Data treatment price indexes

Estimation ML/Bayesian estimation
1

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})

Thanks in advance.

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?

2

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
3

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.