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frbuseview.nw
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\documentclass{book}
\usepackage{noweb}
\usepackage{hyperref}
\hypersetup{final=true}
\usepackage[toc,page]{appendix}
\usepackage{multicol}
\usepackage{framed}
\usepackage{xcolor}
\let\oldquote=\quote
\let\endoldquote=\endquote
\colorlet{shadecolor}{orange!15}
\renewenvironment{quote}{\begin{shaded*}\begin{oldquote}}{\end{oldquote}\end{shaded*}}
\title{Reverse Engineering the Eview Code in the FRB/US Model}
\author{Gary Young}
\begin{document}
\pagestyle{noweb}
\frontmatter
\maketitle
\tableofcontents
\mainmatter
\chapter{Introduction}
\chapter{FRB/US Package}
\section{example1 program}
<<frbus example1>>=
' Program for simple simulation under VAR expectations
'
' See FRB/US Simulation Basics document for information about
' this program
' *************************************************************
' Initial filename and parameter settings
' *************************************************************
' Subroutines
include ../subs/master_library
' Workfile
%wfstart = "1975q1"
%wfend = "2030q4"
%mainpage = "main"
wfcreate(wf=aaa,page={%mainpage}) q {%wfstart} {%wfend}
' FRB/US model name and location
%varmod = "stdver"
%varpath = "../mods/"
' Input datbase
%dbin = "../data/longbase"
' Simulation range
%simstart = "2020q1"
%simend = "2025q4"
' ****************************************************************
' Retrieve data, model equations and coefficients, set
' policy options, and compute tracking residuals
' ****************************************************************
' Load equations and coefficients
ld_frbus_eqs(modelname=%varmod,modelpath=%varpath)
ld_frbus_cfs(modelname=%varmod,modelpath=%varpath)
' Load data
dbopen %dbin as longbase
fetch(d=longbase) *
' Set monetary policy rule
smpl @all
call set_mp("dmpintay")
' Turn off zero bound and policy thresholds; hold policymaker's
' perceived equilibrium real interest rate constant
smpl @all
dmptrsh = 0
rffmin = -9999
drstar = 0
' Set fiscal policy
smpl @all
call set_fp("dfpsrp")
' Set _aerr variables to zero
smpl @all
{%varmod}.makegroup(a,n) endog @endog
call groupnew("endog","_aerr")
call group2zero("endog_aerr")
' Standard solution options
{%varmod}.solveopt(o=b,g=12,z=1e-12)
' Assign baseline tracking add factors
%suftrk = "_0"
smpl %simstart %simend
{%varmod}.addassign @all
{%varmod}.addinit(v=n) @all
{%varmod}.scenario(n,a={%suftrk}) "track"
{%varmod}.solve
scalar mm = @max(@abs(xgap{%suftrk}-xgap))
if mm > .0001 then
statusline dynamic tracking simulation failed for {%varmod}
stop
endif
' *************************************************************
' Simulate a shock to monetary policy rule
' *************************************************************
%sufsim = "_1"
{%varmod}.scenario(n,a={%sufsim}) "sim"
smpl %simstart %simstart
rffintay_aerr = rffintay_aerr + 1
smpl %simstart %simend
{%varmod}.solve
'***********************************************************
' Make a graph
'***********************************************************
smpl %simstart %simend
series zero = 0
series d_rff = rff{%sufsim} - rff
series d_rg10 = rg10{%sufsim} - rg10
series d_lur = lur{%sufsim} - lur
series d_pic4 = pic4{%sufsim} - pic4
graph fig1a.line zero d_rff
fig1a.addtext(t,just(c),font("arial",12)) Federal Funds Rate
fig1a.legend -display
graph fig1b.line zero d_rg10
fig1b.addtext(t,just(c),font("arial",12)) 10-Year Treasury Yield
fig1b.legend -display
graph fig1c.line zero d_lur
fig1c.addtext(t,just(c),font("arial",12)) Unemployment Rate
fig1c.legend -display
graph fig1d.line zero d_pic4
fig1d.addtext(t,just(c),font("arial",12)) Inflation Rate (4-Quarter)
fig1d.legend -display
graph fig1.merge fig1a fig1b fig1c fig1d
fig1.addtext(t,just(c),font("Arial",16)) Macroeconomic Effects of Funds Rate Perturbation\r(VAR Expectations)
fig1.align(2,1,1.25)
show fig1
@
\section{example2 program}
<<frbus example2>>=
' Program for simple simulation with MCE expectations
'
' The switch variables %mcvars_wp and %mcvars_all control whether
' the assumption of MC expectations extends beyond the financial
' sector
' See the Simulation Basics document for information about
' this program
' *************************************************************
' Initial filename and parameter settings
' *************************************************************
' Subroutines
include ../subs/master_library
include ../subs/mce_solve_library
' Workfile
%wfstart = "1975q1"
%wfend = "2100q4"
%mainpage = "main"
wfcreate(wf=aaa,page={%mainpage}) q {%wfstart} {%wfend}
' FRB/US model names and locations
%varmod = "stdver"
%varpath = "../mods/"
%mcemod = "pfver"
%mcepath = "../mods/"
' Input datbase
%dbin = "../data/longbase"
' Simulation range
%simstart = "2020q1"
%simend = "2069q4"
' ****************************************************************
' Retrieve data, model equations and coefficients, set
' policy options, and compute tracking residuals
' ****************************************************************
' Specify MC expectations variables
%mcvars_wp = "yes"
%mcvars_all = "no"
' MCE asset pricing
%zvars = "zdivgr zgap05 zgap10 zgap30 zrff5 zrff10 zrff30 zpi10 zpi10f zpic30 zpib5 zpic58 "
' MCE elsewhere
if %mcvars_wp = "yes" and %mcvars_all = "no" then
%zvars = %zvars + "zpicxfe zpieci "
endif
if %mcvars_all = "yes" then
%zvars = %zvars + "zpicxfe zpieci "
%zvars = %zvars + "zecd zeco zeh zgapc2 zlhp zpi5 zvpd zvpi zvps zxbd zxbi zxbs zyh zyhp zyht zynid "
endif
' Load equations and coefficients
call mce_load_frbus("mce_vars=%zvars,mod_b=%varmod,path_b=%varpath,mod_f=%mcemod,path_f=%mcepath")
' Load data
dbopen %dbin as longdata
fetch(d=longdata) *
' Data for extra variables associated with MC expectations
smpl @all
call make_frbus_mcevars(%zvars)
' Set monetary policy
smpl @all
call set_mp("dmpintay")
' Turn off zero bound and policy thresholds; hold policymaker's
' perceived equilibrium real interest rate constant
smpl @all
dmptrsh = 0
rffmin = -9999
drstar = 0
' Set fiscal policy
smpl @all
call set_fp("dfpsrp")
' Set _aerr variables to zero
smpl @all
{%varmod}.makegroup(a,n) endog @endog
call groupnew("endog","_aerr")
call group2zero("endog_aerr")
' Standard solution options
{%varmod}.solveopt(o=b,g=12,z=1e-12)
{%mcemod}.solveopt(o=b,g=12,z=1e-12)
' Assign baseline tracking add factors
%suftrk = "_0"
smpl %simstart %simend
{%varmod}.addassign @all
{%varmod}.addinit(v=n) @all
{%varmod}.scenario(n,a={%suftrk}) "track"
{%varmod}.solve
scalar mm = @max(@abs(xgap{%suftrk}-xgap))
if mm > .0001 then
statusline dynamic tracking simulation failed for {%varmod}
stop
endif
{%mcemod}.addassign @all
{%mcemod}.addinit(v=n) @all
' *************************************************************
' Simulate a monetary policy shock
' *************************************************************
%sufsim = "_1"
{%varmod}.scenario(n,a={%sufsim}) "sim"
{%mcemod}.scenario(n,a={%sufsim}) "sim"
smpl %simstart %simstart
rffintay_a = rffintay_a + 1
%modstr = "mod_b=%varmod,mod_f=%mcemod,mce_vars=%zvars"
%algstr = "meth=qnewton"
%simstr = "type=single"
smpl %simstart %simend
call mce_run(%modstr,%algstr,%simstr)
'***********************************************************
' Make a graph
'***********************************************************
smpl %simstart %simstart + 39
series zero = 0
series d_rff = rff{%sufsim} - rff
series d_rg10 = rg10{%sufsim} - rg10
series d_lur = lur{%sufsim} - lur
series d_pic4 = pic4{%sufsim} - pic4
graph fig1a.line zero d_rff
fig1a.addtext(t,just(c),font("arial",12)) Federal Funds Rate
fig1a.legend -display
graph fig1b.line zero d_rg10
fig1b.addtext(t,just(c),font("arial",12)) 10-Year Treasury Yield
fig1b.legend -display
graph fig1c.line zero d_lur
fig1c.addtext(t,just(c),font("arial",12)) Unemployment Rate
fig1c.legend -display
graph fig1d.line zero d_pic4
fig1d.addtext(t,just(c),font("arial",12)) Inflation Rate (4-Quarter)
fig1d.legend -display
graph fig1.merge fig1a fig1b fig1c fig1d
%title = " Macroeconomic Effects of Funds Rate Shock\r"
if %mcvars_wp = "no" and %mcvars_all = "no" then
%title = %title + "(MC Expectations in Asset Pricing)"
endif
if %mcvars_wp = "yes" and %mcvars_all = "no" then
%title = %title + "(MC Expectations in Asset Pricing and Price-Wage Setting)"
endif
if %mcvars_all = "yes" then
%title = %title + "(MC Expectations in All Sectors)"
endif
fig1.addtext(t,just(c),font("Arial",16)) {%title}
fig1.align(2,1,1.25)
show fig1
@
\section{example3 program}
<<frbus example3>>=
' Program for simulation under VAR expectations that illustrates how
' to set the monetary policy options that impose the zero lower bound
' on the funds rate and delay the liftoff of the funds rate from the
' ZLB until either the unemployment rate falls below a threshold or
' inflation rises above a threshold.
'
' See FRB/US Simulation Basics document for general information about
' this program.
' Additional notes:
' 1. The scenario involves a set of negative aggregate demand
' shocks and a positive risk premium shock that start in 2003q3,
' when the baseline (historical) funds rate is about one percent.
' The shocks are equal to the equation errors actually observed
' in the four quarters starting in 2008q4.
' 2. To impose the ZLB set %zb = "yes" (rather than "no")
' 3. To impose the policy liftfoff threshold conditions set both
' %zb = "yes" and %threshold = "yes". For illustrative purposes
' and reflecting the baseline conditions in 2003 and the years
' that immediately follow, the inflation threshold is set to 3.0
' and the unemployment threshold is set to 7.0, subject to the
' the adjustments described next.
' 4. Because the threshold conditions only make sense once the ZLB is
' binding, unemployment is above its threshold level (lurtrsh),
' and inflation is below its threshold (pitrsh), which is not the
' case in the initial simulation quarters, the program turns on the
' threshold code (using dmptrsh) in the 5th simulation quarter,
' at which point these conditions hold. In addition, for the threshold
' code to work properly, the endogenous switch variable dmptr must be
' zero in the quarter prior to the quarter in which the threshold code is
' turned on. This is accomplished by setting the baseline data on dmptr
' to zero and by setting the unemployment and inflation thresholds
' (lurtrsh, pitrsh) to values in the first four simulation quarters that
' would not flip the dmptr switch to one.
' 4. Choose one of the five available policy rules by setting
' %policy to one of rffintay, rfftay, rfftlr, rffalt, or rffgen.
' 5. If neither the ZLB or thresholds are imposed, the monetary policy
' equations have baseline-tracking adds and the simulation is
' a standard deviations-from-baseline exercise.
' 6. If either the ZLB or thresholds are imposed, the add factors on
' monetary policy equations are set to zero after the tracking adds
' are computed so that the ZLB and threshold conditions are based on the
' actual simulated outcomes for the funds rate and inflation and unemployment,
' not their deviations from baseline.
' *************************************************************
' Initial filename and parameter settings
' *************************************************************
' Subroutines
include ../subs/master_library
' Workfile
%wfstart = "1975q1"
%wfend = "2012q4"
%mainpage = "main"
wfcreate(wf=aaa,page={%mainpage}) q {%wfstart} {%wfend}
' FRB/US model name and location
%varmod = "stdver"
%varpath = "../mods/"
' Input datbase
%dbin = "../data/longbase"
' Simulation range
%simstart = "2003q3"
%simend = "2008q2"
' Policy
%zb = "yes"
%threshold = "yes"
%policy = "rfftay"
' ****************************************************************
' Retrieve data, model equations and coefficients, set
' policy options, and compute tracking residuals
' ****************************************************************
' Load equations and coefficients
ld_frbus_eqs(modelname=%varmod,modelpath=%varpath)
ld_frbus_cfs(modelname=%varmod,modelpath=%varpath)
' Load data
dbopen %dbin as longbase
fetch(d=longbase) *
' Set monetary policy rule
smpl @all
%policydmp = @replace(%policy,"rff","dmp")
call set_mp(%policydmp)
' Set ZLB
if %zb = "yes" then
rffmin = .125
else
rffmin = -9999
endif
' Set threshold variables
if %threshold = "yes" then
if %zb = "no" then
@uiprompt("When policy thresholds are imposed, the zero bound must also be imposed")
stop
endif
smpl @all
call dateshift(%simstart,%quarter4,3)
' thresholds (dmptrsh and dmptr) not active in first 4 qtrs
smpl %simstart - 1 %quarter4
dmptrsh = 0
lurtrsh = -9999
pitrsh = 9999
dmptr = 0
' thresholds (dmptrsh and dmptr) active starting in qtr 5
smpl %quarter4 + 1 %simend
dmptrsh = 1
lurtrsh = 7.0
pitrsh = 3.0
smpl @all
else
smpl @all
dmptrsh = 0
endif
smpl @all
drstar = 0
' Set fiscal policy
smpl @all
call set_fp("dfpsrp")
' Set _aerr variables to zero
smpl @all
{%varmod}.makegroup(a,n) endog @endog
call groupnew("endog","_aerr")
call group2zero("endog_aerr")
' Standard solution options
{%varmod}.solveopt(o=b,g=12,z=1e-12)
' Assign baseline tracking add factors
%suftrk = "_0"
smpl %simstart 2012q4
{%varmod}.addassign @all
{%varmod}.addinit(v=n) @all
{%varmod}.scenario(n,a={%suftrk}) "track"
{%varmod}.solve
scalar mm = @max(@abs(xgap{%suftrk}-xgap))
if mm > .0001 then
statusline dynamic tracking simulation failed for {%varmod}
stop
endif
' Set monetary policy add factors to zero when ZLB or threshold are
' imposed
if %zb = "yes" then
smpl @all
{%policy}_a = 0
rffrule_a = 0
rffe_a = 0
if %threshold = "yes" then
dmptpi_a = 0
dmptlur_a = 0
dmptmax_a = 0
dmptr_a = 0
endif
endif
' *************************************************************
' Simulation
' *************************************************************
%sufsim = "_1"
{%varmod}.scenario(n,a={%sufsim}) "sim"
' shock values are taken from equation residuals for 2008q4-2009q3
eco_a.fill(o=%simstart) -.006, -.006, -.011, -.001
ecd_a.fill(o=%simstart) -.091, -.018, -.021, .029
eh_a.fill(o=%simstart) -.076, -.078, -.040, .073
epd_a.fill(o=%simstart) -.096, -.062, .014, .032
eps_a.fill(o=%simstart) -.018, -.046, -.036, -.017
rbbbp_a.fill(o=%simstart) 2.70, 0.38, -0.89, -1.35
smpl %simstart %simend
{%varmod}.solve
'***********************************************************
' Make a graph
'***********************************************************
smpl %simstart %simend
graph fig1a.line rff rff{%sufsim}
fig1a.addtext(t,just(c),font("arial",12)) Federal Funds Rate
fig1a.legend -display
graph fig1b.line rg10 rg10{%sufsim}
fig1b.addtext(t,just(c),font("arial",12)) 10-Year Treasury Yield
fig1b.legend -display
graph fig1c.line lur lur{%sufsim}
fig1c.addtext(t,just(c),font("arial",12)) Unemployment Rate
fig1c.legend -display
graph fig1d.line pic4 pic4{%sufsim}
fig1d.addtext(t,just(c),font("arial",12)) Inflation Rate (4-Quarter)
fig1d.legend -display
%title = "Macroeconomic Effects of Negative AD Shock\r(VAR Expectations"
%title = %title + "; Policy = " + %policy + ")"
if %zb = "yes" and %threshold = "no" then
%title = %title + "\r(ZLB Imposed)"
endif
if %zb = "yes" and %threshold = "yes" then
%title = %title + "\r(ZLB and Thresholds Imposed)"
endif
graph fig1.merge fig1a fig1b fig1c fig1d
fig1.addtext(t,just(c),font("Arial",16)) {%title}
fig1.addtext(b,just(c),font("Arial",16)) Blue: Actual; Red: Simulated
fig1.align(2,1,1.25)
show fig1
@
\section{example4 program}
<<frbus example4>>=
' This MCE example program illustrates:
'
' 1. how to use a monetary policy rule that is not one of the policy
' alternatives included in FRB/US;
' 2. how to add new MCE expectations variables;
' 3. how to drop one of the regular FRB/US equations as part of the process
' of loading the model
' Most of the code needed illustrate these issues is located between
' the "start of new code" and "end of new code" comments below
' The switch variables %mcvars_wp and %mcvars_all control whether
' the assumption of MC expectations extends beyond the financial
' sector
' See the Simulation Basics document for information about
' this program
' *************************************************************
' Initial filename and parameter settings
' *************************************************************
' Subroutines
include ../subs/master_library
include ../subs/mce_solve_library
' Workfile
%wfstart = "1975q1"
%wfend = "2100q4"
%mainpage = "main"
wfcreate(wf=aaa,page={%mainpage}) q {%wfstart} {%wfend}
' FRB/US model names and locations
%varmod = "stdver"
%varpath = "../mods/"
%mcemod = "pfver"
%mcepath = "../mods/"
' Input datbase
%dbin = "../data/longbase"
' Simulation range
%simstart = "2010q1"
%simend = "2069q4"
' ****************************************************************
' Retrieve data, model equations and coefficients, set
' policy options, and compute tracking residuals
' ****************************************************************
' Specify MC expectations variables
%mcvars_wp = "no"
%mcvars_all = "yes"
' MCE asset pricing
%zvars = "zdivgr zgap05 zgap10 zgap30 zrff5 zrff10 zrff30 zpi10 zpi10f zpic30 zpib5 zpic58 "
' MCE elsewhere
if %mcvars_wp = "yes" and %mcvars_all = "no" then
%zvars = %zvars + "zpicxfe zpieci "
endif
if %mcvars_all = "yes" then
%zvars = %zvars + "zpicxfe zpieci "
%zvars = %zvars + "zecd zeco zeh zgapc2 zlhp zpi5 zvpd zvpi zvps zxbd zxbi zxbs zyh zyhp zyht zynid "
endif
' Load equations and coefficients
' drop one of the FRB/US monetary policy rule equations (rffgen) so that it can be
' replaced below with an alternative rule
%allbut = "rffgen"
call mce_load_frbus("mce_vars=%zvars,mod_b=%varmod,path_b=%varpath,mod_f=%mcemod,path_f=%mcepath,allbut=%allbut")
' Load data
dbopen %dbin as longdata
fetch(d=longdata) *
' *****************************************************************************
' *****************************************************************************
' start of new code (aside from the change above to mce_load_frbus and
' the change below to the call to set_mp)
' Code a first-difference interest rate rule as rffgen. The first-difference rule depends on
' the expected output gap three quarters ahead (zgap3) and on expected 4-qtr inflation three
' quarters ahead (zpic43). The name of each new expectation must start with a "z".
{%varmod}.append rffgen-rffgen_aerr = rffe(-1) + .5*(zpic43-pitarg) + .5*(zgap3-zgap3(-4))
' Add the MCE definitions of zgap3 and zpic43 to the forward-looking model,
' noting that the MCE names of these variables must start with a "w" rather than a "z".
{%mcemod}.append wgap3-wgap3_aerr = xgap2(3)
{%mcemod}.append wpic43-wpic43_aerr = picx4(3)
' Add expectations error equations to the MCE model
{%mcemod}.append ezgap3 = zgap3-wgap3
{%mcemod}.append ezpic43 = zpic43-wpic43
' Add to the backward-looking model simple equations for the new expectations variables.
' Technically, these equations should be the appropriate VAR expectations formulas, but
' because in this program these expectations will always be MCE, the form of their
' backward-looking identities is not very important.
{%varmod}.append zgap3-zgap3_aerr = .5*xgap2(-1)
{%varmod}.append zpic43-zpic43_aerr = .5*picx4(-1)+.5*ptr(-1)
' Add the new MCE variables to the %zvars string
%zvars = %zvars + " zgap3 zpic43"
' Define baseline values of the new expectations variables
smpl @all
series zgap3 = xgap2(3)
series zpic43 = picx4(3)
' Make sure that the baseline data for rffgen matches the baseline data for rffe
rffgen = rffe
' end of new code
' *****************************************************************************
' *****************************************************************************
' Data for extra variables associated with MC expectations
smpl @all
call make_frbus_mcevars(%zvars)
' Set monetary policy to use the first-difference policy rule (coded as rffgen)
smpl @all
call set_mp("dmpgen")
' Turn off zero bound and policy thresholds; hold policymaker's
' perceived equilibrium real interest rate constant
smpl @all
dmptrsh = 0
rffmin = -9999
drstar = 0
' Set fiscal policy
smpl @all
call set_fp("dfpsrp")
' Set _aerr variables to zero
smpl @all
{%varmod}.makegroup(a,n) endog @endog
call groupnew("endog","_aerr")
call group2zero("endog_aerr")
' Standard solution options
{%varmod}.solveopt(o=b,g=12,z=1e-12)
{%mcemod}.solveopt(o=b,g=12,z=1e-12)
' Assign baseline tracking add factors
%suftrk = "_0"
smpl %simstart %simend
{%varmod}.addassign @all
{%varmod}.addinit(v=n) @all
{%varmod}.scenario(n,a={%suftrk}) "track"
{%varmod}.solve
scalar mm = @max(@abs(xgap{%suftrk}-xgap))
if mm > .0001 then
statusline dynamic tracking simulation failed for {%varmod}
stop
endif
{%mcemod}.addassign @all
{%mcemod}.addinit(v=n) @all
' *************************************************************
' Simulate the effects of a one-percent consumption shock
' *************************************************************
%sufsim = "_1"
{%varmod}.scenario(n,a={%sufsim}) "sim"
{%mcemod}.scenario(n,a={%sufsim}) "sim"
smpl %simstart %simstart
eco_a = eco_a + .01
%modstr = "mod_b=%varmod,mod_f=%mcemod,mce_vars=%zvars"
%algstr = "meth=qnewton"
%simstr = "type=single"
smpl %simstart %simend
call mce_run(%modstr,%algstr,%simstr)
'***********************************************************
' Make a graph
'***********************************************************
smpl %simstart %simstart + 39
series zero = 0
series d_rff = rff{%sufsim} - rff
series d_rg10 = rg10{%sufsim} - rg10
series d_lur = lur{%sufsim} - lur
series d_pic4 = pic4{%sufsim} - pic4
graph fig1a.line zero d_rff
fig1a.addtext(t,just(c),font("arial",12)) Federal Funds Rate
fig1a.legend -display
graph fig1b.line zero d_rg10
fig1b.addtext(t,just(c),font("arial",12)) 10-Year Treasury Yield
fig1b.legend -display
graph fig1c.line zero d_lur
fig1c.addtext(t,just(c),font("arial",12)) Unemployment Rate
fig1c.legend -display
graph fig1d.line zero d_pic4
fig1d.addtext(t,just(c),font("arial",12)) Inflation Rate (4-Quarter)
fig1d.legend -display
graph fig1.merge fig1a fig1b fig1c fig1d
%title = " Macroeconomic Effects of a Shock to Consumption\r"
if %mcvars_wp = "no" and %mcvars_all = "no" then
%title = %title + "(MC Expectations in Asset Pricing)"
endif
if %mcvars_wp = "yes" and %mcvars_all = "no" then
%title = %title + "(MC Expectations in Asset Pricing and Price-Wage Setting)"
endif
if %mcvars_all = "yes" then
%title = %title + "(MC Expectations in All Sectors)"
endif
fig1.addtext(t,just(c),font("Arial",16)) {%title}
fig1.align(2,1,1.25)
show fig1
@
\section{ocpolicy program}
<<frbus ocpolicy>>=
' Routine to simulate how the SEP baseline forecast would change if
' policymakers commit to a path for the federal funds rate that is
' determined by optimal-control (OC) techniques to minimize a
' quadratic loss function.
'
' Detailed information on the mechanics of the OC algorithm and the
' various required and optional parameters that set up and guide its
' execution is available in the MCE Solve Users Guide in the
' documentation directory. Most relevant is the part of section 5
' that describes the "opt" simulation type as well as table 7.
' As specified below, the loss function penalizes equally weighted
' squared deviations of the unemployment rate from the natural rate,
' squared deviations of inflation from a 2 percent, and squared
' quarterly changes in the funds rate.
' In the SEP baseline, agents with model-consistent (MC) expectations
' are initially assumed to project that the funds rate will follow the
' baseline path and to set their baseline expectations
' accordingly. At the start of the optimal control simulation, however,
' these agents immediately and fully revise their expectations to be
' consistent with the revision to the funds rate path that occurs under
' optimal control -- that is, agents have rational expectations and
' announced policy actions are completely credible.
'
' The experiment can be run with the zero lower bound (ZLB) imposed
' (%zerobound = "yes") or not imposed (%zerobound = "no"). When
' the ZLB is imposed, a penalty term is added to the loss function.
' *************************************************************
' Initial filename and parameter settings
' *************************************************************
' Subroutines
include ../subs/master_library
include ../subs/mce_solve_library
' Workfile
%wfstart = "1975q1"
%wfend = "2100q4"
%mainpage = "main"
wfcreate(wf=aaa,page={%mainpage}) q {%wfstart} {%wfend}
' FRB/US model names and locations
%varmod = "stdver"
%varpath = "../mods/"
%mcemod = "pfver"
%mcepath = "../mods/"
' Input datbase
%dbin = "../data/longbase"
' Simulation range
%simstart = "2014q4"
%simend = "2070q4"
' Primary loss function parameters: The value of the policy instrument
' is chosen optimally from %drvstart to %drvend (60 qtrs) to minimize
' the loss function from %evlstart to %evlend (80 qtrs). The three
' arguments of the period loss function are weighted by the the
' weight parameters and over time losses are discounted at the rate
' %discount
%evlstart = %simstart
%drvstart = %simstart
call dateshift(%evlstart,%evlend,79)
call dateshift(%drvstart,%drvend,59)
%discount = ".99"
%u_weight = "1.0"
%p_weight = "1.0"
%r_weight = "1.0"
' Optionally impose the zero lower bound
%zerobound = "yes"
' ****************************************************************
' Retrieve data, model equations and coefficients, set
' policy options, and compute tracking residuals
' ****************************************************************
' Specify MC expectations variables
%mcvars_wp = "yes"
%mcvars_all = "no"
' MCE asset pricing
%zvars = "zdivgr zgap05 zgap10 zgap30 zrff5 zrff10 zrff30 zpi10 zpi10f zpic30 zpib5 zpic58 "
' MCE elsewhere
if %mcvars_wp = "yes" and %mcvars_all = "no" then
%zvars = %zvars + "zpicxfe zpieci "
endif
if %mcvars_all = "yes" then
%zvars = %zvars + "zpicxfe zpieci "
%zvars = %zvars + "zecd zeco zeh zgapc2 zlhp zpi5 zvpd zvpi zvps zxbd zxnfbi zxnfbs zyh zyhp zyht zynid "
endif
' Load equations and coefficients
call mce_load_frbus("mce_vars=%zvars,mod_b=%varmod,path_b=%varpath,mod_f=%mcemod,path_f=%mcepath")
' Add a ugap equation
{%varmod}.append ugap - ugap_aerr = lur - lurnat
' Load data
dbopen %dbin as longdata
fetch(d=longdata) *
' Define SEP-consistent ustar and ugap series; this step is needed because
' the baseline value of lurnat may not be fully SEP-consistent in the
' short-to-medium ruun
smpl @all
series ustar = lurnat
smpl %simstart 2025q4
ustar = 5.35
smpl @all
series ugap = lur-ustar
series ugap_aerr = 0
' Data for extra variables associated with MC expectations
smpl @all
call make_frbus_mcevars(%zvars)
' Set monetary policy option (the residual on the equation of
' the chosen option is the OC policy instrument)
smpl @all
call set_mp("dmptay")
' Initially turn off zero lower bound; if %zerobound = "yes", it will be
' imposed below by adding a penalty term to the loss function.
smpl @all
rffmin = -9999
' Turn off policy thresholds
dmptrsh = 0
' Let the perceived equilibrium real interest rate vary
drstar = 1
' Set fiscal policy so that it is exogenous for first 20 qtrs and then
' turns on debt targeting rule
smpl %simstart %simstart + 19
call set_fp("dfpex")
smpl %simstart + 20 %simend
call set_fp("dfpdbt")
' Set _aerr variables to zero
smpl @all
{%varmod}.makegroup(a,n) endog @endog
call groupnew("endog","_aerr")
call group2zero("endog_aerr")
' Standard solution options
{%varmod}.solveopt(o=b,g=12,z=1e-12)
{%mcemod}.solveopt(o=b,g=12,z=1e-12)
' Assign baseline tracking add factors
%suftrk = "_0"
smpl %simstart %simend
{%varmod}.addassign @all
{%varmod}.addinit(v=n) @all
{%varmod}.scenario(n,a={%suftrk}) "track"
{%varmod}.solve
scalar mm = @max(@abs(xgap{%suftrk}-xgap))
if mm > .0001 then
statusline dynamic tracking simulation failed for {%varmod}
stop
endif
{%mcemod}.addassign @all
{%mcemod}.addinit(v=n) @all
'*************************************************************
' optimal policy setup
'*************************************************************
' The policy instrument is a time varying constant in the equation
' for the selected policy rule
group opt_instrus rfftay_aerr
' Loss function variables (unemployment gap, 4-qtr PCE inflation,
' and the first difference of the federal funds rate)
group opt_targs ugap pic4 delrff
' The desired paths of the loss function variables are specified in
' series with "_t" suffix.
smpl @all
series ugap_t = 0
series delrff_t = 0
series pic4_t = 2.0
' The weights on the loss function arguments are specified in
' series with "_w" suffix.
series ugap_w = @val(%u_weight)
series pic4_w = @val(%p_weight)