131 lines
4.3 KiB
Modula-2
131 lines
4.3 KiB
Modula-2
// This program replicates figure 11.3.1 from chapter 11 of RMT2 by Ljungqvist and Sargent
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// This is a commented version of the program given in the handout.
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// Note: y_ records the simulated endogenous variables in alphabetical order
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// ys0_ records the initial steady state
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// ys_ records the terminal steady state
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// We check that these line up at the end points
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// Note: y_ has ys0_ in first column, ys_ in last column, explaining why it is 102 long;
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// The sample of size 100 is in between.
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// Warning: we align c, k, and the taxes to exploit the dynare syntax. See comments below.
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// So k in the program corresponds to k_{t+1} and the same timing holds for the taxes.
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//Declares the endogenous variables;
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var c k;
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//declares the exogenous variables // investment tax credit, consumption tax, capital tax, government spending
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varexo taui tauc tauk g;
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parameters bet gam del alpha A;
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bet=.95; // discount factor
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gam=2; // CRRA parameter
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del=.2; // depreciation rate
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alpha=.33; // capital's share
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A=1; // productivity
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// Alignment convention:
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// g tauc taui tauk are now columns of ex_. Because of a bad design decision
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// the date of ex_(1,:) doesn't necessarily match the date in y_. Whether they match depends
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// on the number of lag periods in endogenous versus exogenous variables.
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// In this example they match because tauc(-1) and taui(-1) enter the model.
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// These decisions and the timing conventions mean that
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// y_(:,1) records the initial steady state, while y_(:,102) records the terminal steady state values.
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// For j > 2, y_(:,j) records [c(j-1) .. k(j-1) .. G(j-1)] where k(j-1) means
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// end of period capital in period j-1, which equals k(j) in chapter 11 notation.
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// Note that the jump in G occurs in y_(;,11), which confirms this timing.
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// the jump occurs now in ex_(11,1)
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model;
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// equation 11.3.8.a
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k=A*k(-1)^alpha+(1-del)*k(-1)-c-g;
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// equation 11.3.8e + 11.3.8.g
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c^(-gam)= bet*(c(+1)^(-gam))*((1+tauc(-1))/(1+tauc))*((1-taui)*(1-del)/(1-taui(-1))+
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((1-tauk)/(1-taui(-1)))*alpha*A*k(-1)^(alpha-1));
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end;
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initval;
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k=1.5;
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c=0.6;
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g = 0.2;
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tauc = 0;
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taui = 0;
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tauk = 0;
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end;
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steady; // put this in if you want to start from the initial steady state, comment it out to start from the indicated values
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endval; // The following values determine the new steady state after the shocks.
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k=1.5;
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c=0.4;
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g =.4;
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tauc =0;
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taui =0;
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tauk =0;
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end;
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steady; // We use steady again and the enval provided are initial guesses for dynare to compute the ss.
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// The following lines produce a g sequence with a once and for all jump in g
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shocks;
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// we use shocks to undo that for the first 9 periods and leave g at
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// it's initial value of 0
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var g;
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periods 1:9;
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values 0.2;
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end;
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// now solve the model
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simul(periods=100);
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// Note: y_ records the simulated endogenous variables in alphabetical order
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// ys0_ records the initial steady state
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// ys_ records the terminal steady state
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// check that these line up at the end points
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y_(:,1) -ys0_(:)
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y_(:,102) - ys_(:)
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// Compute the initial steady state for consumption to later do the plots.
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co=ys0_(var_index('c'));
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ko = ys0_(var_index('k'));
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// g is in ex_(:,1) since it is stored in alphabetical order
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go = ex_(1,1)
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// The following equation compute the other endogenous variables use in the plots below
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// Since they are function of capital and consumption, so we can compute them from the solved
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// model above.
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// These equations were taken from page 333 of RMT2
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rbig0=1/bet;
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rbig=y_(var_index('c'),2:101).^(-gam)./(bet*y_(var_index('c'),3:102).^(-gam));
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rq0=alpha*A*ko^(alpha-1);
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rq=alpha*A*y_(var_index('k'),1:100).^(alpha-1);
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wq0=A*ko^alpha-ko*alpha*A*ko^(alpha-1);
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wq=A*y_(var_index('k'),1:100).^alpha-y_(var_index('k'),1:100).*alpha*A.*y_(var_index('k'),1:100).^(alpha-1);
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sq0=(1-ex_(1,4))*A*alpha*ko^(alpha-1)+(1-del);
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sq=(1-ex_(1:100,4)')*A*alpha.*y_(var_index('k'),1:100).^(alpha-1)+(1-del);
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//Now we plot the responses of the endogenous variables to the shock.
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figure
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subplot(2,3,1)
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plot([ko*ones(100,1) y_(var_index('k'),1:100)' ]) // note the timing: we lag capital to correct for syntax
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title('k')
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subplot(2,3,2)
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plot([co*ones(100,1) y_(var_index('c'),2:101)' ])
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title('c')
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subplot(2,3,3)
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plot([rbig0*ones(100,1) rbig' ])
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title('R')
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subplot(2,3,4)
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plot([wq0*ones(100,1) wq' ])
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title('w/q')
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subplot(2,3,5)
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plot([sq0*ones(100,1) sq' ])
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title('s/q')
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subplot(2,3,6)
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plot([rq0*ones(100,1) rq' ])
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title('r/q')
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