Bias approximation and reduction in vector autoregressive models

Abstract: In the last few decades, vector autoregressive (VAR) models have gained tremendous popularity as an all-purpose tool in econometrics and other disciplines. Some of their most prominent uses are for forecasting, causality tests, tests of economic theories, hypothesis-seeking, data characterisation, innovation accounting, policy analysis, and cointegration analysis. Their popularity appears to be attributable to their flexibility relative to other models rather than to their virtues per se. In addition, analysts often use VAR models as benchmark models.VAR modeling has not gone uncriticised, though. A list of relevant arguments against VAR modelling can be found in Section 2.3 of this thesis. There is one additional problem which is rarely mentioned though, namely the often heavily biased estimates in VAR models. Although methods to reduce this bias have been available for quite some time, it has probably not been done before, at least not in any systematic way. The present thesis attempts to systematically examine the performance of bias-reduced VAR estimates, using two existing and one newly derived approximation to the bias.The thesis is orginanised as follows. After a short introductory chapter, a brief history of VAR modelling can be found in Chapter 2 together with a review of different representations and a compilation of criticisms against VAR models. Chapter 3 reports the results of very extensive Monte Carlo experiments serving dual purposes: Firstly, the simulations will reveal whether or not bias really poses a serious problem, because if it turns out that biases appear only by exception or are mainly insignificant, there would be little need to reduce the bias. Secondly, the same data as in Chapter 3 will be used in Chapter 4 to evaluate the bias approximations, allowing for direct comparison between bias-reduced and original estimates. Though Monte Carlo methods have been (rightfully) criticised for being too specific to allow for any generalisation, there seems to be no good alternative to analyse small-sample properties of complicated estimators such as these.Chapter 4 is in a sense the core of the thesis, containing evaluations of three bias approximations. The performance of the bias approximations is evaluated chiefly using single regression equations and 3D surfaces. The only truly new research result in this thesis can also be found in Chapter 4; a second-order approximation to the bias of the parameter matrix in a VAR(p) model. Its performance is compared with the performance of two existing first-order approximations, and all three are used to construct bias-reduced estimators, which are then evaluated.Chapter 5 holds an application of US money supply and inflation in order to find out whether the results in Chapter 4 can have any real impacts. Unfortunately though, bias reduction appears not to make any difference in this particular case. Chapter 6 concludes.