Estimating the validity of administrative variables

Administrative data have become more important for both official statistics and academic research. One possible problem with such data is that they are biased and have a low validity. Although this problem is often mentioned in a qualitative respect, the validity is seldom quantitatively measured. This article presents a method to estimate the validity of administrative variables. By applying the classical test theory, the validity can be determined by using linked survey and administrative data which should measure the same concepts. This idea is elaborated with an empirical example in which the construct validity of age, gender, educational attainment and wages is determined simultaneously. A linear structural equations model with a measurement component is used to compute the construct validity. The analyses reveal that educational attainment and wages show some bias, but not higher than the bias found in the survey.     

Estimating the shirking model with variable effort

We show in a theoretical efficiency wage model where firms differ in monitoring intensity that the impact of monitoring intensity on wages is ambiguous, a result that mirrors evidence from the empirical literature. We argue that to correctly specify the impact of monitoring on wages, the interaction between monitoring and effort needs to be modelled. Results using a worker, firm panel from Ghana which contains reasonable effort and monitoring proxies show that the return to effort is higher in poorly monitored sectors as the theory suggests.     

Estimating structural equation models with non-normal variables by using transformations

We discuss structural equation models for non-normal variables. In this situation the maximum likelihood and the generalized least-squares estimates of the model parameters can give incorrect estimates of the standard errors and the associated goodness-of-fit chi-squared statistics. If the sample size is not large, for instance smaller than about 1000, asymptotic distribution-free estimation methods are also not applicable. This paper assumes that the observed variables are transformed to normally distributed variables. The non-normally distributed variables are transformed with a Box–Cox function. Estimation of the model parameters and the transformation parameters is done by the maximum likelihood method. Furthermore, the test statistics (i.e. standard deviations) of these parameters are derived. This makes it possible to show the importance of the transformations. Finally, an empirical example is presented.     

Estimating the autocorrelated error model with trended data

A Monte Carlo study of the small sample properties of various estimators of the linear regression model with first-order autocorrelated errors. When independent variables are trended, estimators using Ttransformed observations (Prais-Winsten) are much more efficient than those using T–1 (Cochrane–Orcutt). The best of the feasible estimators isiterated Prais-Winsten using a sum-of-squared-error minimizing estimate of the autocorrelation coefficient ?. None of the feasible estimators performs well in hypothesis testing; all seriously underestimate standard errors, making estimated coefficients appear to be much more significant than they actually are.     

Estimating regression equations with common explanatory variables but unequal numbers of observations

It is well known that generalised least-squares estimators of a set of regression equations coincide with ordinary least-squares estimators when the explanatory variables are the same in all equations and there are equal numbers of observations. This paper is concerned with the case of unequal numbers of observations and it is shown that the above result no longer holds. Appropriate estimators are derived and their small-sample properties are investigated analytically. The results are of practical importance because the data patterns discussed can easily arise in econometric studies.     

A threshold stochastic volatility model with explanatory variables

In this paper, we introduce a threshold stochastic volatility model with explanatory variables. The Bayesian method is considered in estimating the parameters of the proposed model via the Markov chain Monte Carlo (MCMC) algorithm. Gibbs sampling and Metropolis–Hastings sampling methods are used for drawing the posterior samples of the parameters and the latent variables. In the simulation study, the accuracy of the MCMC algorithm, the sensitivity of the algorithm for model assumptions, and the robustness of the posterior distribution under different priors are considered. Simulation results indicate that our MCMC algorithm converges fast and that the posterior distribution is robust under different priors and model assumptions. A real data example was analyzed to explain the asymmetric behavior of stock markets.     

Estimating the returns to education for Australian youth via rank-order instrumental variables

This paper employs the rank-order instrumental variable (IV) procedure of Vella and Verbeek [Vella, F., Verbeek, M., 1997. Using rank order as an instrumental variable: an application to the return to schooling, CES Discussion Paper 97.10, K.U. Leuven.] to estimate the returns to education for Australian youth. The attraction of this approach is that it can account for the endogeneity of schooling in the wage equation via the use of instrumental variables without the use of exclusion restrictions. We find, after accounting for the endogeneity of schooling, that an additional year of schooling is associated with an increase in wages of approximately 8%. Furthermore, we find that the rank-order IV approach is able to identify the presence of endogeneity in this particular empirical example. However, despite this, the adjusted estimate of how schooling affects wage is close to the ordinary least squares (OLS) estimate.     

An Econometric Analysis of I(2) Variables

This paper provides a selective survey of the recent literature dealing with I(2) variables in economic time series, that is, processes that require to be differenced twice in order to become stationary. With reference to particular economic models intuition is provided of why I(2)-and polynomial cointegration are features likely to occur in economics. The properties of I(2) series are discussed and I review topics such as: Testing for double unit roots, representations of I(2) cointegrated systems, and hypothesis testing in single equations as well as in systems of equations. Different data sets are used to illustrate the various econometric and statistical techniques.     

Testing the purchasing power parity through I(2) cointegration techniques

This paper contributes to the empirical literature on the purchasing power parity (PPP) over the post‐Bretton Woods period by providing a time‐series based interpretation of the controversial evidence characterizing the dynamics of real exchange rates. It is shown that the persistence of deviations from the PPP between a set of European countries and the United States may be empirically attributed to the presence of I(2) stochastic trends in prices using Consumer Price Indices. Interestingly, the slow adjustment towards the equilibrium can be modelled through ‘integral‐proportional’ equilibrium correction models and this evidence can be partly reconciled with theories where the inflation rate reduces the markup of profit‐maximizing firms acting on imperfectly competitive markets. Copyright © 2005 John Wiley & Sons, Ltd.     

A note on the multiple indicator-multiple cause model with several latent variables

Jöreskog/Goldberger [1975] use a maximum likelihood procedure to estimate the parameters of a model in which one observes multiple indicators and multiple causes of a single latent variable. This note extends their analysis to cover the case of several latent variables.     

Estimating and testing a quantile regression model with interactive effects

This paper proposes a quantile regression estimator for a model with interactive effects potentially correlated with covariates. We provide conditions under which the estimator is asymptotically Gaussian and we investigate the finite sample performance of the method. An approach to testing the specification against a competing fixed effects specification is introduced. The paper presents an application to study the effect of class size and composition on educational attainment. The evidence suggests that while smaller classes are beneficial for low performers, larger classes are beneficial for high performers. The fixed effects specification is rejected in favor of the interactive effects specification.     

Estimating predictions,prediction errors and their standard deviations using constructed variables

Increasing use has been made of predictive tests for assessing model adequacy, but it is sometimes difficult to generate predictions and their standard errors in dynamic or simultaneous equation models. Following earlier suggestions by Salkever and Fuller, this paper shows how the requisite information may be obtained by the use of specially constructed variables in a regression framework. The main use of the method will be in those situations where prediction information is not available as a standard option in econometric packages.     

Trend stationarity in the I(2) cointegration model

A vector autoregressive model for I(2) processes which allows for trend-stationary components and restricts the deterministic part of the process to be at most linear is defined. A two-step statistical analysis of the model is derived. The joint test of I(1) and I(2) cointegrating ranks is shown to be asymptotically similar with respect to the drift terms and the asymptotic distribution is tabulated. The cointegrating parameters are shown to be mixed Gaussian and an application for UK monetary data illustrates the proposed analysis.     

Common trends and cycles in I(2) VAR systems

This paper analyzes common cycles in I(2) vector autoregressive (VAR) systems. We consider different choices of stationary variables extracted from a VAR, including deviations from equilibria. This extension is based on the equilibrium dynamics representation of the system, introduced in this paper. Inference on the number of common features is addressed via reduced rank regression, as well as estimation of the cofeature relations and testing. An application to Australian prices is presented; it is found that the deviation from one equilibrium relation is an innovation process, whereas no common cycles can be obtained for the acceleration rates.     

Estimating latent class model parameters for filter questions with skip patterns

Filter questions with skip patterns have been widely used in survey research, and latent class models (LCM) are often used to analyze this type of categorical data. The LCM parameters are usually estimated by means of an EM (expectation maximization) algorithm. When the pattern is present, the non-response of the skip pattern cannot be treated as random missingness. We thus propose a modified algorithm to estimate the latent class parameters when non-response is present, and the approach is attractive for two reasons. First, the latent class model with the algorithm is very flexible in the sense that it can model the association of variables with the skip patterns under study. Secondly, the algorithm can be easily implemented using any computer language. An empirical example is used to demonstrate the usefulness of the algorithm. The algorithm may also be flexibly generalized to more complex surveys, for example, polytomous responses.     

Analysing I(2) Systems by Transformed Vector Autoregressions*

We characterize the restrictions imposed by the minimal I(2)‐to‐I(1) transformation that underlies much applied work, e.g. on money demand relationships or open‐economy pricing relationships. The relationship between the parameters of the original I(2) vector autoregression, including the coefficients of polynomially cointegrating relationships, and the transformed I(1) model is characterized. We discuss estimation of the transformed model subject to restrictions as well as the more commonly used approach of unrestricted reduced rank regression. Only a minor loss of efficiency is incurred by ignoring the restrictions in the empirical example and a simulation study. A properly transformed vector autoregression thus provides a practical and effective means for inference on the parameters of the I(2) model.     

The Instability of the Money Demand Function: An I(2) Interpretation

Some studies have suggested that although money and prices appear to be I(2) processes, real money balances are I(1) and this transformation preserves an important long-run relationship between money and prices. In this paper we present evidence indicating that the success of such a nominal-to-real transformation depends upon the particular monetary aggregate under consideration. It turns out that imposing long-run price homogeneity does not remove all I(2) components from a model of aggregate broad UK M4, but it does prove successful in the case of sectoral components of M4. Since recent research on money demand functions finds more stable relationships between sectoral components of M4 and aggregate demand, our analysis seems to point to a direct link between the existence of I(2) components and the stability of different money demand functions.     

Regime shifts in stock–flow I(2)–I(1) systems: the case of US fiscal sustainability

In the last two decades, fiscal sustainability has been tested through the use of non‐stationary time series analysis. Two different approximations can be found in the literature: first, a univariate approach that has focused on the stochastic properties of the stock of debt and, second, a multivariate one that has focused on the long‐run properties of the flows of expenditures and revenues, i.e., in the stochastic properties of the deficit. In this paper we unify these approaches considering the stock–flow system that fiscal variables configure. Our approach involves working in an I(2) stochastic processes framework. Given the possibility of the existence of regime shifts in the sustainability of US deficit that the literature has pointed out, we develop a new statistic that can be applied to test several types of I(2) cointegration and multicointegration relationships allowing for regime shifts. To test for these kinds of changing long‐run relationships we propose the use of a residual‐based Dickey–Fuller class of statistic that accounts for one structural break. We show that consistent estimates of the break fraction can be obtained through the minimization of the sum of squared residuals when there is I(2) cointegration. The finite sample performance of the proposed statistic is investigated by Monte Carlo simulations. The econometric methodology is applied to assess whether the US fiscal deficit and debt are sustainable. Copyright © 2010 John Wiley & Sons, Ltd.