Timing problem in prices in Euler equations

[mpina]

Hello, I have been trying for a while to reproduce Corsetti, Dedula and Leduc (2008) without success. I think the error is in lines 97- 103, where the Euler equations for countries H and F are located. Currently, the mod file only runs if I set R, capital rental rate, as predetermined (R(-1)) in the budget constraint, but that is inconsistent with R(+1) in the Euler equations. If I fix this inconsistency, the model doesn’t run (blanchard-kahn).

I have tried moving the timing of capital variables kh, kf, kn1 and kn2, the timing of r (real interest rate), and simplifying equations, but nothing. The model is not that big so maybe the error is obvious for someone else.

I attach the .mod, the steady state file, and the derivation file in pdf. If anyone can take a look, it would be greatly appreciated. Thank you

CDL08.mod (9.9 KB)
CDL08_steadystate.m (8.1 KB)

equations.pdf (261.4 KB)

[jpfeifer]

You did not make the timing, but it looks like the reason is:

Timing of capital in two sector economy

Hello all, I am building a two-sectoral model, and I have a question about the timing of sectoral-capital variables: In my model, T and N are sectors, hence kT is capital in sector T and kN is capital in sector N. Then, I assume that the economy’s aggregate capital is simply: k = kT + kN. However, I assume only one law of motion for aggregate capital such that: k = (1-delta)*k(-1) + i - written in Dynare language. It is clear to me that k is a predetermined variable and should be treated as su…

[mpina]

Hello Professor, thanks for your reply. I fixed the capital as suggested by setting

k1(-1)  = kH + kN1; and
k2(-1)  = kF + kN2;

My problem remains the same. I think the problem may come from the timing of prices (r and R1,R2) in the Euler equations and budget constraint (BC).

With the following lines, the code runs, but I think it is wrong because R1 (and R2, for the foreign country) and r should be in expectation in the Euler equation.

Euler equation

lamb1*pHbar  = exp(-nu1)*lamb1(+1) *(pHbar(+1)*(1-DELTA) + R1 );    
lamb1             = exp(-nu1)*lamb1(+1) *(1+r) ;

BC

pH1*cH1 + pF1*cF1 + pN1*cN1 + bH + pHbar*iH = w1*l1 + R1(-1) *k1(-1) + (1+r(-1))*bH(-1); 

I think that the correct setup should be
Euler equation

lamb1*pHbar  = exp(-nu1)*lamb1(+1) *(pHbar(+1)*(1-DELTA) + R1(+1)  );    
lamb1             = exp(-nu1)*lamb1(+1) *(1+r(+1) ) ;

BC

pH1*cH1 + pF1*cF1 + pN1*cN1 + bH + pHbar*iH = w1*l1 + R1*k1(-1) + (1+r)*bH(-1); 

But this last setup yields 8 eigenvalues>1 for 7 forward looking variables and colinear relationships in all prices, so I’m stuck here. What should be the correct timing here? Thank you

[jpfeifer]

The return to capital is almost never predetermined. If that “fixes” your timing issue, you still have not found the correct timing.