SolvingMicroDSOPs-clean-clean.sty

% Contains raw latex versions of most commands
% When used with demacro, generates document where LaTeX can mostly
% be rendered by plain markdown etc.

% Define various generically useful terms and items
\renewcommand{\avg}{\bar}
\providecommand{\cov}{}\renewcommand{\cov}{\textup{cov}}
\renewcommand{\Abve}{\bar}
\renewcommand{\Belw}{\underline}
\renewcommand{\CDF}{\mathcal{F}}
\renewcommand{\GroFac}{\Omega} % Generic for growth factor
\renewcommand{\GroRte}{\omega} % Generic for growth rate 
\renewcommand{\Lvl}{\mathbf}   % Levels of variables are bold

% Constrained
\renewcommand{\cnstr}[1]{\grave{#1}}

% Levels are boldface
\renewcommand{\aLvl}{\mathbf{a}}
\renewcommand{\bLvl}{\mathbf{b}}
\renewcommand{\cLvl}{\mathbf{c}}
\renewcommand{\dLvl}{\mathbf{d}}
\renewcommand{\eLvl}{\mathbf{e}}
\renewcommand{\fLvl}{\mathbf{f}}
\renewcommand{\gLvl}{\mathbf{g}}
\renewcommand{\hLvl}{\mathbf{h}}
\renewcommand{\iLvl}{\mathbf{i}}
\renewcommand{\jLvl}{\mathbf{j}}
\renewcommand{\kLvl}{\mathbf{k}}
\renewcommand{\mLvl}{\mathbf{m}}
\renewcommand{\nLvl}{\mathbf{n}}
\renewcommand{\pLvl}{\mathbf{p}}
\renewcommand{\qLvl}{\mathbf{q}}
\renewcommand{\rLvl}{\mathbf{r}}
\renewcommand{\sLvl}{\mathbf{s}}
\renewcommand{\tLvl}{\mathbf{t}}
\renewcommand{\uLvl}{\mathbf{u}}
\renewcommand{\vLvl}{\mathbf{v}}
\renewcommand{\wLvl}{\mathbf{w}}
\renewcommand{\xLvl}{\mathbf{x}}
\renewcommand{\yLvl}{\mathbf{y}}
\renewcommand{\zLvl}{\mathbf{z}}

\renewcommand{\ALvl}{\mathbf{A}}
\renewcommand{\BLvl}{\mathbf{B}}
\renewcommand{\CLvl}{\mathbf{C}}
\renewcommand{\DLvl}{\mathbf{D}}
\renewcommand{\ELvl}{\mathbf{E}}
\renewcommand{\FLvl}{\mathbf{F}}
\renewcommand{\GLvl}{\mathbf{G}}
\renewcommand{\HLvl}{\mathbf{H}}
\renewcommand{\ILvl}{\mathbf{I}}
\renewcommand{\JLvl}{\mathbf{J}}
\renewcommand{\KLvl}{\mathbf{K}}
\renewcommand{\LLvl}{\mathbf{L}}
\renewcommand{\MLvl}{\mathbf{M}}
\renewcommand{\NLvl}{\mathbf{N}}
\renewcommand{\OLvl}{\mathbf{O}}
\renewcommand{\PLvl}{\mathbf{P}}
\renewcommand{\QLvl}{\mathbf{Q}}
\renewcommand{\RLvl}{\mathbf{R}}
\renewcommand{\SLvl}{\mathbf{S}}
\renewcommand{\TLvl}{\mathbf{T}}
\renewcommand{\ULvl}{\mathbf{U}}
\renewcommand{\VLvl}{\mathbf{V}}
\renewcommand{\WLvl}{\mathbf{W}}
\renewcommand{\XLvl}{\mathbf{X}}
\renewcommand{\YLvl}{\mathbf{Y}}
\renewcommand{\ZLvl}{\mathbf{Z}}

% Functions are Roman not italicized
\renewcommand{\aFunc}{\mathrm{a}}
\renewcommand{\bFunc}{\mathrm{b}}
\renewcommand{\cFunc}{\mathrm{c}}
\renewcommand{\dFunc}{\mathrm{d}}
\renewcommand{\eFunc}{\mathrm{e}}
\renewcommand{\fFunc}{\mathrm{f}}
\renewcommand{\hFunc}{\mathrm{h}}
\renewcommand{\iFunc}{\mathrm{i}}
\renewcommand{\jFunc}{\mathrm{j}}
\renewcommand{\kFunc}{\mathrm{k}}
\renewcommand{\mFunc}{\mathrm{m}}
\renewcommand{\nFunc}{\mathrm{n}}
\renewcommand{\pFunc}{\mathrm{p}}
\renewcommand{\sFunc}{\mathrm{s}}
\renewcommand{\rFunc}{\mathrm{r}}
\renewcommand{\uFunc}{\mathrm{u}}
\renewcommand{\vFunc}{\mathrm{v}}
\renewcommand{\wFunc}{\mathrm{w}}
\renewcommand{\xFunc}{\mathrm{x}}
\renewcommand{\yFunc}{\mathrm{y}}
\renewcommand{\zFunc}{\mathrm{z}}

\renewcommand{\AFunc}{\mathrm{A}}
\renewcommand{\BFunc}{\mathrm{B}}
\renewcommand{\CFunc}{\mathrm{C}}
\renewcommand{\DFunc}{\mathrm{D}}
\renewcommand{\EFunc}{\mathrm{E}}
\renewcommand{\FFunc}{\mathrm{F}}
\renewcommand{\GFunc}{\mathrm{G}}
\renewcommand{\HFunc}{\mathrm{H}}
\renewcommand{\IFunc}{\mathrm{I}}
\renewcommand{\JFunc}{\mathrm{J}}
\renewcommand{\KFunc}{\mathrm{K}}
\renewcommand{\LFunc}{\mathrm{L}}
\renewcommand{\MFunc}{\mathrm{M}}
\renewcommand{\NFunc}{\mathrm{N}}
\renewcommand{\OFunc}{\mathrm{O}}
\renewcommand{\PFunc}{\mathrm{P}}
\renewcommand{\QFunc}{\mathrm{Q}}
\renewcommand{\RFunc}{\mathrm{R}}
\renewcommand{\SFunc}{\mathrm{S}}
\renewcommand{\TFunc}{\mathrm{T}}
\renewcommand{\UFunc}{\mathrm{U}}
\renewcommand{\VFunc}{\mathrm{V}}
\renewcommand{\WFunc}{\mathrm{W}}
\renewcommand{\XFunc}{\mathrm{X}}
\renewcommand{\YFunc}{\mathrm{Y}}
\renewcommand{\ZFunc}{\mathrm{Z}}
% Ratios to permanent income are normal face
\renewcommand{\aNrm}{a}
\renewcommand{\bNrm}{b}
\renewcommand{\cNrm}{c}
\renewcommand{\dNrm}{d}
\renewcommand{\eNrm}{e}
\renewcommand{\fNrm}{f}
\renewcommand{\hNrm}{h}
\renewcommand{\iNrm}{i}
\renewcommand{\jNrm}{j}
\renewcommand{\kNrm}{k}
\renewcommand{\mNrm}{m}
\renewcommand{\pNrm}{p}
\renewcommand{\rNrm}{s}
\renewcommand{\sNrm}{s}
\renewcommand{\vNrm}{v}
\renewcommand{\yNrm}{y}
\renewcommand{\zNrm}{z}

\renewcommand{\ANrm}{A}
\renewcommand{\BNrm}{B}
\renewcommand{\CNrm}{C}
\renewcommand{\DNrm}{D}
\renewcommand{\ENrm}{E}
\renewcommand{\FNrm}{F}
\renewcommand{\HNrm}{H}
\renewcommand{\INrm}{I}
\renewcommand{\JNrm}{J}
\renewcommand{\KNrm}{K}
\renewcommand{\MNrm}{M}
\renewcommand{\PNrm}{P}
\renewcommand{\SNrm}{S}
\renewcommand{\VNrm}{V}
\renewcommand{\YNrm}{Y}
\renewcommand{\ZNrm}{Z}

\renewcommand{\RNrm}{\mathcal{R}}
% Ind and Agg varaibles begin with lower case
\renewcommand{\tranShkInd}{\theta}   % 
\renewcommand{\tranShk}{\tranShkInd}   % 
\renewcommand{\tranShkAgg}{\Theta}   % 
\renewcommand{\permShkInd}{\psi}     % 
\renewcommand{\permShk}{\permShkInd} % 
\renewcommand{\PermShkAgg}{\Psi}     % 
\renewcommand{\tranShkAgg}{\Theta}   % 
\renewcommand{\std}{\sigma}
\renewcommand{\tranShkIndStd}{\std_{\tranShkInd}}     % 
\renewcommand{\tranShkIndVar}{\std^{2}_{\tranShkInd}} % 
\renewcommand{\tranShkAggStd}{\std_{\tranShkAgg}}     %
\renewcommand{\tranShkAggVar}{\std^{2}_{\tranShkAgg}} %

% Combo variables (combining Ind and Agg) 
\renewcommand{\PermShk}{\mathbf{\Psi}}
\renewcommand{\PermShkStd}{\std_{\PermShk}}
\renewcommand{\PermShkVar}{\std^{2}_{\PermShk}}
\renewcommand{\PermLvl}{\pLvl}
\renewcommand{\PermLvlAgg}{\PLvl}

% More specialized variables
\renewcommand{\TranShkAll}{\pmb{\xi}} 
\renewcommand{\TranShkMin}{\underline{\xi}}
\renewcommand{\TranShkMax}{\overline{\xi}}
\renewcommand{\TranShkStd}{\std_{\TranShk}}
\renewcommand{\TranShkVar}{\std^{2}_{\TranShk}}
\renewcommand{\TranShkEmp}{\pmb{\theta}}    
\renewcommand{\TranShkEmpMin}{}\renewcommand{\TranShkEmpMin}{\underline{\TranShkEmp}}    
\renewcommand{\TranShkEmpMax}{}\renewcommand{\TranShkEmpMax}{\overline{\TranShkEmp}}    
\renewcommand{\IncUnemp}{\mu}  % Income in unemployment

\renewcommand{\permLvlAgg}{\mathrm{P}}      % 
\renewcommand{\permLvlInd}{\mathrm{p}}      % 

\renewcommand{\MPCmin}{{\uline{\kappa}}}
\renewcommand{\MPCmax}{{\bar{\kappa}}}
\renewcommand{\MPCmaxmax}{{\bar{\bar{\kappa}}}}
\renewcommand{\MPCmaxmin}{{\hat{\underline{\kappa}}}}
\renewcommand{\MPCminmin}{{\underline{\kappa}}}
\renewcommand{\Opt}{\tilde}
\renewcommand{\permGroFacAgg}{\mathrm{G}}
\renewcommand{\permGroFacInd}{\mathsf{G}}
\renewcommand{\PermGroFac}{\mathcal{G}}
\renewcommand{\PermGroFacAdj}{\underline{\PermGroFac}}
\renewcommand{\PermGroFacuAdj}{\underline{\underline{\PermGroFac}}}
\renewcommand{\PermGroRte}{g}

\renewcommand{\Alive}{\mathcal{L}}\renewcommand{\Alive}{\mathcal{L}}
\renewcommand{\RfreeAgg}{}\renewcommand{\RfreeAgg}{\Agg{\Rfree}}

\renewcommand{\DeprFac}{\daleth}
\renewcommand{\deprRte}{\delta} % 
\renewcommand{\DiscFac}{\beta}
\renewcommand{\DiscFacAlt}{\beth}
\renewcommand{\DiscAltuAdj}{{\underline{\underline{\beth}}}}
\renewcommand{\DiscAlt}{}\renewcommand{\DiscAlt}{\beth}
\renewcommand{\DiscFacRaw}{\beta}
\renewcommand{\DiscFacLiv}{\underline{\DiscFacRaw}}
\renewcommand{\discRte}{\vartheta} % 

\renewcommand{\APFac}{\text{\pmb{\Thorn}}} % Former \Pat
\renewcommand{\APFacDefn}{\hyperlink{APFacDefn}{\textrm{APF}}}

\renewcommand{\GPFacRaw}{\APFac_{\PermGroFac}}
\renewcommand{\GPFacNrm}{\APFac_{\PermGroFacAdj}}
\renewcommand{\RPFac}{\APFac_{\Rfree}}

\renewcommand{\RPRte}{\text{\thorn}_{\rfree}}
\renewcommand{\GPRte}{\text{\thorn}_{\PermGroRte}}
\renewcommand{\APRte}{\text{\thorn}}


\renewcommand{\EPermShkInv}{\Ex[\PermShk^{-1}]}  % Formerly EpShkInv
\renewcommand{\InvEPermShkInv}{\underline{\PermShk}} % Formerly InvEpShkInv
\renewcommand{\uInvEuPermShk}{\underline{\underline{\PermShk}}} % Formerly {\uInvEpShkuInv}

\renewcommand{\RfreeEff}{\bar{\Rfree}} % Blanchard-adjusted interest rate

\renewcommand{\PopnGroFac}{\Xi}
\renewcommand{\PopnGroRte}{\xi}
\renewcommand{\PopnLvl}{\pmb{\mathrm{N}}}
  
\renewcommand{\LivPrb}{\Alive}
\renewcommand{\livPrb}{\ell}

\renewcommand{\cncl}{}
\renewcommand\cncl[1]{{\cancel{#1}}}

\renewcommand{\pNotZero}{(1-\pZero)}

\renewcommand{\CARA}{{\alpha}}
\renewcommand{\CRRA}{\rho}
\renewcommand{\diePrb}{{\mathsf{d}}} % Continuous time death rate 
\renewcommand{\DiePrb}{{\mathsf{D}}} % Discrete-time one-period death rate
\renewcommand{\Ex}{{\mathbb{E}}} % Expectations operator defined in econtex.cls
\renewcommand{\Mean}{{\mathbb{M}}} % Mean
\renewcommand{\MPC}{{\kappa}}
\renewcommand{\MPCFunc}{\pmb{\kappa}}
\renewcommand{\pZero}{\wp}

\renewcommand{\rfree}{\mathsf{r}}   % The net return rate on the safe asset
\renewcommand{\Rfree}{\mathsf{R}}   % The return factor on the safe asset 
\renewcommand{\RSave}{{\underline{\Rfree}}}
\renewcommand{\rsave}{{\underline{\rfree}}}
\renewcommand{\RBoro}{{\bar{\Rfree}}}
\renewcommand{\rboro}{{\bar{\rfree}}}

\renewcommand{\Risky}{{\mathbf{R}}}  % The return factor on the risky asset
\renewcommand{\risky}{{\mathbf{r}}}  % The arithmetic return rate E[\Risky] - 1
\renewcommand{\riskyELog}{\risky}     % The arithmetic return rate \Risky - 1
\renewcommand{\riskyELev}{\boldsymbol{r}} % The geometric  return rate \log \Risky
\renewcommand{\riskyshare}{{\varsigma}}
\renewcommand{\riskyvar}{\std^{2}_{\risky}}
\renewcommand{\Rport}{\mathfrak{R}}    % Portfolio -weighted return
\renewcommand{\rport}{\mathfrak{r}}

\renewcommand{\uPPP}{{{\mathrm{u}^{\prime\prime\prime}}}}
\renewcommand{\uPP}{{{\mathrm{u}^{\prime\prime}}}}
\renewcommand{\uP}{{{\mathrm{u}^{\prime}}}}
\renewcommand{\util}{u}

\renewcommand{\Kap}{{K}}
\renewcommand{\kap}{k}

\renewcommand{\leiShare}{\zeta} % 

\renewcommand{\MPSmin}{\pZero^{1/\CRRA} \RPFac}
\renewcommand{\MPSmax}{\RPFac}

\renewcommand{\PDV}{{\mathbb{P}}} % 
\renewcommand{\Wage}{{\mathsf{W}}}
\renewcommand{\wage}{{\mathsf{w}}}

\renewcommand{\TaxLev}{T}
\renewcommand{\Tax}{}
\renewcommand{\TaxFree}{{\cancel{\Tax}}}

\renewcommand{\Alt}{\grave}

\renewcommand{\urate}{{\mho}}
\renewcommand{\erate}{{\cancel{\mho}}}
\renewcommand{\unins}{\upsilon}

\renewcommand{\Labor}{}\renewcommand{\Labor}{\mathrm{L}}
\renewcommand{\labor}{}\renewcommand{\labor}{\ell}

\renewcommand{\EEndMap}{{\mathsf{E}}}
\renewcommand{\TMap}{\mathscr{T}}

\renewcommand{\CEndFunc}{{\mathfrak{C}}}
\renewcommand{\cEndFunc}{{\mathfrak{c}}}

\renewcommand{\uFuncInv}{\rotatebox{180}{$\uFunc$}}
\renewcommand{\muFuncInv}{\rotatebox{180}{$\uFunc$}}

\renewcommand{\Hi}{\overline}
\renewcommand{\Lo}{\underline}

\renewcommand{\Rnorm}{{\mathcal{R}}}    % Normalized version of riskless return factor
\renewcommand{\rnorm}{{\mathit{r}}}    % Normalized version of riskless rate of return

\renewcommand{\EpremLog}{\varphi} % Not using regular \eprem because want to distinguish between \varphi = log E_{t}[\Phi_{t+1}] and \phi_{t} = E[\log \Phi_{t}]
\renewcommand{\EPrem}{\pmb{\varphi}} % equity premium
\renewcommand{\eprem}{\phi} % log equity premium

\renewcommand{\weight}{\omega}

\renewcommand{\FDist}{{\mathcal{F}}}
\renewcommand{\fDist}{{\mathcal{f}}}

\renewcommand{\aMin}{{\underline{\aNrm}}}

\renewcommand{\FDist}{}\renewcommand{\FDist}{\mathcal{F}}
\renewcommand{\fDist}{}\renewcommand{\fDist}{\mathcal{f}}

\renewcommand{\Nrml}{}\renewcommand{\Nrml}{\mathcal{N}}