Covariance between stochastic discount factor and inflation

Dear all,

Thank you in advance for your helpful advice.

I’m trying to price long-term real/nominal bond with New Keynesian DSGE model, to calculate the inflation risk premium, and to see how demand/supply shock may change the sign of the premium.

As is known, the positive inflation premium is accompanied by the negative covariance between ‘SDF from t to t+1’ and ‘inverse of cummulative inflation from t to t+1’. That is cov( SDF(t,t+1), 1/INF(t,t+1) ) < 0.

In the dynare code attached below (which is the mod file for BOE working paper 326, obtained from the BOE website). There exist negative inflation premium (-0.1406). Therefore I expected to get positive cov( SDF(t,t+1), 1/INF(t,t+1) ), or negative cov( SDF(t,t+1), INF(t,t+1) ).

In the code, DPSW(the authors) defined the stochastic discount factor and 1-period ahead inflation as

sdf = bet*(mu/mu(-1)); pi0_1 = pi(+1);

To get the covariance using the dynare, I added 1 period ahead sdf as

sdf0_1 = sdf(+1);

And I run the code and check the theoretical moments from


but the cov(sdf0_1, pi0_1) from oo._var was not negative, which is inconsistent with the paper.

I think I may have made some mistake using the dynare to calculate the covariance between future sdf and inflation. Can anyone help me to find where I did wrong.

Thank you always.

DPSW_WP_4.mod (37.3 KB)