IRFs: Timing Issue


I have replicated an RBC-model and essentially most of the IRFs turn out as in the paper. However, some of the predetermined variables respond to the shock on impact while in the paper their response is lagged by one period. I am not sure what could be the reason for this because I use the exact timing-convention as in the paper. I am not very experienced with solving DSGE-models, but could it potentially be a matter of the solution-method?

Any hints or suggestions would be very much appreciated…

Remark: there is no physical capital accumulation in the model, but a fixed asset that enters the agent’s period-by-period budget constraint with periods ‘t’ and ‘t-1’. I keep the same timing in Dynare.

Denote the fixed asset with b. The predetermined fixed asset that cannot move would be b(-1). But b is the amount of the fixed asset chosen this period, with which you enter the next period, where it cannot be changed anymore. For capital, you would have

Here, k(-1) is the predetermined capital stock used for production today, while k is the capital stock used next period, but determined by today’s investment. What Dynare plots in the IRFs is k, not k(-1) (it is the stock at the end of the period). It will naturally move, because it is determined by investment today. However, in terms of the stock at the beginning of period notation most papers use (and you seem to be thinking of), the timing is shifted by one period. In contrast, the capital stock used for production, i.e. k(-1), only moves with a one period delay and is really fixed at time t.

Thank you for the explanation.

If I understand you correctly: Given a stock at the beginning of period notation, what is plotted for period t usually corresponds to the value of period t-1, i.e. b_{t-1} ? Is that what you mean with the timing is shifted by one period?

No, compared to the beginning of period stock notation, what is plotted is b_{t+1} as this corresponds to Dynare’s b (your b_{t-1} would correspond to b(-2)).

Thank you, now it’s clear.