Test Of Overidentifying Restrictions Research Articles

Standard Errors for Calibrated Parameters

Abstract Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive conservative standard errors and confidence intervals for the structural parameters that are valid even under the worst-case correlation structure. In the over-identified case, we show that the moment weighting scheme that minimizes the worst-case estimator variance amounts to a moment selection problem with a simple solution. Finally, we develop tests of over-identifying or parameter restrictions. We apply our methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model.

A Heteroscedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates

This article proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and instruments to be larger than the sample size. The test is scale-invariant and robust to heteroscedastic errors. To construct the final test statistic, we first introduce a test based on the maximum norm of multiple parameters that could be high-dimensional. The theoretical power based on the maximum norm is higher than that in the modified Cragg-Donald test, the only existing test allowing for large-dimensional covariates. Second, following the principle of power enhancement, we introduce the power-enhanced test, with an asymptotically zero component used to enhance the power to detect some extreme alternatives with many locally invalid instruments. Finally, an empirical example of the trade and economic growth nexus demonstrates the usefulness of the proposed test.

TRADE OPENNESS, INVESTMENT FREEDOM- SELECTED COUNTRY RISK INDICATORS, IMPACT ON FOREIGN DIRECT INVESTMENTS, A PANEL VECTOR AUTOREGRESSION MODEL APPROACH

We employ a panel vector autoregression model (PVAR) selecting as endogenous variables Foreign Direct Investments percent of GDP, Trade Openness and Investment Freedom for a database comprised of European Countries. The data are collected from the Global Economy database. We compare different PVAR models changing the input of desired lags. We test the Hansen test for over-identifying restrictions and we generate the Generalised impulse response functions. The article uses a Hahn Kuehrsteiner Panel Var estimation estimating a stationarity PVAR with fixed effects. Econometric analysis shows a significant impact of trade openness and investment freedom indicators on foreign direct investment in Europe.

Tests for independence between categorical variables

I prove the numerical equivalence between Pearson’s independence test statistic for categorical variables and the Lagrange Multiplier and overidentifying restrictions test statistics in several popular linear and non-linear regression models. I also show that its asymptotically equivalent Likelihood Ratio test is numerically identical in the non-linear regression models, and that the heteroskedasticity-robust Wald test statistic in the multivariate linear probability model and the moment condition model coincide with the Wald test statistic in the conditional multinomial model. Finally, I show that all these equivalences also apply to serial independence tests in discrete Markov chains. • Pearson’s independence test is numerically equivalent to the LM in regression models. • LR test is numerically identical in the non-linear regression models. • Heteroskedastic Wald test in LPM and GMM coincide with Wald in multinomial model. • All these equivalences apply to serial independence tests in discrete Markov chains.

Identifying factor‐augmented vector autoregression models via changes in shock variances

SummaryThis study proposes a method to identify factor‐augmented vector autoregression models without imposing uncorrelatedness or any timing restrictions among observed and unobserved factors in the vector autoregression system. To this end, we utilize changes in unconditional shock variances following Rigobon (2003). The proposed method can incorporate both observed and unobserved factors in the structural vector autoregression system and allows the contemporaneous matrix to be fully unrestricted. We derive the asymptotic distribution of the impulse response estimator and consider a bootstrap inference method. We also provide two diagnostic tools: a test for the identification condition and a class of overidentifying restrictions tests. A Monte Carlo experiment shows that the asymptotic and bootstrap methods yield a satisfactory coverage rate when the shock of an observed factor is analyzed, although the bootstrap method is more accurate. We apply the proposed method to an empirical example for the effects of U.S. monetary policies on asset prices. A contractionary monetary policy shock induces positive and hump‐shaped interest rate responses along the maturity dimension and negative but insignificant stock price responses.

Remittances, Trade Balance and Economic Growth in West Africa Sub-region

The impacts remittances and trade balance has on growth in West Africa sub-region was examine for the period 2007 to 2019. To this end, based on relevant theory a model was drawn. However, prior to estimation, reliability and validity of the data set was examined. This was followed by unit root test which shows that all variables attained stationarity at their first difference while Cointegration test indicated that there exists a long-run convergence among the variables. System Generalised Method of Moment estimation revealed that remittances inflows significantly and positively impact economic growth while trade balance exerted a negative and significant impact on economic growth. The over-identifying restrictions test of J-Statistics revealed that the instrument of measurement employed was valid. It was recommended among others that policy makers in West Africa should implement policies that continually encourage remittances inflow to the sub-region while ensuring that trade deficits emanates from productive investment.

Testing Overidentifying Restrictions with High-Dimensional Data and Heteroskedasticity

This paper proposes a new test of overidentifying restrictions (called the Q test) with high-dimensional data. This test is based on estimation and inference for a quadratic form of high-dimensional parameters. It is shown to have the desired asymptotic size and power properties under heteroskedasticity, even if the number of instruments and covariates is larger than the sample size. Simulation results show that the new test performs favorably compared to existing alternative tests (Chao et al., 2014; Kolesar, 2018; Carrasco and Doukali, 2021) under the scenarios when those tests are feasible or not. An empirical example of the trade and economic growth nexus manifests the usefulness of the proposed test.

Testing overidentifying restrictions with many instruments and heteroscedasticity using regularised jackknife IV

Summary This paper proposes a new overidentifying restrictions test in a linear model when the number of instruments (possibly weak) may be smaller or larger than the sample size n or even infinite in a heteroscedastic framework. The proposed J test combines two techniques: the jackknife method and the regularisation technique which consists in stabilising the projection matrix. We theoretically show that our new test achieves the asymptotically correct size in the presence of many instruments. The simulation results demonstrate that our modified J statistic test has better empirical properties in small samples than existing J tests. We also propose a regularised F-test to assess the strength of the instruments, which is robust to heteroscedasticity and many instruments.

Inference in second-order identified models

We explore the local power properties of different test statistics for conducting inference in moment condition models that only identify the parameters locally to second order. We consider the conventional Wald and LM statistics, and also the Generalized Anderson–Rubin (GAR) statistic (Anderson and Rubin, 1949; Dufour, 1997; Staiger and Stock, 1997; Stock and Wright, 2000), KLM statistic (Kleibergen, 2002; Kleibergen, 2005) and the GMM extension of Moreira (2003) (GMM-M) conditional likelihood ratio statistic. The GAR, KLM and GMM-M statistics are so-called “identification robust” since their (conditional) limiting distribution is the same under first-order, weak and therefore also second order identification. For inference about the model specification, we consider the identification-robust J statistic (Kleibergen, 2005), and the GAR statistic. Interestingly, we find that the limiting distribution of the Wald statistic under local alternatives not only depends on the distance to the null hypothesis but also on the convergence rate of the Jacobian. We specifically analyse two empirically relevant models with second order identification. In the panel autoregressive model of order one, our analysis indicates that the Wald test of a unit root value of the autoregressive parameter has better power compared to the corresponding GAR test which, in turn, dominates the KLM, GMM-M and LM tests. For the conditionally heteroskedastic factor model, we compare Kleibergen (2005) J and the GAR statistics to Hansen (1982) overidentifying restrictions test (previously analysed in this context by Dovonon and Renault, 2013) and find the power ranking depends on the sample size. Collectively, our results suggest that tests with meaningful power can be conducted in second-order identified models.

Testing distributional assumptions using a continuum of moments

We propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test, which takes into account the correlation between influence functions for different argument values. We derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size. We show its consistency against any deviation from the null, study its local power and compare it with existing tests. An extensive Monte Carlo exercise confirms that our proposed tests display good power in finite samples against a variety of alternatives.

A note on a cross-sectional GMM estimator in the presence of an observable common shock

This paper studies property of a modified GMM estimator employed for a single cross-section of data that are strongly dependent due to an observed stochastic common shock. The estimator is shown to be asymptotically mixed normal. Statistical inference can be conducted with a Wald test. An overidentifying restrictions test is suggested.

Testing overidentifying restrictions with a restricted parameter space

We show that the standard test for testing overidentifying restrictions, which compares the J-statistic (Hansen, 1982) to χ2 critical values, does not control asymptotic size when the true parameter vector is allowed to lie on the boundary of the (optimization) parameter space. We also propose a modified J-statistic that, under the null hypothesis, is asymptotically χ2 distributed, such that the resulting test does control asymptotic size.

Does Mandatory Ifrs Adoption and Macroeconomic Factors Affect Cost of Equity Capital? Empirical Evidence From South African Listed Firms

Purpose: This paper investigates the collaboration of International Financial Reporting Standards (IFRS) adopted and macroeconomic variables interaction with information asymmetry, analysts following and managerial opportunism affecting the cost of equity capital, and also influence investor’s decision taking on companies in South Africa.
 Design/Approach: A sample of 49 listed Johannesburg mining and manufacturing firms was extracted from archival database of INET BFA/IRESS SA, Morningstar, and Anupedia. A leverage fixed effects panel data set of firms from 2001 to 2014 was examined, which shows that Breusch-Lagrange Multiplier tests and the test of over-identifying restrictions used, form the basis of the content analysis of the most recent IFRS effect after mandatory adoption. We used a hand-collected dataset between 2000 and 2015.
 Findings: Our findings suggest that a significant association is found between IFRS and its interactions with managerial opportunism and integrity but with a reasonable statistical effect. However, the IFRS adoption effect on the cost of equity capital of South African firms’ has no significant effect.
 Practical implications: This study reveals that most firms report more, the credibility of annual financial statements which may not be sufficient because of the qualitative data for an assessment of managerial opportunism, information asymmetry and analysts following. Of such myopia of company managers, their reputation causes agency problems and as a result, shareholders interest is mainly focused on improving reporting standards
 Originality: The research considers dual harmonizing facets: first, that the interaction with IFRS adoption and economic factors impact on the cost of equity capital may be so pathetic and obvious; and second, that IFRS moderation impacts on the cost of equity capital in Sub- Saharan African. This finding should be meaningful to managers, analysts, policymakers, and supervisory bodies in nations with similar capital structure decisions and socioeconomic systems.

The Determinants of Sovereign Risk Premium in African Countries

This paper investigates the determinants of the sovereign risk premium in African countries. We employ the dynamic fixed effects model to determine the key drivers of sovereign bond spreads. Country-specific effects are fixed and the inclusion of dummy variables using the Bai–Perron multiple structural break test is significant at a 5% level. For robustness, the time-series generalized method of moments (GMM) is used where the null hypothesis of the Sargan Test of over-identifying restrictions (OIR) and the Arellano–Bond Test of no autocorrelation are not rejected. This implies that the instruments used are valid and relevant. In addition, there is no autocorrelation in the error terms. Our results show that the exchange rate, Money supply/GDP (M2/GDP) ratio, and trade are insignificant. Furthermore, our findings indicate that public debt/GDP ratio, GDP growth, inflation rate, foreign exchange reserves, commodity price, and market sentiment are significant at a 5% and 10% level.

Alternative over-identifying restriction test in the GMM estimation of panel data models

A new over-identifying restriction test in the generalized method of moments (GMM) estimation of panel data models is proposed. In contrast to the conventional over-identifying restriction test, where the sample covariance matrix of the moment conditions is used in the weighting matrix, the proposed test uses a block diagonal weighting matrix constructed from the efficient optimal weighting matrix. It is shown that the proposed test statistic asymptotically follows the weighted sum of the chi-square distribution with one degree of freedom. A detailed local power analysis is provided for dynamic panel data models, and it is demonstrated that the new test has a comparable power to the conventional J test in many cases. The Monte Carlo simulations reveal that the proposed test has a substantially better size property than the conventional test does.

Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems

Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood estimation are presented, and asymptotic properties sketched. The techniques are illustrated using the analysis of the PPP and UIP between Switzerland and the US.

On bootstrap validity for specification testing with many weak instruments

This paper studies the asymptotic validity of bootstrapping the J test of over-identifying restrictions and the Anderson–Rubin (AR) test under many/many weak instrument sequences. We show that the (residual-based) bootstrap consistently estimates the limiting distributions of interest under these asymptotic frameworks. Interestingly, such bootstrap validity holds even if the bootstrap cannot mimic well certain important properties in the model. In addition, the studied bootstrap procedures are easy to implement in practice because they do not require an a priori choice between the conventional asymptotics and the many/many weak instrument asymptotics. Monte Carlo simulation shows that the bootstrap techniques provide a more reliable method to approximate the null distribution of the J and AR test statistics under many/many weak instruments.

Asymptotic [formula omitted] and [formula omitted] tests in an efficient GMM setting

This paper considers two-step efficient GMM estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator. We propose a simple and easy-to-implement modification to the trinity of test statistics in the two-step efficient GMM setting and show that the modified test statistics are all asymptotically F distributed under the so-called fixed-smoothing asymptotics. The modification is multiplicative and involves the J statistic for testing over-identifying restrictions. This leads to convenient asymptotic F tests whose critical values, i.e., the standard F critical values, are readily available from standard statistical tables and programming environments. For testing a single restriction with a one-sided alternative, an asymptotic t test theory using the standard t distribution as the reference distribution is also developed.

Core and Periphery in the European Monetary Union: Bayoumi and Eichengreen 25 years later

Bayoumi and Eichengreen (1993) establish a EMU core–periphery pattern using 1963–1988 data. We use same methodology, sample, window length (1989–2015), and a novel over-identifying restriction test to ask whether the EMU strengthened or weakened the core–periphery pattern. Our results suggest the latter.

On the effect of weighting matrix in GMM specification test

In this paper, we study the finite sample behavior of an over-identifying restriction test, the J test, in generalized method of moments(GMM). We consider two variants of the J test, one with centered weighting matrix and the other with uncentered weighting matrix. We demonstrate that the finite sample distribution of J test with centered weighting matrix is close to F distribution whereas that with uncentered weighting matrix is close to beta distribution and that both are far different from chi-square distribution. Using this, we demonstrate why competing simulation results relating to the size property is reported in the context of dynamic panel data and covariance structure models.