AN EMPIRICAL EVALUATION OF DIFFERENT ESTIMATION TECHNIQUES OF COINTEGRATING VECTORS

Abstract

Many macroeconomic series are in general nonstationary. When these series are regressed with each other, spurious results occur unless the series are cointegrated. One source of non-stationarity is the presence of one or more unit roots. Thus a common practice is to verify that all the variables employed in the static regression are of the same order of integration prior to the estimation of the cointegrating vectors. The dissertation begins with a literature survey on testing for unit roots and cointegration and a critique of these tests. It is pointed out that these tests have low power and tends to give contradictory results. Monte Carlo evidence suggests that no test is unambiguously superior to all the others. Applied workers still need to use judgement and economic theory regarding cointegration properties of a set of variables. There are many estimation methods to use in estimating cointegrating vectors and different method tends to give different estimates. Monte Carlo studies do not indicate that any single method is superior to the others. These studies impose unit root assumption in the series generated but in practice integrated time series is not the only source of non-stationarity. Another way to evaluate these estimation methods is through application. The main objective of this dissertation is to use five methods to estimate a standard model. The five estimation methods are Ordinary Least Squares (OLS) Method, Unrestricted Error Correction Model (ECM) Method, Fully Modified Ordinary Least Squares (FM) Method, Engle-Yoo Three Step Estimation (3-STEP) Method and Johansen's Vector Autoregression Maximum Likelihood (JOHAN) Estimation Method. Two sets of time series data, annual Canada and China data, are used in the empirical work. The model considered is a demand model. Demand model was chosen because economic theory has been well developed in this area. Two models are used. One is a logarithmic linear model and the second one is a relative price and real expenditure model. The estimation methods are evaluated based on the standard errors of the estimates, the number of occurrences of estimates with wrong signs and of extreme values. The empirical work indicates that the ECM method does not perform well even though it has incorporated dynamics features in the estimation. This method tend to produce estimates with wrong signs and high standard errors. The Engle-Yoo Three Step Method is supposedly superior to the OLS method but the empirical work indicates otherwise. This method tends to convert an OLS estimates with correct sign to a wrong one. Its estimates also have high standard errors. The JOHAN method has the worse performances in the empirical work. It tends to give wrong signs and extreme values for its estimates. It is discovered that OLS and FM works well in most of the cases. These two methods tend to give estimates with reasonable values and correct signs. Although the OLS estimates have smaller standard errors, they are known to be biased, especially in small sample. Thus the dissertation favours FM in estimating cointegrating vectors.