How to compute steady state analytically for open economy model When the condition for international risk sharing is not met?

Stochastic simulations
1

Now I only know the procedure how to calculate the steady-state when the international risk-sharing condition is met, in this case，consumption in both countries is equal,which makes computing the steady state simple,because I can use both Equilibrium condition and the condition that both countries consume the same to compute.However, When the condition for international risk sharing is not met,the above computing procedure can not be adopted.Can anyone recommend textbooks or papers to help me solve this problem? I would be very grateful 。

2

Can you elaborate a bit more? Risk sharing alone is not sufficient. You also need to assume identical initial wealth to have identical consumption in steady state.

3

Okey.I write my computing process and my questions in the word file.You can check it.
Computing process.pdf (526.1 KB)

4

That is too much detail. You cannot expect people to wade through your full attempt at steady state computation.

5

Sorry,I misunderstood what you meant.Now could I ask another question? I run dynare for my model,it says:Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file …
Found 45 equation(s).
Evaluating expressions…done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs …
done
Preprocessing completed.

Randomize initial guess…

Residuals of the static equations:

Equation number 1 : NaN : 1
Equation number 2 : NaN : 2
Equation number 3 : NaN : 3
Equation number 4 : NaN : 4
Equation number 5 : NaN : 5
Equation number 6 : NaN : 6
Equation number 7 : NaN : delta
Equation number 8 : NaN : deltastar
Equation number 9 : NaN : ch
Equation number 10 : NaN : cf
Equation number 11 : NaN : cfstar
Equation number 12 : NaN : chstar
Equation number 13 : NaN : 13
Equation number 14 : NaN : 14
Equation number 15 : NaN : s
Equation number 16 : NaN : ca
Equation number 17 : NaN : 17
Equation number 18 : NaN : y
Equation number 19 : NaN : ystar
Equation number 20 : NaN : mc
Equation number 21 : NaN : mcstar
Equation number 22 : NaN : pho
Equation number 23 : NaN : s1
Equation number 24 : NaN : s2
Equation number 25 : NaN : pfostar
Equation number 26 : NaN : s1star
Equation number 27 : NaN : s2star
Equation number 28 : NaN : 28
Equation number 29 : NaN : 29
Equation number 30 : NaN : pih
Equation number 31 : NaN : pifstar
Equation number 32 : NaN : taod
Equation number 33 : NaN : mdta
Equation number 34 : NaN : ph
Equation number 35 : NaN : pf
Equation number 36 : NaN : 36
Equation number 37 : NaN : 37
Equation number 38 : NaN : vh
Equation number 39 : NaN : vfstar
Equation number 40 : NaN : a
Equation number 41 : NaN : ddelta
Equation number 42 : NaN : adelta
Equation number 43 : NaN : astar
Equation number 44 : NaN : 44
Equation number 45 : NaN : 45

错误使用 print_info (line 32)
The steady state has NaNs or Inf.

出错 steady (line 102)
print_info(info,options_.noprint, options_);

出错 primitive.driver (line 593)
steady;

出错 dynare (line 281)
primitive.mod (5.4 KB)

evalin('base',[fname '.driver']);
6

That typically happens when your exogenous processes are not correctly specified. In your case, a is zero, but you have mc = w/a;

7

Thank you! Now it says:ERROR: primitive.mod: line 107, cols 17-19: syntax error, unexpected LOG.I don’t know where I go wrong. Thank you for your help.
primitive.mod (5.4 KB)

8

Thank you! Now it says:mpossible to find the steady state (the sum of square residuals of the static equations is 0.0048). Either the model doesn’t
have a steady state, there are an infinity of steady states, or the guess values are too far from the solution
primitive.mod (5.4 KB)
.I don’t know where I go wrong. Thank you for your help.

9

I would recommend computing the steady state analytically. That allows cross-checking with the entered equations to see whether there is still a mistake.

10

Thank you for your recommendation.Now I am facing a new problem:The exchange rate (Q) is identical to 1 in this model.
pcp.mod (7.4 KB)
But not in the model.
two_country.mod (7.9 KB)
However The equations for determining exchange rates are the same for these two models.The only difference is that an equation is in exponential form.

11

I cannot run your code because files are missing and some parameter values are not set (they probably were in an external file).

12

Sorry!Please see
pcp.mod (7.4 KB)
and
two_country.mod (7.9 KB)

13

I am not sure I understand. It seems you did an exp()-substitution. This takes the log of everything. log(1) is zero, which is what the model shows.

14

syntax error, unexpected ‘;’
LLCPdeng.mod (10.6 KB)
This is a simple problem.But I can’t solve it right now.Looking forward to your help.Thank you!

15

In line 137, there is a bracket that never closes.

16

I found it according to your clue.Thanks a lot.