I guess you are right that capital is not predetermined anymore in this case due to the presence of tau.

I would recommend testing the different timing options in a simple model through looking at the impulse response functions. I tried to implement this setting into the Cooley-Prescott-model. There you can see that my proposed timing is wrong. When I shock tau_k_shock, it only affects capital used in the next period, while klag, which is the capital used in this period is unaffected. But because the shock realized today is known to affect capital used tomorrow, the endogenous variables c and i already move today.

```
var yobs iobs c k lab z klag tau_shock;
varexo e e2;
//predetermined_variables k;
parameters bet del alp rho the tau rho_tau;
bet = 0.987;
the = 0.357;
del = 0.012;
alp = 0.4;
tau = 2;
rho = 0.95;
rho_tau = 0.9;
model;
(c^the*(1-lab)^(1-the))^(1-tau)/c=bet*((c(+1)^the*(1-lab(+1))^(1-the))^(1-tau)/c(+1))*(1+alp*exp(z(+1))*k^(alp-1)*lab(+1)^(1-alp)-del);
c=the/(1-the)*(1-alp)*exp(z)*k(-1)^alp*lab^(-alp)*(1-lab);
yobs=exp(z)*k(-1)^alp*lab^(1-alp);
k=exp(tau_shock(+1))*(exp(z)*k(-1)^alp*lab^(1-alp)-c+(1-del)*k);
iobs=exp(z)*k(-1)^alp*lab^(1-alp)-c;
z=rho*z(-1)+e;
tau_shock=rho_tau*tau_shock(-1)+e2;
klag=k(-1);
end;
initval;
k = 1;
klag=k;
c = 1;
lab = 0.3;
z = 0;
e = 0;
end;
shocks;
var e2; stderr 1;
end;
steady;
stoch_simul(order=1,irf=40);
```

Hence, I would try to make K non-predetermined by using:

```
Y = K^alpha;
K = Tau*(I(-1)+(1-d)*K(-1));
```

In the Cooley-Prescott-Model this would be

[code]var yobs iobs c k lab z klag tau_shock;

varexo e e2;

//predetermined_variables k;

parameters bet del alp rho the tau rho_tau;

bet = 0.987;

the = 0.357;

del = 0.012;

alp = 0.4;

tau = 2;

rho = 0.95;

rho_tau = 0.9;

model;

(c^the*(1-lab)^(1-the))^(1-tau)/c=bet*((c(+1)^the*(1-lab(+1))^(1-the))^(1-tau)/c(+1))*(1+alp*exp(z(+1))*k(+1)^(alp-1)**lab(+1)^(1-alp)-del);*

c=the/(1-the)(1-alp)*exp(z)**k(-1)^alp*lab^(-alp)(1-lab);

yobs=exp(z)*k^alp*lab^(1-alp);

k=exp(tau_shock)(exp(z(-1))*k(-1)^alp*lab(-1)^(1-alp)-c(-1)+(1-del)*k(-1));*

iobs=exp(z)*k^alp*lab^(1-alp)-c;

z=rhoz(-1)+e;

tau_shock=rho_tau*tau_shock(-1)+e2;

klag=k(-1);

end;

initval;

k = 1;

klag=k;

c = 1;

lab = 0.3;

z = 0;

e = 0;

end;

shocks;

var e2; stderr 1;

end;

steady;

stoch_simul(order=1,irf=40);[/code]