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(edited) I am estimating a Central Bank reaction function using GMM using monthly data.

Following the literature, I used lagged values of each variable as instruments (are there other feasible options?)

Variables: gdp growth monthly forecast, monthly cpi inflation, difference between domestic interbank market and federal funds rate, exchange rate, oil price. All data are on monthly basis, and for frequent data I use the value at the end of the month. Deviation are computed with a one-sided HP filter, a part inflation, where I just subtract the inflation target from cpi inflation.

  1. How could I chose the optimal lag? I thought to fit each variable in a AR model, use information criteria to chose the lag, and then use this lag number for the instruments.

  2. For data in which I have more frequent data, could I use daily lags as instruments? Let us say that in my equation I have the exchange rate, of which I have daily data. The variable I want to instrument is "exchange rate the last day of the month" Could I use as instrument "exchange rate one day before the end of the month", "exchange rate two days before the end of the month" and "exchange rate three days before the end of the month"?

Up to now as instrument for the "exchange rate the last day of the month" I used "exchange rate the last day of the month before", "exchange rate the last day of two months before", and exchange rate the last day of three months before"

Thanks for your help!

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  • $\begingroup$ Could you clarify the problem? This might depend on specifics, that is what variables are you using at what frequency etc. there are some rule of thumbs and you can use information criteria but without details there is no much to be said there. Also, are you using data on different frequencies in a single model? You should not be doing that in GMM or most standard models for that matter $\endgroup$
    – 1muflon1 ♦
    Commented Nov 1, 2021 at 11:32
  • $\begingroup$ Variables: gdp growth monthly forecast, monthly cpi inflation, difference between domestic interbank market and federal funds rate, exchange rate, oil price. Deviation are computed with a one-sided HP filter, a part inflation, where I just subtract the inflation target from cpi inflation. Up to now I always used only monthly data, but I was wondering if I could use more frequent data, when available, for identification. The model itself would remain on a monthly basis, as I don’t have more frequent data for some variables (like gdp growth), and anyway the CB does not change the rates daily. $\endgroup$
    – Khairon
    Commented Nov 1, 2021 at 12:32
  • $\begingroup$ please edit your question instead of posting that in comments $\endgroup$
    – 1muflon1 ♦
    Commented Nov 1, 2021 at 12:39
  • $\begingroup$ Ok, I have done, I hope it is clear. $\endgroup$
    – Khairon
    Commented Nov 1, 2021 at 12:50

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