Introduction to Econometric Methods (Spring 2021)
econ2228.04 & econ2228.05
Christopher Maxwell Maloney Hall, 337
This is an introductory course in the use of econometric methods, with an emphasis on empirical applications. Our focus will be on learning to do econometrics, not just learning about econometrics.
While the course will cover the development of the formal tools of econometric analysis (simple and multiple regression analysis, estimation, inference, categorical variables, functional forms and so forth), we will also spend quite a bit of time on empirical methods (posing questions, building datasets, running regressions, supplementing datasets, running more regressions, etc … until we can confidently say something about the questions at hand). As such, an important part of the course will be a set of empirical exercises and an empirical research project in which students will be building their own datasets and applying the various econometric methods developed in the course.
Prerequisites: An introductory statistics course such as EC 151. No exceptions. Students should also have an understanding of basic Excel (which will be used at times to assemble datasets and verify calculations) and basic calculus.[1] I also assume that you've had some previous exposure to Stata, the computer language that we will be using to run regressions (you should have seen Stata in EC151). (See below for more about Stata.)
Welcome to OnlineU! Due to circumstances beyond our control, the course has been moved online for the semester. This is relatively new to me (this will be just my second full semester @ OnlineU), and so I'll be learning along the way. But I am excited by the emphasis in online education on learning by doing… which is, I think, the best way to learn econometrics!
I have historically used lots of handouts in the course (more below), but I've never used the more traditional OnlineU tools (slideshows, videos, Zoom calls, etc) and so it's been a challenge to redevelop/reformat/restructure content for OnlineU. I continue to post the handouts to Canvas, but you'll now also find slideshows (with and without narration) as well as videos. While I believe I've landed on a structure that should work well, this is definitely a work in progress. And so feel free to make suggestions/comments… and don’t be surprised if things change over the course of the semester.
The course structure: I have divided the course content into about a dozen self-paced Units, each of which concludes with some sort of assignment, which is typically a short online quiz or assignment designed to assess your progress. Schedules will be posted to Canvas, and I will post weekly videos to Canvas to keep students on-track with the material, assignments, deliverables, etc etc. We may also have ad hoc Zoom calls from time to time, in which I'll review the schedule, answer questions, summarize recent units/material, preview upcoming units/material, etc etc.
Course reference text: As mentioned above, the course is built around a set of handouts/slideshows/videos, which are posted to Canvas. To simplify things for you, I have also self-published the handouts through Amazon. I will post the Amazon link when everything is up and running. I sell the book at my cost, which will probably be less than $10 (it's 372 8.5 x 11 pages), and will only make it available for you all for about two weeks or so (I'll let you know when it's available.[2]) As well, I have printed hardcopies for everyone. Those copies are free to you and currently sitting in a box outside my office @ Maloney 337. Feel free to drop by a grab a copy; let me know if the cupboard is bare and I'll replenish the supply.
Some additional texts: There is no need to purchase any of these (most are available at O’Neill). I list them because it is sometimes useful to see different presentations of the material.
· Jeffrey M. Wooldridge, Introductory Econometrics: A Modern Approach, 7^{th} ed., Cengage Learning, 2019.
· Angrist, Joshua D. and Jörn-Steffen Pischke, Mastering 'Metrics: The Path from Cause to Effect, 2014.
· Stock, James H. and Mark W. Watson, Introduction to Econometrics, 4^{th} ed., Addison-Wesley, 2019.
· Studenmund, A.H., Using Econometrics: A Practical Guide, 7^{th} ed., Pearson, 2017.
· Bailey, Michael A., Real Econometrics: The Right Tools to Answer Important Questions, 2^{nd} ed., Oxford, 2019.
· Ashley, Richard, Fundamentals of Applied Econometrics, Wiley, 2012.
Grading (Exams: 66%; Research Project: 15%; Exercises/qFlips/Quizzes: 14%; Labs: 5%):
· Exams (66%): Three exams: Two mid-term exams and one optional final exam.
Anticipated dates (these may change):
- Mid Term Exam #1: Thurs, March 18^{th } – OLS Analytics and Assessment
- Mid Term Exam #2: Thurs, May 6^{th } (last week in the semester) – OLS Estimation and Inference + Topics
- Optional Final Exam: TBD
Exam weights and the optional final exam:
- If you decide to take the optional final exam, then each mid-term exam counts for 18% of your course grade, and the final exam counts for the remaining 30% (so the exam weights are: 18%-18%-30%).
- If you decide not to take the optional final exam, each mid-term exam counts for 33% of your course grade.
You must commit to taking the final exam at the time you receive the exam. To allow you to make a fully informed decision about whether or not to take the (optional) final exam, conditional course grades, which assume that you are not taking the final exam, will be posted to Canvas as quickly as possible after the end of classes.
There are no make-up exams in this course. If you miss either mid-term exam, then you must take the final exam (exam weights will be adjusted proportionately). All exam grades are curved.
· Research Project (15%): Replicate an econometric analysis that has been published in an academic journal. More details below.
· Exercises/qFlips/Quizzes (14%): There will be about four Exercises over the course of the semester. These are team projects, which you will typically have two weeks to complete. As well, there will be about ten quizzes or short assignments (I call them q(uick)Flips), which will typically follow each Unit. Course grades for Exercises/qFlips/Quizzes will be curved (after dropping the lowest score… it's OK to miss one; don’t miss two!). More details below.
· econ2227 Labs (5%): Course-wide labs, focused on using Stata in empirical/econometric analysis. Lab scores will be curved.
Canvas: In the past, I have not used Canvas for the course, except to post course-related scores and grades. Instead, all course-related material (other than scores and grades) was posted to the oh-so-spiffy (not!) course website: http://www.cmaxxsports.com/ec228 . (To access the website, just google ec228.) Last year, however, I started migrating content from my website to Canvas. That process is now almost complete, so while we will use the website a bit, almost all of the course content can/will now be found on the Canvas website. (You should not expect my ec228 website to be up-to-date or complete.)
Accommodations: If you are a student with a documented disability seeking reasonable accommodations in this course, please contact Kathy Duggan (x2-8093; dugganka@bc.edu) at the Connors Family Learning Center regarding learning disabilities and ADHD, or staff in the Disability Services Office regarding all other types of disabilities, including temporary disabilities. Advance notice and appropriate documentation are required for accommodations.
Academic Integrity: You will be held to Boston College’s standards of academic integrity. If you have any questions as to what that means, see BC's academic integrity policies webpage.[3]
Pass/Fail: It is perfectly fine, of course, to take the course Pass/Fail… but it is definitely not OK to do so and shirk on group projects/exercises. That is not fair to your teammates… and they will come to hate you! Accordingly: If you are taking the course Pass/Fail, please let me know at the start of the semester, and I will monitor goings-on and make adjustments if necessary.
The Research Project (15% of your course grade): This is an empirical project, which will kick off with team assignments at around the time of the first mid-term exam. In the past, there have been two phases to the project: I) Replication and II) Improvement.
However, at OnlineU, I've dropped Phase II, and so the Project is now focused solely on replicating an existing published piece of econometric analysis… of your choosing. [4]
Team assignments: The Research Project kicks off a week with team assignments after the Ides of March and around the time of the first mid-term exam. I will assign the teams, which will likely have three members each. If some of you would like to work together, let me know before MT #1 on March 18^{th} . I will try my best to honor all such requests.
· Kickoff/Team assignments: Project teams assigned by Mon. Mar. 22^{nd}
Topic selection: Topics should showcase interesting econometric analysis, and need not be restricted to topics in Economics. It’s important to get an early start, as empirical research is always slow going!. To help you in that regard, I’ll ask teams to email me a one paragraph description of their topic/paper of interest, within two weeks of team assignments. I will compile and circulate those blurbs and we'll discuss them at some point.
· Topic selection (due Weds. Apr 7^{th} , about two weeks after Team assignments)
Replication: Replicate both the summary statistics of interest presented in the paper (to show that you have indeed replicated the construction of the dataset) as well as at least one set of regression results of interest.
Your end-of-semester deliverable will be a PowerPoint presentations (or the equivalent), which should be concise and to the point; shorter is always better.
Your PowerPoint presentation should discuss your data sources in detail and how your dataset was constructed. (I will say more about the format of the deliverable when teams are assigned.) Credit will reflect in part the level of difficulty.[5] In some cases you may be able to obtain data from the original authors, which obviously greatly simplifies the replication phase. You can do that if you want, but since building datasets is hard work, you won’t get much credit for your efforts … certainly not as much as you would had you built the dataset yourself.
At the end of the semester teammates will assess their own and each other's performance using the posted Peer Evaluation form. Students’ grades will reflect both their individual performance as well as the quality of the final PowerPoint presentation.
· Replication (due Fri., Apr 30^{th}, about three class-weeks after Topic selection)
Leave plenty of time for Replication. You’ll find this far more challenging and time consuming than you could ever imagine.
Shirkers take notice. I repeat: Peer evaluation forms will be distributed at the end of the semester, so that team members can assess each other’s performance… as well as their own.
Empirical work is slow going. Be sure to leave yourself enough time to complete the assignment to your satisfaction.
Exercises/qFlips/Quizzes (14% of your course grade; grades on Exercises/qFlips/Quizzes are curved):
Exercises: There will be four or so empirical exercises, which together with qFlips and Quizzes (see following) count towards 14% of your course grade. Exercises will be team assignments, usually with two students per team, and are graded on a 10 point scale. I will assign teams, which will differ from Exercise to Exercise. Answers are submitted online (one set per team).
In some cases, the Exercises are designed to give you practice with the techniques and tools we have developed in the course… other times, they are designed to introduce you to new material, which we have not yet covered in the course. These will take some time to complete, so please do not leave them until the last moment. A good rule of thumb is that Exercises will take about a week to complete… so budget your time accordingly (no sympathy for teams getting a late start).
qFlips: We will have about a half dozen custom tailored qFlips this semester. They will typically be self-paced online assignments, and are designed to give you some rudimentary practice with concepts and applications that we are covering in the course. Most, but not all, of these will be team assignments; I will assign teams, which will typically have two members.
Quizzes: There will also be four or so Canvas quizzes over the course of the semester. These will be multiple choice exams and typically feature about eight questions. Quizzes are to be completed individually (though they are open book; open notes; open lifelines; open etc etc etc).
Each qFlip and Quiz is graded on a two point scale (1/5^{th} the value of an Exercise). I anticipate close to perfect scores on these as they are primarily designed to reinforce the learning of the Unit material. (Grading: I will drop your lowest qFlip/Quiz score, just in case you inadvertently miss a deadline; but do not miss two deadlines!)
The Labs (5% of your course grade): There will be nine or so one-hour sections of Econ2227 econometrics labs, taught by excellent BC Econ graduate student instructors. The lab sections will focus on the use of Stata in empirical analysis generally, and econometric analysis specifically. While I am always happy to tackle Lab questions, you should know that the 2227 labs are completely independent of the 2228 courses. Lab scores will be curved.
Course Topics (I have posted course notes/handouts for each Unit… and slideshows and videos too! As well, you may want to consult the Wooldridge text.)
Introduction
Unit 1 – Introduction & Getting Started: Estimating the relationship between x and y; causality v. correlation; data types; economic v. statistical significance; robust analysis (how many regressions did you run?); art v. science; sample statistics (sample means, variances, standard deviations, covariances, and correlations); standardizing data; OLS as minimization of SSRs (FOCs and SOCs)
Simple Linear Regression (OLS/SLR) Models
Unit 2 – OLS/SLR analytics (single explanatory variable): In the beginning (SLR.1: the data generation process); residuals and sum squared residuals (SSR); OLS, FOCs and SOCs, Sample Regression Function (SRF), predictions and residuals; economic significance/meaningfulness (elasticity and beta regressions)
Unit 3 – OLS/SLR assessment: Sum Squared Explained (SSE) and Sum Squared Total (SST); SST = SSE + SSR (w/ constant term in the model); Goodness of Fit (GOF) metrics - Coefficient of Determination (R^{2}), Mean Squared Error (MSE) and Root MSE (RMSE); comparing SLR models using GOF metrics
Multiple Linear Regression (MLR) Models
Unit 4 – OLS/MLR analytics I (adding, and subtracting, explanatory variables): Comparing SLR and MLR analytics; interpreting coefficients I – ceteris paribus (partial effects and the SRF); interpreting coefficients II – partial correlations (WhatsLeft and WhatsNew); an overview of omitted variable bias (endogeneity)
Unit 5 – OLSMLR assessment: Comparing SLR and MLR assessment (GOF metrics); shortcomings of R^{2}; adjusted R^{2}; comparing MLR models using GOF metrics
Unit 6 – OLS/MLR analytics II: The collinearity regression; multicollinearity, R^{2}_{j}'s and Variance Inflation Factors (VIFs); Omitted variable bias/impact (endogeneity); simple v. partial correlations
Mid-Term Exam #1 (about here)
Way-Too-Fast Review of Statistics
Unit 7 – Review of Estimation and Inference: Our focus will be on estimation of the population mean; LUEs (Linear Unbiased Estimators); BLUEs (Best Linear Unbiased Estimators); point and interval estimators; standard errors, t statistics, p-values; confidence levels; critical values; confidence intervals; hypothesis testing; significance levels
Estimation and Inference in Regression Analysis
Unit 8 – SLR Estimation: Gauss-Markov assumptions (SLR.1 – SLR.5); Population Regression Function (PRF); conditional means; means, variances, standard deviations and standard errors of OLS estimators (intercepts and slopes); unbiasedness (OLS coefficients; MSE); LUEs; homoskedasticity; BLUE: The Gauss-Markov Theorem
Unit 8a – Heteroskedasticity: Issues (OLS standard errors no longer correct; LUE but not BLUE); White-corrected standard errors (robust inference); working towards BLUE (weighted least squares… but where do those weights come from?)
Unit 9 – SLR Inference: Add SLR.6 to the mix; normally distributed errors; variances, standard deviations and standard errors; t statistics; t-tests (Null hypotheses); p values; confidence intervals; hypothesis tests; economic v. statistical significance (elasticities v. p-values); Convergence I (t stats and R^{2})
Unit 10 – MLR Estimation and Inference: Compare to SLR; What's new? … Not much!; now MLR.1-MLR.5; n-k-1; multicollinearity, standard errors and Variance Inflation Factors (VIFs); MLR.6; heteroskedasticity and robust standard errors
Topics
Unit 11 – Dummy Variables and Fixed Effects: Dummies revisited; on the RHS and on the LHS; uses on the RHS (slope and intercept dummies); quieting the endogeneity critics (fixed effects); Examples (sovereign debt ratings, gender bias in wages, and death penalty deterrence)
Unit 12 – F-tests and Convergence: Extension of t-tests to more complicated null hypotheses; testing linear restrictions with the F(q, n-k-1) distribution; Convergence II: connects Goodness-of-Fit metrics and inference stats (t stats and incremental R^{2}, SSR and SSE); reported F stats (for the regression) and associated p values; relation to adjusted R^{2}; Babies and bathwater; Chow tests; machine learning
Mid-Term Exam #2 (about here)
Further Topics
Unit 13 – Linear Probability Models (LPMs) and Functional Forms: Dummies on the LHS; Linear Probability Models (LPMs); exploring functional forms (quantile dummies; linear splines; logarithms and exponentials; polynomials; cubic splines, and fixed effects)
Unit 14 – Further Topics I: Differences-in-Differences (Deflategate; NBA Referee Own-Race Bias); Regression Discontinuity Designs (Highway Fatalities & Daylight Savings Time); Instrumental Variables (The Oregon Health Insurance Experiment (Medicaid)); Maximum Likelihood Estimation (MLE); limited dependent variables; logit and probit models; censored and truncated regression models
Unit 15 – Further Topics II: OLS asymptotics (large sample properties; consistency; convergence in distribution); misspecified models; proxy variables; missing data; outliers; non-random samples; forecasting and prediction intervals;
Stata @ Boston College
There are a large number of statistical software packages that you can use to do econometric analysis. We will use Stata, one of the more popular packages and the package that receives the most support at Boston College.
I will be providing more details as the semester develops, but for now: Stata is available to BC students through the “application server”, known as the apps server.. In the past you've needed Citrix Receiver installed on your computer to access the apps server (and if you were not connected to the BC network, you also needed to use VPN to access the apps server). But those days are over. You can now use the "Light Version" of Citrix Receiver to directly access the apps server (no need to install the Citrix Receiver or VPN.) To learn how to do this, go to http://www.bc.edu/offices/help/teaching/app_server.html .
Alternatively, and to avoid traffic jams with Citrix and the apps server, you may want to purchase a six-month Stata IC license for $48 (sorry, but small Stata will not suffice for econ2228). For details, go to: https://www.stata.com/order/new/edu/profplus/student-pricing/
We will devote some time to learning how to use Stata to build datasets and run regressions. You will discover that building datasets is long, hard, tedious and unrewarding work… and running regressions is relatively quick and easy… and fun!
Stata Resources
As the semester progresses, you may find the following resources of interest:
· Encountering Stata questions/issues/features?… just Google it (always include “UCLA”).
And here are a few sites that might be helpful (the pdfs are posted to the course website):
· http://fmwww.bc.edu/GStat/docs/StataIntro.pdf
· https://stats.idre.ucla.edu/stata/modules/
· http://dss.princeton.edu/training/StataTutorial.pdf
· https://stats.idre.ucla.edu/stata/
· … and don’t forget YouTube: https://www.youtube.com/results?search_query=stata
Examples and datasets (bcuse may be helpful here… I’ll explain in class):
· http://fmwww.bc.edu/gstat/examples/wooldridge/wooldridge.html
· http://fmwww.bc.edu/ec-p/data/wooldridge/datasets.list.html
· http://fmwww.bc.edu/ec-p/data/ecfindata.php
· https://stats.idre.ucla.edu/other/dae/
· https://stats.idre.ucla.edu/other/annotatedoutput/
Also: Ben Lambert’s full course in econometrics videos are terrific and come with a British accent!
· https://www.youtube.com/user/SpartacanUsuals/playlists
[1] The course website and Canvas site contain a few links to online materials and tutorials.
[2] Let me know if you'd like a copy and are not able to purchase it through Amazon, and we can discuss shipping options.
[3] https://www.bc.edu/content/bc-web/academics/sites/university-catalog/policies-procedures.html#academic_integrity_policies
[4] Published here means published in an academic journal (so no unpublished senior theses, web blogs, or the like).
[5] If you want a sense of degree of difficulty, just ask.