Daron Acemoglu, Simon Johnson, and James A. Robinson. The colonial origins of comparative development: an empirical investigation. American Economic Review, 91(5):1369–1401, December 2001. URL: https://www.aeaweb.org/articles?id=10.1257/aer.91.5.1369.
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[AC03]
Jérôme Adda and Russell Cooper. Dynamic Economics: Quantitative Methods and Applications. MIT Press, 2003.
Orazio Attanasio, Sarah Cattan, Emla Fitzsimons, Costas Meghir, and Marta Rubio-Codina. Estimating the production function for human capital: results from a randomized control trial in colombia. American Economic Review, 110(1):48–85, January 2020. URL: https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.20150183.
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[BMM19]
Martha J. Bailey, Olga Malkova, and Zoë M. McLaren. Does access to family planning increase children's opportunities? evidence from the war on poverty and the early years of title x. Journal of Human Resources, 54(4):825–856, Fall 2019. URL: https://jhr.uwpress.org/content/54/4/825.
William A. Brock and Leonard J. Mirman. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory, 4(3):479–513, June 1972.
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[DM04]
Russell Davidson and James G. MacKinnon. Econometric Theory and Methods. Oxford University Press, 2004.
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[DS93]
Darrell Duffie and Kenneth J. Singleton. Simulated moment estimation of markov models of asset prices. Econometrica, 61(4):929–952, July 1993.
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[EP17]
Richard W. Evans and Kerk L. Phillips. Advantages of an ellipse when modeling leisure utility. Computational Economics, 51(3):513–533, March 2017.
GitHub. Octoverse 2022: the state of open source software. Report, GitHub, Inc., November 17 2022. URL: https://octoverse.github.com/.
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[GvanRossum01]
David Goodger and Guido van Rossum. Pep 257–Docstring conventions. Python Enhancement Proposal 257, Python Steering Council, May 29 2001. URL: https://peps.python.org/pep-0257.
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[GM96]
Christian Gourieroux and Alain Monfort. Simulation-based Econometric Methods. Oxford University Press, 1996.
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[HJ20]
Jeffrey Humpherys and Tyler J. Jarvis. Foundations of Applied Mathematics: Algorithms, Approximation, Optimization. Volume 2. SIAM, Society for Industrial and Applied Mathematics, 2020.
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[JWHT17]
Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. An Introduction to Statistical Learning with Applications in R. Springer Texts in Statistics. Springer, 2017.
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[Jud98]
Kenneth L. Judd. Numerical Methods in Economics. MIT Press, 1998.
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[Kea10]
Michael P. Keane. Structural vs. atheoretic approaches to econometrics. Journal of Econometrics, 156(1):3–20, May 2010.
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[LSalanie93]
G. Laroque and B. Salanié. Simulation based estimation models with lagged latent variables. Journal of Applied Econometrics, 8(Supplement):119–133, December 1993.
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[LI91]
Bong-Soo Lee and Beth Fisher Ingram. Simulation estimation of time series models. Journal of Econometrics, 47(2-3):197–205, February 1991.
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[McF89]
Daniel McFadden. A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica, 57(5):995–1026, September 1989.
Whitney K. Newey and Kenneth D. West. A simple, positive, semi-definite, heteroskedasticy and autocorrelation consistent covariance matrix. Econometrica, 55(3):703–708, May 1987.
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[Rus87]
John Rust. Optimal replacement of gmc bus engines: an empirical model of harold zurcher. Econometrica, 55(5):999–1033, September 1987. URL: https://www.jstor.org/stable/1911259.
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[Rus10]
John Rust. Comments on: `structural vs. atheoretic approaches to econometrics'. Journal of Econometrics, 156(1):21–24, May 2010.
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+[SS23a]
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Thomas J. Sargent and John Stachurski. Simple linear regression. In QuantEcon Python Lectures: A First Course in Quantitative Economics With Python, chapter 36. 2023. URL: https://intro.quantecon.org/simple_linear_regression.html.
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+[SS23b]
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Thomas J. Sargent and John Stachurski. Https://python.quantecon.org/ols.html. In QuantEcon Python Lectures: Intermediate Quantitative Economics with Python, chapter 79. 2023. URL: https://python.quantecon.org/ols.html.
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[Smi20]
Anthony A. Jr. Smith. Indirect inference. In Matias Vernengo, Esteban Perez Caldentey, and Barkley J. Rosser Jr., editors, New Palgrave Dictionary of Economics. Palgrave MacMillan, 2020. URL: http://www.econ.yale.edu/smith/palgrave7.pdf.
BYU ACME. Animations and 3d plotting in matplotlib. In BYU ACME 2023-2024 Incoming Senior Materials, chapter 5. 2023. URL: https://acme.byu.edu/2023-2024-materials.
Guido van Rossum, Barry Warsaw, and Nick Coghlan. Pep 8–Style guide for python code. Python Enhancement Proposal 8, Python Steering Council, July 5 2001. URL: https://peps.python.org/pep-0008.
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[WikipediaContributors20a]
Wikipedia Contributors. "Git". Wikipedia, The Free Encyclopedia, 2020. [Online; accessed 19-August-2020]. URL: https://en.wikipedia.org/wiki/Git.
GitHub or GitHub.com is a cloudsource code management service platform designed to enable scalable, efficient, and secure version controlled collaboration by linking localGit version controlled software development by users. GitHub’s main business footprint is hosting a collection of millions of version controlled code repositories. In addition to being a platform for distributed version control system (DVCS), GitHub’s primary features include code review, project management, continuous integrationunit testing, GitHub actions, and associated web page (GitHub pages) and documentation hosting and deployment.
Integrated development environment or IDE is a software application that comsolidates many of the functions of software development under one program. IDE’s often include a code editor, object memory and identification, debugger, and build automation tools. (See IDE Wikipedia entry[Wikipedia Contributors, 2020].)
Integrated development environment or IDE is a software application that comsolidates many of the functions of software development under one program. IDE’s often include a code editor, object memory and identification, debugger, and build automation tools. (See IDE Wikipedia entry[Wikipedia Contributors, 2020].)
The focus of this chapter is to give the reader a basic introduction to the standard empirical methods in data science, policy analysis, and economics. I want each reader to come away from this chapter with the following basic skills:
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Difference between correlation and causation
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Standard data description
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Basic understanding of linear regression
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What do regression coefficients mean?
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What do standard errors mean?
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How can I estimate my own linear regression with standard errors?
Ideas behind bigger extensions of linear regression
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Instrumental variables (omitted variable bias)
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Logistic regression
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Multiple equation models
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Panel data
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Time series data
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Vector autoregression
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+
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In the next chapter Basic Machine Learning, I give a more detailed treatment of logistic regression as a bridge to learning the basics of machine learning.
Any paper that uses data needs to spend some ink summarizing and describing the data. This is usually done in tables. But it can also be done in cross tabulation, which is descriptive statistics by category. The most common types of descriptive statistics are the following:
The research question of the paper “The Colonial Origins of Comparative Development: An Empirical Investigation” [Acemoglu et al., 2001] is to determine whether or not differences in institutions can help to explain observed economic outcomes. How do we measure institutional differences and economic outcomes? In this paper:
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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 Serivces Group.
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These variables and other data used in the paper are available for download on Daron Acemoglu’s webpage.
The following cells downloads the data from [Acemoglu et al., 2001] from the file maketable1.dta and displays the first five observations from the data.
The pandas.DataFrame.head method returns the first \(n\) forws of a DataFrame with column headings and index numbers. The default is n=5.
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df1.head()
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shortnam
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euro1900
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excolony
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avexpr
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logpgp95
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cons1
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cons90
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democ00a
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cons00a
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extmort4
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logem4
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loghjypl
+
baseco
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+
+
+
+
0
+
AFG
+
0.000000
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1.0
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NaN
+
NaN
+
1.0
+
2.0
+
1.0
+
1.0
+
93.699997
+
4.540098
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NaN
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NaN
+
+
+
1
+
AGO
+
8.000000
+
1.0
+
5.363636
+
7.770645
+
3.0
+
3.0
+
0.0
+
1.0
+
280.000000
+
5.634789
+
-3.411248
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1.0
+
+
+
2
+
ARE
+
0.000000
+
1.0
+
7.181818
+
9.804219
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NaN
+
NaN
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NaN
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NaN
+
NaN
+
NaN
+
NaN
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NaN
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+
+
3
+
ARG
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60.000004
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1.0
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6.386364
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9.133459
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1.0
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6.0
+
3.0
+
3.0
+
68.900002
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4.232656
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-0.872274
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1.0
+
+
+
4
+
ARM
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0.000000
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0.0
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NaN
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7.682482
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NaN
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NaN
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NaN
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NaN
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NaN
+
NaN
+
NaN
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NaN
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+
+
+
+
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How many observations are in this dataset? What are the different countries in this dataset?
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print("The number of observations (rows) in the dataset is:",df1.size)
+print("")
+print("A list of all the",len(df1["shortnam"].unique()),
+ 'unique countries in the "shortnam" variable is:')
+print(df1["shortnam"].unique())
+
For this problem, you will use the 397 observations from the Auto.csv dataset in the /data/basic_empirics/ folder of the repository for this book.[2] This dataset includes 397 observations on miles per gallon (mpg), number of cylinders (cylinders), engine displacement (displacement), horsepower (horsepower), vehicle weight (weight), acceleration (acceleration), vehicle year (year), vehicle origin (origin), and vehicle name (name).
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Import the data using the pandas.read_csv() function. Look for characters that seem out of place that might indicate missing values. Replace them with missing values using the na_values=... option.
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Produce a scatterplot matrix which includes all of the quantitative variables mpg, cylinders, displacement, horsepower, weight, acceleration, year, origin. Call your DataFrame of quantitative variables df_quant. [Use the pandas scatterplot function in the code block below.]
Compute the correlation matrix for the quantitative variables (\(8\times 8\)) using the pandas.DataFrame.corr() method.
+
Estimate the following multiple linear regression model of \(mpg_i\) on all other quantitative variables, where \(u_i\) is an error term for each observation, using Python’s statsmodels.api.OLS() function.
Which of the coefficients is statistically significant at the 1% level?
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Which of the coefficients is NOT statistically significant at the 10% level?
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Give an interpretation in words of the estimated coefficient \(\hat{\beta}_6\) on \(year_i\) using the estimated value of \(\hat{\beta}_6\).
+
+
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Looking at your scatterplot matrix from part (2), what are the three variables that look most likely to have a nonlinear relationship with \(mpg_i\)?
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Estimate a new multiple regression model by OLS in which you include squared terms on the three variables you identified as having a nonlinear relationship to \(mpg_i\) as well as a squared term on \(acceleration_i\).
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Report your adjusted R-squared statistic. Is it better or worse than the adjusted R-squared from part (4)?
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What happened to the statistical significance of the \(displacement_i\) variable coefficient and the coefficient on its squared term?
+
What happened to the statistical significance of the cylinders variable?
+
+
+
Using the regression model from part (5) and the .predict() function, what would be the predicted miles per gallon \(mpg\) of a car with 6 cylinders, displacement of 200, horsepower of 100, a weight of 3,100, acceleration of 15.1, model year of 1999, and origin of 1?
For this problem, you will use the 397 observations from the Auto.csv dataset in the /data/BasicEmpirMethods/ folder of the repository for this book.[1] This dataset includes 397 observations on miles per gallon (mpg), number of cylinders (cylinders), engine displacement (displacement), horsepower (horsepower), vehicle weight (weight), acceleration (acceleration), vehicle year (year), vehicle origin (origin), and vehicle name (name).
-
-
Import the data using the pandas.read_csv() function. Look for characters that seem out of place that might indicate missing values. Replace them with missing values using the na_values=... option.
-
Produce a scatterplot matrix which includes all of the quantitative variables mpg, cylinders, displacement, horsepower, weight, acceleration, year, origin. Call your DataFrame of quantitative variables df_quant. [Use the pandas scatterplot function in the code block below.]
Compute the correlation matrix for the quantitative variables (\(8\times 8\)) using the pandas.DataFrame.corr() method.
-
Estimate the following multiple linear regression model of \(mpg_i\) on all other quantitative variables, where \(u_i\) is an error term for each observation, using Python’s statsmodels.api.OLS() function.
Which of the coefficients is statistically significant at the 1% level?
-
Which of the coefficients is NOT statistically significant at the 10% level?
-
Give an interpretation in words of the estimated coefficient \(\hat{\beta}_6\) on \(year_i\) using the estimated value of \(\hat{\beta}_6\).
-
-
-
Looking at your scatterplot matrix from part (2), what are the three variables that look most likely to have a nonlinear relationship with \(mpg_i\)?
-
-
Estimate a new multiple regression model by OLS in which you include squared terms on the three variables you identified as having a nonlinear relationship to \(mpg_i\) as well as a squared term on \(acceleration_i\).
-
Report your adjusted R-squared statistic. Is it better or worse than the adjusted R-squared from part (4)?
-
What happened to the statistical significance of the \(displacement_i\) variable coefficient and the coefficient on its squared term?
-
What happened to the statistical significance of the cylinders variable?
-
-
-
Using the regression model from part (5) and the .predict() function, what would be the predicted miles per gallon \(mpg\) of a car with 6 cylinders, displacement of 200, horsepower of 100, a weight of 3,100, acceleration of 15.1, model year of 1999, and origin of 1?
Good documentation is critical to the ability of yourself and others to understand and disseminate your work and to allow others to reproduce it. As Eagleson’s Law of Programming implies in Observation 2 above, one of the biggest benefits of good documentation might be to the core maintainers and original code writers of a project. Despite the aspiration that the Python programming language be easy and intuitive enough to be its own documentation, we have often found than any not-well-documented code written by ourselves that is only a few months old is more likely to require a full rewrite rather than incremental additions and improvements.
Python scripts allow for two types of comments: inline comments (which are usually a line or two at a time) and docstrings, which are longer blocks set aside to document the source code. We further explore other more extensive types of documentation including README files, Jupyter notebooks, cloud notebooks, Jupyter Books, and published documentation forms.
“PEP 257–Docstring Conventions” differentiates between inline comments, which use the # symbol, and one-line docstrings, which use the """...""" format [Goodger and van Rossum, 2001]. An block of code with inline comments might look like:
+
“PEP 257–Docstring Conventions” differentiates between inline comments, which use the # symbol, and one-line docstrings, which use the """...""" format [Goodger and van Rossum, 2001]. An block of code with inline comments might look like:
# importsimportnumpyasnp
@@ -497,7 +497,7 @@
Contents
A few notes on this documentation of the FOC_savings function. First, see that the docstring starts of with a clear description of what the function does. Second, you can see the :math tags that allow you to write LaTeX equations that will be rendered in the documentation. Docstrings written using reStructuredText markup can be compiled through various packages to render equations and other formatting options. Third, the Args and Returns sections are used to document the arguments and return values of the function.
-
“PEP 257–Docstring Conventions” give suggested format and usage for docstrings in Python [Goodger and van Rossum, 2001]. And there are two main styles for writing docstrings, the [Google style]*(https://sphinxcontrib-napoleon.readthedocs.io/en/latest/example_google.html) and the NumPy style. While there are other ways to write docstrings (even those that meet PEP 257 standards), these two styles are so commonly used and are compatible with the Sphinx documentation package that we recommend using one of these two styles. OG-Core used the Google style, so you might adopt that to be consistent.
+
“PEP 257–Docstring Conventions” give suggested format and usage for docstrings in Python [Goodger and van Rossum, 2001]. And there are two main styles for writing docstrings, the [Google style]*(https://sphinxcontrib-napoleon.readthedocs.io/en/latest/example_google.html) and the NumPy style. While there are other ways to write docstrings (even those that meet PEP 257 standards), these two styles are so commonly used and are compatible with the Sphinx documentation package that we recommend using one of these two styles. OG-Core used the Google style, so you might adopt that to be consistent.
This chapter was coauthored by Jason DeBacker and Richard W. Evans.
Python stops the computation process when it encounters an error. Sometimes you want to describe certain errors with descriptive error messages. And sometimes you want your code to move past errors while saving them and including descriptive error messages. Other times, you want to ensure that no errors occur and that your program stops and informs you in the case of an error.
Python’s error handling, assertion functionality, traceback capability, and type hinting are powerful methods to make sure your code does what you expect it to do, breaks when you expect it to break, and moves past issues when you don’t want the computation to stop.
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The iframe below contains a PDF of the BYU ACME open-access lab entitled, “Exceptions and File Input/Output”. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 8 below has you work through the problems in this BYU ACME lab. The Python file (exceptions_fileIO.py) and associated text files (.txt) associated with this lab are stored in the ./code/Exceptions_FileIO/ directory.
+
The iframe below contains a PDF of the BYU ACME open-access lab entitled, “Exceptions and File Input/Output”. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 8 below has you work through the problems in this BYU ACME lab. The Python file (exceptions_fileIO.py) and associated text files (.txt) associated with this lab are stored in the ./code/Exceptions_FileIO/ directory.
-
The iframe below contains a PDF of the BYU ACME open-access lab entitled, “Pandas 2: Plotting”. In spite of having “Pandas” in the title, we include this lab here in this Matplotlib chapter because all of the plotting uses the Matplotlib package. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 38 below has you work through the problems in this BYU ACME lab. A Jupyter notebook file template (matplotlib2.ipynb) used in the lab is stored in the ./code/Matplotlib2/ directory. The budget.csv and crime_data.csv data files are stored in the ./data/Pandas1 directory, which were used in the “Pandas 1: Introduction” lab. And the other data file used in this lab college.csv is stored in the ./data/Pandas3 directory, which was used in the “Pandas 3: Grouping” lab.
+
The iframe below contains a PDF of the BYU ACME open-access lab entitled, “Pandas 2: Plotting”. In spite of having “Pandas” in the title, we include this lab here in this Matplotlib chapter because all of the plotting uses the Matplotlib package. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 38 below has you work through the problems in this BYU ACME lab. A Jupyter notebook file template (matplotlib2.ipynb) used in the lab is stored in the ./code/Matplotlib2/ directory. The budget.csv and crime_data.csv data files are stored in the ./data/Pandas1 directory, which were used in the “Pandas 1: Introduction” lab. And the other data file used in this lab college.csv is stored in the ./data/Pandas3 directory, which was used in the “Pandas 3: Grouping” lab.
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The following iframe contains a PDF of the BYU ACME open-access lab entitled, “Advanced NumPy”, which contains content and exercises that build off of the previous BYU ACME NumPy lab. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 16 below has you work through the problems in this BYU ACME lab. A Python file template (advanced_numpy.py) used in the lab are stored in the ./code/AdvancedNumPy/ directory.
+
The following iframe contains a PDF of the BYU ACME open-access lab entitled, “Advanced NumPy”, which contains content and exercises that build off of the previous BYU ACME NumPy lab. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 16 below has you work through the problems in this BYU ACME lab. A Python file template (advanced_numpy.py) used in the lab are stored in the ./code/AdvancedNumPy/ directory.
-
The iframe below contains a PDF of the BYU ACME open-access lab entitled, “Pandas 3: Grouping”. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 24 below has you work through the problems in this BYU ACME lab. The data files used in this lab are stored in the ./data/Pandas3/ directory. A Jupyter notebook file template (pandas3.ipynb) used in the lab is stored in the ./code/Pandas3/ directory.
+
The iframe below contains a PDF of the BYU ACME open-access lab entitled, “Pandas 3: Grouping”. You can either scroll through the lab on this page using the iframe window, or you can download the PDF for use on your computer. See [BYU ACME, 2023]. Exercise 24 below has you work through the problems in this BYU ACME lab. The data files used in this lab are stored in the ./data/Pandas3/ directory. A Jupyter notebook file template (pandas3.ipynb) used in the lab is stored in the ./code/Pandas3/ directory.
+
+
+
+