The choice of a foreign price measure in a Bayesian estimated new-Keynesian model for Israel

We estimate a small DSGE model by full information Bayesian techniques on the basis of Israeli data from 1995 to 2006. The model was first developed and estimated by means of classical GMM in Argov and Elkayam (2010), and since then it has been used at the Bank of Israel for monetary policy analysis. It is widely believed that in 2007 (out of sample year) as elsewhere worldwide, inflation rose in Israel due to high commodity prices in global markets. However, our baseline model attributes most of the high inflation in 2007 to supply shocks. One conjecture is that this model's result derives from the inappropriate original use of the unit value of imported consumer goods (which do not include unprocessed food and energy) as the main foreign price measure. We test this conjecture by re-estimating the model with various other foreign price measures that typically do reflect the global rise in commodity prices and compare the log-marginal likelihoods. We find that no other price measure outperforms the original choice in the sample period. Only the foreign trade-weighted CPI equals the performance of the original choice while improving the 2007 interpretation of inflation, and should therefore be considered the main foreign price measure. The proposed methodology for comparing the suitability of alternative measures for observable variables can be applied to any model with exogenous variables that are characterized by univariate equations.