Mathematics Preparation

Mathematics provides economists with a set of tools that they use for many purposes. First,

mathematics enables economists to prove rigorously the logical connection between

concepts, which is especially crucial in situations where words alone are imprecise or

potentially misleading. Second, mathematics makes it easy to combine several simple

models into a larger model, allowing economists to analyze complex economic systems that

involve interacting parts. For example, macroeconomists study the interactions between

the goods market (involving production and consumption of goods and the setting of prices),

the labor market (involving employment and wages), and the money market (involving

assets, such as cash and bonds, and interest rates). Third, mathematics allows economists

to formulate and test their theories quantitatively. Quantitative testing means that

economic theories must satisfy a demanding standard before they become accepted.

Finally, because economic theories are quantitative, economists can offer quantitative

policy prescriptions.

Because “marginal” conditions hold a central place among economists’ analytical tools,

concentrators are required to demonstrate competence in single-variable calculus by taking

Math 1a or by placing out of it. Single-variable calculus is the prerequisite for the less math

intensive intermediate economic theory courses, Ec 1010a and 1010b.

Although a student can understand virtually all the basic concepts in economics with single

variable calculus, deeper understanding, and understanding of more difficult concepts,

requires more mathematical preparation. And while math beyond the level of first-semester

calculus is not required for the concentration, it is highly recommended. The more-math

intensive intermediate economic theory courses, Ec 1011a and 1011b, require multivariable

calculus at the level of Math 20 or 21a. Math 20 covers multivariable calculus and linear

algebra together, focuses on economic and social science applications, and serves as a last

math course for many economics concentrators. Math 21a covers multivariable calculus as

part of a sequence leading to higher-level math courses, though it can be taken alone.

Students who want to pursue graduate work in economics should take multivariable calculus

(Math 21a), linear algebra (Math 21b), a course that emphasizes writing proofs (Math 101),

and real analysis (Math 112). (Students with very strong math backgrounds may substitute

Math 23ab for 21ab. A student with an extremely strong math background would be

prepared for graduate work in economics after taking Math 25ab or 55ab.)

Ec 10 (formerly Social Analysis 10)

Ideally, students intending to concentrate in Economics spend their first year at Harvard

taking Ec 10, the full-year introduction to current economic issues and to basic economic

principles and methods. (If you did not take Ec 10 as a freshman, you may still concentrate

in economics. You may take all of Ec 10 during the summer at Harvard or take it as a

sophomore. Sit down with one of the concentration advisors to help you plan your courses

so that you will fulfill your concentration requirements without a problem.)

All concentrators are required to either take Ec 10 or demonstrate proficiency at

introductory economics, most typically by a combined score of ten on the Macroeconomics.

and Microeconomics Advanced Placement examinations or a score of 7 on the Higher Level

examination toward the International Baccalaureate. If you meet these requirements, you

may skip Ec 10 and go on to the intermediate theory courses (Ec 1010ab or Ec 1011ab), but

you must replace those credit hours with two other half courses. If you received a five on

one AP economics exam, you may skip that half of Ec 10, but again, must replace it with

one additional half course. Most eligible students who go on to the intermediate theory

courses do very well, but you do not have to skip Ec 10; you may take it if you wish. It is a

personal choice, and we suggest that you speak with one of the concentration advisors to

help you with your decision. (Note that a student who uses macro and/or micro AP exam

scores as part of the basis on which to activate Advanced Standing will not get Harvard

credit for taking Ec 10, or for the semester of Ec 10 represented by the exam taken.)

Ec 10 is taught in sections of 20 students or so, with course-wide lectures on a variety of

topics about 10 times a semester. Unless replaced by course-wide lectures, sections meet

for three one-hour classes each week, on Mondays, Wednesdays, and Fridays. The section

based orientation of the courses is very important because sections teach the principal tools

of economics in an environment in which students can ask questions freely. All sections

cover the same basic course material.

Course-wide lectures are usually given by faculty experts on the specific topic addressed

(e.g., Greg Mankiw on macroeconomics, David Laibson on behavioral economics, Andrei

Shleifer on finance, Richard Freeman on labor). The lectures focus on current economic

problems and policy issues, in coordination with the material being taught in section. Each

lecture is discussed at the following section meeting.

Section leaders are graduate students in Economics, as well as law, business, and public

policy students with strong economics backgrounds and high teaching ratings. Teacher

training sections and videotape reviews of individual sections maintain high pedagogical

standards in the course.

Examinations cover both lecture and section material. There are usually two one-hour

exams and one final each term. One of the hour exams and both finals are course-wide

exams, in which all students taking Ec 10 solve the same problems and write on the same

essay questions. Most sections assign roughly five problem sets per term.

There are no prerequisites for Ec 10. It is not a highly mathematical course. However, it

uses a lot of graphs and some simple algebra. It does not use calculus. Ec 10 cannot be

taken pass/fail by a student intending to concentrate in Economics.

Sophomore Tutorial

Because Economics has so many concentrators, even upper-level courses can be large in

size. But much of what one learns about an analytical subject like economics comes

ultimately from active discovery, which is often better accomplished in a small group

setting. Ec 970, Sophomore Tutorial, is taught in sections of about eight to ten students, and

provides a key opportunity for such active learning. Ec 970 is offered in the spring. As the

name suggests, almost all concentrators take the tutorial during their sophomore year;

however, under certain circumstances (e.g., if you transferred into the department late), it

may be postponed to junior or senior year. To enroll in Ec 970, you must have completed Ec

10, Stat 100 (or its equivalent), and Ec 1010a/1011a. You also must be concurrently enrolled

in (or have already completed) Ec 1010b/1011b. If you do not meet those prerequisites, you

will need to enroll in tutorial in either your junior or senior year. Ec 970 may not be taken

pass/fail.

The goals of Ec 970 are to build on the foundations laid in the principles, statistics, and

intermediate theory courses by applying frameworks of economic analysis to specific

subject areas, to help students develop an effective style for writing analytical economics

papers, and to practice the arts of analysis, communication, argument, and listening.

In a typical year, there are 25 to 30 different tutorials to choose from. The vast majority of

students are assigned to one of their top four tutorial choices. Topics vary from year to year.

Recent topics have been behavioral finance, experimental methods and psychology in

economics, economics of professional sports, and law and economics. An overwhelming

majority of tutorials receive high student evaluations, and sophomore tutorial is often one

of a student’s favorite classes in the department.

Intermediate Theory Courses

The Economics Department offers two intermediate microeconomic and macroeconomic

theory course tracks. The Ec 1010 track is intended for students who find mathematical

formulations as much of an obstacle as a help to understanding economics; knowledge of

Math 1a is expected. But many students with higher levels of mathematical preparation

take Ec 1010 courses when they believe that the courses are especially well taught. The Ec

1011 track is intended for students who find mathematical formulations of economic

principles a significant aid in understanding and using them. It uses mathematics at

approximately the level of Math 20/21a. Students who have taken Ec 1010a and 1010b have

sufficient preparation for almost all upper-level undergraduate economics courses. A

handful of upper-level undergraduate economics courses have Ec 1011a or 1011b as a

prerequisite. Students are free to mix and match courses from the different tracks:

combining 1011a with 1010b, or 1010a with 1011b.

Ideally, concentrators should have finished the intermediate micro and macro courses by

the end of their sophomore year. Whether or not a particular upper-level economics course

has Ec 1010 as a formal prerequisite, students who have taken intermediate micro and

macro usually do better and learn more in upper-level courses than students who have not.

Concentrators must demonstrate their command of the basic tools of economic analysis by

receiving a B-/C+ average (that is, a 2.5 grade point average) or better in both intermediate

theory courses. Students who do not meet this standard are required to reinforce their

understanding of macro and micro theory by satisfactorily completing (i.e., receiving at

least a C- in) Ec 975: Tutorial—Theory Review. Ec 975 is not intended as a review for

students who feel weak in their overall economics courses. It is required of, and limited to,

students who receive below a B-/C+ average in the intermediate theory courses. Students

who must take the course are notified by the Undergraduate Office. If you are unsure,

speak to the Undergraduate Program Administrator. Students do not receive economics

course credit for Ec 975.

In the years when 975 is not offered, students who receive below a C+/B- average in the

intermediate series must (unofficially) retake the portion/s of the series in which they got

below a B- and receive at least a B- the second time around. Since such students will not

officially be enrolled in the course, the grade and credit hours will not count for Harvard

credit towards graduation or fulfilling Ec electives in the concentration, nor will it be

factored into your Ec GPA for honors if you choose to pursue them. Students’ fulfillment of

this requirement will be tracked internally by the Economics’ Department and students will

not receive a degree in Economics until this requirement is met.

Statistics and Econometrics

The ability to interpret quantitative data and to understand statistical arguments is

essential to understanding the economy. Statistical methods help economists to summarize

data, to analyze empirical relationships, to test theories, and to make predictions. Because

virtually all research in economics involves at least some statistics, economics

concentrators must take a course in statistics (Stat 100, 104, or 110) before they may take

Ec 970, Sophomore Tutorial. For this reason, most economics concentrators take the course

in statistics in their freshman year or in the fall of their sophomore year.

Stat 100 introduces students to statistical tools like hypothesis testing, parameter

estimation, and regression analysis. The main intent is to enable students to read

contemporary economic literature and to understand how statistical procedures are used to

summarize information. Stat 100 is essential for fully understanding much of the reading in

upper-level Economics courses.

An alternative to Stat 100 is Stat 104, which covers somewhat more material at a faster

pace in a smaller class. Stat 104 is pitched at a slightly higher level and draws on

applications from economics and other social sciences.

Students who have completed multivariable calculus (Math 20 or 21a) and who wish to

understand statistics at a deeper level can fulfill their statistics requirement by taking

(instead of Stat 100 or 104) Stat 110 (often, but not necessarily, followed by Stat 111). Stat

110 covers probability theory, which provides a mathematical foundation for statistics. Stat

111, which requires linear algebra (Math 20 or 21b), builds statistical theory from this

foundation. Stat 111 draws more directly from Stat 110 but has fewer economic applications

and less emphasis on standard econometric methods than Ec 1126.

Stat 101 is not an option. The Economics Department does not give any credit for high

school statistics or the statistics AP exam. Courses taken to meet the Economics

Department’s statistics and econometrics requirements cannot be taken pass/fail by

Economics concentrators.

In addition to a basic course in statistics, the department requires all concentrators to take

Ec 1123 or 1126 (Ec 1127 can also be substituted). These courses are designed to introduce

concentrators to econometrics – the statistical concepts and quantitative methods that are

especially important for economists. Econometrics typically plays a central role in an

economics senior thesis, so students who plan to write a thesis fulfill their econometrics

requirement before senior year.

Ec 1123 provides students with an understanding of econometric techniques and an ability

to apply them using standard software packages. Ec 1123 is less mathematical and more

applied than Ec 1126, covering the essential methods for conducting research in economics.

Ec 1123 provides students with most of the basic tools to write an empirical honors thesis.

Ec 1123 assumes a mathematics preparation at the level of Math 1a.

Ec 1126 goes further into the fundamentals of probability theory and problems of statistical

inference. It is more mathematical and more theoretical than Ec 1123, employing both

multivariable calculus and linear algebra (Math 20 or both Math 21a and 21b). Ec 1126

emphasizes understanding the general framework of econometric theory and covers several

important recent contributions and applications. Like Ec 1123, Ec 1126 provides students

with the basic tools to write an empirical honors thesis, while also providing a rigorous

introduction to econometric methodology. Preparation at the Math 20 level is a prerequisite

for Ec 1126. Students should also have taken, or be taking, the intermediate

microeconomics and macroeconomics courses.