ENH: Add link checker to GitHub Actions Workflow (#120)

* ENH: Add link checker to GitHub Actions Workflow

* Reference and link fix

* fix all broken links

* update missing links

* update stationary density

* update infinite horizon

Co-authored-by: Humphrey Yang <u6474961@anu.edu.au>

Author: mmcky

.github/workflows/linkcheck.yml

@@ -0,0 +1,44 @@
+name: Link Checker [Anaconda, Linux]
+on:
+  pull_request:
+    types: [opened, reopened]
+  schedule:
+    # UTC 12:00 is early morning in Australia
+    - cron:  '0 12 * * *'
+jobs:
+  link-check-linux:
+    name: Link Checking (${{ matrix.python-version }}, ${{ matrix.os }})
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        os: ["ubuntu-latest"]
+        python-version: ["3.9"]
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v2
+      - name: Setup Anaconda
+        uses: conda-incubator/setup-miniconda@v2
+        with:
+          auto-update-conda: true
+          auto-activate-base: true
+          miniconda-version: 'latest'
+          python-version: 3.9
+          environment-file: environment.yml
+          activate-environment: quantecon
+      - name: Download "build" folder (cache)
+        uses: dawidd6/action-download-artifact@v2
+        with:
+          workflow: cache.yml
+          branch: main
+          name: build-cache
+          path: _build
+      - name: Link Checker
+        shell: bash -l {0}
+        run: jb build lectures --path-output=./ --builder=custom --custom-builder=linkcheck
+      - name: Upload Link Checker Reports
+        uses: actions/upload-artifact@v2
+        if: failure()
+        with:
+          name: linkcheck-reports
+          path: _build/linkcheck

lectures/BCG_complete_mkts.md

@@ -58,7 +58,7 @@ This simplification of BCG’s setup helps us by
 - introducing `Big K, little k` issues in a simple context that will
   recur in the BCG incomplete markets environment
 
-A Big K, little k analysis also played roles in [this quantecon lecture](https://python.quantecon.org/cass_koopmans.html) as well  as
+A Big K, little k analysis also played roles in [this quantecon lecture](https://python.quantecon.org/cass_koopmans_1.html) as well  as
 [here](https://python.quantecon.org/rational_expectations.html) and {doc}`here <dyn_stack>`.
 
 ### Setup

lectures/_static/quant-econ.bib

@@ -170,7 +170,6 @@ @Article{Ross_78
   pages={453-475},
   month={July},
   keywords={},
-  doi={10.1086/296008},
   abstract={No abstract is available for this item.},
   url={https://ideas.repec.org/a/ucp/jnlbus/v51y1978i3p453-75.html}
 }
@@ -297,7 +296,7 @@ @Article{townsend
   year =1983
 }
 
-@Article{sargent91,
+@Article{sargent91_equilibrium,
   author ={Thomas J. Sargent},
   title ={Equilibrium with Signal Extraction from Endogenous Variables},
   journal ={Journal of Economic Dynamics and Control},
@@ -306,7 +305,7 @@ @Article{sargent91
   year =1991
 }
 
-@Inproceedings{singleton,
+@Inproceedings{singleton87,
   author ={Kenneth J. Singleton},
   title ={Asset Prices in a Time-Series Model with Disparately Informed
   Competitive Traders},
@@ -2378,7 +2377,7 @@ @Article{Hansen_2012_Eca
   pages={911-967},
   month={May},
   keywords={},
-  doi={ECTA8070},
+  doi={10.3982/ECTA8070},
   abstract={No abstract is available for this item.},
   url={https://ideas.repec.org/a/ecm/emetrp/v80y2012i3p911-967.html}
 }

lectures/additive_functionals.md

@@ -230,7 +230,7 @@ with an initial condition for $y_0$.
 
 While {eq}`ftaf` is not a first order system like {eq}`old1_additive_functionals`, we know that it can be mapped  into a first order system.
 
-* For an example of such a mapping, see [this example](https://python-intro.quantecon.org/linear_models.html#Second-order-Difference-Equation).
+* For an example of such a mapping, see [this example](https://python.quantecon.org/linear_models.html#second-order-difference-equation).
 
 In fact, this whole model can be mapped into the additive functional system definition in {eq}`old1_additive_functionals` -- {eq}`old2_additive_functionals`  by appropriate selection of the matrices $A, B, D, F$.
 

lectures/discrete_dp.md

@@ -195,7 +195,7 @@ For each $\sigma \in \Sigma$, define
 * $r_{\sigma}$ by $r_{\sigma}(s) := r(s, \sigma(s))$)
 * $Q_{\sigma}$ by $Q_{\sigma}(s, s') := Q(s, \sigma(s), s')$
 
-Notice that $Q_\sigma$ is a [stochastic matrix](https://python-intro.quantecon.org/finite_markov.html#Stochastic-Matrices) on $S$.
+Notice that $Q_\sigma$ is a [stochastic matrix](https://python.quantecon.org/finite_markov.html#stochastic-matrices) on $S$.
 
 It gives transition probabilities of the *controlled chain* when we follow policy $\sigma$.
 
@@ -211,7 +211,7 @@ If we think of $r_\sigma$ as a column vector, then so is $Q_\sigma^t r_\sigma$,
 Comments
 
 * $\{s_t\} \sim Q_\sigma$ means that the state is generated by stochastic matrix $Q_\sigma$.
-* See [this discussion](https://python-intro.quantecon.org/finite_markov.html#Multiple-Step-Transition-Probabilities) on computing expectations of Markov chains for an explanation of the expression in {eq}`ddp_expec`.
+* See [this discussion](https://python.quantecon.org/finite_markov.html#multiple-step-transition-probabilities) on computing expectations of Markov chains for an explanation of the expression in {eq}`ddp_expec`.
 
 Notice that we're not really distinguishing between functions from $S$ to $\mathbb R$ and vectors in $\mathbb R^n$.
 
@@ -913,7 +913,7 @@ plt.show()
 #### Dynamics of the Capital Stock
 
 Finally, let us work on [Exercise
-2](https://python-intro.quantecon.org/optgrowth.html#Exercise-1), where we plot
+2](https://python.quantecon.org/optgrowth.html#exercises), where we plot
 the trajectories of the capital stock for three different discount
 factors, $0.9$, $0.94$, and $0.98$, with initial
 condition $k_0 = 0.1$.

lectures/knowing_forecasts_of_others.md

@@ -1573,8 +1573,8 @@ it enlists the Kalman filter and invariant subspace methods for
 solving systems of Euler
 equations <sup><a href=#footnote1 id=footnote1-link>[5]</a></sup> .
 
-As [[Sin87](https://python-advanced.quantecon.org/zreferences.html#id27)],
-[[Kas00](https://python-advanced.quantecon.org/zreferences.html#id24)], and [[Sar91](https://python-advanced.quantecon.org/zreferences.html#id26)] also
+As {cite}`singleton87`,
+[[Kas00](https://python-advanced.quantecon.org/zreferences.html#id24)], and {cite}`sargent91_equilibrium` also
 found, the equilibrium is fully revealing: observed prices tell
 participants in industry $ i $ all of the information held by
 participants in market $ -i $ ($ -i $ means not $ i $).
@@ -1595,7 +1595,7 @@ those forecasts are the same as their own, they know them.
 
 ### Further historical remarks
 
-Sargent [[Sar91](https://python-advanced.quantecon.org/zreferences.html#id26)] proposed a way to compute an equilibrium
+Sargent {cite}`sargent91_equilibrium` proposed a way to compute an equilibrium
 without making Townsend’s approximation.
 
 Extending the reasoning of [[Mut60](https://python-advanced.quantecon.org/zreferences.html#id110)], Sargent noticed that it is possible to

lectures/lucas_model.md

@@ -44,7 +44,7 @@ What is the correct price to pay for such a claim?
 
 The elegant asset pricing model of Lucas {cite}`Lucas1978` attempts to answer this question in an equilibrium setting with risk-averse agents.
 
-While we mentioned some consequences of Lucas' model [earlier](https://python-intro.quantecon.org/markov_asset.html#Risk-Neutral-Pricing), it is now time to work through the model more carefully and try to understand where the fundamental asset pricing equation comes from.
+While we mentioned some consequences of Lucas' model [earlier](https://python.quantecon.org/markov_asset.html#risk-neutral-pricing), it is now time to work through the model more carefully and try to understand where the fundamental asset pricing equation comes from.
 
 A side benefit of studying Lucas' model is that it provides a beautiful illustration of model building in general and equilibrium pricing in competitive models in particular.
 

lectures/permanent_income_dles.md

@@ -272,7 +272,7 @@ permanent income model.
 The state vector in the LQ problem is
 $\begin{bmatrix} z_t \\ b_t \end{bmatrix}$.
 
-Consequently, the relevant elements of econ1.Sc are the same as in
+Consequently, the relevant elements of `econ1.Sc` are the same as in
 $-F$ occur when we apply other approaches to the same model in the lecture
 [Optimal Savings II: LQ Techniques](https://python-intro.quantecon.org/perm_income_cons.html) and [this Jupyter
 notebook](http://nbviewer.jupyter.org/github/QuantEcon/QuantEcon.notebooks/blob/master/permanent_income.ipynb).

lectures/robustness.md

@@ -150,7 +150,7 @@ This will involve crafting a *skinnier* set at the cost of  a lower *level* (at
 
 ### Inspiring Video
 
-If you want to understand more about why one serious quantitative researcher is interested in this approach, we recommend [Lars Peter Hansen's Nobel lecture](http://www.nobelprize.org/mediaplayer/index.php?id=1994).
+If you want to understand more about why one serious quantitative researcher is interested in this approach, we recommend [Lars Peter Hansen's Nobel lecture](https://www.nobelprize.org/prizes/economic-sciences/2013/hansen/lecture/).
 
 ### Other References
 
@@ -165,7 +165,7 @@ For simplicity, we present ideas in the context of a class of problems with line
 
 To fit in with [our earlier lecture on LQ control](https://python-intro.quantecon.org/lqcontrol.html), we will treat loss minimization rather than value maximization.
 
-To begin, recall the [infinite horizon LQ problem](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon), where an agent chooses a sequence of controls $\{u_t\}$ to minimize
+To begin, recall the [infinite horizon LQ problem](https://python.quantecon.org/lqcontrol.html#infinite-horizon), where an agent chooses a sequence of controls $\{u_t\}$ to minimize 
 
 ```{math}
 :label: rob_sih
@@ -312,7 +312,7 @@ $$
 $$
 
 The operator $\mathcal B$ is the standard (i.e., non-robust) LQ Bellman operator, and $P = \mathcal B(P)$ is the standard matrix Riccati equation coming from the
-Bellman equation --- see [this discussion](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon).
+Bellman equation --- see [this discussion](https://python.quantecon.org/lqcontrol.html#infinite-horizon).
 
 Under some regularity conditions (see {cite}`HansenSargent2008`), the operator $\mathcal B \circ \mathcal D$
 has a unique positive definite fixed point, which we denote below by $\hat P$.
@@ -445,7 +445,7 @@ subject to {eq}`rob_lomf`.
 
 What's striking about this optimization problem is that it is once again an LQ discounted dynamic programming problem, with $\mathbf w = \{ w_t \}$ as the sequence of controls.
 
-The expression for the optimal policy can be found by applying the usual LQ formula ([see here](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon)).
+The expression for the optimal policy can be found by applying the usual LQ formula ([see here](https://python.quantecon.org/lqcontrol.html#infinite-horizon)).
 
 We denote it by $K(F, \theta)$, with the interpretation $w_{t+1} = K(F, \theta) x_t$.
 
@@ -610,7 +610,7 @@ subject to
 x_{t+1} = (A + C K) x_t + B u_t
 ```
 
-Once again, the expression for the optimal policy can be found [here](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon) --- we denote
+Once again, the expression for the optimal policy can be found [here](https://python.quantecon.org/lqcontrol.html#infinite-horizon) --- we denote
 it by $\tilde F$.
 
 (rb_eq)=
@@ -1147,7 +1147,7 @@ K(\hat F, \theta) = (\theta I - C'\hat P C)^{-1} C' \hat P  (A - B \hat F)
 \beta (A - B \hat F)' \tilde P (A - B \hat F)
 ```
 
-(revisit [this discussion](https://python-intro.quantecon.org/lqcontrol.html#Infinite-Horizon) if you don't know where {eq}`rb_a2be` comes from) and the optimal policy is
+(revisit [this discussion](https://python.quantecon.org/lqcontrol.html#infinite-horizon) if you don't know where {eq}`rb_a2be` comes from) and the optimal policy is
 
 $$
 w_{t+1} = - \beta (\beta \theta I + \beta C' \tilde P C)^{-1}

lectures/stationary_densities.md

@@ -283,7 +283,7 @@ $\sigma(x) = s f(x)$ is strictly positive for all $s$ as required)
 
 ### Distribution Dynamics
 
-In [this section](https://python-intro.quantecon.org/finite_markov.html#Marginal-Distributions) of our lecture on **finite** Markov chains, we
+In [this section](https://python.quantecon.org/finite_markov.html#marginal-distributions) of our lecture on **finite** Markov chains, we
 asked the following question: If
 
 1. $\{X_t\}$ is a Markov chain with stochastic matrix $P$
@@ -292,7 +292,7 @@ asked the following question: If
 then what is the distribution of $X_{t+1}$?
 
 Letting $\psi_{t+1}$ denote the distribution of $X_{t+1}$, the
-answer [we gave](https://python-intro.quantecon.org/finite_markov.html#Marginal-Distributions) was that
+answer [we gave](https://python.quantecon.org/finite_markov.html#marginal-distributions) was that
 
 $$
 \psi_{t+1}[j] = \sum_{i \in S} P[i,j] \psi_t[i]
@@ -333,7 +333,7 @@ This operator is usually called the *Markov operator* corresponding to $p$
 Unlike most operators, we write $P$ to the right of its argument,
 instead of to the left (i.e., $\psi P$ instead of $P \psi$).
 This is a common convention, with the intention being to maintain the
-parallel with the finite case --- see [here](https://python-intro.quantecon.org/finite_markov.html#Marginal-Distributions)
+parallel with the finite case --- see [here](https://python.quantecon.org/finite_markov.html#marginal-distributions)
 ```
 
 With this notation, we can write {eq}`statd_fdd` more succinctly as $\psi_{t+1}(y) = (\psi_t P)(y)$ for all $y$, or, dropping the $y$ and letting "$=$" indicate equality of functions,
@@ -516,7 +516,7 @@ Notice that the sequence of densities shown in the figure seems to be
 converging --- more on this in just a moment.
 
 Another quick comment is that each of these distributions could be interpreted
-as a cross-sectional distribution (recall [this discussion](https://python-intro.quantecon.org/finite_markov.html#Example-2:-Cross-Sectional-Distributions)).
+as a cross-sectional distribution (recall [this discussion](https://python.quantecon.org/finite_markov.html#example-2-cross-sectional-distributions)).
 
 ## Beyond Densities
 
@@ -606,7 +606,7 @@ The general case is relatively similar --- references are given below.
 
 ### Theoretical Results
 
-Analogous to [the finite case](https://python-intro.quantecon.org/finite_markov.html#Stationary-Distributions), given a stochastic kernel $p$ and corresponding Markov operator as
+Analogous to [the finite case](https://python.quantecon.org/finite_markov.html#stationary-distributions), given a stochastic kernel $p$ and corresponding Markov operator as
 defined in {eq}`def_dmo`, a density $\psi^*$ on $S$ is called
 *stationary* for $P$ if it is a fixed point of the operator $P$.