%ASSET_RUN.M %[gx,hx,gxx,hxx,gss,hss] = asset_run_linear(eta) computes a first- or second-order approximation (depending on the value assigned to the variable approx in the program ASSET_MODEL.M)to the policy function of the Burnside asset pricing model as described in ``Accuracy of stochastic perturbation methods: the case of asset pricing models," by F. Collard and M. Juillard, JEDC, 25, June 2001, 979-999. % %(c) Stephanie Schmitt-Grohe and Martin Uribe % %January 22, 2002 % % %The solution is of the form % %xp = h(x,sigma) + sigma* eta * ep % %y = g(x,sigma) % %The quadratic approximation to these functions are (in tensor notation) [Notation: x is x_t and xp is x_t+1, variables are expressed in log-deviations from their steady state value] % %xp^i = hx^i_a x_a + 1/2 [hxx^i_ab x_a x_b + hss^i sigma^2] + sigma* eta^i_c ep_c % %y^i = gx^i_a x_a + 1/2 [gxx^i_ab x_a x_b + gss^i sigma^2] % %where % % hx is nx by nx % gx is ny by nx % hxx is nx by nx by nx % gxx is ny by nx by nx % eta is nx by ne % gss is ny by 1 % hss is nx by 1 % sigma is a positive scalar % %Calls: asset_model.m gx_hx.m gxx_hxx.m gss_hss.m % %(c) Stephanie Schmitt-Grohe and Martin Uribe %Date January 22, 2002 [fx,fxp,fy,fyp,fypyp,fypy,fypxp,fypx,fyyp,fyy,fyxp,fyx,fxpyp,fxpy,fxpxp,fxpx,fxyp,fxy,fxxp,fxx,eta]=asset_model; [gx,hx] = gx_hx(fy,fx,fyp,fxp) [gxx,hxx] = gxx_hxx(fx,fxp,fy,fyp,fypyp,fypy,fypxp,fypx,fyyp,fyy,fyxp,fyx,fxpyp,fxpy,fxpxp,fxpx,fxyp,fxy,fxxp,fxx,hx,gx) [gss,hss] = gss_hss(fx,fxp,fy,fyp,fypyp,fypy,fypxp,fypx,fyyp,fyy,fyxp,fyx,fxpyp,fxpy,fxpxp,fxpx,fxyp,fxy,fxxp,fxx,hx,gx,gxx,eta)