 Calibration procedure

Good afternoon everyone,

I would like to know what is the mainstream way to calibrate the factor share and substitution elasticities in a “growth dynamic general equilibrium model” (deterministic). I have two options:

1. Calibrate my factor shares (and other parameters, and steady state values for endogenous variables) on long-run averages from 1978 to 2017 and estimate my elasticities of substitution on 1978-2017 time series.

2. Calibrate my factor shares on the year 2017, which has a (nearly) zero output gap, so we can define it as the steady state of the economy to reproduce, and my elasticities on 1978-2017 time series. I personally prefer that one because it allows me to have “actual” steady state values for endogenous variables and parameters reflecting the current state of the economy I’m studying. The first option would underestimate or overestimate some steady state values as it takes long-run averages from 1978 to 2017.

Best

The answer depends on your prior about what happened in the data. Usually, we think that the long-run average is a good estimator of the mean, i.e. steady state in your model. If you think that this is not the case, e.g. due to a trend in the data that makes the mean an inappropriate estimator, then you should use more recent data.

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Yes I have a trend in my capital, debt, energy consumption and GDP data… So on your advice, I’ll take the year 2017 as the steady state of my model.

Thanks!

It’s not about trends per se. In a Cobb-Douglas function, the share parameters refer to a ratio of trending variables. You only have a problem if that ratio has a trend.

I don’t get it then. I have CES functions. If I say that 2017 has a zero output-gap, can I state that this year is my steady state? Because if I take long-run averages as the steady state, my averages for endogenous variables are usually not close to the values of the latest years. I am afraid my model won’t be able to simulate correctly actual data.

Thanks

Having a 0 output gap does not imply you are in steady state. Only if all variables are at their steady stae values and not just output, that will be the case. If you are willing to make these additional assumptions, then go ahead.

Hum okay. It looks tricky. Better use long-run averages then. But for example :
a) The long-run average of my GDP is 1700 billion euros while the GDP is at 2000 billion euros in 2017,
b) The long-run average of the debt is at 1412 billion euros while the 2017 value is at 2000 billion euros
c) The long-run average of consumption is at 1000 billion euros while the 2017 value is at 1200 billion euros
d) Taxes have also a huge huge gap between long-run averages and 2017 data.

If I put long-run averages values as my initial steady state, my economy is going to be far from its current state… That’s what I’m afraid of.

Best regards,

Sorry, but I don’t understand what you are doing. You started talking about factor shares, now you talk about trending levels. Those are very different objects.

Let me reformulate my issue.

1. What you are saying is that I should calibrate the factor shares on long-run averages. I get that.

2. Before writing down my steady state values for endogenous variables on Dynare, I have to find the SS of my model from FOCs and parameters only. However, my parameters are calibrated on long-run averages, hence the SS values for the endogenous variables will (?) mimic long-run averages as well. The issue is that, this SS values will be far from the actual 2017/2018 levels. Plus, I fix my exogenous variables on 2017 values…

Thanks A steady state cannot contain a trend. If your model variables are trending, you first need to conceptualize what a steady state means in that context (usually something like a balanced growth path)

Okay. Does that mean I should integrate some growth content in my steady-state equations? And should I put these new “balanced growth path” equations in the steady_state file?

One last question: if so, do I have to calibrate the parameters on these new equations, or can I still use the steady-state equations to calibrate my model?

I think I have the answer there : https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_nonstationary.mod

Thanks

Hi prof Pfeifer, may I revive this thread…so, for example, if you want to calibrate \alpha to target some ratio, say \frac{Y_t}{K_t}, Y_t and K_t can have a trend (in levels in the data), but their ratio should not, right?

If \frac{Y_t}{K_t} has a trend over the entire sample, then there is a problem as you said. In this case, maybe one can just focus on ratios in the last period of the sample?

1. Yes, if Y_t and K_t are indeed cointegrated as in most models, then their ratio is constant.
2. Focusing on the end of the sample is sometimes valid, particularly if there is more like a break than a continuous (and unmodeled) trend.
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