# Transitional Dynamics

Hi everyone.

Actually I’m doing a transitional dynamics exercise with a large scale OLG model which features two different types of households (natives and migrants). This of course imply a set of Euler equations and budget constraints for each generation and for each type of household. I’m calibrating the model in 1950, however at that time my assumption is that migrants were not present in the economy, but they start to show up just in the 1990. Therefore for the first 40 periods (1950-1990) when I’m doing transitional dynamics, I’m setting the migrant population to zero (the population dynamics is completely exogenous) so that they are not affecting the determination of aggregates and prices in the economy. However, although the population is set to zero, the “representative agent” for migrants is still there in 1950 (Euler equations and budget constraints are active), therefore individual consumption and asset for migrants are positive although the population is zero. This would imply that when migrants show up in 1990, their consumption and asset choices are affected by their previous ones although they were not present in the economy, right?

I’m wondering if I’m doing things right. If not, is there a way to completely shut off the Euler equations and budget constraints for the first 40 periods, or any advices? Or this implies a regime switching from a model without migrants to a model with migrants?

Thanks.

Alex.

This sounds like a nonstationary model case. I am not sure this can be meaningfully done in one simulation. If migration expected to happen? If not, you could start with a simulation without migrants and then combine it with an economy where they are present.

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A little background of why i am doing this. In principle my time span of interest is from 1990 onwards. However, a referee pointed me out that with perfect foresight, the anticipation could lead to boosted quantitative results in the first periods of simulation, and he suggested me to follow Kruger & Ludwig 2007, where they start doing the simulation many periods before the period of interest by calibrating an artificial steady state to avoid the anticipation effect. Fine the method. However, in my case, if i do that, migrants are not present in 1950 and I end up with the problem mentioned above.

Yes the model is not stationary, the only source of growth comes from TFP growth.

I thought of doing the simulation in the two cases you mentioned, i tried with an exogenous variable that regulate the shift from the economy without migrants to the one with migrants (so that to preserve one .mod file), but this lead to converge problem (on the forward looking part of the euler equation). Otherwise how can i combine two different .mod files in perfect foresight in Dynare as you are saying?

Alex.

If the problem is anticipation, you could try the
`perfect_foresight_with_expectation_errors_solver`
in Dynare 6.

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I have a code to simulate a sequence of MIT shocks in PF, is it the same thing right?

However, given the non stationarity of the economy I think i cannot simulate the economy with fully unexpected paths, rather i have to assume that the path for the productivity must be somehow expected (or from the beginning of the simulation till the final SS or starting from a specific period of time in the future till the final SS) so that to keep the economy along the BGP during the transitional dynamics. Regarding the other exogenous variables instead they are unexpected shocks at each time t. Right?

Yes, it’s equivalent to a sequence of MIT shocks.

You are correct. From what you describe, you need to combine expected and MIT shocks.

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Thanks a lot Johannes.

I have achieved what I wanted by updating at each time t the growth path of the TFP.
So there are two cases:

1. temporary: the agents are hit by unexpected shocks and they think these are temporary. The same apply for the TFP growth, the agents think the new path is temporary, and from t+1 (after the shock) they think the TFP growth will be back to the previous balanced path.
2. permanent: the same but the agents think the exo variables will remain to the shock level forever, included the TFP growth to its new balanced path.

Basically i update the BGP at every period of time t.