The estimation of simultaneous equation models under conditional heteroscedasticity

In this paper we extend the setting analysed in Hahn and Hausman (2002a) by allowing for conditionally heteroscedastic disturbances. We start by considering the type of conditional variance-covariance matrices proposed by Engle and Kroner (1995) and we show that, when we impose a GARCH specification in the structural model, some conditions are needed to have a GARCH process of the same order in the reduced form equations. Later, we propose a modified-2SLS and a modified-3SLS procedures where the conditional heteroscedasticity is taken into account, that are more asymptotically efficient than the traditional 2SLS and 3SLS estimators. We recommend to use these modified-2SLS and 3SLS procedures in practice instead of alternative estimators like LIML/FIML, where the non-existence of moments leads to extreme values (in case we are interested in the structural form). We show theoretically and with simulation that in some occasions 2SLS, 3SLS and our proposed 2SLS and 3SLS procedures can have very severe biases, and we present the bias correction mechanisms to apply in practiceSimultaneous equations, conditional heteroscedasticity

A comparison of bias approximations for the 2SLS estimator

We consider the bias of the 2SLS estimator in the linear instrumental variables regression with one endogenous regressor only. By using asymptotic expansion techniques we approximate 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments. The resulting approximation encompasses existing bias approximations, which are valid in particular cases only. Simulations show that the developed approximation gives an accurate description of the 2SLS bias in case of either weak or many instruments or both.

A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). With multiple instruments, two-stage least squares (2SLS) estimand is a weighted average of different LATEs. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroskedasticity-robust variance estimator would be inconsistent, and 2SLS standard errors based on such estimators would be incorrect. I derive the correct asymptotic distribution, and propose a consistent asymptotic variance estimator by using the result of Hall and Inoue (2003, Journal of Econometrics) on misspecified moment condition models. This can be used to correctly calculate the standard errors regardless of whether there is more than one LATE or not

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.Institutions, Growth, 2SLS, OLS, G2SLS Random effects IV regression and Panel Fixed (within) IV regression, cross-country data, Hausman test, Overidentification test

Inference regarding multiple structural changes in linear models estimated via two stage least squares

In this paper, we extend Bai and Perron’s (1998, Econometrica, p.47-78) framework for multiple break testing to linear models estimated via Two Stage Least Squares (2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the resulting estimated break point fractions. We show that various F-statistics for structural instability based on the 2SLS estimator have the same limiting distribution as the analogous statistics for OLS considered by Bai and Perron (1998). This allows us to extend Bai and Perron’s (1998) sequential procedure for selecting the number of break points to the 2SLS setting. Our methods also allow for structural instability in the reduced form that has been identified a priori using data-based methods. As an empirical illustration, our methods are used to assess the stability of the New Keynesian Phillips curve.unknown break points; structural change; instrumental variables; endogenous regressors; structural stability tests; new Keynesian Phillips curve

Bayesian Model Averaging for Model Implied Instrumental Variable Two Stage Least Squares Estimators

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, non-iterative estimator for latent variable models. Associated with this estimator are equation specific tests of model misspecification. We propose an extension to the existing MIIV-2SLS estimator that utilizes Bayesian model averaging which we term Model-Implied Instrumental Variable Two-Stage Bayesian Model Averaging (MIIV-2SBMA). MIIV-2SBMA accounts for uncertainty in optimal instrument set selection, and provides powerful instrument specific tests of model misspecification and instrument strength. We evaluate the performance of MIIV-2SBMA against MIIV-2SLS in a simulation study and show that it has comparable performance in terms of parameter estimation. Additionally, our instrument specific overidentification tests developed within the MIIV-2SBMA framework show increased power to detect model misspecification over the traditional equation level tests of model misspecification. Finally, we demonstrate the use of MIIV-2SBMA using an empirical example.Comment: 31 pages, 8 figures, supplementary materials available upon reques

Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances

In this paper we extend the setting analysed in Hahn and Hausman (2002a) by allowing for conditionally heteroscedastic disturbances. We start by considering the type of conditional variance-covariance matrices proposed by Engle and Kroner (1995) and we show that, when we impose a GARCH specification in the structural model, some conditions are needed to have a GARCH process of the same order in the reduced form equations. Later, we propose a modified-2SLS and a modified-3SLS procedures where the conditional heteroscedasticity is taken into account, that are more asymptotically efficient than the traditional 2SLS and 3SLS estimators. We recommend to use these modified-2SLS and 3SLS procedures in practice instead of alternative estimators like LIML/FIML, where the non-existence of moments leads to extreme values (in case we are interested in the structural form). We show theoretically and with simulation that in some occasions 2SLS, 3SLS and our proposed 2SLS and 3SLS procedures can have very severe biases, and we present the bias correction mechanisms to apply in practiceSimultaneous Equations, conditionally heteroscedastic disturbances

The Causal Relationship between ICT and FDI

foreign direct investment, information and communication technology, stationarity, cointegration, causality, LSDV, 2SLS