Merge branch 'main' into update-tex-macros

Author: mmcky

.github/workflows/ci.yml

@@ -21,10 +21,22 @@ jobs:
       - name: Display Pip Versions
         shell: bash -l {0}
         run: pip list
+      - name: Download "build" folder (cache)
+        uses: dawidd6/action-download-artifact@v2
+        with:
+          workflow: publish.yml
+          branch: main
+          name: build-cache
+          path: _build
       - name: Build HTML
         shell: bash -l {0}
         run: |
           jb build lectures --path-output ./
+      - name: Save Build as Artifact
+        uses: actions/upload-artifact@v1
+        with:
+          name: _build
+          path: _build
       - name: Preview Deploy to Netlify
         uses: nwtgck/[email protected]
         with:

.github/workflows/publish.yml

@@ -43,6 +43,11 @@ jobs:
           github_token: ${{ secrets.GITHUB_TOKEN }}
           publish_dir: _build/html/
           # cname: python.quantecon.org
+      - name: Upload "_build" folder (cache)
+        uses: actions/upload-artifact@v2
+        with:
+          name: build-cache
+          path: _build
       # - name: Prepare lecture-python.notebooks sync
       #   shell: bash -l {0}
       #   run: |

.gitignore

@@ -0,0 +1,2 @@
+_build/
+lectures/_build/

environment.yml

@@ -3,10 +3,10 @@ channels:
   - default
 dependencies:
   - python=3.8
-  - anaconda=2020.07
+  - anaconda=2020.11
   - pip
   - pip:
-    - git+https://github.com/executablebooks/jupyter-book
+    - jupyter-book
     - sphinxext-rediraffe
     - sphinx-multitoc-numbering
     - quantecon-book-theme

lectures/_config.yml

@@ -5,14 +5,41 @@ description: This website presents a set of lectures on quantitative economic mo
 
 execute:
   execute_notebooks: "cache"
-  timeout: 60
+  timeout: 600
+
+bibtex_bibfiles:
+   - _static/quant-econ.bib
+
+bibtex_bibfiles:
+   - _static/quant-econ.bib
 
 html:
   baseurl: https://python.quantecon.org/
 
 sphinx:
   extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_tojupyter]
   config:
+    nb_render_priority:
+      html:
+      - "application/vnd.jupyter.widget-view+json"
+      - "application/javascript"
+      - "text/html"
+      - "text/latex"
+      - "image/svg+xml"
+      - "image/png"
+      - "image/jpeg"
+      - "text/markdown"
+      - "text/plain"
+      jupyter:
+      - "application/vnd.jupyter.widget-view+json"
+      - "application/javascript"
+      - "text/html"
+      - "text/latex"
+      - "image/svg+xml"
+      - "image/png"
+      - "image/jpeg"
+      - "text/markdown"
+      - "text/plain"
     html_favicon: _static/lectures-favicon.ico
     html_theme: quantecon_book_theme
     html_static_path: ['_static']
@@ -31,6 +58,7 @@ sphinx:
         Macros:
           "argmax" : "arg\\,max"
           "argmin" : "arg\\,min"
+    mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
     rediraffe_redirects:
       index_toc.md: intro.md
     tojupyter_static_file_path: ["source/_static", "_static"]

lectures/cake_eating_numerical.md

@@ -72,7 +72,8 @@ where $u$ is the CRRA utility function.
 The analytical solutions for the value function and optimal policy were found
 to be as follows.
 
-```{literalinclude} _static/lecture_specific/cake_eating_numerical/analytical.py
+```{code-cell} python3
+:load: _static/lecture_specific/cake_eating_numerical/analytical.py
 ```
 
 Our first aim is to obtain these analytical solutions numerically.

lectures/cass_koopmans_2.md

@@ -195,7 +195,7 @@ all other dates $t=1, 2, \ldots, T$.
 There are  sequences of prices
 $\{w_t,\eta_t\}_{t=0}^T= \{\vec{w}, \vec{\eta} \}$
 where $w_t$ is a wage or rental rate for labor at time $t$ and
-$eta_t$ is a rental rate for capital at time $t$.
+$\eta_t$ is a rental rate for capital at time $t$.
 
 In addition there is are intertemporal prices that work as follows.
 
@@ -397,7 +397,7 @@ verify** approach.
 In this lecture {doc}`Cass-Koopmans Planning Model <cass_koopmans_1>`, we  computed an allocation $\{\vec{C}, \vec{K}, \vec{N}\}$
 that solves the planning problem.
 
-(This allocation will constitute the **Big** $K$  to be in the present instance of the *Big** $K$ **, little** $k$ trick
+(This allocation will constitute the **Big** $K$  to be in the present instance of the **Big** $K$ **, little** $k$ trick
 that we'll apply to  a competitive equilibrium in the spirit of [this lecture](https://lectures.quantecon.org/py/rational_expectations.html#)
 and  [this lecture](https://lectures.quantecon.org/py/dyn_stack.html#).)
 
@@ -835,9 +835,9 @@ for T in T_arr:
     for i, ax in enumerate(axs.flatten()):
         ax.plot(paths[i])
         ax.set(title=titles[i], ylabel=ylabels[i], xlabel='t')
-        if titles[i] is 'Capital':
+        if titles[i] == 'Capital':
             ax.axhline(k_ss, lw=1, ls='--', c='k')
-        if titles[i] is 'Consumption':
+        if titles[i] == 'Consumption':
             ax.axhline(c_ss, lw=1, ls='--', c='k')
 
 plt.tight_layout()
@@ -871,9 +871,9 @@ for γ in γ_arr:
     for i, ax in enumerate(axs.flatten()):
         ax.plot(paths[i], label=f'$\gamma = {γ}$')
         ax.set(title=titles[i], ylabel=ylabels[i], xlabel='t')
-        if titles[i] is 'Capital':
+        if titles[i] == 'Capital':
             ax.axhline(k_ss, lw=1, ls='--', c='k')
-        if titles[i] is 'Consumption':
+        if titles[i] == 'Consumption':
             ax.axhline(c_ss, lw=1, ls='--', c='k')
 
 axs[0, 0].legend()
@@ -893,7 +893,7 @@ Vice-versa for lower $\gamma$.
 
 We return to  Hicks-Arrow prices and  calculate how they are related to  **yields**  on loans of alternative maturities.
 
-This will let us plot a **yield curve** that graphs   yields  on bonds of  maturities $j=1, 2, \ldots$ against :math:j=1,2, ldots`.
+This will let us plot a **yield curve** that graphs   yields  on bonds of  maturities $j=1, 2, \ldots$ against $j=1,2, \ldots$.
 
 The formulas we want are:
 

lectures/coleman_policy_iter.md

@@ -267,7 +267,8 @@ As in our {doc}`previous study <optgrowth_fast>`, we continue to assume that
 
 This will allow us to compare our results to the analytical solutions
 
-```{literalinclude} _static/lecture_specific/optgrowth/cd_analytical.py
+```{code-cell} python3
+:load: _static/lecture_specific/optgrowth/cd_analytical.py
 ```
 
 As discussed above, our plan is to solve the model using time iteration, which
@@ -278,7 +279,8 @@ For this we need access to the functions $u'$ and $f, f'$.
 These are available in a class called `OptimalGrowthModel` that we
 constructed in an {doc}`earlier lecture <optgrowth_fast>`.
 
-```{literalinclude} _static/lecture_specific/optgrowth_fast/ogm.py
+```{code-cell} python3
+:load: _static/lecture_specific/optgrowth_fast/ogm.py
 ```
 
 Now we implement a method called `euler_diff`, which returns
@@ -374,7 +376,8 @@ Here is a function called `solve_model_time_iter` that takes an instance of
 `OptimalGrowthModel` and returns an approximation to the optimal policy,
 using time iteration.
 
-```{literalinclude} _static/lecture_specific/coleman_policy_iter/solve_time_iter.py
+```{code-cell} python3
+:load: _static/lecture_specific/coleman_policy_iter/solve_time_iter.py
 ```
 
 Let's call it:
@@ -439,7 +442,8 @@ Compute and plot the optimal policy.
 
 We use the class `OptimalGrowthModel_CRRA` from our {doc}`VFI lecture <optgrowth_fast>`.
 
-```{literalinclude} _static/lecture_specific/optgrowth_fast/ogm_crra.py
+```{code-cell} python3
+:load: _static/lecture_specific/optgrowth_fast/ogm_crra.py
 ```
 
 Let's create an instance:

lectures/complex_and_trig.md

@@ -310,7 +310,7 @@ eq1 = Eq(x1/x0 - r * cos(ω+θ) / cos(ω), 0)
 print(f'ω = {ω:1.3f}')
 
 # Solve for p
-eq2 = Eq(x0 - 2 * p * cos(ω))
+eq2 = Eq(x0 - 2 * p * cos(ω), 0)
 p = nsolve(eq2, p, 0)
 p = np.float(p)
 print(f'p = {p:1.3f}')

lectures/egm_policy_iter.md

@@ -160,12 +160,14 @@ where
 
 This will allow us to make comparisons with the analytical solutions
 
-```{literalinclude} _static/lecture_specific/optgrowth/cd_analytical.py
+```{code-cell} python3
+:load: _static/lecture_specific/optgrowth/cd_analytical.py
 ```
 
 We reuse the `OptimalGrowthModel` class
 
-```{literalinclude} _static/lecture_specific/optgrowth_fast/ogm.py
+```{code-cell} python3
+:load: _static/lecture_specific/optgrowth_fast/ogm.py
 ```
 
 ### The Operator
@@ -216,7 +218,8 @@ grid = og.grid
 
 Here's our solver routine:
 
-```{literalinclude} _static/lecture_specific/coleman_policy_iter/solve_time_iter.py
+```{code-cell} python3
+:load: _static/lecture_specific/coleman_policy_iter/solve_time_iter.py
 ```
 
 Let's call it:

lectures/exchangeable.md

@@ -53,7 +53,7 @@ that are
 Understanding the distinction between these concepts is essential for appreciating how Bayesian updating
 works in our example.
 
-You can read about exchangeability [here](https://en.wikipedia.org/wiki/Exchangeable_random_variables)
+You can read about exchangeability [here](https://en.wikipedia.org/wiki/Exchangeable_random_variables).
 
 Below, we'll often use
 
@@ -116,10 +116,10 @@ $$
 Using the laws of probability, we can always factor such a joint density into a product of conditional densities:
 
 $$
-\begin{align}
-  p(W_T, W_{T-1}, \ldots, W_1, W_0)    = & p(W_T | W_{t-1}, \ldots, W_0) p(W_{T-1} | W_{T-2}, \ldots, W_0) \cdots  \cr
-  & p(W_1 | W_0) p(W_0)
-\end{align}
+\begin{aligned}
+  p(W_T, W_{T-1}, \ldots, W_1, W_0)    = & p(W_T | W_{T-1}, \ldots, W_0) p(W_{T-1} | W_{T-2}, \ldots, W_0) \cdots  \cr
+  & \quad \quad \cdots p(W_1 | W_0) p(W_0)
+\end{aligned}
 $$
 
 In general,
@@ -140,16 +140,14 @@ and partial history $W_{t-1}, \ldots, W_0$ contains no information about the pro
 
 So in the IID case, there is **nothing to learn** about the densities of future random variables from past data.
 
-In the general case, there is something go learn from past data.
+In the general case, there is something to learn from past data.
 
-We turn next to an instance of this general case in which there is something to learn from past data.
+We turn next to an instance of this general case.
 
 Please keep your eye out for **what** there is to learn from past data.
 
 ## A Setting in Which Past Observations Are Informative
 
-We now turn to a setting in which there **is** something to learn.
-
 Let $\{W_t\}_{t=0}^\infty$ be a sequence of nonnegative
 scalar random variables with a joint probability distribution
 constructed as follows.
@@ -174,15 +172,15 @@ of them once and for all and then drew an IID sequence of draws from that distri
 
 But our decision maker does not know which of the two distributions nature selected.
 
-The decision maker summarizes his ignorance about this by picking a **subjective probability**
+The decision maker summarizes his ignorance with a **subjective probability**
 $\tilde \pi$ and reasons as if  nature had selected $F$ with probability
 $\tilde \pi \in (0,1)$ and
 $G$ with probability $1 - \tilde \pi$.
 
 Thus, we  assume that the decision maker
 
 - **knows** both $F$ and $G$
-- **doesnt't know** which of these two distributions that nature has drawn
+- **doesn't know** which of these two distributions that nature has drawn
 - summarizing his ignorance by acting  as if or **thinking** that nature chose distribution $F$ with probability $\tilde \pi \in (0,1)$ and distribution
   $G$ with probability $1 - \tilde \pi$
 - at date $t \geq 0$ has observed  the partial history $w_t, w_{t-1}, \ldots, w_0$ of draws from the appropriate joint
@@ -276,7 +274,7 @@ as a **prior probability** that nature selected probability distribution $F$.
 DeFinetti {cite}`definetti` established a related representation of an exchangeable process created by mixing
 sequences of IID Bernoulli random variables with parameters $\theta$ and mixing probability $\pi(\theta)$
 for a density $\pi(\theta)$ that a Bayesian statistician would interpret as a prior over the unknown
-Bernoulli paramter $\theta$.
+Bernoulli parameter $\theta$.
 
 ## Bayes' Law
 
@@ -287,7 +285,7 @@ But how can we learn?
 
 And about what?
 
-The answer to the *about what* question is about $\tilde pi$.
+The answer to the *about what* question is about $\tilde \pi$.
 
 The answer to the *how* question is to use  Bayes' Law.
 
@@ -302,7 +300,7 @@ $$
 \pi = \mathbb{P}\{q = f \}
 $$
 
-where we regard $\pi$ as the decision maker's **subjective probability**  (also called a **personal probability**.
+where we regard $\pi$ as the decision maker's **subjective probability**  (also called a **personal probability**).
 
 Suppose that at $t \geq 0$, the decision maker has  observed a history
 $w^t \equiv [w_t, w_{t-1}, \ldots, w_0]$.
@@ -484,18 +482,18 @@ learning_example()
 ```
 
 Please look at the three graphs above created for an instance in which $f$ is a uniform distribution on $[0,1]$
-(i.e., a Beta distribution with parameters $F_a=1, F_b=1$, while  $g$ is a Beta distribution with the default parameter values $G_a=3, G_b=1.2$.
+(i.e., a Beta distribution with parameters $F_a=1, F_b=1$), while  $g$ is a Beta distribution with the default parameter values $G_a=3, G_b=1.2$.
 
-The graph in the left  plots the likehood ratio $l(w)$ on the coordinate axis against $w$ on the coordinate axis.
+The graph on the left  plots the likelihood ratio $l(w)$ on the coordinate axis against $w$ on the ordinate axis.
 
 The middle graph plots both $f(w)$ and $g(w)$  against $w$, with the horizontal dotted lines showing values
 of $w$ at which the likelihood ratio equals $1$.
 
-The graph on the right side plots arrows to the right that show when Bayes' Law  makes $\pi$ increase and arrows
+The graph on the right plots arrows to the right that show when Bayes' Law  makes $\pi$ increase and arrows
 to the left that show when Bayes' Law make $\pi$ decrease.
 
 Notice how the length of the arrows, which show the magnitude of the force from Bayes' Law impelling $\pi$ to change,
-depend on both the prior probability $\pi$ on the ordinate axis and the evidence in the form of the current draw of
+depends on both the prior probability $\pi$ on the ordinate axis and the evidence in the form of the current draw of
 $w$ on the coordinate axis.
 
 The fractions in the colored areas of the middle graphs are probabilities under $F$ and $G$, respectively,
@@ -532,7 +530,7 @@ assumptions about nature's choice of distribution:
 - that nature permanently draws from $G$
 
 Outcomes depend on a peculiar property of likelihood ratio processes that are discussed in
-[this lecture](https://python-advanced.quantecon.org/additive_functionals.html)
+[this lecture](https://python-advanced.quantecon.org/additive_functionals.html).
 
 To do this, we create some Python code.