A. NO FISCAL POLICY


Ramsey Steady State
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(a) To run the cashless economy, edit STRUCTURAL_PARAMETERS.M and set at the very bottom NUH=0 and NUF=0;
(b) Set inital guess for ramsey optimal gross nominal quarterly interest rate at X0=1.04^(1/4) (cashless economy) and X0=1.0342^(1/4) (monetary economy) and save it in x0.mat.  
(c) Run RAMSEY_SS.M this program saves output in ramsey_ss.mat

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Welfare
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(1) Run ramsey_f.m This program saves output in ramsey_f.mat. It computes analytical expressions for f and its first and 2nd derivatives (fx, fxp, ...) Although the derivatives are taken with respect to the log of a number of variables, f and its derivatives are expressed in terms of the levels of its arguments. So, in evaluating these functions one must use levels. 

(2) run ramsey_run.m This program saves output in ramsey_run.mat. It computes a second-order accurate approximation to lifetime utility (a) conditional on the initial period being the deterministic ramsey steady state and (b) unconditionally. Welfare  values and parameters necessary for computing welfare costs are stored in the file welfare_ramsey.mat for use in other programs.

Welfare under a Taylor rule or Inflation Targeting
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(1) Run competitive_f.m This program saves output in competitive_f.mat. It computes analytical expressions for f and its first and 2nd derivatives (fx, fxp, ...) Although the derivatives are taken with respect to the log of a number of variables, f and its derivatives are expressed in terms of the levels of its arguments. So, in evaluating these functions one must use levels. 
(2) In the workspace, create a string: economy=`taylor' for a Taylor rule with inflation coefficient of 1.5 and an output coefficient of 0.5. Or set economy = `taylor_simple' for a Taylor rule with inflation coefficient of 1.5 and an output coefficient of zero. Or set economy=`inflation_targeting' for a policy that sets $\hat{pi}_t=0$.
(3) run competitive_run(economy):  This program saves output in "economy"_run.mat. It computes a second-order accurate approximation to lifetime utility (a) conditional on the initial period being the deterministic ramsey steady state and (b) unconditionally.  In addition, it computes the welfare costs of both of these welfare concepts relative to the Ramsey allocation. 

Optimized Interest Rate Rules
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(1) Create two strings, named feature1 and feature2 in the matlab workspace. Set feature1='smoothing' or 'no_smoothing' for a interest rate feedback rule with or without interest rate inertia,i.e.,  $\alpha_R\neq0$ or $\alpha_R=0$. Set feature2='crule',  'brule',  'frule', or 'drule' to select a contemporaneous looking, a backward-looking, a forward-looking, or a difference interest rate rule. 
(2) Execute competitive_optimized(feature1, feature2). This program finds the policy coefficients that maxmize welfare from a timeless perspective, i.e., coefficients that maximize the unconditional expectation of lifetime utility. The optimized rule coefficients are written to a .mat file named: optimized_feature1_feature2.mat. The initial guess for the optimized coefficients is given in competitive_optimized.m in the variable MONET_POL0 = [3 0];
(3) In the matlab workspace create a string: economy='optimized_feature1_feature2'. For example, set economy = 'optimized_no_smoothing_crule'.  
(4) run competitive_run(economy):  This program saves output in "economy"_run.mat. It computes a second-order accurate approximation to lifetime utility (a) conditional on the initial period being the deterministic ramsey steady state and (b) unconditionally.  In addition, it computes the welfare costs of both of these welfare concepts relative to the Ramsey allocation. 

Second Moments
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(1) In the workspace, create a string variable called economy which can take the following values: 
ramsey or 
taylor or
taylor_simple or
inflation_targeting or
optimized_smoothing_crule(/brule/frule/drule)
optimized_no_smoothing_crule(/brule/frule/drule)
(2) Run moments(economy). It saves the output under the name 'economy_moments.mat'.  The output of moments is a table with standard deviations in its first column and different variables accross rows. 



B. FISCAL POLICY
Follow instructions in A. with small modificaitons