I have a silly question. The timing of the interest rate on government debt ® and the rental rate of capital ® in NK_baseline.mod (the replication of Fernandez-Villaverde (2009)), while both government debt and capital are predetermined variables, are different; R(-1) and r in the consumer budget constraint. Thus the FOC,
The timing difference, is this common to use? This, I think, is problematic when I have fiscal policy in the model. If I add a government budget constraint using the government debt timing on NK_baseline.mod and the original paper, R(-1)*b(-1), this won’t work; the rank condition isn’t verified. When I declared the debt as predetermined variable and use the same timing as the capital, for example,
g + Rb = tax(ldw+r*k) + b(+1)*PI(+1) + lumpsum;
the Euler equation is now
This, however, is working when the Taylor rule is defined as
But, really, the Taylor rule looks really weird with (+1) in it. Do you have any thoughts on this? Did I make any mistake on something? Can you suggest how can I fix this problem? Any comments will be very much appreciated. Thank you!
Note: I let g, tax, and lumpsum as completely exogenous, so the government budget constraint determines debt.