Hi,

I’ve started working on models where international trade of assets is subject to imperfections. That is, some models assume complete financial markets, which gives rise to the Backus-Smith consumption-risk sharing relation

`q=UC_star/UC`

where q - real exchange rate, UC_star - foreign marginal utility of consumption and UC - domestic. But it typically fails to explain negative correlation between the domestic consumption and the real exchange rate and it leads to a very stable (low volatility) and rapidly mean-reverting real exchange rate (whereas in reality real exchange rates of floating currencies are extremely persistent).

So one of the ways of enhancing the model is to introduce portfolio adjustment costs. In that case, the expected change in the real exchange rate is defined from an augmented UIP condition expressed in real terms:

`1+dDELTA(-1)=(r_star(-1)/r(-1))*(q/q(-1));`

where r is the domestic real interest rate:

```
1=beta*r*(UC(+1)/UC);
```

dDELTA is the slope of portfolio adjustment costs:

```
dDELTA=phi*(OMEGA(+1)-STEADY_STATE(OMEGA));
```

OMEGA is the portfolio position and r_star is the foreign real interest rate given exogenously:

```
log(r_star)=(1-rho_star)*log(1/beta)+rho_star*log(r_star(-1))+sigma_star*u_star;
```

The problem is that I keep getting collinearity warnings of all the equations above when I use the augmented UIP, but not the Backus-Smith relation and I don’t understand why. The rest of the model runs smoothly without any problems and the impulse response functions seem smooth and sensible regardless of which version I use.

However, some of the results don’t make sense and in some cases the endo_simul leads to a very large gap between the theoretical mean (steady state) and the sample mean (from the simulated series over say 10000 observations).

Any idea why I might be getting such results? Many thanks.