Data preparation for estimation

Estimation ML/Bayesian estimation
1

Hi, I finally constructed an RBC model with 3 sectors tradable goods, nontradable goods, and final goods. There are a few extensions from standard open economy RBC model. There are two financial frictions: a costly banking sector and working capital constraint for firms. It is a stationary model with no trend growth and there is no inflation in the model.

Now I want to estimate the model. This will be my first estimation attempt so sorry for my trivial questions in advance. I know that there should be as many observable variables as shocks. I have six shocks in the model and I will have measurement error so I choose 7 observables: tradable sector production, nontradable sector production, tradable sector investment, nontradable sector investment, world interest rate, domestic interest rate, foreign debt.

My question is regarding the preparation of the data. Should I use per capita or level production, and should I detrend the data? Since there is no trend growth should I use level production or demean it? Regarding interest rates, should I use nominal or real interest rates?

Any help would be appreciated…

2
  1. Your data must not have trends. Either use growth rates or detrend the data, e.g. using a one-sided HP filter
  2. Your model will not feature population growth, so you need to use per capita or per worker variables.
  3. If it’s an RBC model, the model will not have a counterpart to the nominal interest rate. Hence, you need to use the real interest rate
3

Thank you very much for your help…

4

some follow up questions: can I use quadratically detrended as Schmitt-Grohé? and should I take logarithm of the variables? I use real interest rate of US for calibration of world interest rate and the value is negative. Then there exists an indeterminacy error for the model. So can I use nominal for calibration?

5
  1. Yes, a quadratic trend is fine.
  2. Yes, you need to log exponentially growing variables. Otherwise, the trend would not even be close to linear.
  3. How come your interest is negative? That does not really make sense.
6

Prof. Pfeifer, I define interest rate faced by domestic agents as r =r* + risk premium where r* is US interest rate and risk premium is a function of deviation of debt level from equilibrium as Schmitt-Grohé defined. r* is a fixed parameter. I wanted to calibrate r* using data of US interest rate. I took 3 months Treasury Bill rate as nominal interest rate. To calculate expected inflation, I averaged GDP deflator inflation of time t and 3 preceding periods. Then calculated real interest rate by substracting expected inflation from nominal interest rate. Finally I calculated the arithmetic mean of the sample period: 2000:q1-2015q3. But the result is a negative value…

7

The real interest rate is a function of expected inflation, not past inflation. That type of approximation error that comes via the proxy seems to be problematic in your case. What happens when you replace the expected inflation by its actual realization?

8

I followed “Credit decomposition and business cycles in emerging market economies” 2016 paper by İnci Gümüş and Bahar Bahadır for the calculation of expected inflation. Replacing the expected inflation changes the magnitude, but still gives negative value.

9

Then you cannot use this for calibration. It does not make sense to use this a sample