A simple test of exogeneity for recursively structured VAR models

Abstract

The restriction of exogeneity of certain variables in structural VAR models is rarely tested for consistency with the actual data. The reason is obvious: such a test requires estimates of the structural parameters. This paper proposes a solution for models that assume long-run or contemporaneous recursive structures in identification. We show that in such cases, the exogeneity restriction can be assessed statistically using the well-known Granger non-causality test which is conveniently performed in the reduced-form VAR model. Two empirical examples are offered to demonstrate the usefulness of this result.

Acknowledgements

The author thanks the editor and an associate editor of the journal, and also Lance Fisher for his helpful comments on earlier versions of the paper. This work was supported by Yonsei Business and Economics Research Fund. The usual disclaimer applies.

Notes

¹ See Johansen and Juselius (1990) for a likelihood ratio test on α and Toda and Phillips (1993 and 1994) for a sequential test of long-run non-causality, and then short-run non-causality.

² In their actual implementation, IS and LM shocks are not separately identified, and reported instead are the combined effects of these two shocks labeled as aggregate demand shocks.

³ The other domestic variables in their model are real GDP, real effective exchange rate, real wage, inflation, and short and long-term interest rates.

⁴ The VAR model in levels is fitted to the US data with a lag length of 8 and to the Australian data with a lag length of 7. The last lags in both models are added deliberately as prescribed by Dolado and Lutkepohl. The usual Wald test is performed on the coefficients of the first 7 lags for the USA and 6 lags for Australia.

⁵ An exception is that labour supply shocks now explain a much smaller portion of the variability in real interest rates.