Taylor rule estimation, Choice of Deflator

General DSGE Modeling
1

Dear Prof @jpfeifer,

My goal is to estimate Taylor rule parameters for 3 different rule Specifications and analyse the fit. I am also using quarterly data from two periods, the first period spans 20 years and the second period spans 10 years.
I am using a basic NK DSGE model with price rigidity and habit formation with only consumption and Investment in Y.
I have assumed prices of investment and consumption to be the same, hence Y=C+I holds.
I am having confusions regarding the preparation of data.
The method in mind:
Subtract NX and Govt expenditure from nominal GDP, and divide the series by GDP deflator and population.
For consumption, use nominal PCE divided by GDP deflator and population.
Should I be using inflation in GDP deflator as my inflation data?
But Central Bank in India targets CPI, so wouldn’t it make the whole study baseless?
Can I deflate my GDP and Consumption series with CPI and use that data?
Can I deflate both series with GDP deflator and use CPI inflation in the model for Pi?

Or should I have different prices for Investment and Y in my model and use the value added Identity? Even in that case, I am subtracting NX and Government expenditure from Y, so can I still use the deflator( since now I am explicitly modelling different prices for each component)

I am also estimating steady state inflation and discount factor.Since I am estimating inflation and beta together, shouldnt my interest rate series be
\hat R = \log(Rdata) + \log(\Pi)-\log(\beta) ? where R is gross p.q interest rate.(Log deviation from ss)
I need to see the effectiveness of the inflation targeting regime, would you suggest estimating the ss inflation and comparing with the official target or putting the target as ss inflation in the model and then analysing the estimated coefficients?
Wouldn’t introducing a positive inflation target make my model non stationary?

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  1. That is a difficult question with no definitive answer. Obviously, the model does not satisfy the properties of the data and you need to live with the resulting inconsistencies. I don’t have particular insights into Indian data, but the big question will be how different CPI and GDP deflator are and what causes this. If you remove G and NX, consumption will be responsible for about 80% of output. Using the CPI to deflate everything may then not be worst idea.
  2. You could try to estimate a slow moving inflation target. That would be informative about the commitment of the central bank to inflation targeting.
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  1. But I have to be consistent with the deflator I choose and the inflation data, if I am using GDP deflator, inflation should be between calculated on GDP deflator, is that correct?
    2)Are you suggesting that I should model target inflation as an AR1 process?
    Also, @jpfeifer , please try to answer my other questions in the post, however silly you find them, whenever you find time.
    Thank you for replying to all my posts as well as the other posts and helping out the community so much.
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  1. As I wrote above, at least one inconsistency will remain. Either you will incorrectly deflate the real aggregates with the CPI deflator or you will assign the wrong inflation target to the central bank. I don’t know what is worse.
  2. Yes, an AR(1) for the target should do the trick.
  3. What are your other questions that remain? Numbering is often helpful.
  4. Why would a positive inflation target render the model non-stationary? The Fisher equation usually provides a stationary solution for all real variables, regardless of the inflation level.