We estimate a small DSGE model by full information Bayesian techniques on Israeli data from 1995 to 2006. The model was first developed and estimated by classical GMM in Argov and Elkayam (2007). We extend the model by: (1) Separating the fuel component from the CPI; (2) Estimating trends and natural rates simultaneously with the parameters; (3) Adopting an optimization-based approach to modeling imported inflation. Testing the model's fit we find that it replicates the main cross-correlations observed in the data. In terms of forecast performance we find that simple VARs outperform our model, which outperforms a na?ve RW. Analyzing the source of variation in the data, and specifically inflation, we find that exchange-rate shocks play a major role (accounting for 67% of the variation in CPI inflation).

Our baseline model attributes most of the high inflation in 2007 to supply shocks, whereas it has been widely accepted that inflation rose in Israel due to high commodity prices in the global markets. One conjecture is that the original use of the unit value of imported consumer goods (which do not include unprocessed food and energy) as the main foreign price measure was not appropriate. 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 therefore should be considered for the main foreign price measure.

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