econ-ark · dedwar65 · Oct 26, 2023 · Oct 26, 2023 · Nov 27, 2023 · Jan 5, 2024
diff --git a/.DS_Store b/.DS_Store
diff --git a/Notes/.#math.tex b/Notes/.#math.tex
@@ -0,0 +1 @@
+[email protected]
diff --git a/Notes/.DS_Store b/Notes/.DS_Store
diff --git a/Notes/BeqRefs.bib b/Notes/BeqRefs.bib
diff --git a/Notes/Equations/#DeNardi_2004# b/Notes/Equations/#DeNardi_2004#
@@ -0,0 +1 @@
+ \quad &
diff --git a/Notes/Equations/Abel_1985 b/Notes/Equations/Abel_1985
@@ -0,0 +1,8 @@
+\begin{equation}
+\begin{aligned}
+\max \quad & U(c_1) + (1-p) \delta U(c_2) \\
+\text{s.t.} \quad & W = B + Y - T - c_1 \\
+\end{aligned}
+\end{equation}
+
+where $B$ is determined by (i) $R, W$, (ii) the number of children, $G$, and most importantly (iii) the number of periods the household has survived \textit{before} the terminal period \footnote{in which case, they consume everything because they don't care about leaving bequests.} .
diff --git a/Notes/Equations/Barro_1974 b/Notes/Equations/Barro_1974
@@ -0,0 +1,9 @@
+The utility function of the member of the $i$th generation has the form
+
+\begin{equation}
+\begin{aligned}
+U_i =  U(c_{i}^{y}, c_{i}^{o}, U_{i+1}^{*} ) \\
+\end{aligned}
+\end{equation}
+
+where $U_{i+1}^{*}$ is the attainable utility of $i$'s immediate descendant.
diff --git a/Notes/Equations/Cagetti_2003 b/Notes/Equations/Cagetti_2003
@@ -0,0 +1,8 @@
+\begin{equation}
+\begin{aligned}
+\max_{W_{t+1}, C_t} \quad & \mathbb{E} \bigg( \sum_{t=0}^{\tilde{T}} \beta^t e^{Z_t \theta} \frac{C_{t}^{1-\gamma}}{1-\gamma} + \beta^{\tilde{T}+1} e^{Z_{\tilde{T}} \theta} S(W_{\tilde{T} +1}) \bigg) \\
+\text{s.t.} \quad & W_{t+1} = R W_t + Y_t - C_t + B_t\\
+\end{aligned}
+\end{equation}
+
+where the utility from bequests is specified as $$ S(W) = \alpha \frac{W^{1-\gamma}}{1-\gamma}.$$ 
diff --git a/Notes/Equations/Cagetti_2006 b/Notes/Equations/Cagetti_2006
@@ -0,0 +1,7 @@
+\begin{equation}
+\begin{aligned}
+W_{r}(a) = \max_{c,a'} \quad & \{ u(c) + \beta \pi_0 \mathbb{E} W_r(a') + \eta \beta (1 - \pi_0) \mathbb{E}V(a', y', \theta')  \} \\
+\end{aligned}
+\end{equation}
+
+where $\eta$ is the weight on the utility of the descendants. If $\eta = 1$, the household behaves as a dynasty.
diff --git a/Notes/Equations/Cagetti_2008 b/Notes/Equations/Cagetti_2008
@@ -0,0 +1,9 @@
+\begin{equation}
+\begin{aligned}
+U = \quad & \mathbb{E} \bigg\{ \sum_{t=1}^{N} \beta^t \bigg( \Pi_{j=1}^{t}s_t \bigg) u(c_t) \bigg \} \\
+V(x,t) = \max_{c,a'} \quad & \{ u(c) + \beta s_{t+1} \mathbb{E}[v(x', t+1) |x ] \} \\
+\text{s.t.} \quad & W = B + Y - T - c_1 \\
+\end{aligned}
+\end{equation}
+
+where $x=(a,z)$ and $T$ are accidental bequests left by all deceased in a period, which are \textit{assumed to be redistributed by the government to all people alive}.
diff --git a/Notes/Equations/Carroll_1998 b/Notes/Equations/Carroll_1998
@@ -0,0 +1,6 @@
+\begin{equation}
+\begin{aligned}
+\max_{c_t} \quad & u(c_T) + v(w_{T+1}) \\
+\text{s.t.} \quad & w_{T+1} = w_T - c_T \\
+\end{aligned}
+\end{equation}
diff --git a/Notes/Equations/DeNardi_2004 b/Notes/Equations/DeNardi_2004
@@ -0,0 +1,8 @@
+\begin{equation}
+\begin{aligned}
+\phi(b) = \phi_1\bigg(1 + \frac{b}{\phi_2} \bigg)^{1-\sigma} \\
+\end{aligned}
+\end{equation}
+
+where $\phi_1$ reflects the parent's concern about leaving bequests and $\phi_2$ measures the extent to which bequests are luxury goods.  
+
diff --git a/Notes/Equations/DeNardi_2016 b/Notes/Equations/DeNardi_2016
@@ -0,0 +1,7 @@
+\begin{equation}
+\begin{aligned}
+\phi(b) = \phi_1 \bigg[(b + \phi_2)^{1-\gamma} - 1 \bigg] \\
+\end{aligned}
+\end{equation}
+
+where $\phi_1$ measures the strength of bequest motivess and $\phi_2$ measures the extent to which bequests are luxury goods. When $\phi_2 > 0$, the marginal utility of small bequests is bounded.  
diff --git a/Notes/Equations/Dynan_2004 b/Notes/Equations/Dynan_2004
@@ -0,0 +1,7 @@
+\begin{equation}
+\begin{aligned}
+V(B_{is}) = \frac{\mu [(B_{is} + YL_{is}^{c})^{1-\gamma} -1]}{1-\gamma} \\
+\end{aligned}
+\end{equation}
+
+where $\mu$ is the trade-off parameter between own consumption and bequests $B_{is}$  and $YL^{c}_{is}$ is the value of the next generation's lifetime earnings.
diff --git a/Notes/Equations/Gourinchas_2002 b/Notes/Equations/Gourinchas_2002
@@ -0,0 +1,8 @@
+\begin{equation}
+\begin{aligned}
+V_{\tau}(X_{\tau}, P_{\tau}, Z_{\tau}) \quad & = \max_{c_{\tau}, \ldots, c_{T}} \bigg[ \sum_{t=\tau}^{T} \beta^{t-\tau} v(Z_t) \frac{C_{t}^{1-\rho}}{1-\rho} + \beta^{T+1-\tau} \kappa v(Z_{T+1}) (X_{T+1} + h P_{T+1})^{1-\rho} \bigg] \\
+\text{s.t.} \quad & X_{t+1} = R (X_t - C_t) + Y_{t+1} \\
+\end{aligned}
+\end{equation}
+
+where $X_{T+1}$ is cash on hand and $H_{T+1}$ is illiquid wealth in the first year of retirement.
diff --git a/Notes/Equations/Saez_2017 b/Notes/Equations/Saez_2017
@@ -0,0 +1,7 @@
+\begin{equation}
+\begin{aligned}
+U_i(c_i, k_i, z_i) = c_i + a_i(k_i) - h_i(z_i) + \delta_i(k_{i}^{init} - k_i)
+\end{aligned}
+\end{equation}
+
+where utility for may be specified as $$ a_i(k) = \eta_i \frac{k_i^{\gamma}}{\gamma}  $$. 
diff --git a/Notes/Equations/Straub_2019 b/Notes/Equations/Straub_2019
@@ -0,0 +1,5 @@
+\begin{equation}
+\begin{aligned}
+U(a) = \frac{(\frac{a}{o})^{1-\Sigma} - 1}{1 - \Sigma}
+\end{aligned}
+\end{equation}
diff --git a/Notes/auto/BeqRefs.el b/Notes/auto/BeqRefs.el
@@ -0,0 +1,25 @@
+(TeX-add-style-hook
+ "BeqRefs"
+ (lambda ()
+   (LaTeX-add-bibitems
+    "Laitner2002-hu"
+    "Gokhale2001-dj"
+    "Abel1985-ef"
+    "Barro1974-mp"
+    "Saez2018-we"
+    "Auclert2023-ot"
+    "De_Nardi2010-tt"
+    "Michaillat2021-po"
+    "Straub_undated-fx"
+    "Straub_undated-gy"
+    "Dynan2004-bu"
+    "Dynan2002-za"
+    "De_Nardi2004-xs"
+    "De_Nardi2016-yi"
+    "Carroll1998-tz"
+    "Cagetti2008-cc"
+    "Cagetti2006-pu"
+    "Cagetti2003-yp"
+    "Gourinchas2002-lq"))
+ '(or :bibtex :latex))
+
diff --git a/Notes/auto/bequests_lit_rev.el b/Notes/auto/bequests_lit_rev.el
@@ -0,0 +1,42 @@
+(TeX-add-style-hook
+ "bequests_lit_rev"
+ (lambda ()
+   (TeX-add-to-alist 'LaTeX-provided-package-options
+                     '(("inputenc" "utf8") ("biblatex" "backend=bibtex" "style=authoryear")))
+   (add-to-list 'LaTeX-verbatim-macros-with-braces-local "path")
+   (add-to-list 'LaTeX-verbatim-macros-with-braces-local "url")
+   (add-to-list 'LaTeX-verbatim-macros-with-braces-local "nolinkurl")
+   (add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperbaseurl")
+   (add-to-list 'LaTeX-verbatim-macros-with-braces-local "hyperimage")
+   (add-to-list 'LaTeX-verbatim-macros-with-braces-local "href")
+   (add-to-list 'LaTeX-verbatim-macros-with-delims-local "path")
+   (TeX-run-style-hooks
+    "latex2e"
+    "./Equations/Abel_1985"
+    "./Equations/Cagetti_2008"
+    "./Equations/Barro_1974"
+    "./Equations/Cagetti_2006"
+    "./Equations/Carroll_1998"
+    "./Equations/Cagetti_2003"
+    "./Equations/Gourinchas_2002"
+    "./Equations/DeNardi_2004"
+    "./Equations/Dynan_2004"
+    "./Equations/DeNardi_2016"
+    "./Equations/Saez_2017"
+    "./Equations/Straub_2019"
+    "article"
+    "art10"
+    "color"
+    "hyperref"
+    "amsmath"
+    "amsfonts"
+    "dirtytalk"
+    "inputenc"
+    "biblatex")
+   (TeX-add-symbols
+    '("doi" 1)
+    '("doilink" 1))
+   (LaTeX-add-bibliographies
+    "BeqRefs"))
+ :latex)
+
diff --git a/Notes/bequests_lit_rev-blx.bib b/Notes/bequests_lit_rev-blx.bib
@@ -0,0 +1,11 @@
+@Comment{$ biblatex control file $}
+@Comment{$ biblatex bcf format version 3.10 $}
+% Do not modify this file!
+%
+% This is an auxiliary file used by the 'biblatex' package.
+% This file may safely be deleted. It will be recreated as
+% required.
+
+@Control{biblatex-control,
+  options = {3.10:0:0:1:0:1:1:0:0:1:0:2:3:1:3:1:0:0:3:1:79:+:+:nyt},
+}
diff --git a/Notes/bequests_lit_rev.aux b/Notes/bequests_lit_rev.aux
@@ -0,0 +1,142 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\bibstyle{biblatex}
+\bibdata{bequests_lit_rev-blx,BeqRefs}
+\citation{biblatex-control}
+\abx@aux@refcontext{nyt/global//global/global}
+\citation{Laitner2002-hu}
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+\gdef \@abspage@last{5}