Kalman Filter estimation with lags of state variables in observation equation
Dear Stata Users:
I am trying to estimate potential output using a backward looking Phillips curve. However as lags of the output gap (which include lags of the state unobservable variable potential output, which is part of the estimation procedure) enter this observation equation, stata returns an error warning of the presence of lagged state variables (not allowed under sspace syntax).
I can trick stata by defining an additional state equation with an auxiliary variable equal to lagged potential output and including a constraint setting its coefficient equal to 1, and then using this auxiliary variable in my observation equation (Phillips curve), without getting an error message.
However I am concerned that by doing this I might be overparametrizing the model, by forcing Stata to estimate and additional state equation of a variable that I already know, which might change the estimation. Let me know your ideas.
constraint 1 [lgdp]yp = 1 //coefficient of potential output in equation decomposing observed output in cyclical and long run term
constraint 2 [lgdp]yc = 1 // coefficient of cyclical component in equation decomposing observed output in cyclical and long run term
constraint 3 [yp]l.yp = 1 // eq 4: coefficient of y*(t-1) constraint in potential output law of motion modeled as a random walk
constraint 4 [yp]l.g = 1 // eq 4: coefficient of g(t-1) constraint on coefficient on growth rate of potential output, in law of motion of potential output
constraint 5 [g]l.g = 1 // eq 5: coefficient of g(t-1) constraint on coefficient on growth rate of potential output, in its law of motion
constraint 6 [var(yc)]_cons = 1600*[var(g)]_cons // set ratio of variances lambda HP filter = 1600
constraint 7 [ypL]l.yp = 1 // ypL is potential ouput in t-1. In order to cheat Stata because does not allow lags in measurement equations
constraint 8 [inflagap]ypL = -[inflagap]l.lgdp // eq 7: set same coef.*(-1) for y*(t-1) and y(t-1)
sspace (yp L.yp L.g, state noconstant noerror) /// eq. 4
(g L.g , state noconstant) /// eq. 5
(yc, state noconstant) /// eq. 6
(ypL l.yp, state noconstant noerror) /// auxiliry eq. to cheat stata: creates y*(t-1)
(inflagap l.inflagap ypL l.lgdp m2_growth tcn_growth, noconstant) /// eq. 7
(lgdp yp yc, noconstant noerror), /// eq. 3
constraints(1 2 3 4 5 6 7 8) difficult /// constraints on coefficients
I am trying to estimate potential output using a backward looking Phillips curve. However as lags of the output gap (which include lags of the state unobservable variable potential output, which is part of the estimation procedure) enter this observation equation, stata returns an error warning of the presence of lagged state variables (not allowed under sspace syntax).
I can trick stata by defining an additional state equation with an auxiliary variable equal to lagged potential output and including a constraint setting its coefficient equal to 1, and then using this auxiliary variable in my observation equation (Phillips curve), without getting an error message.
However I am concerned that by doing this I might be overparametrizing the model, by forcing Stata to estimate and additional state equation of a variable that I already know, which might change the estimation. Let me know your ideas.
constraint 1 [lgdp]yp = 1 //coefficient of potential output in equation decomposing observed output in cyclical and long run term
constraint 2 [lgdp]yc = 1 // coefficient of cyclical component in equation decomposing observed output in cyclical and long run term
constraint 3 [yp]l.yp = 1 // eq 4: coefficient of y*(t-1) constraint in potential output law of motion modeled as a random walk
constraint 4 [yp]l.g = 1 // eq 4: coefficient of g(t-1) constraint on coefficient on growth rate of potential output, in law of motion of potential output
constraint 5 [g]l.g = 1 // eq 5: coefficient of g(t-1) constraint on coefficient on growth rate of potential output, in its law of motion
constraint 6 [var(yc)]_cons = 1600*[var(g)]_cons // set ratio of variances lambda HP filter = 1600
constraint 7 [ypL]l.yp = 1 // ypL is potential ouput in t-1. In order to cheat Stata because does not allow lags in measurement equations
constraint 8 [inflagap]ypL = -[inflagap]l.lgdp // eq 7: set same coef.*(-1) for y*(t-1) and y(t-1)
sspace (yp L.yp L.g, state noconstant noerror) /// eq. 4
(g L.g , state noconstant) /// eq. 5
(yc, state noconstant) /// eq. 6
(ypL l.yp, state noconstant noerror) /// auxiliry eq. to cheat stata: creates y*(t-1)
(inflagap l.inflagap ypL l.lgdp m2_growth tcn_growth, noconstant) /// eq. 7
(lgdp yp yc, noconstant noerror), /// eq. 3
constraints(1 2 3 4 5 6 7 8) difficult /// constraints on coefficients
