Refactor McCall lecture: Emphasize persistent and transitory wage shocks

lectures/_static/quant-econ.bib

@@ -2711,3 +2711,25 @@ @article{fischer2024improving
   journal={arXiv preprint arXiv:2410.16076},
   year={2024}
 }
+
+@article{MaCurdy1982,
+  title={The use of time series processes to model the error structure of earnings in a longitudinal data analysis},
+  author={MaCurdy, Thomas E.},
+  journal={Journal of Econometrics},
+  volume={18},
+  number={1},
+  pages={83--114},
+  year={1982},
+  publisher={Elsevier}
+}
+
+@article{Meghir2004,
+  title={Income variance dynamics and heterogeneity},
+  author={Meghir, Costas and Pistaferri, Luigi},
+  journal={Econometrica},
+  volume={72},
+  number={1},
+  pages={1--32},
+  year={2004},
+  publisher={Wiley Online Library}
+}

lectures/_toc.yml

@@ -67,7 +67,7 @@ parts:
   - file: mccall_model_with_separation
   - file: mccall_model_with_sep_markov
   - file: mccall_fitted_vfi
-  - file: mccall_correlated
+  - file: mccall_persist_trans
   - file: career
   - file: jv
   - file: odu

lectures/mccall_fitted_vfi.md

@@ -132,7 +132,7 @@ $$
 
 where $\psi$ is the standard normal density.
 
-Here we are thinking of $v_u$ as a function on all of $\RR_+$.
+Here we are thinking of $v_u$ as a function on all of $\mathbb{R}_+$.
 
 
 ### Fitting
@@ -473,33 +473,6 @@ This makes economic sense: when the value of being unemployed rises (through hig
 ```{exercise}
 :label: mfv_ex2
 
-Let us now consider how the agent responds to an increase in volatility.
-
-To try to understand this, compute the reservation wage when the wage offer distribution is uniform on $(m - s, m + s)$ and $s$ varies.
-
-The idea here is that we are holding the mean constant and spreading the support.
-
-(This is a form of *mean-preserving spread*.)
-
-Use `s_vals = jnp.linspace(1.0, 2.0, 15)` and `m = 2.0`.
-
-State how you expect the reservation wage to vary with $s$.
-
-Now compute it - is this as you expected?
-```
-
-```{solution-start} mfv_ex2
-:class: dropdown
-```
-
-Maybe add an exercise that explores a pure increase in volatility.
-
-```{solution-end}
-```
-
-```{exercise}
-:label: mfv_ex3
-
 Create a plot that shows how the reservation wage changes with the risk aversion parameter $\gamma$.
 
 Use `γ_vals = jnp.linspace(1.2, 2.5, 15)` and keep all other parameters at their default values.
@@ -508,7 +481,7 @@ How do you expect the reservation wage to vary with $\gamma$? Why?
 
 ```
 
-```{solution-start} mfv_ex3
+```{solution-start} mfv_ex2
 :class: dropdown
 ```
 

lectures/mccall_model_with_sep_markov.md

@@ -1,16 +1,14 @@
 ---
-jupyter:
-  jupytext:
-    default_lexer: ipython3
-    text_representation:
-      extension: .md
-      format_name: markdown
-      format_version: '1.3'
-      jupytext_version: 1.17.2
-  kernelspec:
-    display_name: Python 3 (ipykernel)
-    language: python
-    name: python3
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.17.2
+kernelspec:
+  display_name: Python 3 (ipykernel)
+  language: python
+  name: python3
 ---
 
 (mccall_with_sep_markov)=
@@ -22,7 +20,7 @@ jupyter:
 </div>
 ```
 
-
++++
 
 # Job Search III: Search with Separation and Markov Wages
 
@@ -104,6 +102,7 @@ $$
     \right]
 $$
 
++++
 
 ## Computational Approach
 
@@ -121,6 +120,7 @@ $$
 
 2. Substitute into the unemployed agent's Bellman equation to get:
 
++++
 
 $$
     v_u(w) = 
@@ -137,6 +137,7 @@ $$
 
 The optimal policy turns out to be a reservation wage strategy: accept all wages above some threshold.
 
++++
 
 ## Code
 
@@ -334,6 +335,7 @@ plt.show()
 
 Can you provide an intuitive economic story behind the outcome that you see in this figure?
 
++++
 
 ## Employment Simulation
 
@@ -492,7 +494,7 @@ This is because she uses the wage $w$ from her last job to draw a new wage offer
 via $P(w, \cdot)$, and positive correlation means that a high current $w$ is
 often leads a high new draw.
 
-
++++
 
 ## The Ergodic Property
 
@@ -545,6 +547,7 @@ As a result, we can study steady-state unemployment either by:
 
 Often the second approach is better for our purposes, since it's easier to parallelize.
 
++++
 
 ## Cross-Sectional Analysis