How to estimate NAIRU in a state space model of the econometrics toolbox

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lovejesus
lovejesus 2016-6-16
回答： Hang Qian 2016-8-19
I would like to estimate the a time-varying nairu from the Philipps Curve: pi_t = pi*_t + beta*(u_t - u*_t) + e_t
pi_t: inflation
pi*_t: trend inflation
u_t: observed unemployment rate
u*_t: unobserved nairu
---------------------------------------------------
state equations are:
pi*_t = pi*_t-1 + v_1t
u*_t = u*_t-1 + v_2t
-------------------------------------------
N = 184 %# observations
m = 2 %# state equations
A = zeros(m);
A(1,1) = 1;
A(2,2) = NaN;
% Define the state-disturbance-loading matrix.
B = zeros(m);
B(1,1) = 0.001;
B(2,2) = 0.001;
% Define the measurement-sensitivity matrix.
C = zeros(N,m);
C(1,1) = 1;
C(1,2) = 1;
% Define the observation-innovation matrix.
D = zeros(N);
D(1,1) = 0.025;
params0 = -.3;
StateType = [2;2];
Mdl = ssm(A,B,C,D,'StateType',StateType);
Beta0 = [-.3];
[EstMdl1,estParams,EstParamCov,logL,Output] ...
= estimate(Mdl,yt,params0,'Predictors',Z,'Beta0',Beta0,'Display',{'params','diagnostics','full'})
filteredX = filter(EstMdl1,yt,'Predictors',Z,'Beta',estParams(end));
Z = observed unemployment series ---------------------------------------------------------------------------------------
Above the code I have created and it does not give me any reasonable results.
Does anyone have any suggestions?

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回答（1 个）

Hang Qian
Hang Qian 2016-8-19
It seems that the constructed SSM is not exactly the same as the one described in the equations. Usually C and D is a low-dimension matrix (say, C appears to be a 1-by-2 vector in this case), it is unnecessary to stack N observations in a giant matrix.
To check whether A,B,C,D construct a desired state-space model, consider disp(Mdl) and the model will be displayed on the screen equation by equation.
Also, I would not let the software guess both initial states, which are diffuse. I would incorporate priors on where the two random-walk states should start in that state-space model.
Regards,
- Hang Qian

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