Forecasting - 1st and 2nd order approximation
Posted: Tue Oct 24, 2006 11:50 pm[This follows an earlier question but identifies a possible bug in DYNARE]
The RBC model enclosed includes a variable (v) that is the expected discounted sum of another endogenous variable (ut). When using the instruction 'forecast' with the second order approximation over 250 periods, the forecasted path of variable (ut) is uniformally above its steady state value, while the forecast of variable (v) at time 1 decreases below its steady state value. This seems odd since variable (v) is just the expected discounted sum of (ut), written as a difference equation.
Another way of identifying the same problem is to run FORECAST with the deterministic shock set =0 for any period. Then (ut) is uniformally below its value in the previous exercise while the forecast of (v) at time 1 is above its value in the previous exercise.
note:
1) this problem only arises for long enough forecast
2) setting the stochastic shocks ' variance to zero does not affect result
I am inclined to think there is a problem with the way the FORECAST instruction works with second order approximation.
ENCLOSED:
- rbc model file
- exogenous deterministic shock path file
The RBC model enclosed includes a variable (v) that is the expected discounted sum of another endogenous variable (ut). When using the instruction 'forecast' with the second order approximation over 250 periods, the forecasted path of variable (ut) is uniformally above its steady state value, while the forecast of variable (v) at time 1 decreases below its steady state value. This seems odd since variable (v) is just the expected discounted sum of (ut), written as a difference equation.
Another way of identifying the same problem is to run FORECAST with the deterministic shock set =0 for any period. Then (ut) is uniformally below its value in the previous exercise while the forecast of (v) at time 1 is above its value in the previous exercise.
note:
1) this problem only arises for long enough forecast
2) setting the stochastic shocks ' variance to zero does not affect result
I am inclined to think there is a problem with the way the FORECAST instruction works with second order approximation.
ENCLOSED:
- rbc model file
- exogenous deterministic shock path file