Why Calvo parameters are so high in my estimation?

Rui · October 12, 2017, 4:14pm

Dear Prof.

I am trying to estimate a middle scale NK-DSGE model with Japan and US data, 7 series, growth rate of output, growth rate of consumption, growth rate of wage, growth rate of investment, labor hours index and policy rate.

I used mode_compute=4 and successful estimated all parameters. but I have some problems about two Calvo parameters for wage and price rigidity. The model I used has a stochastic growth trend. xi_p and xi_w are near 1, these values are not reasonable.
parameters
prior mean post. mean 90% HPD interval prior pstdev

sigma 1.000 theta 0.500 chi 2.000 zetainv 4.000 mu 1.000 phiy 0.075 lambda_p 0.200 gamma_p 0.500 xi_p 0.500 gamma_w 0.500 xi_w 0.500 phi_r 0.800 phi_pi 1.500 phi_y 0.125 pi_star 0.150 z_star 0.200 RN_star 0.500 L_star 2.000 rho_b 0.500 rho_i 0.500 rho_w 0.500 rho_g 0.500 rho_p 0.500 3.7749 2.3107 5.2315 gamm 0.5000
0.8691 0.8204 0.9185 beta 0.1500
2.1490 1.3056 2.9663 gamm 0.5000
8.1778 6.0267 10.2268 gamm 1.0000
0.3673 0.2244 0.5034 gamm 0.5000
0.1853 0.0698 0.3018 beta 0.0500
0.2708 0.1689 0.3708 gamm 0.0500
0.7540 0.5897 0.9460 beta 0.2500
0.9785 0.9688 0.9876 beta 0.2500
0.6961 0.4844 0.9175 beta 0.2500
0.9756 0.9547 0.9990 beta 0.2500
0.7291 0.6727 0.7836 beta 0.1000
1.4640 1.3076 1.6174 gamm 0.1000
0.2598 0.1628 0.3609 gamm 0.0500
0.2358 0.1200 0.3396 gamm 0.0500
0.1634 0.1191 0.2033 gamm 0.0500
0.6589 0.5603 0.7578 gamm 0.0500
1.9586 1.9185 1.9992 norm 1.0000
0.2472 0.0985 0.3915 beta 0.2000
0.7406 0.6696 0.8179 beta 0.2000
0.3802 0.0992 0.6278 beta 0.2000
0.9834 0.9760 0.9914 beta 0.2000
0.0842 0.0115 0.1578 beta 0.2000

standard deviation of shocks
prior mean post. mean 90% HPD interval prior pstdev

mu_b 0.500 7.7915 4.6284 10.8363 invg Inf
mu_i 0.500 1.8427 1.3232 2.3637 invg Inf
mu_w 0.500 0.3056 0.2728 0.3388 invg Inf
mu_g 0.500 0.8941 0.7835 1.0039 invg Inf
mu_p 0.500 0.0957 0.0834 0.1081 invg Inf
mu_r 0.500 0.2982 0.2565 0.3383 invg Inf
mu_z 0.500 0.4864 0.4198 0.5521 invg Inf
Data and mod file.zip (63.2 KB)

I hope someone can give me some help about how to fix this problem, because these two parameters are very important.

jpfeifer · October 12, 2017, 7:03pm

It’s hard to tell. There is nothing immediately suspicious, except for the somewhat strange series for pi_obs, which has a pronounced downward trend initially and then settles to a lower level without much movement.
That being said, compared with much of the literature, you use a relatively wide prior for the Calvo parameters. Try the Smets/Wouters (2007) prior with mean 0.5 and standard deviation 0.1 instead of 0.25

Rui · October 13, 2017, 1:19am

@jpfeifer Thank you for your advice.

The series of inflation rate I used is exactly same to Smets and Wouters (2007) , Gross Domestic Product: Implicit Price Deflator (GDPDEF), and the inflation rate is calculated as 100*log(GDPEDF_t-GDPDEF_t-1).

The mode can be found at mode_compute=4 and mcmc begun to run. I am still waiting the results of estimation, but the mode found before mcmc is still very high even I set the prior std of Calvo parameters to a very low value, 0.05~0.1.