Exogeneity in structural equation models

The practical relevance of several concepts of exogeneity of treatments for the estimation of causal parameters based on observational data are discussed. We show that the traditional concepts, such as strong ignorability and weak and super-exogeneity, are too restrictive if interest lies in average effects (i.e. not on distributional effects of the treatment). We suggest a new definition of exogeneity, KL-exogeneity. It does not rely on distributional assumptions and is not based on counterfactual random variables. As a consequence it can be empirically tested using a proposed test that is simple to implement and is distribution-free.     

Testing constancy of the error covariance matrix in vector models

In this paper a Lagrange multiplier test of the hypothesis that the covariance matrix of a multivariate time series model is constant over time is considered. It is assumed that under the alternative, the error variances are time-varying, whereas the correlations remain constant over time. Under the parameterized alternative hypothesis the variances may change continuously as a function of time or some observable stochastic variables. Small-sample properties of the test statistic are investigated by simulation. The assumption of constant correlations does not appear overly restrictive.     

Identification of simultaneous equation models with measurement error

This paper establishes identification conditions for a simultaneous equation model in which some of the exogenous variables are measured with error. It is assumed that observational information is confined to the covariance matrix of the observed variables and that prior information on the structural coefficients and error variances takes the form of zero restrictions. The primary result is an easily-applied assignment condition for checking whether or not there are an adequate number and variety of prior restrictions to identify the structural parameters.     

Identification of simultaneous equation models with measurement error: a computerized evaluation

Rank conditions for identification in structural models are often difficult evaluate. Here we consider simultaneous equation models with measurement error and we show that previously published rank conditions for identification are not well-suited for evaluation. An alternative rank condition is derived and a computer algebra program is presented that takes care of both the construction and the computation of the rank of the relevant Jacobian matrix. It uses the parameter restrictions as input in order to characterize the identification situation of the individual parameters in the output.     

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.     

Testing for serial correlation in simultaneous equation models: Some further results

In this paper approximate counterparts of the exact tests earlier proposed by the authors are examined. Type 1 error probabilities and test powers are estimated and compared using Monte Carlo experiments. The effect on the Type 1 error probabilities of the misspecification which results when serial correlation is present elsewhere in the system is also investigated.     

Well-posedness of measurement error models for self-reported data

This paper considers the widely admitted ill-posed inverse problem for measurement error models: estimating the distribution of a latent variable $X^1$ from an observed sample of $X$, a contaminated measurement of $X^1$. We show that the inverse problem is well-posed for self-reporting data under the assumption that the probability of truthful reporting is nonzero, which is supported by empirical evidences. Comparing with ill-posedness, well-posedness generally can be translated into faster rates of convergence for the nonparametric estimators of the latent distribution. Therefore, our optimistic result on well-posedness is of importance in economic applications, and it suggests that researchers should not ignore the point mass at zero in the measurement error distribution when they model measurement errors with self-reported data. We also analyze the implications of our results on the estimation of classical measurement error models. Then by both a Monte Carlo study and an empirical application, we show that failing to account for the nonzero probability of truthful reporting can lead to significant bias on estimation of the latent distribution.     

Robustness of normal theory statistics in structural equation models*

A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.     

Testing equality of variances in the analysis of repeated measurements

The problem of comparing the precisions of two instruments using repeated measurements can be cast as an extension of the Pitman-Morgan problem of testing equality of variances of a bivariate normal distribution. Hawkins (1981) decomposes the hypothesis of equal variances in this model into two subhypotheses for which simple tests exist. For the overall hypothesis he proposes to combine the tests of the subhypotheses using Fisher's method and empirically compares the component tests and their combination with the likelihood ratio test. In this paper an attempt is made to resolve some discrepancies and puzzling conclusions in Hawkins's study and to propose simple modifications.
The new tests are compared to the tests discussed by Hawkins and to each other both in terms of the finite sample power (estimated by Monte Carlo simulation) and theoretically in terms of asymptotic relative efficiencies.     

Testing for structural stability of factor augmented forecasting models

Mild factor loading instability, particularly if sufficiently independent across the different constituent variables, does not affect the estimation of the number of factors, nor subsequent estimation of the factors themselves (see e.g.  Stock and Watson (2009)). This result does not hold in the presence of large common breaks in the factor loadings, however. In this case, information criteria overestimate the number of breaks. Additionally, estimated factors are no longer consistent estimators of “true” factors. Hence, various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings. However, forecast failure of factor augmented models can be due to either factor loading instability, regression coefficient instability, or both. To address this issue, we develop a test for the joint hypothesis of structural stability of both factor loadings and factor augmented forecasting model regression coefficients. Our proposed test statistic has a chi-squared limiting distribution, and we are able to establish the first order validity of (block) bootstrap critical values. Empirical evidence is also presented for 11 US macroeconomic indicators.     

Evaluating estimation methods for ordinal data in structural equation modeling

This study examined the performance of two alternative estimation approaches in structural equation modeling for ordinal data under different levels of model misspecification, score skewness, sample size, and model size. Both approaches involve analyzing a polychoric correlation matrix as well as adjusting standard error estimates and model chi-squared, but one estimates model parameters with maximum likelihood and the other with robust weighted least-squared. Relative bias in parameter estimates and standard error estimates, Type I error rate, and empirical power of the model test, where appropriate, were evaluated through Monte Carlo simulations. These alternative approaches generally provided unbiased parameter estimates when the model was correctly specified. They also provided unbiased standard error estimates and adequate Type I error control in general unless sample size was small and the measured variables were moderately skewed. Differences between the methods in convergence problems and the evaluation criteria, especially under small sample and skewed variable conditions, were discussed.     

The impact of desirability and feasibility on entrepreneurial intentions: A structural equation model

There is general agreement that attitudes towards entrepreneurship are determinant factors to decide to be an entrepreneur. In this context, this research is focused on analyzing the relationship between desirability and feasibility on university student’s intentions to create a new firm in Catalonia. A structural equation model supported by Krueger & Brazeal’s Model was tested with different groups of students. The main results reveal most of university students consider desirable to create a new firm, although the perception of feasibility is not positive. Also, there is a statistical significant and positively relationship between credibility and the intention to create a new firm.

The impact of on-site mentoring on expatriate socialization: a structural equation modelling approach

While the literature on expatriate adjustment has focused on the importance of back-home mentors and their instrumentality for future career advancement, this research explores the importance of on-site mentors for the effective socialization of expatriates into their current overseas assignments. Using a sample of 179 expatriates located in nineteen countries, this paper presents a structural equation model illustrating the relationships among mentoring received, expatriate socialization and socialization outcomes. Amount of mentoring received positively impacts on expatriate socialization, which in turn positively influences job attitudes, intention to finish the expatriate assignment and expatriate understanding of global business issues. Using Hofstede's typology of national cultures, this research also suggests that the international context of the overseas assignment affects how much on-site mentoring expatriates receive. Specifically, expatriates are more likely to receive mentoring in small power distance, weak uncertainty avoidance and individualistic cultures.     

Linear indices in nonlinear structural equation models: best fitting proper indices and other composites

Quality & Quantity - The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a...     

Nonparametric testing for smooth structural changes in panel data models

Detecting and modeling structural changes in time series models have attracted great attention. However, relatively little effort has been paid to the testing of structural changes in panel data models despite their increasing importance in economics and finance. In this paper, we propose a new approach to testing structural changes in panel data models. Unlike the bulk of the literature on structural changes, which focuses on detection of abrupt structural changes, we consider smooth structural changes for which model parameters are unknown deterministic smooth functions of time except for a finite number of time points. We use nonparametric local smoothing method to consistently estimate the smooth changing parameters and develop two consistent tests for smooth structural changes in panel data models. The first test is to check whether all model parameters are stable over time. The second test is to check potential time-varying interaction while allowing for a common trend. Both tests have an asymptotic $N(0,1)$ distribution under the null hypothesis of parameter constancy and are consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points alternatives. Simulation studies show that the tests provide reliable inference in finite samples and two empirical examples with respect to a cross-country growth model and a capital structure model are discussed.     

The impact of non-normality,sample size and estimation technique on goodness-of-fit measures in structural equation modeling: evidence from ten empirical models of travel behavior

Ten empirical models of travel behavior are used to measure the variability of structural equation model goodness-of-fit as a function of sample size, multivariate kurtosis, and estimation technique. The estimation techniques are maximum likelihood, asymptotic distribution free, bootstrapping, and the Mplus approach. The results highlight the divergence of these techniques when sample sizes are small and/or multivariate kurtosis high. Recommendations include using multiple estimation techniques and, when sample sizes are large, sampling the data and reestimating the models to test both the robustness of the specifications and to quantify, to some extent, the large sample bias inherent in the χ ² test statistic.     

Estimation of variances in orthogonal finite discrete spectrum linear regression models

The Invariant Quadratic Estimators, the Maximum Likelihood Estimator (MLE) and Restricted Maximum Likelihood Estimator (REML) of variances in an orthogonal Finite Discrete Spectrum Linear Regression Model (FDSLRM) are derived and the problems of unbiasedness and consistency of these estimators are investigated.Acknowledgement. The research was supported by the grants 1/0272/03, 1/0264/03 and 2/4026/04 of the Slovak Scientific Grant Agency VEGA.     

Discrete factor approximations in simultaneous equation models: estimating the impact of a dummy endogenous variable on a continuous outcome

This paper contains a Monte Carlo evaluation of estimators used to control for endogeneity of dummy explanatory variables in continuous outcome regression models. When the true model has bivariate normal disturbances, estimators using discrete factor approximations compare favorably to efficient estimators in terms of precision and bias; these approximation estimators dominate all the other estimators examined when the disturbances are non-normal. The experiments also indicate that one should liberally add points of support to the discrete factor distribution. The paper concludes with an application of the discrete factor approximation to the estimation of the impact of marriage on wages.     

Testing the constancy in varying-coefficient regression models

Two hypothesis testing problems are considered in this paper to check the constancy of the coefficients in the varying-coefficient regression model. Tests for the two corresponding hypothesis testing problems are derived by two p-values. The proposed p-values can be thought as the generalized p-values, which are given by linear interpolation based on fiducial method. When all of the coefficients are constants, the p-value is uniformly distributed on interval (0, 1). Furthermore, the bound of the difference between the cumulative distribution function of the p-value and the uniform distribution on (0, 1) is given, which tends to 0 under some conditions. Meanwhile, the proposed tests are proved to be consistent under mild conditions. In addition, the proposed new method could be extended to include a broader range of hypotheses. Some good finite sample performances of the tests are investigated by simulations, in which a comparison with other test is given. Finally, a simple example based on real data is given to illustrate the application of our test, different result was obtained based on the proposed test.