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

@article{Orcutt_Winokur_69,

issn = {00129682, 14680262},

url = {http://www.jstor.org/stable/1909199},

abstract = {Monte Carlo techniques are used to study the first order autoregressive time series model with unknown level, slope, and error variance. The effect of lagged variables on inference, estimation, and prediction is described, using results from the classical normal linear regression model as a standard. In particular, use of the t and x^2 distributions as approximate sampling distributions is verified for inference concerning the level and residual error variance. Bias in the least squares estimate of the slope is measured, and two bias corrections are evaluated. Least squares chained prediction is studied, and attempts to measure the success of prediction and to improve on the least squares technique are discussed.},

author = {Guy H. Orcutt and Herbert S. Winokur},

journal = {Econometrica},

and David Cass {cite}`Cass` used to analyze optimal growth.

The model can be viewed as an extension of the model of Robert Solow

described in [an earlier lecture](https://lectures.quantecon.org/py/python_oop.html)

described in [an earlier lecture](https://python-programming.quantecon.org/python_oop.html)

but adapted to make the saving rate be a choice.

(Solow assumed a constant saving rate determined outside the model.)

The preceding approach to imposing stability on a system of potentially unstable linear difference equations is not limited to linear quadratic dynamic optimization problems.

For example, the same method is used in our [Stability in Linear Rational Expectations Models](https://python.quantecon.org/re_with_feedback.html#Another-perspective) lecture.

For example, the same method is used in our [Stability in Linear Rational Expectations Models](https://python.quantecon.org/re_with_feedback.html#another-perspective) lecture.

Let's try to solve the model described in that lecture by applying the `stable_solution` function defined in this lecture above.

To solve this problem, one can use either calculus or the theory of orthogonal

projections.

The solution is known to be $\hat x = (A'A)^{-1}A'y$ --- see for example chapter 3 of [these notes](https://lectures.quantecon.org/_downloads/course_notes.pdf).

The solution is known to be $\hat x = (A'A)^{-1}A'y$ --- see for example chapter 3 of [these notes](https://python.quantecon.org/_static/lecture_specific/linear_algebra/course_notes.pdf).

### More Columns than Rows

Treisman's main source of data is *Forbes'* annual rankings of billionaires and their estimated net worth.

The dataset `mle/fp.dta` can be downloaded from [here](https://lectures.quantecon.org/_downloads/mle/fp.dta)

The dataset `mle/fp.dta` can be downloaded from [here](https://python.quantecon.org/_static/lecture_specific/mle/fp.dta)

or its [AER page](https://www.aeaweb.org/articles?id=10.1257/aer.p20161068).

```{code-cell} python3

As an example, we will replicate results from Acemoglu, Johnson and Robinson's seminal paper {cite}`Acemoglu2001`.

* You can download a copy [here](https://economics.mit.edu/files/4123).

* You can download a copy [here](http://economics.mit.edu/files/4123).

In the paper, the authors emphasize the importance of institutions in economic development.

- economic outcomes are proxied by log GDP per capita in 1995, adjusted for exchange rates.

- institutional differences are proxied by an index of protection against expropriation on average over 1985-95, constructed by the [Political Risk Services Group](https://www.prsgroup.com/).

These variables and other data used in the paper are available for download on Daron Acemoglu's [webpage](https://economics.mit.edu/faculty/acemoglu/data/ajr2001).

These variables and other data used in the paper are available for download on Daron Acemoglu's [webpage](http://economics.mit.edu/faculty/acemoglu/data/ajr2001).

We will use pandas' `.read_stata()` function to read in data contained in the `.dta` files to dataframes

method.

Note that an observation was mistakenly dropped from the results in the

original paper (see the note located in maketable2.do from Acemoglu's webpage), and thus the

original paper (see the note located in `maketable2.do` from Acemoglu's webpage), and thus the

coefficients differ slightly.

```{code-cell} python3

(For an alternative approach, using Python's default row-major ordering, see [this

lecture by Alfred

Galichon](https://www.math-econ-code.org/mec-optim-b04).)

Galichon](https://www.math-econ-code.org/dynamic-programming).)

**Interpreting the warning:**

import numpy as np

```

We'll also use the LQ class from QuantEcon.py.

We'll also use the LQ class from `QuantEcon.py`.

```{code-cell} ipython

from quantecon import LQ

Dynamic mode decomposition was introduced by {cite}`schmid2010`,

You can read more about Dynamic Mode Decomposition here [[KBBWP16](https://python.quantecon.org/zreferences.html#id24)] and here [[BK19](https://python.quantecon.org/zreferences.html#id25)] (section 7.2).

You can read more about Dynamic Mode Decomposition here {cite}`DMD_book` and here [[BK19](https://python.quantecon.org/zreferences.html#id25)] (section 7.2).

We want to fit a **first-order vector autoregression**