Improved instrumental variables estimation of simultaneous equations under conditionally heteroskedastic disturbances

Abstract

SUMMARYIn this paper we develop estimation techniques and a specification test for the validity of instrumental variables allowing for conditionally heteroskedastic disturbances. We propose modified two-stage least squares (2SLS) and modified 3SLS procedures where the conditional heteroskedasticity is taken into account, which are natural extensions of the traditional 2SLS and 3SLS estimators and which achieve a lower variance. We recommend the use of these modified 2SLS and 3SLS procedures in practice instead of alternative estimators like limited-information maximum likelihood/full-information maximum likelihood, where the non-existence of moments leads to extreme values, and also for ease of computation. It is shown theoretically and with simulation that in some cases 2SLS, 3SLS and our modified 2SLS and 3SLS procedures can have very severe biases (including the weak instruments case), and we present bias correction procedures to apply in practice along the lines of Flores-Lagunes (2007). Our new estimation procedures can also be used to extend the test for weak instruments of Stock and Yogo (2005) and to allow for conditional heteroskedasticity. Finally, we show the usefulness of our estimation procedures with an application to the demand and supply of fish.

The impact of pre-announced day-to-day interventions on the Colombian exchange rate

“…Significance levels are very similar for the traditional Tobit regression in column (1), though the coefficients differ, and the results in column (2) are similar to those in column (1). We Table 3 presents the main results for the estimation of equation 2, according to the methodology proposed by Iglesias and Phillips (2012). The number of observations in Table 2 for the reaction function (1000) is different from the number in 35 This last result contrasts with the surveys reported by Murcia and Rojas (2012), Graph 14, according to which the impact of discretionary -dirty interventions should be higher than the impact of other types of intervention, like…”

“…We use daily information for 2is carried out according to the multistep methodology proposed by Iglesias and Phillips (2012) for the case of simultaneous equations under GARCH disturbances. The first step consists of applying a traditional 2SLS, the second step estimates the conditional variance…”

The impact of pre-announced day-to-day interventions on the colombian exchange rate

“…t q ∆ and t s , and yearly information for * π . The estimation of the parameters of equations (1) and (2) is carried out according to the multistep methodology proposed by Iglesias and Phillips (2012) for the case of simultaneous equations under GARCH disturbances. The first step consists of applying a traditional 2SLS, the second step estimates the conditional variance 2 2,t σ associated with the GARCH model in equation (4), and the last step estimates the parameters of expression (2), obtained from the following standardized version of the equation: Fiorentini (1998) for Tobit models with GARCH errors.…”

“…We obtained disc t I ɵ from column (3) -Tobit-GARCH-and used it in the estimation of equation (2) for the determinants of t s ∆ . Table 2 The reaction function of the central bank ( Table 3 presents the main results for the estimation of equation (2), according to the methodology proposed by Iglesias and Phillips (2012). The number of observations in Table 2 for the reaction function (1000) is different from the number in Also, the coefficients are very similar for the four specifications employed.…”

The institutional basis of efficiency in resource-rich countries

“…14 The earlier working paper version of this paper utilized IV-GMM methods as a check against the 3SLS formulation specifically to deal with heteroskedasticity. However, with the advances in bootstrap theory and programming shown in papers such as Iglesias and Phillips (2012), a conscious decision was made in this version to retain the 3SLS framework for reasons of efficiency and consistency. 15 In order to ensure small bias in our estimates, and given the large number of observations in most of our equations, the bootstrap for each equation has been set to between 1,000 and 2,500 repetitions, to correspond with the data size.…”