reverse-shooting

Matlab scripts for reverse shooting
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iv.m (3233B)

      1 % iv	[u,N,K,stdest,b,vcv,sOID]=iv(y,x,w,title,depv,indv,instv)
      2 %	Instrumental Variables Estimation (Works with Panel data also)
      3 %
      4 %		y = dependent variable 		Nx1
      5 %		x = rhs variables		NxK
      6 %		w = instruments			NxJ  J>=K
      7 
      8 function [u,N,K,stdest,beta,vcv,sOID]=iv(y,x,w,title,depv,indv,instv);
      9 
     10 sOID=[];
     11 
     12 Pw = w*inv(w'*w)*w';		% The projection matrix for w
     13 xxinv = inv(x'*Pw*x);
     14 beta  = xxinv*x'*Pw*y;
     15 u  = y-x*beta;			% Use the real x's here!
     16 
     17 % Now, just copy the remainder from ols.m
     18 
     19 if x(:,1) ~= 1; disp 'No constant term in regression'; end;
     20 if exist('prevest')~=1; prevest=0; end;
     21 if title == 0; title = 'Instrumental Variables Estimation'; end;
     22 if depv == 0; depv = '        '; end;
     23 
     24 [N K] = size(x);
     25 if indv == 0; indv=vdummy('x',K); end;
     26 
     27 
     28 dof   = N-K-prevest;
     29 sigma2=u'*u/dof;
     30 stdest=sqrt(sigma2);
     31 vcv   =sigma2*xxinv;
     32 se    =sqrt(diag(vcv));
     33 tstat = beta./se;
     34 ybar  = 1/N*(ones(N,1)'*y);
     35 rsq   = 1-(u'*u)/(y'*y - N*ybar^2);
     36 rbar  = 1-sigma2/((y'*y - N*ybar^2)/(N-1));
     37 
     38 % Compute White robust standard errors
     39  
     40 robvcv=zeros(K,K);
     41 xhat=Pw*x;
     42 for i=1:N
     43         robvcv = robvcv + u(i)^2*xhat(i,:)'*xhat(i,:);
     44 end % i
     45 robvcv = (N/(dof))*xxinv*robvcv*xxinv;
     46 roberr = sqrt(diag(robvcv));
     47 trob   = beta./roberr;
     48 
     49 
     50 % Test of OID Restrictions (See Econometrics Notes, Newey Section (end) back
     51 % of page 5:  Based on quadratic form for W'e/sqrt(T).
     52 
     53 dofOID=size(w,2)-size(x,2);
     54 if dofOID>0;
     55    sOID=(w'*u)'*inv(sigma2*w'*w)*(w'*u);
     56    pval=1-chi2cdf(sOID,dofOID);
     57 end;
     58 
     59 % Hausman-Wu test versus OLS;  Problem:  often VV is not invertible (pd)
     60 %bols = inv(x'*x)*x'*y;
     61 %q=bols-beta;
     62 %VV=sigma2*(xxinv - inv(x'*x));
     63 %det(VV)
     64 %sHW=q'*inv(VV)*q;
     65 %pHW=1-chi2cdf(sHW,K);
     66 
     67 disp '=============================================================================';
     68 disp ' ';
     69 disp ' ';
     70 disp '         ------------------------------------------------------------';
     71 fprintf(['                   ', title, '\n']);
     72 disp '         ------------------------------------------------------------';
     73 disp ' ';
     74 fprintf(['       NOBS:  ', num2str(N),'                Dependent Variable: ',depv,'\n']);
     75 fprintf(['   RHS Vars:  ', num2str(K),'\n']);
     76 fprintf(['     D of F:  ', num2str(dof), '\n']);
     77 disp ' ';
     78 fprintf(['  R-Squared:  ', num2str(rsq)]);
     79 fprintf(['                        S.E.E.:  ', num2str(stdest), '\n']);
     80 fprintf(['     RBar^2:  ', num2str(rbar)]);
     81 fprintf(['                   Residual SS:  ', num2str(u'*u), '\n']);
     82 disp ' ';
     83 if dofOID>0;
     84    fprintf('  OverID Test -- Statistic: %6.2f  DoF: %4.0f  Pval: %6.3f\n',[sOID dofOID pval]);
     85 end;
     86 %fprintf('  Hausman-Wu Test -- Stat:  %6.2f  DoF: %4.0f  Pval: %6.3f\n',[sHW K pHW]);
     87 disp ' ';
     88 disp '                             Standard              Robust     Robust';
     89 disp 'Variable          Beta         Error    t-stat      Error     t-stat';
     90 disp '--------          ----       --------   ------     ------     ------';
     91 disp ' ';
     92 fmt='%16.6f %12.6f %8.2f %12.6f %8.2f';
     93 results=[beta se tstat roberr trob];
     94 for i=1:K;
     95         fprintf(indv(i,:));
     96         fprintf(1,fmt,results(i,:));
     97         fprintf('\n');
     98 end
     99 disp ' ';
    100 fprintf('Instruments: ');
    101 say(instv);  % List the instruments
    102 disp ' ';
    103 disp '=============================================================================';
    104 %end;  % if PRINT==0