misc

Misc edits

Author: jstac

lectures/_config.yml

@@ -1,7 +1,7 @@
-title: Introductory Computational Economics and Finance
+title: An Introduction to Quantitative Economics and Finance
 author: Thomas J. Sargent & John Stachurski
 logo: _static/qe-logo.png
-description: This website presents an undergraduate set of lectures computational economics, designed and written by Thomas J. Sargent and John Stachurski.
+description: This website presents introductory lectures on computational economics, designed and written by Thomas J. Sargent and John Stachurski.
 
 parse:
   myst_enable_extensions:  # default extensions to enable in the myst parser. See https://myst-parser.readthedocs.io/en/latest/using/syntax-optional.html

lectures/_toc.yml

@@ -4,7 +4,8 @@ parts:
 - caption: Introduction
   numbered: true
   chapters:
-  - file: intro_economics
+  - file: about
+  - file: long_run_growth
   - file: inequality
 - caption: Tools & Techniques
   numbered: true

lectures/about.md

@@ -0,0 +1,69 @@
+# About these Lectures
+
+
+## About
+
+This lecture series introduces quantitative economics using elementary
+mathematics and statistics plus computer code written in
+[Python](https://www.python.org/).  
+
+The lectures emphasize simulation and visualization through code as a way to
+convey ideas, rather than focusing on mathematical details.
+
+Although the presentation is quite novel, the ideas are rather foundational.
+
+We emphasize the deep and fundamental importance of economic theory, as well
+as the value of analyzing data and understanding stylized facts.
+
+The lectures can be used for university courses, self-study, reading groups or
+workshops. 
+
+Researchers and policy professionals might also find some parts of the series
+valuable for their work.  
+
+We hope the lectures will be of interest to students of economics
+who want to learn both economics and computing, as well as students from
+fields such as computer science and engineering who are curious about
+economics.
+
+## Level
+
+The lecture series is aimed at undergraduate students. 
+
+The level of the lectures varies from truly introductory (suitable for first
+year undergraduates or even high school students) to more intermediate.
+
+The
+more intermediate lectures require comfort with linear algebra and some
+mathematical maturity (e.g., calmly reading theorems and trying to understand
+their meaning).  
+
+In general, easier lectures occur earlier in the lecture
+series and harder lectures occur later.
+
+We assume that readers have covered the easier parts of the QuantEcon lecture
+series [on Python
+programming](https://python-programming.quantecon.org/intro.html).  
+
+In
+particular, readers should be familiar with basic Python syntax including
+Python functions. Knowledge of classes and Matplotlib will be beneficial but
+not essential.  
+
+## Credits
+
+In building this lecture series, we had invaluable assistance from research
+assistants at QuantEcon, as well as our QuantEcon colleages.  Without their
+help this series would not have been possible.
+
+In particular, we sincerely thank and give credit to
+
+- [Aakash Gupta](https://github.com/AakashGfude)
+- [Shu Hu](https://github.com/shlff)
+- [Smit Lunagariya](https://github.com/Smit-create)
+- [Matthew McKay](https://github.com/mmcky)
+- [Maanasee Sharma](https://github.com/maanasee)
+- [Humphrey Yang](https://github.com/HumphreyYang)
+
+We also thank Noritaka Kudoh for encouraging us to start this project and providing thoughtful suggestions.
+

lectures/intro_economics.md renamed to lectures/long_run_growth.md

@@ -9,7 +9,7 @@ kernelspec:
   name: python3
 ---
 
-# Introduction to Economics
+# Long Run Growth
 
 ```{index} single: Introduction to Economics
 ```
@@ -18,10 +18,33 @@ kernelspec:
 :depth: 2
 ```
 
-## World Bank Data - GDP Per Capita (Current US$)
+## Overview
 
+This lecture is about how different economies grow over the long run.
 
-GDP per capita is gross domestic product divided by midyear population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in current U.S. dollars.
+As we will see, some countries have had very different growth experiences
+since the end of WWII.
+
+References:
+
+* https://www.imf.org/en/Publications/fandd/issues/Series/Back-to-Basics/gross-domestic-product-GDP
+* https://www.stlouisfed.org/open-vault/2019/march/what-is-gdp-why-important
+* https://wol.iza.org/articles/gross-domestic-product-are-other-measures-needed
+
+
+One drawback of focusing on GDP growth is that it makes no allowance for
+depletion and degradation of natural resources. 
+
+
+GDP per capita is gross domestic product divided by population. 
+
+GDP is the sum of gross value added by all resident producers in the economy
+plus any product taxes and minus any subsidies not included in the value of
+the products.
+
+We use World Bank data on GPD per capita in current U.S. dollars.
+
+We require the following imports.
 
 ```{code-cell} ipython3
 import pandas as pd
@@ -31,26 +54,13 @@ import matplotlib.pyplot as plt
 import numpy as np
 ```
 
-```{code-cell} ipython3
-wbi = pd.read_csv("datasets/GDP_per_capita_world_bank.csv")
-```
 
-## Histogram comparison between 1960, 1990, 2020
+The following code reads in the data into a pandas data frame.
 
 ```{code-cell} ipython3
-def get_log_hist(data, years):
-    filtered_data = data.filter(items=['Country Code', years[0], years[1], years[2]])
-    log_gdp = filtered_data.iloc[:,1:].transform(lambda x: np.log(x))
-    max_log_gdp = log_gdp.max(numeric_only=True).max()
-    min_log_gdp = log_gdp.min(numeric_only=True).min()
-    log_gdp.hist(bins=16, range=[min_log_gdp, max_log_gdp], log=True)
+wbi = pd.read_csv("datasets/GDP_per_capita_world_bank.csv")
 ```
 
-```{code-cell} ipython3
-## All countries
-wbiall = wbi.drop(['Country Name' , 'Indicator Name', 'Indicator Code'], axis=1)
-get_log_hist(wbiall, ['1960', '1990', '2020'])
-```
 
 ## Comparison of GDP between different Income Groups
 
@@ -112,7 +122,7 @@ wbi_filtered_umi_lmi = filter_country_list_data(wbi, country_list_umi_lmi)
 wbi_filtered_umi_lmi.plot()
 ```
 
-### Plot for lower middle income
+Here is a plot for lower middle income countries.
 
 ```{code-cell} ipython3
 # Vietnam, Pakistan (Lower middle income)
@@ -121,11 +131,30 @@ wbi_filtered_lmi = filter_country_list_data(wbi, country_list_lmi)
 wbi_filtered_lmi.plot()
 ```
 
-### Plot for lower middle income and low income
+Here is a plot for lower middle income and low income
 
 ```{code-cell} ipython3
 # Pakistan, Congo (Lower middle income, low income)
 country_list_lmi_li = ['PAK', 'COD']
 wbi_filtered_lmi = filter_country_list_data(wbi, country_list_lmi_li)
 wbi_filtered_lmi.plot()
 ```
+
+
+
+## Histogram comparison between 1960, 1990, 2020
+
+```{code-cell} ipython3
+def get_log_hist(data, years):
+    filtered_data = data.filter(items=['Country Code', years[0], years[1], years[2]])
+    log_gdp = filtered_data.iloc[:,1:].transform(lambda x: np.log(x))
+    max_log_gdp = log_gdp.max(numeric_only=True).max()
+    min_log_gdp = log_gdp.min(numeric_only=True).min()
+    log_gdp.hist(bins=16, range=[min_log_gdp, max_log_gdp], log=True)
+```
+
+```{code-cell} ipython3
+## All countries
+wbiall = wbi.drop(['Country Name' , 'Indicator Name', 'Indicator Code'], axis=1)
+get_log_hist(wbiall, ['1960', '1990', '2020'])
+```

lectures/markov_chains.md

@@ -255,6 +255,8 @@ Then we can address a range of questions, such as
 
 We'll cover such applications below.
 
+
+
 ### Defining Markov Chains
 
 So far we've given examples of Markov chains but now let's define them more
@@ -306,6 +308,9 @@ chain $\{X_t\}$ as follows:
 
 By construction, the resulting process satisfies {eq}`mpp`.
 
+
+
+
 ## Simulation
 
 ```{index} single: Markov Chains; Simulation
@@ -859,8 +864,10 @@ Importantly, the result is valid for any choice of $\psi_0$.
 
 Notice that the theorem is related to the law of large numbers.
 
+TODO -- link to our undergrad lln and clt lecture
+
 It tells us that, in some settings, the law of large numbers sometimes holds even when the
-sequence of random variables is [not IID](iid_violation).
+sequence of random variables is not IID.
 
 
 (mc_eg1-2)=
@@ -905,15 +912,15 @@ n_state = P.shape[1]
 fig, axes = plt.subplots(nrows=1, ncols=n_state)
 ψ_star = mc.stationary_distributions[0]
 plt.subplots_adjust(wspace=0.35)
-
 for i in range(n_state):
     axes[i].grid()
-    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black', 
-                    label = fr'$\psi^*({i})$')
+    axes[i].set_ylim(ψ_star[i]-0.2, ψ_star[i]+0.2)
+    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black',
+                    label = fr'$\psi^*(X={i})$')
     axes[i].set_xlabel('t')
-    axes[i].set_ylabel(f'fraction of time spent at {i}')
+    axes[i].set_ylabel(fr'average time spent at X={i}')
 
-    # Compute the fraction of time spent, starting from different x_0s
+    # Compute the fraction of time spent, for each X=x
     for x0, col in ((0, 'blue'), (1, 'green'), (2, 'red')):
         # Generate time series that starts at different x0
         X = mc.simulate(n, init=x0)
@@ -942,8 +949,6 @@ $$
 The diagram of the Markov chain shows that it is **irreducible**
 
 ```{code-cell} ipython3
-:tags: [hide-input]
-
 dot = Digraph(comment='Graph')
 dot.attr(rankdir='LR')
 dot.node("0")
@@ -971,16 +976,15 @@ mc = MarkovChain(P)
 n_state = P.shape[1]
 fig, axes = plt.subplots(nrows=1, ncols=n_state)
 ψ_star = mc.stationary_distributions[0]
-
 for i in range(n_state):
     axes[i].grid()
     axes[i].set_ylim(0.45, 0.55)
-    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black', 
-                    label = fr'$\psi^*({i})$')
+    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black',
+                    label = fr'$\psi^*(X={i})$')
     axes[i].set_xlabel('t')
-    axes[i].set_ylabel(f'fraction of time spent at {i}')
+    axes[i].set_ylabel(fr'average time spent at X={i}')
 
-    # Compute the fraction of time spent, for each x
+    # Compute the fraction of time spent, for each X=x
     for x0 in range(n_state):
         # Generate time series starting at different x_0
         X = mc.simulate(n, init=x0)
@@ -1074,7 +1078,6 @@ In the case of Hamilton's Markov chain, the distribution $\psi P^t$ converges to
 P = np.array([[0.971, 0.029, 0.000],
               [0.145, 0.778, 0.077],
               [0.000, 0.508, 0.492]])
-
 # Define the number of iterations
 n = 50
 n_state = P.shape[0]
@@ -1094,8 +1097,8 @@ for i in range(n):
 # Loop through many initial values
 for x0 in x0s:
     x = x0
-    X = np.zeros((n, n_state))
-    
+    X = np.zeros((n,n_state))
+
     # Obtain and plot distributions at each state
     for t in range(0, n):
         x =  x @ P
@@ -1104,10 +1107,10 @@ for x0 in x0s:
         axes[i].plot(range(0, n), X[:,i], alpha=0.3)
 
 for i in range(n_state):
-    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black', 
-                    label = fr'$\psi^*({i})$')
+    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black',
+                    label = fr'$\psi^*(X={i})$')
     axes[i].set_xlabel('t')
-    axes[i].set_ylabel(fr'$\psi({i})$')
+    axes[i].set_ylabel(fr'$\psi(X={i})$')
     axes[i].legend()
 
 plt.show()
@@ -1144,9 +1147,9 @@ for x0 in x0s:
         axes[i].plot(range(20, n), X[20:,i], alpha=0.3)
 
 for i in range(n_state):
-    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black', label = fr'$\psi^*({i})$')
+    axes[i].axhline(ψ_star[i], linestyle='dashed', lw=2, color = 'black', label = fr'$\psi^* (X={i})$')
     axes[i].set_xlabel('t')
-    axes[i].set_ylabel(fr'$\psi({i})$')
+    axes[i].set_ylabel(fr'$\psi(X={i})$')
     axes[i].legend()
 
 plt.show()
@@ -1292,7 +1295,7 @@ In this exercise,
 
 1. show this process is asymptotically stationary and calculate the stationary distribution using simulations.
 
-1. use simulations to demonstrate ergodicity of this process.
+1. use simulation to show ergodicity.
 
 ````
 
@@ -1320,7 +1323,7 @@ codes_B =  ( '1','2','3','4','5','6','7','8')
 np.linalg.matrix_power(P_B, 10)
 ```
 
-We find that rows of the transition matrix converge to the stationary distribution 
+We find rows transition matrix converge to the stationary distribution
 
 ```{code-cell} ipython3
 mc = qe.MarkovChain(P_B)
@@ -1341,17 +1344,17 @@ ax.axhline(0, linestyle='dashed', lw=2, color = 'black', alpha=0.4)
 
 
 for x0 in range(8):
-    # Calculate the fraction of time for each worker
+    # Calculate the average time for each worker
     X_bar = (X == x0).cumsum() / (1 + np.arange(N, dtype=float))
     ax.plot(X_bar - ψ_star[x0], label=f'$X = {x0+1} $')
     ax.set_xlabel('t')
-    ax.set_ylabel(r'fraction of time spent in a state $- \psi^* (x)$')
+    ax.set_ylabel(fr'average time spent in a state $- \psi^* (X=x)$')
 
 ax.legend()
 plt.show()
 ```
 
-Note that the fraction of time spent at each state quickly converges to the probability assigned to that state by the stationary distribution.
+We can see that the time spent at each state quickly converges to the stationary distribution.
 
 ```{solution-end}
 ```
@@ -1449,9 +1452,10 @@ However, another way to verify irreducibility is by checking whether $A$ satisfi
 
 Assume A is an $n \times n$ $A$ is irreducible if and only if $\sum_{k=0}^{n-1}A^k$ is a positive matrix.
 
-(see more: {cite}`zhao_power_2012` and [here](https://math.stackexchange.com/questions/3336616/how-to-prove-this-matrix-is-a-irreducible-matrix))
+(see more at \cite{zhao_power_2012} and [here](https://math.stackexchange.com/questions/3336616/how-to-prove-this-matrix-is-a-irreducible-matrix))
 
 Based on this claim, write a function to test irreducibility.
+
 ```
 
 ```{solution-start} mc_ex3