policy frontier

[yanking]

Dear all,
I am trying to draw a policy frontier (or Taylor curve) by assuming loss function as "lambda * var(inflation) + (1-lambda) * var(y)".
But I don't knwo how can I get it?
Can anyone offer me an complete example for refering!
Any helps will be really appreciated.

Best,
yanking

[jpfeifer]

Do you have a reference for what you are trying to achieve?

[yanking]

Dear Professor jpfeifer,thanks for your reply!
Such as viewtopic.php?f=1&t=6766&p=19563&hilit=policy+frontier#p19563,This is a problem that appeared long ago in this forom,but hasn't been solved till now.Another example is Iacoviello, Matteo(2007),"House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle",But he computed his policy frontier completely with matlab program.
What I need is how to solve this problem with dynare platform conbineded with simple matlab codes.

[yanking]

Sorry,Iacoviello, Matteo(2005),

[jpfeifer]

I see. Do you already have the mod-file for which you want to compute this?

[jpfeifer]

Starting with the unstable version of 12/18/2016 (Dynare 4.5), the following code should work for your mod-file

Code: Select all

% make loop silent
options_.nofunctions=1;
options_.nocorr=1;
options_.noprint=1;
options_.irf=0;
options_.silent_optimizer=1;

options_.osr.opt_algo=9;

% find position of variables in variable_weights
y_pos=strmatch('y_hat',M_.endo_names,'exact');
pi_pos=strmatch('pi_hat',M_.endo_names,'exact');

% find position of variables in var_list_
y_pos_var_list_=strmatch('y_hat',var_list_,'exact');
pi_pos_var_list_=strmatch('pi_hat',var_list_,'exact');

weight_grid=0:0.01:1;
n_grid_points=length(weight_grid);
var_y=NaN(n_grid_points,1);
var_pi=NaN(n_grid_points,1);
for grid_iter=1:n_grid_points
    M_.osr.variable_weights(pi_pos,pi_pos) = weight_grid(grid_iter);
    M_.osr.variable_weights(y_pos,y_pos) = (1-weight_grid(grid_iter));
    oo_.osr = osr(var_list_,M_.osr.param_names,M_.osr.variable_indices,M_.osr.variable_weights);
    if oo_.osr.error_indicator==0
        var_y(grid_iter)=oo_.var(y_pos_var_list_,y_pos_var_list_);
        var_pi(grid_iter)=oo_.var(pi_pos_var_list_,pi_pos_var_list_);
    end
end
figure
plot(var_y,var_pi)

[zhanshuo]

Hi, Prof Pfeifer, I add your above code to my mod file and it does not work, since the var_list_ is empty.
So shall I write names of all variables into var_list_?
Thanks.

[jpfeifer]

In that case, you should be able to replace

Code: Select all

var_list_

with

Code: Select all

M_.endo_names

[zhanshuo]

Thanks, dear Prof. Pfeifer , it finally works!

[john949]

Prof. Pfeifer,

Could you please clarify whether the above code you provided re-computes the Optimal Simple Rule every time the weight in the grid is changed, or whether it merely computes the unconditional variances of inflation and output gap implied by the Optimal Simple Rule calculated using the OSR routine for a particular value of "lambda" (say, 0.5) chosen prior to running the code you provided?

Thank you very much.

[jpfeifer]

Hi,
in the above code within the loop

Code: Select all

    M_.osr.variable_weights(pi_pos,pi_pos) = weight_grid(grid_iter);
    M_.osr.variable_weights(y_pos,y_pos) = (1-weight_grid(grid_iter));
    oo_.osr = osr(var_list_,M_.osr.param_names,M_.osr.variable_indices,M_.osr.variable_weights);


resets the weights and then recomputes the OSR for these particular weights.

[john949]

Prof. Pfeifer, thank you very much for such a prompt reply.

And just to confirm, if one runs

Code: Select all

optim_weights;
pi_hat 0.5;
y_hat 0.5;
end;

osr_params phiR phipi phiY;

osr_params_bounds;
phiR, 0, 0.99;
phipi, 1, 100;
phiY, 0, 100;
end;

osr(opt_algo=9);

prior to the code you provided, would the above-stated parameter bounds be respected in the re-computation of the OSR within the loop as the weight in the loss function is varied?

[jpfeifer]

Yes, because the resulting

Code: Select all

M_.osr.param_bounds

is not altered subsequently.

[john949]

Thank you.