Character unrecognized in simulation

Perfect foresight simulations
25

Yes I tried, it gives me the same trend for Hours without shocks. That’s a lot strange… It goes from 0.03064 to nearly 0.44, way too much… I don’t see any household working 11-hours a day :slight_smile:

What is also triggering is that the interest rate and the rental rate of capital do not co-move for 4 periods… But after period 4, it is all fine. Without shocks, the two variables co-move for all periods.

Thanks @jpfeifer

26

Then you should debug with a simpler model to find out why hours are non-stationary.

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27

Good afternoon @jpfeifer,

I’ve tried many things to debug the model.

The model works perfectly if I put a steady command after initval and write some shocks after it. The economy grows perfectly. If I put an arbitrary initial point, without writing the steady command, the solver fails.

My question is the following: in the Solow non-stationary you say that one cannot put a steady command after initval-block when the model exhibits a BGP. But mine works perfectly well if I do so. What’s the catch here?

Thank you.

Best regards

28

The steady command will compute the steady state conditional on the value of the exogenous variables. If it does not work without the command, this suggests that the value of the endogenous states deviates too far from the their steady state/BGP values.

29

Thanks @jpfeifer

I’m trying to write a steady-state-model file. I’ve followed your paper with Born (2014) such that I normalized output to 1. How do you write output in the steady state model in that case then, if normalized to 1? My first hint is: Output=1*(1+g)^t , with g the economic growth rate

Best regards

30

I have never tried this as your steady state will change over time given the growth rate. But I guess that you are right that the steady state will be conditional on the exogenous growth rate.

31

Thanks @jpfeifer . I’ve done it, and it gives all the BGP values I found by hand.

I have two further questions, if it’s ok:

  • When specifying BGP equations in initval, initval only computes the BGP values for period 0, then for period 1 to T the model block takes over, am I right?

  • I have a decreasing return rate of capital through time. Does this say that at period 0, r is not at its BGP value; or that my model is misspecified? I reckon that r should be constant along the BGP.

Thank you again. Very much appreciated.

Best regards

32
  1. initval does not compute anything. Only the steady-command after a block does. If you call it after a block, the steady state will be computed conditional on the state values provided in that block. I don’t know what you mean with

For those periods, you only supply starting values for the solver. The values for the exogenous states are never changed. They are always what you set them to be.
2. That is hard to tell. You must have an idea what your model is supposed to generate. But yes, usually rates of return do not have trends.

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33

Thank you @jpfeifer

I’ve checked, the ratio capital-output is not constant but trending in the simulations, which could explain the decreasing rate of return.

What’s triggering is that even with a simpler model and no shocks, the economy is growing.

Here is a “simpler” model with no shocks: BGP1.mod (7.2 KB)

Best regards

34

I cannot really help you here. This seems to be an economic issue within your model. You as the model builder need to try to understand what is going on. Why is your growth not consistent with the Kaldor facts?

35

I actually have no clue here. I use a standard model with CES functions, and a log-utility function. I think the issue here is with K. Indeed, K grows (while it shouldn’t in the presence of no shocks) giving a decreasing r and increasing Y. But why, I really don’t know.

Does the normalized constant in the production function Y_norma (such as Born and Pfeifer, 2014) need to be recalibrated every year? I’ve followed your paper and fixed Y_norma such that Y is equal to 1.

Thank you @jpfeifer

36

No, but with CES production functions, you can only have trend growth in labor augmenting technology. That follows from Uzawa’s theorem.

37

I am aware of that. I only have trend growth for labor augmenting technology and demographics growth. Even when I take out trend growth, the economy somewhat grows…

38

So does it come from demographics?

40

It’s bizarre that Dynare still manages to find a solution for all the simulations despite Uzawa’s theorem.

Actually the simulations gives me a capital to output ratio growing through time, which is what I observe empirically for the EU. IS it some kind of unbalanced growth path?

41

Dynare does not care about balanced or unbalanced growth as long as the FOCs are satisfied. You need to think hard why Uzawa’s theorem does not apply in your context.

42

Thank you. That’s what I’ve been doing today. My analytical model, on paper, satisfies Uzawa’s theorem. I’ve built it accordingly.

My second guess is the way I coded it on Dynare. I’m on that atm.

Thank you for your help again. I appreciate it a lot.

best regards

43

One last question @jpfeifer . Theoretically speaking, does one have to necessarily build a growth model according to Uzawa’s theorem (in the context of perfect foresight)? Or can it deviate from it ?

44

No, you can deviate from it. The argument for using balanced growth is usually an empirical one.

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