Overidentification Tests Research Articles

Sieve Semiparametric Two-Step GMM Under Weak Dependence

This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen's (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided.

Sieve semiparametric two-step GMM under weak dependence

This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen’s (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided.

Inference in Near Singular Regression

This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in conditions such as growth convergence. Structural equation models are also considered and limit theory is derived for the corresponding instrumental variable estimator, Wald test statistic, and overidentification test when the regressors are endogenous.

Revisiting Mendelian randomization studies of the effect of body mass index on depression.

Mendelian Randomization studies, which use genetic instrumental variables (IVs) as quasi-experiments to estimate causal effects, report inconsistent findings regarding effects of body mass index (BMI) on mental health. We used genetic IV to estimate effects of BMI on depression and evaluated validity of a commonly used IV. Female Nurse's Health Study participants (n=6989, average age 56.4, [Standard Deviation 6.91] years at first depression assessment) self-reported BMI, which was averaged across eight reports prior to depression assessment (mean=24.96, SD 4.50). Genetic instruments included fat mass and obesity-associated protein (FTO) alleles, melanocortin receptor 4 (MC4R) alleles, and polygenic risk scores based on 32 established polymorphisms for BMI. Depression was assessed using multiple symptom measures, scaled to the Geriatric Depression Scale 15, averaged across up to 7 biennial waves. We used over-identification tests to assess the validity of genetic IVs. In conventional estimates, each additional BMI point predicted 0.024 (95% Confidence Interval (CI): 0.020-0.029) higher average depression scores. Genetic IV estimates were not significant when based on FTO (beta: 0.064, CI: -0.014, 0.142), MC4R (beta: 0.005, CI: -0.146, 0.156), polygenic score excluding FTO (beta=-0.003, 95%-CI -0.051, 0.045), or mechanism-specific scores. The over-identification test comparing IV estimates based on FTO to estimates based on the polygenic score excluding FTO rejected equality of estimated effects (P=0.014). Results provide no evidence against a null effect of BMI on depression and call into question validity of FTO as an instrument for BMI in Mendelian Randomization studies.

The effect of a mixed passive and active labour market policy: Evidence from an Italian programme for dismissed workers

Liste di Mobilita (LM) is an Italian labour market programme targeted to dismissed workers. It combines an active component for all dismissed workers and a passive one to which only workers dismissed by firms with at least 16 employees are entitled; besides, 50% of the residual passive component the worker would have received had s/he remained unemployed is transferred to any firm hiring him/her from the LM. Exploiting a unique panel data set, we identify the causal effect of being eligible for the latter mixed passive and active component on short to mid-run labour market outcomes, via a fuzzy Regression Discontinuity Design. We validate the design by a set of over-identification tests. We find evidence of a negative effect of this component of the program on the short- to mid-run reemployment probability even if it is robust to alternative specification of the estimator only for middle-age women.

The effect of sexual activity on wages

Purpose – The purpose of this paper is to estimate whether sexual activity is associated with wages, and also to estimate potential interactions between individuals’ characteristics, wages and sexual activity. Design/methodology/approach – The central hypothesis behind this research is that sexual activity, alike health indicators and mental well-being, may be thought of as part of an individual’s set of productive traits that affect wages. Using two-stage estimations the author examines the relationship between adult sexual activity and wages. Findings – The author estimates that there is a monotonic relationship between the frequency of sexual activity and wage returns, whilst the returns to sexual activity are higher for those between 26 and 50 years of age. In addition, heterosexuals’ sexual activity does not seem to provide higher or lower wage returns than that of homosexuals, but wages are higher for those health-impaired employees who are sexually active. Over-identification tests, robustness checks, falsification tests, as well as, decomposition analysis and sample selection modelling enhance study’s strength. Social implications – Contemporary social analysis suggests that health, cognitive and non-cognitive skills and personality are important factors that affect wage level. Sexual activity may also be of interest to social scientists, since sexual activity is considered to be a barometer for health, quality of life, well-being and happiness. Originality/value – The paper adds to the literature on the importance of unobserved characteristics in determining labour market outcomes.

The Effect of the Kyoto Protocol on Carbon Emissions

AbstractSince 1997, CO2 emissions have continued to rise in many countries despite their emission caps under the Kyoto Protocol (Kyoto). Failure to meet promised targets, however, does not imply that Kyoto has been pointless. Whether Kyoto has made a difference relative to the counterfactual of “No Kyoto” is an empirical question that requires an instrumental variables strategy. We argue that countries’ ratification of the statutes governing the International Criminal Court is a valid instrument for ratification of Kyoto commitments. In our panel fixed effects estimations, the instrument easily passes weak identification and overidentification tests. It can be plausibly excluded from our second‐stage equations and does not cause CO2 emissions. Our estimates suggest that Kyoto ratification has a quantitatively large (about 10 percent) and robust, though only moderately statistically significant, negative effect on CO2 emissions. We also show that higher fuel prices and a different energy mix in Kyoto countries support this result.

Subsampling tests of parameter hypotheses and overidentifying restrictions with possible failure of identification

We introduce a general testing procedure in models with possible identification failure that has exact asymptotic rejection probability under the null hypothesis. The procedure is widely applicable and in this paper we apply it to tests of arbitrary linear parameter hypotheses as well as to tests of overidentification in time series models given by unconditional moment conditions. The main idea is to subsample classical tests, like for example the Wald or the J test. More precisely, instead of using critical values based on asymptotic theory, we compute data-dependent critical values based on the subsampling technique.We show that under full identification the resulting tests are consistent against fixed alternatives and that they have exact asymptotic rejection probabilities under the null hypothesis independent of identification failure. Furthermore, the subsampling tests of parameter hypotheses are shown to have the same local power as the original tests under full identification.An algorithm is provided that automates the block size choice needed to implement the subsampling testing procedure. A Monte Carlo study shows that the tests have reasonable size properties and often outperform other robust tests in terms of power.

Instrumental Variables in Sociology and the Social Sciences

Instrumental variable (IV) methods provide a powerful but underutilized tool to address many common problems with observational sociological data. Key to their successful use is having IVs that are uncorrelated with an equation's disturbance and that are sufficiently strongly related to the problematic endogenous covariates. This review briefly defines IVs, summarizes their origins, and describes their use in multiple regression, simultaneous equation models, factor analysis, latent variable structural equation models, and limited dependent variable models. It defines and contrasts three methods of selecting IVs: auxiliary instrumental variable, model implied instrumental variable, and randomized instrumental variable. It provides overidentification tests and weak IV diagnostics as methods to evaluate the quality of IVs. I review the use of IVs in models that assume heterogeneous causal effects. Another section summarizes the use of IVs in contemporary sociological publications. The conclusion suggests ways to improve the use of IVs and suggests that there are many areas in which IVs could be profitably used in sociological research.

Efficient minimum distance estimation with multiple rates of convergence

This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations.Possible applications include econometric problems with two dimensions of asymptotics, due to trimming, tail estimation, infill asymptotic, social interactions, kernel smoothing or any kind of regularization.

Gradual Financial Liberalization, Fdi, and Domestic Investment: Evidence From China's Panel Data

We argue that how inward foreign direct investment (FDI) affects domestic investment (DI) depends on the degree of financial deregulation. Utilizing the Chinese experience and its panel data, instrumenting FDI with weather indicators (validity supported by over-identification tests), our limited-information maximum likelihood (LIML) results suggest that both FDI and its interaction with financial deregulation have a significant negative effect on DI. It means FDI significantly crowds out DI in China, and higher degree of financial deregulation reinforces the crowding-out effect. The results are robust even after controlling for other growth factors, and time and province effects.

Current account, productivity and terms of trade shocks in Norway

Economic theory suggests that a permanent rise in terms of trade should result in a permanent rise in the standard of living. The increase comes from a permanent rise in productivity following an efficient reallocation of resources in a frictionless economy. This article presents Norway as a counterexample using three-variable Structural Vector Moving Average (SVMA) with long-run restrictions. The results show that permanent shocks to terms of trade improve the current account and have almost no effect on the output per capita growth. An over-identification test that restricts the permanent shocks to terms of trade to have only temporary effects on output per capita growth cannot be rejected as well. Overall, those shocks that have permanent effects on terms of trade or output per capita growth do not have permanent effects on each other. The empirical evidence suggests that strong intersectoral rigidities to reallocation of resources are present in Norway.

Institutions and Growth Revisited: OLS, 2SLS, G2SLS Random Effects IV Regression and Panel Fixed (within) IV Regression with Cross-Country Data

This paper revisits the Institutions and growth models. Econometric techniques have been applied on cross-country data, just to confirm the apriori knowledge that Institutions effect on growth is positive and highly statistically significant. This evidence was confirmed by all four models. OLS proved as a better technique for our data than 2SLS, this simply because overidentification test showed that instrument cannot be considered exogenous, also Hausman test showed that OLS is better than 2SLS at 1% and 5% levels of significance. G2SLS estimator and Fixed effects panel estimators just confirmed the results from the OLS and 2SLS. As a proxy variable for institutions we used Rule of law variable, also as instruments were used revolutions and Freedom house rating as well as War casualties variables. Also as conclusion here Trade is insignificant in influence to GDP growth compared with quality of institutions.

Simple and powerful GMM over-identification tests with accurate size

Based on the series long run variance estimator, we propose a new class of over-identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms. We show that when the number of terms used in the series long run variance estimator is fixed, the conventional J statistic, after a simple correction, is asymptotically F -distributed. We apply the idea of the F -approximation to the conventional kernel-based J tests. Simulations show that the J ∗ tests based on the finite sample corrected J statistic and the F -approximation have virtually no size distortion, and yet are as powerful as the standard J tests.

Intra-Continental and Intercontinental Service Trade in the Travel and Tourism Industry

This study investigates the features and determinants of the international travel and tourism service trade between the European, Asian and North American markets from 2000 to 2005. The evolution of bilateral service trade in each of these markets indicates that travel and tourism within continents plays an important role in 36 countries. The study first employs the Breusch–Pagan LM (Lagrange multiplier) test, the Hausman test and the Hausman–Taylor over-identification test to choose the appropriate empirical method. The empirical results reveal that the supply–pull effect from parent countries (the economic size of tourist origins) plays an important role in improving the tourism service exports of the various destinations. In addition, the home countries' exports of travel services are inelastic to the appreciation of their own currencies. Moreover, distribution infrastructures and the adjacency and RTA (ASEAN) dummies are found to have significantly positive contributions in terms of enhancing Asian tourism service exports, whereas the European Union (EU) and NAFTA discourage European and North American tourism exports, respectively.

Narrow Replication of Yogo (2004) Estimating the Elasticity of Intertemporal Substitution when Instruments are Weak

SUMMARY This narrow replication exercise of Yogo (Review of Economics and Statistics 2004; 86(3): 797–810) finds results identical to the original paper, and provides results on overidentification tests for specifications that do not suffer from the weak instruments problem. The null hypothesis of the Sargan test is rejected in several cases, in particular for US and UK quarterly data. When other combinations of instruments are used the null of the Sargan test is rejected again in several cases. These rejections cast doubts on either instrument validity or model specification. Copyright © 2011 John Wiley & Sons, Ltd.

Fifteen years of labour market regulations and policies in Italy: what have we learned from their evaluation?

During the last fifteen years a notable number of labour market interventions took place in Italy, under two main headings: new regulations and implementation of active and/or passive programmes. The paper reviews a fair number of subjectively selected impact evaluation studies published in the last ten years. The framework is provided by counterfactual analysis; preliminary, its barebones are sum up. The focus of the review in on two aspects. First, a blend of empirical and analytical issues critical for credible impact evaluations are discussed. They emerge from the fact that the reviewed studies are carried out in an observational setting, and refer to prospective vs. retrospective evaluation, availability (or lack) of adequate data, over-identification tests in order to corroborate (or falsify) the identifying restriction on which the evaluation strategy rests, and heterogeneous effects. Second, the substantive evidence offered by the reviewed studies is summarized. It points to generally minor policy effects; some tentative explanations for that lack of effectiveness are suggested.

Simple and Powerful GMM Over-Identification Tests with Accurate Size

The paper provides a new class of over-identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms. The tests are based on the series long run variance estimator that is designed to pivotalize the moment restrictions. We show that when the number of terms used in the series long run variance estimator is fixed, the conventional J statistic, after a simple correction, is asymptotically F-distributed. We apply the idea of the F-approximation to the conventional kernel-based J tests. Simulations show that the J* tests based on the finite sample corrected J statistic and the F approximation have virtually no size distortion, and yet are as powerful as the standard J tests.

Accurate and robust tests for indirect inference

In this paper we propose accurate parameter and over-identification tests for indirect inference. Under the null hypothesis the new tests are asymptotically χ2-distributed with a relative error of order n−1. They exhibit better finite sample accuracy than classical tests for indirect inference, which have the same asymptotic distribution but an absolute error of order n−1/2. Robust versions of the tests are also provided. We illustrate their accuracy in nonlinear regression, Poisson regression with overdispersion and diffusion models.

GMM Overidentification Test with First Order Underidentification

This paper revisits the asymptotic theory of GMM when the moment conditions identify a unique parameter true value $\theta^0$ but the rank condition of the Jacobian matrix at $\theta^0$ fails. The possibility in case of nonlinear moment restrictions of such simultaneous global identification but first order under-identification has already been pointed out by Sargan (1983). The contribution of this paper is to provide a general asymptotic theory when one can maintain an assumption of second order identification. While this issue has been addressed in a maximum likelihood context by Lee and Chesher (1986) and Rotnitzky, Cox, Bottai and Robbins (2000), we set the focus on the asymptotic behaviour of the GMM overidentification test statistic $J_T$. We show that with $H$ moment conditions, when the Jacobian matrix of the moment conditions evaluated at $\theta^0$ is of rank $p-1$, where $p$ is the number of parameters, the asymptotic distribution of $J_T$ is a half-half mixture of $\chi^2_{H-p}$ and $\chi^2_{H-(p-1)}$ instead of the standard $\chi^2_{H-p}$. In other words, the distribution of $J_T$ for large sample sizes $T$ has fatter tails, leading to over-rejection of the null of valid moments when using standard critical values. The practical significance of this oversize problem is illustrated by Monte Carlo experiments in the context of a test for common GARCH features proposed by Engle and Kozicki (1993).