High volatility of investment relative to output

[dynare16]

Hello,

I am working on a basic small-scale DSGE, with borrowers and savers and collateralized borrowing constraints (and no nominal rigidities). Both model-generated data and empirical data are in logged terms and hp-filtered. When I compare moments in the data and model-generated moments, I can see that the model generates much higher volatility of investment (relative to output) than in the data.

Is this something commonly found in basic models ? If so, is there a standard way to deal with it, like introducing investment adjustment costs or something similar ?

Thanks a lot

[jpfeifer]

In the very basic models, this is not that common. Investment is the most volatile component of GDP, but you can typically generate volatility commensurate with the data. But there might be amplification mechanisms the make investment more volatile. In these cases, introducing investment adjustment costs often helps.

[dynare16]

Thank you.

So I implemented investment adjustment costs in my model, with the following standard form :

(phi/2)*(I_t/I(t-1) -1)^2.

This affects the capital accumulation equation which becomes k=(1-delta)*k(-1)+i*[1-(phi/2)*(i/i(-1)-1)^2], the first order condition of firms with respect to capital and the firms' budget constraint.

However, this should not affect the steady state, because investment adjustment costs are zero in steady state. But when I run my model using the 'steady' command with the initial values being the steady state values of the model without adjustment costs, the model does not run and I get the usual error message saying that this is impossible to find the steady state. But the initial values should be the good ones, so I don't understand why Dynare can't find the steady state. It does not seem to be any error in my code.

Could it be that the non-linear solver has difficulties dealing with the squared term of the investment adjustment cost, even if it is obvious that this term reduces to zero in steady state ? Should I help by providing a steady state file ?

Thanks again

[jpfeifer]

Use the steady state values from the version without investment adjustment costs as starting values. If they do not solve the model, your implementation is wrong.

[dynare16]

Indeed, I found some problems in my implementation.

I have one last question: it is equivalent to derive the F.O.C of the firm with respect to capital or with respect to investment, right ? As long as I express my capital variable as a function of investment (by using the capital accumulation equation) in the firm's program (or conversely). Because usually the capital is the variable we maximize with respect to but with investment adjustment costs, I find it more convenient to maximize with respect to investment (because adjustment costs are quadratic and it not as easy to express investment as a function of capital) and I juste want to make sure this makes sense.

Many thanks for all your very helpful answers

[jpfeifer]

If you don't substitute out capital by replacing it with investment (which is typically impossible with adjustment costs), you need the derivative with respect to both investment and capital. If that is what you mean, you are right, this is equivalent.