据。     

UK Intra-industry Trade with the EU North and South

This paper tests the traditional country and industry hypotheses of intra-industry trade (IIT) in vertically and horizontally differentiated products in the context of the UK's bilateral trade with EU countries. It distinguishes empirically between IIT in vertically and horizontally differential goods, between trade with EU 'North' and 'South' and between the effects of using GDP proxies and direct measures of national factor endowment differences. The paper shows that the robustness of the results of earlier multi-country studies are open to challenge, that the separation of IIT into vertical and horizontal IIT offers an important innovation to the empirical work in this area and that further development of large numbers models of IIT in quality differentiated goods is required.     

Structural measurement errors in nonseparable models

This paper considers measurement error from a new perspective. In surveys, response errors are often caused by the fact that respondents recall past events and quantities imperfectly. We explore the consequences of limited recall for the identification of marginal effects. Our identification approach is entirely nonparametric, using Matzkin-type nonseparable models that nest a large class of potential structural models. We show that measurement error due to limited recall will generally exhibit nonstandard behavior, in particular be nonclassical and differential, even for left-hand side variables in linear models. We establish that information reduction by individuals is the critical issue for the severity of recall measurement error. In order to detect information reduction, we propose a nonparametric test statistic. Finally, we propose bounds to address identification problems resulting from recall errors. We illustrate our theoretical findings using real-world data on food consumption.     

Which covariates should be controlled in propensity score matching? Evidence from a simulation study

Propensity score matching is a widely‐used method to measure the effect of a treatment in social as well as medicine sciences. An important issue in propensity score matching is how to select conditioning variables in estimation of the propensity scores. It is commonly mentioned that variables which affect both program participation and outcomes are selected. Using Monte Carlo simulation, this paper shows that efficiency in estimation of the Average Treatment Effect on the Treated can be gained if all the available observed variables in the outcome equation are included in the estimation of propensity scores. This result still holds in the presence of non‐sampling errors in the observed control variables.     

Latent variables in econometrics

Unobservable variables in econometrics are represented in one of three ways: by variables contaminated by measurement errors, by proxy variables, or by various manifest indicators and/or causes. This paper contains a discussion of models involving each of these representations, and highlights certain interesting implications that have been insufficiently emphasized or completely unrecognized in the literature.     

DISENTANGLING DEMAND AND SUPPLY SHOCKS IN THE CRUDE OIL MARKET: HOW TO CHECK SIGN RESTRICTIONS IN STRUCTURAL VARS

Sign restrictions have become increasingly popular for identifying shocks in structural vector autoregressive (SVAR) models. So far there are no techniques for validating the shocks identified via such restrictions. Although in an ideal setting the sign restrictions specify shocks of interest, sign restrictions may be invalidated by measurement errors, data adjustments or omitted variables. We model changes in the volatility of the shocks via a Markov switching (MS) mechanism and use this device to give the data a chance to object to sign restrictions. The approach is illustrated by considering a small model for the market of crude oil. Earlier findings that oil supply shocks explain only a very small fraction of movements in the price of oil are confirmed and it is found that the importance of aggregate demand shocks for oil price movements has declined since the mid 1980s. Copyright © 2013 John Wiley & Sons, Ltd.     

Determination of expected cost of equity with the CAPM: Theoretical extension using the law of error propagation

The determination of the expected return on equity based on the capital asset pricing model (CAPM) is an internationally recognized method, although the underlying theory is not without criticism and therefore leaves sufficient room for interpretation. Strictly speaking, the expected return on equity cannot be determined per se, as all parameters of the CAPM have to be estimated and contain measurement errors. The statistical measurement errors would have to be included in the calculation of the expected return on equity. The paper discusses the current view on how the expected return on equity is determined in the Germen‐speaking countries and presents an approach to transfer the measurement errors of the parameter risk‐free rate, market risk premium, and company beta to the calculated return on equity using the Gaussian law of error propagation.     

USING MODEL SELECTION ALGORITHMS TO OBTAIN RELIABLE COEFFICIENT ESTIMATES

This review surveys a number of common model selection algorithms (MSAs), discusses how they relate to each other and identifies factors that explain their relative performances. At the heart of MSA performance is the trade‐off between type I and type II errors. Some relevant variables will be mistakenly excluded, and some irrelevant variables will be retained by chance. A successful MSA will find the optimal trade‐off between the two types of errors for a given data environment. Whether a given MSA will be successful in a given environment depends on the relative costs of these two types of errors. We use Monte Carlo experimentation to illustrate these issues. We confirm that no MSA does best in all circumstances. Even the worst MSA in terms of overall performance – the strategy of including all candidate variables – sometimes performs best (viz., when all candidate variables are relevant). We also show how (1) the ratio of relevant to total candidate variables and (2) data‐generating process noise affect relative MSA performance. Finally, we discuss a number of issues complicating the task of MSAs in producing reliable coefficient estimates.     

Capital use intensity and productivity biases

Measures of productivity growth are often pro-cyclical. This paper focuses on measurement errors in capital inputs, associated with unobserved variations in capital utilization rates, as an explanation for the existence of pro-cyclical patterns in measures of productivity. Recently constructed national and state-specific indexes of inputs, outputs, and productivity in U.S. agriculture for 1949–2002 are used to estimate production functions that include proxy variables for changes in the utilization of durable inputs. The proxy variables include an index of farmers’ terms of trade and an index of local seasonal growing conditions. We find that utilization responses by farmers are significant and bias measures of productivity growth in a pro-cyclical pattern. We quantify the bias, adjust the measures of productivity for the estimated utilization responses, and compare the adjusted and conventional measures.     

Measurement error in causal analysis of panel data: Attenuated versus inflated relationships

The presence of random measurement error is commonly thought to cause attenuation of statistical relationships. While this is an unquestionable truth in bivariate analysis, it cannot be generalized to the multivariate case without qualification. This paper shows that measurement error may give rise to overestimates of parameters in causal analysis whenever there is more than one independent variable and the independent variables are correlated. If the independent variables are not measured with the same amount of reliability, there may also be considerable error in estimates of the relative magnitude of their impact. Both problems are particularly serious when the amount of measurement error is large relative to some of the causal effects such as in panel analysis with lagged dependent variables.