Cosmetical changes

exam/midterm_exam_ss2022.tex

@@ -125,7 +125,7 @@ \subsection*{Exercises}
 Write a Dynare mod file for this model.
 
 \item
-Derive the steady state analytically and include these in a {\texttt{steady{\_}state{\_}model}} block.
+Derive the steady-state analytically and include these in a {\texttt{steady{\_}state{\_}model}} block.
 If you struggle to do that, use an \texttt{initval} block.
 
 \item

exercises/an_schorfheide_identif_bk.tex

@@ -62,7 +62,7 @@ \subsection*{Exercises}
 \item Provide intuition behind each equation of the model.
 How are nominal price rigidities modelled?\\\emph{Hint: Have a look at the relevant parts of the underlying paper.}
 
-\item Write a Dynare mod file for this model. Derive the steady state of all model variables analytically and include these in a \texttt{steady\_state\_model} block.
+\item Write a Dynare mod file for this model. Derive the steady-state of all model variables analytically and include these in a \texttt{steady\_state\_model} block.
 
 \item Explain how theoretical moments are computed based on the first-order policy function.
 

exercises/case_study_ascari_sbordone_2014.tex

@@ -44,7 +44,7 @@
 
 \item The labor disutility parameter, which is unspecified in the paper is set so that labor is 1/3 in the benchmark case.
 
-\item The technology parameter, which is also left unspecified in the published version, is set to 1 in steady state.
+\item The technology parameter, which is also left unspecified in the published version, is set to 1 in steady-state.
 
 \end{itemize}
 

exercises/log_linearization_solution.tex

@@ -16,12 +16,12 @@
   around which the perturbation solution is computed.
 
 \item No, variables in model C behave as the log of variables in model B.
-In addition, in model B, variables have distinct steady state values depending on the parameters of the model,
-  while in model C, the steady state of all variables is zero.
+In addition, in model B, variables have distinct steady-state values depending on the parameters of the model,
+  while in model C, the steady-state of all variables is zero.
 If, however, we would add hat variables to model B,
   then the hat variables would be equivalent between model variants.
 
-\item The exponential transform enables one to write variables in terms of log deviations from their steady state:
+\item The exponential transform enables one to write variables in terms of log deviations from their steady-state:
 \begin{align*}
 x_t = e^{log(x_t)} = e^{log(x_t) - log(x) + log(x)} = x e^{log(x_t)-log(x)} = x e^{\hat{x}_t}
 \end{align*}
@@ -35,7 +35,7 @@
     \begin{align*}
     1 = \beta E_t \left[ \left(\frac{c e^{\hat{c}_{t+1}}}{c e^{\hat{c}_t}}\right)^{-\tau} \frac{1}{\gamma z e^{\hat{z}_{t+1}}} \frac{R e^{\hat{R}_t}}{\pi e^{\hat{\pi}_{t+1}}} \right]
     \end{align*}
-    Note that equation \eqref{eq:AS_B1} in steady state is equal to $1 = \beta \frac{1}{\gamma z}\frac{R}{\pi}$.
+    Note that equation \eqref{eq:AS_B1} in steady-state is equal to $1 = \beta \frac{1}{\gamma z}\frac{R}{\pi}$.
     So we can simplify the previous equation to get equation \eqref{eq:AS_C1}:
     \begin{align*}
     1 &= \mathbb{E}_t \left[e^{-\tau \hat{c}_{t+1} + \tau \hat{c}_{t} + \hat{R}_{t} - \hat{z}_{t+1} - \hat{\pi}_{t+1} }\right]

exercises/nk_model_algebra.tex

@@ -354,7 +354,7 @@
 \begin{align}
 R_t = R \left(\frac{\Pi_t}{\Pi^*}\right)^{\psi_\pi} \left(\frac{y_t}{y}\right)^{\psi_y} e^{\nu_t} \label{eq:NewKeynesian.MonetaryPolicyRule}
 \end{align}
-where $R$ denotes the nominal interest rate in steady state,
+where $R$ denotes the nominal interest rate in steady-state,
   $\psi_\pi$ the sensitivity parameter to inflation deviations,
   $\psi_y$ the feedback parameter of the output gap
   and $\nu_t$ an exogenous deviation to the rule.

exercises/nk_model_algebra_solution.tex

@@ -154,7 +154,7 @@
 \paragraph{First-order condition with respect to $i_t$}
 Setting the derivative of $\pounds^{HH}$ with respect to $i_t$ to zero yields directly equation \eqref{eq:NewKeynesian.EulerInvestment}
 \begin{align*}
-1 = q_t \left( 1 - \frac{\phi_i}{2} \left(\frac{i_t}{i_{t-1}-1}\right)^2 - \phi_i \left(\frac{i_t}{i_{t-1}}-1\right)\left(\frac{i_t}{i_{t-1}}\right) \right)
+1 = q_t \left( 1 - \frac{\phi_i}{2} \left(\frac{i_t}{i_{t-1}}-1\right)^2 - \phi_i \left(\frac{i_t}{i_{t-1}}-1\right)\left(\frac{i_t}{i_{t-1}}\right) \right)
 + \beta E_t \frac{\lambda_{t+1}}{\lambda_t} q_{t+1} \phi_i \left(\frac{i_{t+1}}{i_{t}}-1\right)\left(\frac{i_{t+1}}{i_{t}}\right)^2
 \end{align*}
 \emph{Interpretation:}

exercises/nk_preprocess_steady.tex

@@ -33,7 +33,7 @@
       \end{longtable}
 
 \noindent
-Write a Dynare mod file for this model and compute the steady state of the model either analytically using a \texttt{steady\_state\_model} block
+Write a Dynare mod file for this model and compute the steady-state of the model either analytically using a \texttt{steady\_state\_model} block
   or numerically using an \texttt{initval} block.
 \noindent Additionally, for reporting purposes, add the following equations:
 \begin{align*}

exercises/nk_preprocess_steady_solution.tex

@@ -21,7 +21,7 @@
 \begin{align*}
 {\widetilde{p}} = \left(\frac{1-{{\theta}}\, {{\Pi}}^{{{\epsilon}}-1}}{1-{{\theta}}}\right)^{\frac{1}{1-{{\epsilon}}}}
 \end{align*}
-Now we are able to evaluate \eqref{eq:NewKeynesian.PriceDistortionLoM} in steady state, which becomes:
+Now we are able to evaluate \eqref{eq:NewKeynesian.PriceDistortionLoM} in steady-state, which becomes:
 \begin{align*}
 {p^*} = ({{\widetilde{p}}})^{-{{\epsilon}}} \,\frac{1-{{\theta}}}{1-{{\theta}}\, {{\Pi}}^{{{\epsilon}}}}
 \end{align*}

exercises/nk_simulations_solution.tex

@@ -28,12 +28,12 @@
 In other words, when inflation rises, the central bank rises the nominal interest rate more than one-to-one.
 This guarantees that the real interest rate eventually rises with inflation.
 The increase in the real interest rate creates a counter-effect to inflation,
-  since a higher real interest rate causes a fall in the output gap and in deviations of the marginal cost from the steady state.
+  since a higher real interest rate causes a fall in the output gap and in deviations of the marginal cost from the steady-state.
 This is the underlying economic principle behind the ability of monetary policy to anchor inflation expectations.
 \end{itemize}
 Note that in the mod file, we focus on the hat variables which are defined as \textbf{log deviations from steady-state}.
 This is useful for interpreting the Impulse Response Functions as Dynare plots these in \textbf{deviation from steady-state}.
-So for hat variables this corresponds (at \texttt{order=1}) to \textbf{percentage deviations} from the original level variables from steady state.
+So for hat variables this corresponds (at \texttt{order=1}) to \textbf{percentage deviations} from the original level variables from steady-state.
 
 \paragraph{Technology shock}
 The positive unit shock on total factor productivity has on impact a positive effect on output and consumption,

exercises/simulations_deterministic_vs_stochastic_solution.tex

@@ -1,6 +1,6 @@
 The key difference between stochastic and deterministic models stems from the role of uncertainty.
   In a deterministic world we have perfect knowledge about all future events including policy actions.
-Given some initial data we can derive optimal trajectories leading to a steady state which generates the highest outcome, e.g. total utility flows.
+Given some initial data we can derive optimal trajectories leading to a steady-state which generates the highest outcome, e.g. total utility flows.
 Contrary to that, in a stochastic setting there is always some randomness involved.
 That is, the agents do not know if or when a shock will hit the economy.
 They do, however, build (mathematical) expectations because the probability distribution of those shocks is known to the agents.

progs/dynare/an_schorfheide_identif_bk.mod

@@ -33,7 +33,7 @@ RA      ${r_{A}}$          (long_name='annualized steady-state real interest rat
 PA      ${\pi^{(A)}}$      (long_name='annualized target inflation rate')
 GAMQ    ${\gamma^{(Q)}}$   (long_name='quarterly steady-state growth rate of technology')
 NU      ${\nu}$            (long_name='inverse of elasticity of demand in Dixit Stiglitz aggregator')
-GBAR    ${\bar{g}}$        (long_name='steady state government spending process')
+GBAR    ${\bar{g}}$        (long_name='steady-state government spending process')
 ;
 
 

progs/dynare/an_schorfheide_loglinear.mod

@@ -37,7 +37,7 @@ RA      ${r_{A}}$          (long_name='annualized steady-state real interest rat
 PA      ${\pi^{(A)}}$      (long_name='annualized target inflation rate')
 GAMQ    ${\gamma^{(Q)}}$   (long_name='quarterly steady-state growth rate of technology')
 NU      ${\nu}$            (long_name='inverse of elasticity of demand in Dixit Stiglitz aggregator')
-GBAR    ${\bar{g}}$        (long_name='steady state government spending process')
+GBAR    ${\bar{g}}$        (long_name='steady-state government spending process')
 ;
 
 model;

progs/dynare/an_schorfheide_nonlinear.mod

@@ -45,7 +45,7 @@ RA      ${r_{A}}$          (long_name='annualized steady-state real interest rat
 PA      ${\pi^{(A)}}$      (long_name='annualized target inflation rate')
 GAMQ    ${\gamma^{(Q)}}$   (long_name='quarterly steady-state growth rate of technology')
 NU      ${\nu}$            (long_name='inverse of elasticity of demand in Dixit Stiglitz aggregator')
-GBAR    ${\bar{g}}$        (long_name='steady state government spending process')
+GBAR    ${\bar{g}}$        (long_name='steady-state government spending process')
 ;
 
 

progs/dynare/an_schorfheide_nonlinear_exp.mod

@@ -36,7 +36,7 @@ RA      ${r_{A}}$          (long_name='annualized steady-state real interest rat
 PA      ${\pi^{(A)}}$      (long_name='annualized target inflation rate')
 GAMQ    ${\gamma^{(Q)}}$   (long_name='quarterly steady-state growth rate of technology')
 NU      ${\nu}$            (long_name='inverse of elasticity of demand in Dixit Stiglitz aggregator')
-GBAR    ${\bar{g}}$        (long_name='steady state government spending process')
+GBAR    ${\bar{g}}$        (long_name='steady-state government spending process')
 ;
 
 model;

progs/dynare/nk.mod

@@ -188,7 +188,7 @@ RHONU = 0.5;
 
 @#if USE_INITVAL==1
 %-------------------------------------------------------------------------%
-% computations: steady state with initval block
+% computations: steady-state with initval block
 %-------------------------------------------------------------------------%
 % note that you can compute simple expressions in the initval block and also
 % re-use computed variables in subsequent initial values of other variables,

progs/matlab/Brock_Mirman_ss.m

@@ -4,13 +4,13 @@
 % computes the steady-state of the Brock and Mirman (1972) model analytically
 % =========================================================================
 % INPUTS
-%   - SS     : vector with initial steady state values in declaration order
+%   - SS     : vector with initial steady-state values in declaration order
 %              (usually empty, but might be useful for initial values
 %               or to update endogenous parameters)
 %	- params : vector with values for the parameters in declaration order
 % ----------------------------------------------------------------------
 % OUTPUTS
-%   - SS     : vector with computed steady state values in declaration order
+%   - SS     : vector with computed steady-state values in declaration order
 %	- params : vector with updated values for the parameters in declaration order
 %   - error_indicator: 0 if no error when computing the steady-state
 % =========================================================================

progs/matlab/perturbation_solver_LRE.m

@@ -51,7 +51,7 @@
 nspred   = M_.nspred;   % number of state variables: predetermined and mixed
 dr_order_var       = oo_.dr.order_var;      % declaration order to DR order
 lead_lag_incidence = M_.lead_lag_incidence; % lead_lag_incidence matrix with information about columns in dynamic Jacobian matrix
-steady_state       = oo_.steady_state;      % steady state of endogenous in declaration order
+steady_state       = oo_.steady_state;      % steady-state of endogenous in declaration order
 exo_steady_state   = oo_.exo_steady_state;  % steady-state of exogenous variables
 
 %%%%%%%%%%%%%%%%%%%%

progs/matlab/perturbation_solver_dynare_order1.m

@@ -64,7 +64,7 @@
 nsfwrd   = M_.nsfwrd;   % number of jumper variables: mixed and forward
 dr_order_var       = oo_.dr.order_var;      % declaration order to DR order
 lead_lag_incidence = M_.lead_lag_incidence; % lead_lag_incidence matrix with information about columns in dynamic Jacobian matrix
-steady_state       = oo_.steady_state;      % steady state of endogenous in declaration order
+steady_state       = oo_.steady_state;      % steady-state of endogenous in declaration order
 exo_steady_state   = oo_.exo_steady_state;  % steady-state of exogenous variables
 
 %%%%%%%%%%%%%%%%%%%%

progs/replications/Annicchiarico_DiDio_2015/ann_dio_2015_tbl1_tbl2_no_policy.mod

@@ -49,7 +49,7 @@ TARGET_ZSHARE = 0.20840121;
 l             = 0.2;
 
 %-------------------------------------------------------------------------%
-% computations: steady state and calibration of endogenous parameters
+% computations: steady-state and calibration of endogenous parameters
 %-------------------------------------------------------------------------%
 steady_state_model;
 pz = 0; % no policy regime
@@ -86,6 +86,15 @@ A = a;
 ZSTAR = DELTA_M*m - z; % implicit rest of the world emission share
 TARGET_INTENSITY = z/y;
 CARBON_TAX = pz;
+
+log_y = log(y);
+log_c = log(c);
+log_iv = log(iv);
+log_l = log(l);
+log_mc = log(mc);
+log_z = log(z);
+log_u = log(u);
+log_pz = log(pz);
 end;
 steady;
 save_params_and_steady_state('ann_dio_2015_calib_no_policy.inc');

progs/replications/Annicchiarico_DiDio_2015/ann_dio_2015_tbl2_environmental_policy.mod

@@ -17,7 +17,7 @@ change_type(var)        TARGET_GSHARE;
 @#include "ann_dio_2015_modeleqs.inc"
 
 %-------------------------------------------------------------------------%
-% calibration via new steady state
+% calibration via new steady-state
 %-------------------------------------------------------------------------%
 load_params_and_steady_state('ann_dio_2015_calib_no_policy.inc'); % start from no policy calibration
 

progs/replications/Ascari_Sbordone_2014/Ascari_Sbordone_2014.mod

@@ -6,14 +6,14 @@
  * It provides a replication of the main results of the original paper  
  * in Section 3 (the New Keynesian model with trend inflation). It replicates the Figures:
  * - Figure 7: The Cost of Price dispersion
- * - Figure 8: Trend Inflation and Steady State Variables
+ * - Figure 8: Trend Inflation and Steady-State Variables
  * - Figure 11: The Determinacy Region and Trend Inflation
  * - Figure 13: Impulse Response Functions to a 1 Percent Positive Technology Shock 
  * - Figure 14: Impulse Response Functions to a 1 Percent Positive Monetary Policy Shock 
  *
  * Moreover, it replicates the business cycle moments reported on p. 717. 
  *
- * This mod-file shows how to access steady state variables in order to plot steady state
+ * This mod-file shows how to access steady-state variables in order to plot steady-state
  * dependences on parameters.
  * It also shows how to manually do a stability mapping be iterating over a grid on the parameter space.
  * 
@@ -27,7 +27,7 @@
  * - Following the approach of the published replication files by the authors, the labor disutility parameter, which
  *      is unspecified in the paper is set so that labor is 1/3 in the benchmark case; this normalization is relevant
  *      for the definition of welfare
- * - The technology parameter, which is also left unspecified in the published version is set to in steady state, which 
+ * - The technology parameter, which is also left unspecified in the published version is set to in steady-state, which 
  *      is the natural normalization also used in the official replication files
  * - For the business cycle moments, the technology shock variance is actually 0.45^2 (not 0.45 as reported in the paper), i.e. 
  *      it is consistent with the number reported in Smets/Wouters (2007). Moreover, business cycle moments rely on a Taylor rule 
@@ -106,31 +106,31 @@ parameters trend_inflation
     theta   $\theta$    (long_name='Calvo parameter')
     sigma   $\sigma$    (long_name='Risk aversion')
     epsilon $\varepsilon$   (long_name='Elasticity of substitution')
-    Pi_bar  ${\bar \pi}$    (long_name='gross quarterly steady state inflation')
+    Pi_bar  ${\bar \pi}$    (long_name='gross quarterly steady-state inflation')
     rho_v   ${\rho_\nu}$    (long_name='autocorrelation of monetary shock')
     rho_a   ${\rho_a}$      (long_name='autocorrelation of technology shock')
     rho_zeta ${\rho_\zeta}$ (long_name='autocorrelation of preference shock')
     phi_pi  ${\phi_\pi}$    (long_name='Taylor rule feedback inflation')
     phi_y   ${\phi_y}$      (long_name='Taylor rule output')
-    Y_bar   ${\bar Y}$      (long_name='steady state output, set in steady state model block')
+    Y_bar   ${\bar Y}$      (long_name='steady-state output, set in steady-state model block')
     var_rho ${\varrho}$     (long_name='degree of indexing')
-    i_bar   ${\bar i}$      (long_name='steady state interest rate, set in steady state model block')
+    i_bar   ${\bar i}$      (long_name='steady-state interest rate, set in steady-state model block')
     d_n     ${d_n}$         (long_name='labor disutility parameter')
     rho_i   ${\rho_i}$      (long_name='interest rate smoothing parameter')
     ;
 
 
-%fix labor to 1/3 in zero trend inflation steady state with Frisch elasticity of 1#
+%fix labor to 1/3 in zero trend inflation steady-state with Frisch elasticity of 1#
 beta_ss = 0.99;
 alpha_ss = 0;
 theta_ss = 0.75;
 epsilon_ss = 10;
-sigma_ss = 1; %different utility than log case implies that model utility function and its steady state must be manually changed
+sigma_ss = 1; %different utility than log case implies that model utility function and its steady-state must be manually changed
 phi_par_ss=1;
 var_rho_ss = 0;
 trend_inflation_ss=0;
 
-%%compute labor disutility parameter under benchmark of 0 steady state
+%%compute labor disutility parameter under benchmark of 0 steady-state
 %%inflation
 Pi_bar = (1+0/100)^(1/4); %set Pi_bar to reflect quarterly inflation
 p_star_ss=((1-theta_ss*Pi_bar^((epsilon_ss-1)*(1-var_rho_ss)))/(1-theta_ss))^(1/(1-epsilon_ss));
@@ -483,10 +483,10 @@ verbatim;
     xlabel('Trend Inflation')
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%% Generate Figure 8: Trend Inflation and Steady State Variables
+%%%%%% Generate Figure 8: Trend Inflation and Steady-State Variables
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-    figure('Name','Trend Inflation and Steady State Variables')
+    figure('Name','Trend Inflation and Steady-State Variables')
     trend_inflation_vector=0:0.5:8;
     utility=NaN(length(trend_inflation_vector),1);
     output=NaN(length(trend_inflation_vector),1);
@@ -509,15 +509,15 @@ verbatim;
     subplot(1,3,1)
     plot(trend_inflation_vector,(output-output(1,1))*100)
     xlabel('Trend Inflation')
-    ylabel('Steady state output')
+    ylabel('Steady-state output')
     subplot(1,3,2)
     plot(trend_inflation_vector,(ave_markup-ave_markup(1,1))*100,'-',trend_inflation_vector,(marg_markup-marg_markup(1,1))*100,'--',trend_inflation_vector,(price_adjust_gap-price_adjust_gap(1,1))*100,'.')
     xlabel('Trend Inflation')
     ylabel('SS price adj. gap, marg. and ave. markup')
     subplot(1,3,3)
     plot(trend_inflation_vector,(utility-utility(1,1))./abs(utility(1,1))*100)
     xlabel('Trend Inflation')
-    ylabel('Steady state welfare')
+    ylabel('Steady-state welfare')
 
 end;
 

progs/replications/Ascari_Sbordone_2014/ascari_sbordone_2014_calib_common.inc

@@ -1,5 +1,5 @@
 % fix labor to 1/3 to compute labor disutility parameter under benchmark of
-% zero trend inflation steady state with Frisch elasticity of 1
+% zero trend inflation steady-state with Frisch elasticity of 1
 N_SS = 1/3;
 BETA_SS = 0.99;
 ALPHA_SS = 0;