Over-identifying Restrictions Research Articles

Reversed Economics and Inhumanity of Development Assistance in Africa

Purpose – The purpose of this paper is to assess the aid-development nexus in 52 African countries using updated data (1996-2010) and a new indicator of human development (adjusted for inequality). Design/methodology/approach – The estimation technique used is a Two-Stage-Least Squares Instrumental Variable approach. Instruments include: income-levels, legal-origins and religious-dominations. The first-step consists of justifying the choice of the estimation technique with a Hausman-test for endogeneity. In the second-step, we verify that the instrumental variables are exogenous to the endogenous components of explaining variables (aid dynamic channels) conditional on other covariates (control variables). In the third-step, the strength and validity of the instruments are examined with the Cragg-Donald and Sargan overidentifying restrictions tests respectively. Robustness checks are ensured by: (1) the use of alternative aid indicators; (2) estimation under restricted and unrestricted hypotheses; and (3) adoption of two interchangeable sets of instruments.Findings – The findings broadly indicate that development assistance is detrimental to GDP growth, GDP per capita growth and inequality adjusted human development. Given concerns on the achievement of the MDGs, the relevance of these results point to the deficiency of foreign aid as a sustainable cure to poverty in Africa.Social implications – It is a momentous epoque to solve the second tragedy of foreign aid; it is high time economists and policy makers start rethinking the models and theories on which foreign aid is based. In the meantime, it is up to people who care about the poor to hold aid agencies accountable for piecemeal results.Originality/value – These findings are based on data collected after pioneering works on the aid-development nexus. Usage of the inequality adjusted human development index first published in 2010, corrects past works of the bunch of criticisms inherent in the first index.

An Efficient Minimum Distance Estimator for DSGE Models

Recent studies illustrate that under some conditions dynamic stochastic general equilibrium models can be expressed as structural vector autoregressive models of infinite order. Based on this mapping and the theoretical results about vector autoregressive models of infinite order this paper proposes a minimum distance estimator that: a) matches the k-period responses of the whole vector of the observable variables described by the structural model – caused after a small perturbation to the entire vector of the structural errors – with those observed in the historical data, which have been recovered through the use of a structurally identified vector autoregressive model, and b) minimises the distance between the reduced-form error covariance matrix implied by the structural model and the one estimated in the data. This estimator encompasses those in the literature, is asymptotically consistent, normally distributed and efficient. The J-type overidentifying restrictions statistic that results from this methodology can be used for the evaluation of the structural model. Finally, this study also develops the theory of the bootstrapped version of the estimator and the statistic introduced here. Monte Carlo simulation evidences based on a medium-scale DSGE model reveal very encouraging results for the proposed estimator when it is compared against modern – Bayesian maximum likelihood – and less modern – maximum likelihood and non-efficient IR matching – DSGE estimators.

Equity Prices And Inflation In South Africa: An Empirical Analysis

<p>This paper attempts to assess the indirect relationship between equity prices and inflation in South Africa in order to infer the possible reaction of the monetary authority in the face of excessive changes in equity price or bubble. To this end, use is made of a system equation, rather than a single equation, in the context of cointegrating VAR with over-identifying restrictions. The paper decomposes actual inflation into expected and unexpected components and shows that the two components react differently to the changes in equity prices. Nonetheless, given a weak reaction of expected inflation to the change in equity prices and the fact that monetary authority behaviour is forward-looking in South Africa, the paper concludes that equity prices should not form part of the monetary authority reaction function in South Africa.</p>

On the size distortion of tests after an overidentifying restrictions pretest

SUMMARYIn the linear instrumental variables model, we provide theoretical and Monte Carlo evidence for the size distortion of a two‐stage hypothesis test that uses a test of overidentifying restrictions (OR) in the first stage. We derive a lower bound for the asymptotic size of the two‐stage test. The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of OR used in the first stage does not reject and the test in the second stage rejects. This lower bound can be as large as 1 − εP, where εP is the pretest nominal size, for a parameter space that allows for local non‐exogeneity of the instruments but rules out weak instruments. Copyright © 2011 John Wiley & Sons, Ltd.

Why Gaussian Macro-Finance Term Structure Models are (Nearly) Unconstrained Factor-VARs

This paper explores the impact of simultaneously enforcing the no-arbitrage structure of a Gaussian macro-finance term structure model (MTSM) and accommodating measurement errors on bond yield through filtering on the maximum likelihood estimates of the model-implied conditional distributions of the macro risk factors and bond yields. For the typical yield curves and macro variables studied in this literature, the estimated joint distribution within a canonical MTSM is nearly identical to the estimate from an economic-model-free factor vector-autoregression (factor-VAR), even when measurement errors are large. It follows that a canonical MTSM does not offer any new insights into economic questions regarding the historical distribution of the macro risk factors and yields, over and above what is learned from a factor-VAR. In particular, the discipline of a canonical MTSM is empirically inconsequential for analyses of impulse response functions of bond yields and macro factors or empirical studies of term premiums. These results are rotation-invariant and, therefore, apply to many of the specifications of risk factors in the literature. In deriving these results we develop a new canonical form for MTSMs that is particularly revealing about the nature of the over-identifying restrictions implied by MTSMs relative to yield-based factor models.

Monte Carlo Simulation Of The Portfolio-Balance Model Of Exchange Rates: Finite Sample Properties Of The GMM Estimator

Using Monte Carlo simulation of the Portfolio-balance model of the exchange rates, we report finite sample properties of the GMM estimator for testing over-identifying restrictions in the simultaneous equations model. F-form of Sargans statistic performs better than its chi-squared form while Hansens GMM statistic has the smallest bias.

A New Perspective on Gaussian Dynamic Term Structure Models

In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields. (JEL E43, G12, C13) Dynamic models of the term structure often posit a linear factor structure for a collection of yields, with these yields related to underlying factors P through a no-arbitrage relationship. Does the imposition of no-arbitrage in a Gaussian dynamic term structure model (GDTSM) improve the out-of-sample forecasts of yields relative to those from the unconstrained factor model, or sharpen model-implied estimates of expected excess returns? In practice, the answers to these questions are obscured by the imposition of over-identifying restrictions on the risk-neutral (Q) or historical (P) distributions of the risk factors, or on their market prices of risk, in addition to the cross-maturity restrictions implied by no-arbitrage. 1

Estimating the Effects of Wages on Obesity

To estimate the effects of wages on obesity and body mass. Data on household heads, aged 20 to 65 years, with full-time jobs, were drawn from the Panel Study of Income Dynamics for 2003 to 2007. The Panel Study of Income Dynamics is a nationally representative sample. Instrumental variables (IV) for wages were created using knowledge of computer software and state legal minimum wages. Least squares (linear regression) with corrected standard errors were used to estimate the equations. Statistical tests revealed both instruments were strong and tests for over-identifying restrictions were favorable. Wages were found to be predictive (P < 0.05) of obesity and body mass in regressions both before and after applying IVs. Coefficient estimates suggested stronger effects in the IV models. Results are consistent with the hypothesis that low wages increase obesity prevalence and body mass.

Bayesian methods for instrumental variable analysis with genetic instruments (‘Mendelian randomization’): example with urate transporter SLC2A9 as an instrumental variable for effect of urate levels on metabolic syndrome

The ‘Mendelian randomization’ approach uses genotype as an instrumental variable to distinguish between causal and non-causal explanations of biomarker–disease associations. Classical methods for instrumental variable analysis are limited to linear or probit models without latent variables or missing data, rely on asymptotic approximations that are not valid for weak instruments and focus on estimation rather than hypothesis testing. We describe a Bayesian approach that overcomes these limitations, using the JAGS program to compute the log-likelihood ratio (lod score) between causal and non-causal explanations of a biomarker–disease association. To demonstrate the approach, we examined the relationship of plasma urate levels to metabolic syndrome in the ORCADES study of a Scottish population isolate, using genotype at six single-nucleotide polymorphisms in the urate transporter gene SLC2A9 as an instrumental variable. In models that allow for intra-individual variability in urate levels, the lod score favouring a non-causal over a causal explanation was 2.34. In models that do not allow for intra-individual variability, the weight of evidence against a causal explanation was weaker (lod score 1.38). We demonstrate the ability to test one of the key assumptions of instrumental variable analysis—that the effects of the instrument on outcome are mediated only through the intermediate variable—by constructing a test for residual effects of genotype on outcome, similar to the tests of ‘overidentifying restrictions’ developed for classical instrumental variable analysis. The Bayesian approach described here is flexible enough to deal with any instrumental variable problem, and does not rely on asymptotic approximations that may not be valid for weak instruments. The approach can easily be extended to combine information from different study designs. Statistical power calculations show that instrumental variable analysis with genetic instruments will typically require combining information from moderately large cohort and cross-sectional studies of biomarkers with information from very large genetic case–control studies.

Testing Over-Identifying Restrictions Without Consistent Estimation of the Asymptotic Covariance Matrix

This paper extends Kiefer, Vogelsang, and Bunzel - (2000, Econometrica) and Kiefer and Vogelsang - (2002b, Econometric Theory) to propose a class of over-identifying restrictions (OIR) tests that are robust to heteroskedasticity and serial correlations of unknown form. These OIR tests do not require consistent estimation of the asymptotic covariance matrix and hence avoid choosing the bandwidth in nonparametric kernel estimation. By employing a suitable normalizing matrix to eliminate the nuisance parameters in the limit, these tests remain asymptotically pivotal. As opposed of the conventional OIR test, the proposed tests require only a consistent, but not necessarily optimal, GMM estimator. It is also shown that the asymptotic local power of these tests is invariant with respect to the choice of the weighting matrix for preliminary GMM estimator. Our simulations demonstrate that the proposed tests are properly sized in most cases and may have power comparable with that of the conventional OIR test.

On Bahadur efficiency of empirical likelihood

This paper studies the Bahadur efficiency of empirical likelihood for testing moment condition models. It is shown that under mild regularity conditions, the empirical likelihood overidentifying restriction test is Bahadur efficient, i.e., its p -value attains the fastest convergence rate under each fixed alternative hypothesis. Analogous results are derived for parameter hypothesis testing and set inference problems.

Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity

This paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity. It is based on a jackknife version of the Sargan test statistic, having a numerator that is the objective function minimized by the JIVE2 estimator of Angrist, Imbens, and Krueger (1999). Correct asymptotic critical values are derived for this test when the number of instruments grows large, at a rate up to the sample size. It is also shown that the test is valid when the number instruments is fixed and there is homoskedasticity. This test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix. The asymptotics is based on the heteroskedasticity robust many instrument asymptotics of Chao et. al. (2010).

Nonlinear principal components and long-run implications of multivariate diffusions

We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these NPCs. By exploiting the theory of continuous-time, reversible Markov diffusion processes, we give a different interpretation of these NPCs and the smoothness constraints. When the diffusion matrix is used to enforce smoothness, the NPCs maximize long-run variation relative to the overall variation subject to orthogonality constraints. Moreover, the NPCs behave as scalar autoregressions with heteroskedastic innovations; this supports semiparametric identification and estimation of a multivariate reversible diffusion process and tests of the overidentifying restrictions implied by such a process from low-frequency data. We also explore implications for stationary, possibly nonreversible diffusion processes. Finally, we suggest a sieve method to estimate the NPCs from discretely-sampled data.

Identification of Macroeconomic Factors in Large Panels

This paper presents a dynamic factor model in which the extracted factors and shocks are given a clear economic interpretation. The economic interpretation of the factors is obtained by means of a set of over-identifying loading restrictions, while the structural shocks are estimated following standard practices in the SVAR literature. Estimators based on the EM algorithm are developped. We apply this framework to a large panel of US monthly macroeconomic series. In particular, we identify nine macroeconomic factors and discuss the economic impact of monetary policy stocks. The results are theoretically plausible and in line with other findings in the literature.

Still Puzzling: Evaluating the Price Puzzle in an Empirically Identified Structural Vector Autoregression

The price puzzle is the association in a structural vector autoregression (SVAR) of a contractionary shock to monetary policy with persistent increases in the price level. Various explanations have been investigated separately in the framework of small SVARs without any common set of variables and with ad hoc and casually justified identification schemes. In contrast, here it is addressed in a rich 12-variable SVAR in which various factors that have been mooted as solutions are considered jointly. SVARs for the pre-1980 and post-1990 periods are identified empirically using a graph-theoretic causal search algorithm combined with formal tests of the implied overidentifying restrictions. The transmission mechanism of monetary policy to prices remains puzzling. Whether a price puzzle exists in the pre-1980 depends on whether monetary-policy actions are adequately characterized by movements in the Federal funds rate. If so, there is a price puzzle. But if monetary policy is better characterized through movements in reserves, then there is no price puzzle. In the later period, monetary policy is well characterized by movements in the Federal funds rate, but the response of prices is statistically insignificant. Commonly suggested resolutions, including the inclusion of commodity prices, measures of output gaps, and fuller specification of monetary policy are shown to have causal implications inconsistent with the data. Nevertheless, the evidence suggests that further investigation of the role of the output gap and monetary policy is warranted.

Least orthogonal distance estimator of structural parameters in simultaneous equation models

The aim of this paper is to present a consistent estimator of parameters in simultaneous equation model, based on characteristic roots and vectors of a matrix derived from the so called over-identifying restrictions. The Least Orthogonal Distance Estimator presented here is a more recent development of its original limited information version. The occasion, for reviewing it, has been given by its extension to a full information context which is here completely formalized and by the very encouraging results of recent simulation experiments.

The Information Content of Implied Probabilities to Detect Structural Change

This paper proposes to use implied probabilities resulting from estimation methods based on unconditional moment conditions to detect structural change. The class of GEL estimators (Smith 1997) assigns a set of probabilities to each observation such that moment conditions are satisfled. These restricted probabilities are called implied probabilities. Implied probabilities may also constructed for the standard GMM (Back and Brown 1993). The proposed structural change statistic tests are based on the information content in these implied probabilities. We consider cases of structural change which can occur in the parameters of interest or in the overidentifying restrictions used to estimate these parameters.

A joint serial correlation test for linear panel data models

Abstract This paper proposes a joint error serial correlation test to be applied to linear panel data models after generalised method of moments estimation. This new test is an alternative inferential tool to both the m 2 test of [Arellano, M., Bond, S., 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297] and the overidentifying restrictions test. The proposed test, called the m ( 2 , p ) 2 test, involves an examination of the joint significance of estimates of second to p th-order (first differenced) error serial correlations. The small sample properties of the m ( 2 , p ) 2 test are investigated by means of Monte Carlo experiments. The evidence shows that the proposed test mostly outperforms the conventional m 2 test and has high power when the overidentifying restrictions test does not, under a variety of alternatives including slope heterogeneity and cross section dependence.

Nearly-singular design in GMM and generalized empirical likelihood estimators

Nearly-Singular design relaxes the nonsingularity assumption of the limit weight matrix in GMM, and the nonsingularity of the limit variance matrix for the first order conditions in GEL. The sample versions of these matrices are nonsingular, but in large samples we assume these sample matrices converge to a singular matrix. This can result in size distortions for the overidentifying restrictions test and large bias for the estimators. This nearly-singular design may occur because of the similar instruments in these matrices. We derive the large sample theory for GMM and GEL estimators under nearly-singular design. The rate of convergence of the estimators is slower than root n.

Do coincident indicators have one-factor structure?

The Stock–Watson coincident index of business cycles and its extensions assume a static linear one-factor model for the component indicators. This paper tests that assumption. Since the factor structure restricts the autocovariance matrices of the component indicators, a distance test, or the Hansen–Sargan test of over-identifying restrictions, is applicable. This also gives a GMM counterpart of the Stock–Watson coincident index, or a new composite index (CI) of coincident indicators, as a by-product. For the four US coincident indicators that currently make up the CI, the test strongly rejects the null hypothesis of static linear one-factor structure.