Reduced Rank of Regression Using Generalized Method of Moments Estimators

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Correction Cointegration Model (ECCM) and the Incomplete Simultaneous Equations Model (INSEM).The GMM (2SLS) estimators of the cointegrating vector in the ECCM are shown to have normal limiting distributions.Tests for the number of unit roots can be constructed straightforwardly and have Dickey-Fuller type limiting distributions.Two extensions of the ECCM, which are important in practice, are analyzed.First, cointegration estimators and tests allowing for structural shifts in the variance (heteroscedasticity) of the series are derived and analyzed using both a Generalized Least Squares Estimator and a White Covariance Matrix Estimator. The resulting cointegrating vectors estimators have again normal limiting distributions while the cointegration tests have identical limiting distributions which differ from the Dickey-Fuller type.Second, cointegrating vector estimators and tests are derived which allow for structural breaks in the cointegrating vector and/or multiplicator.The limiting distributions of the estimators are again shown to be normal and the limiting distributions.

Orthogonal statistics and the density of the liml estimator

We show that orthogonalization is helpful for constructing densities of maximum likelihood estimators. We therefore use an orthogonal specification of the reduced form of the instrumental variables regression model to obtain an approximation of the density of the limited information maximum likelihood estimator. The approximation consists of a single infinite sum and is less involved than the expression of the true density. In comparisons with the sampling density the approximation is shown to be accurate indicating the validity of its construction

Reduced Rank of Regression Using Generalized Method of Moments Estimators

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Correction Cointegration Model (ECCM) and the Incomplete Simultaneous Equations Model (INSEM).The GMM (2SLS) estimators of the cointegrating vector in the ECCM are shown to have normal limiting distributions.Tests for the number of unit roots can be constructed straightforwardly and have Dickey-Fuller type limiting distributions.Two extensions of the ECCM, which are important in practice, are analyzed.First, cointegration estimators and tests allowing for structural shifts in the variance (heteroscedasticity) of the series are derived and analyzed using both a Generalized Least Squares Estimator and a White Covariance Matrix Estimator. The resulting cointegrating vectors estimators have again normal limiting distributions while the cointegration tests have identical limiting distributions which differ from the Dickey-Fuller type.Second, cointegrating vector estimators and tests are derived which allow for structural breaks in the cointegrating vector and/or multiplicator.The limiting distributions of the estimators are again shown to be normal and the limiting distributions.GMM;econometric models;regression

Re-examining the consumption-wealth relationship : the role of model uncertainty

This paper discusses the consumption-wealth relationship. Following the recent influential workof Lettau and Ludvigson [e.g. Lettau and Ludvigson (2001), (2004)], we use data on consumption, assets andlabor income and a vector error correction framework. Key …ndings of their work are that consumption doesrespond to permanent changes in wealth in the expected manner, but that most changes in wealth are transitoryand have no e¤ect on consumption. We investigate the robustness of these results to model uncertainty andargue for the use of Bayesian model averaging. We …nd that there is model uncertainty with regards to thenumber of cointegrating vectors, the form of deterministic components, lag length and whether the cointegratingresiduals a¤ect consumption and income directly. Whether this uncertainty has important empirical implicationsdepends on the researcher's attitude towards the economic theory used by Lettau and Ludvigson. If we workwith their model, our findings are very similar to theirs. However, if we work with a broader set of models andlet the data speak, we obtain somewhat di¤erent results. In the latter case, we …nd that the exact magnitudeof the role of permanent shocks is hard to estimate precisely. Thus, although some support exists for the viewthat their role is small, we cannot rule out the possibility that they have a substantive role to play

Evidence on a Real Business Cycle Model with Neutral and Investment-Specific Technology Shocks Using Bayesian Model Averaging

The empirical support for a real business cycle model with two technology shocks is evaluated using a Bayesian model averaging procedure. This procedure makes use of a finite mixture of many models within the class ofvector autoregressive (VAR) processes. The linear VAR model is extendedto permit cointegration, a range of deterministic processes, equilibrium restrictions and restrictions on long-run responses to technology shocks. Wefind support for a number of the features implied by the real business cyclemodel. For example, restricting long run responses to identify technologyshocks has reasonable support and important implications for the short runresponses to these shocks. Further, there is evidence that savings and investment ratios form stable relationships, but technology shocks do not accountfor all stochastic trends in our system. There is uncertainty as to the mostappropriate model for our data, with thirteen models receiving similar support, and the model or model set used has signficant implications for theresults obtained