RDP 9601: Why Does the Australian Dollar Move so Closely with the Terms of Trade? Appendix B: Real Exchange Rate Model B

This appendix explains how the preferred specifications for real exchange rate model B are determined. For a given sample period, we begin with the unrestricted error-correction model defined by equation (7) in the text, reproduced below as model (B1). We then define eight restricted versions of this model derived by imposing sequentially larger sets of exclusion restrictions. Specifically, we have the following real exchange rate models:

Note that model (B8) is simply exchange rate model A. For a given sample period, let _i R_k be the set of exclusion restrictions that reduces model (Bi) to model (Bk), for i = 1, …, 9 and k = i +1, …, 9. Then, model (Bp) is the preferred specification, when at the 10 per cent level of significance, all of the exclusion restrictions _l R_m, l = 1, 2, …, p−1, m = l + 1, …, p are accepted and at least one of the exclusion restrictions _l R_p+1, l = 1, 2, …, p, is rejected. The exclusion restrictions are tested assuming the OLS variance-covariance matrix.