# Data treatment price indexes

Hi everyone

Smets and Wouters (2007) use nominal variables and adjust all variables by the GDP deflator since the economy has only one final good. In this case P_{t} represents the price of the final good (GDP deflator), and at the same time \Pi_{t} = \frac{P_{t}}{P_{t-1}}, so they use the log-difference of the GDP deflator as the inflation rate.

In my case, I want to define the measurement equations for the price indexes of the different goods, and I would like to know if I should adjust. For example, for tradable goods in real terms we have p_{t}^T = \frac{P^T_{t}}{P_{t}}. So, if I take the first log-difference of the export price index (FRED: IQ) as observable, which of the following measurement equations is correct?

Let X_{t} = 100 \times [ln(\text{FRED: IQ}_{t}) - ln(\text{FRED: IQ}_{t-1}) ]

1. X_{t} = ln(\frac{p_{t}^T}{p_{t- 1}^T})
2. X_{t} = ln(\frac{p_{t}^T}{p_{t- 1}^T}) - ln(\Pi_{t})

Another question: is it correct to transform the nominal to real observable variables using the GDP deflator, but to use the CPI as the observable variable of inflation?

When setting up an observation equation we typically try to have a correspondence between data and model concepts. As far as I see your export price index should be deflated by the GDP deflator before you can apply equation (1). If you want to stay with non-deflated export prices you may specify X_t =\ln(\frac{p^T_t}{p^T_{t-1}})+\ln(\Pi_t).

1 Like

Indeed, the “export price index” from Fred seems to be the deflator for export goods from chain weighted data and therefore should correspond to P_t^T, i.e. it is not expressed in terms of the final good. To link it to p_t^T, you need to add back the GDP deflator. Thus, @Max1 is correct. But be careful with the 100 you added. You need to be consistent.