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Copy file name to clipboardExpand all lines: lectures/aiyagari.md
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@@ -70,7 +70,7 @@ The primary reference for this lecture is {cite}`Aiyagari1994`.
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A textbook treatment is available in chapter 18 of {cite}`Ljungqvist2012`.
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A continuous time version of the model by SeHyoun Ahn and Benjamin Moll can be found [here](http://nbviewer.jupyter.org/github/QuantEcon/QuantEcon.notebooks/blob/master/aiyagari_continuous_time.ipynb).
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A continuous time version of the model by SeHyoun Ahn and Benjamin Moll can be found [here](https://nbviewer.org/github/QuantEcon/QuantEcon.notebooks/blob/master/aiyagari_continuous_time.ipynb).
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## The Economy
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Let's look at how we might compute such an equilibrium in practice.
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To solve the household's dynamic programming problem we'll use the [DiscreteDP](https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/markov/ddp.py) class from [QuantEcon.py](http://quantecon.org/quantecon-py).
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To solve the household's dynamic programming problem we'll use the [DiscreteDP](https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/markov/ddp.py) class from [QuantEcon.py](https://quantecon.org/quantecon-py/).
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Our first task is the least exciting one: write code that maps parameters for a household problem into the `R` and `Q` matrices needed to generate an instance of `DiscreteDP`.
Copy file name to clipboardExpand all lines: lectures/coleman_policy_iter.md
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Differentiating with respect to $y$, and then evaluating at the optimum yields {eq}`cpi_env`.
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(Section 12.1 of [EDTC](http://johnstachurski.net/edtc.html) contains full proofs of these results, and closely related discussions can be found in many other texts.)
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(Section 12.1 of [EDTC](https://johnstachurski.net/edtc.html) contains full proofs of these results, and closely related discussions can be found in many other texts.)
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Differentiability of the value function and interiority of the optimal policy
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imply that optimal consumption satisfies the first order condition associated
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In this lecture, we review some of the theory of Markov chains.
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We will also introduce some of the high-quality routines for working with Markov chains available in [QuantEcon.py](http://quantecon.org/quantecon-py).
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We will also introduce some of the high-quality routines for working with Markov chains available in [QuantEcon.py](https://quantecon.org/quantecon-py/).
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Prerequisite knowledge is basic probability and linear algebra.
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(We are assuming here that the state space $S$ is finite; if not more assumptions are required)
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For proof of this result, you can apply [Brouwer's fixed point theorem](https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem), or see [EDTC](http://johnstachurski.net/edtc.html), theorem 4.3.5.
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For proof of this result, you can apply [Brouwer's fixed point theorem](https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem), or see [EDTC](https://johnstachurski.net/edtc.html), theorem 4.3.5.
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There can be many stationary distributions corresponding to a given stochastic matrix $P$.
Copy file name to clipboardExpand all lines: lectures/lake_model.md
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We take a period to be a month.
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We set $b$ and $d$ to match monthly [birth](http://www.cdc.gov/nchs/fastats/births.htm) and [death rates](http://www.cdc.gov/nchs/fastats/deaths.htm), respectively, in the U.S. population
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We set $b$ and $d$ to match monthly [birth](https://www.cdc.gov/nchs/fastats/births.htm) and [death rates](https://www.cdc.gov/nchs/fastats/deaths.htm), respectively, in the U.S. population
Copy file name to clipboardExpand all lines: lectures/linear_algebra.md
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$i,j$-th element the inner product of the $i$-th row of $A$ and the
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$j$-th column of $B$.
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There are many tutorials to help you visualize this operation, such as [this one](http://www.mathsisfun.com/algebra/matrix-multiplying.html), or the discussion on the [Wikipedia page](https://en.wikipedia.org/wiki/Matrix_multiplication).
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There are many tutorials to help you visualize this operation, such as [this one](https://www.mathsisfun.com/algebra/matrix-multiplying.html), or the discussion on the [Wikipedia page](https://en.wikipedia.org/wiki/Matrix_multiplication).
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If $A$ is $n \times k$ and $B$ is $j \times m$, then
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to multiply $A$ and $B$ we require $k = j$, and the
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### Further Reading
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The documentation of the `scipy.linalg` submodule can be found [here](http://docs.scipy.org/doc/scipy/reference/linalg.html).
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The documentation of the `scipy.linalg` submodule can be found [here](https://docs.scipy.org/doc/scipy/reference/linalg.html).
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Chapters 2 and 3 of the [Econometric Theory](http://www.johnstachurski.net/emet.html) contains
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Chapters 2 and 3 of the [Econometric Theory](https://johnstachurski.net/emet.html) contains
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a discussion of linear algebra along the same lines as above, with solved exercises.
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If you don't mind a slightly abstract approach, a nice intermediate-level text on linear algebra
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The benefit relative to linear regression is that it allows more flexibility in the probabilistic relationships between variables.
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Here we illustrate maximum likelihood by replicating Daniel Treisman's (2016) paper, [Russia's Billionaires](http://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20161068), which connects the number of billionaires in a country to its economic characteristics.
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Here we illustrate maximum likelihood by replicating Daniel Treisman's (2016) paper, [Russia's Billionaires](https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20161068), which connects the number of billionaires in a country to its economic characteristics.
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The paper concludes that Russia has a higher number of billionaires than
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economic factors such as market size and tax rate predict.
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As an example, we will replicate results from Acemoglu, Johnson and Robinson's seminal paper {cite}`Acemoglu2001`.
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* You can download a copy [here](http://economics.mit.edu/files/4123).
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* You can download a copy [here](https://web.archive.org/web/20220901051300/http://economics.mit.edu/files/4123).
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In the paper, the authors emphasize the importance of institutions in economic development.
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- economic outcomes are proxied by log GDP per capita in 1995, adjusted for exchange rates.
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- 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/).
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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).
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These variables and other data used in the paper are available for download on Daron Acemoglu's [webpage](https://web.archive.org/web/20220901063129/http://economics.mit.edu/faculty/acemoglu/data/ajr2001).
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We will use pandas' `.read_stata()` function to read in data contained in the `.dta` files to dataframes
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We have demonstrated basic OLS and 2SLS regression in `statsmodels` and `linearmodels`.
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If you are familiar with R, you may want to use the [formula interface](http://www.statsmodels.org/dev/example_formulas.html) to `statsmodels`, or consider using [r2py](https://rpy2.github.io/) to call R from within Python.
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If you are familiar with R, you may want to use the [formula interface](https://www.statsmodels.org/dev/example_formulas.html) to `statsmodels`, or consider using [r2py](https://rpy2.github.io/) to call R from within Python.
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```
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These lectures are built on `linux` instances through `github actions` so are
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executed using the following [hardware specifications](https://docs.github.com/en/actions/reference/specifications-for-github-hosted-runners#supported-runners-and-hardware-resources)
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executed using the following [hardware specifications](https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners#supported-runners-and-hardware-resources)
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