Abstract
This article presents an analysis of the mathematics course requirements and recommendations for prospective students seeking entry into economics PhD programs in the United States. We find that applicants must complete seven mathematics courses to safely assume that they have enough math credits for admission to most programs. Using National Research Council (NRC) rankings of economics departments according to the level of research activity, we find no strong evidence that the mathematics courses required and recommended are dependent upon the level of academic research conducted by the faculty in the respective PhD programs.
Introduction
Research in economics frequently involves mathematical analyses. Therefore, in preparing new economists, economics PhD programs require prospective students to possess substantial mathematics knowledge and skills upon entering their programs. Even though this is generally a known fact to prospective doctoral students, they often wonder how advanced their mathematical training need to be to enter a PhD program. They also might wonder if the mathematics requirements are uniform across all PhD programs in economics. This article attempts to answer these questions. Previously, we collected and published a data set on mathematics requirements and recommendations for admission into economics PhD programs in the United States (Milkman & Marjadi, 2017). We identified a set of eleven mathematics and statistics courses commonly mentioned in descriptions of the admission requirements of economics PhD programs in the United States. Those courses are Calculus 1, Calculus 2, Multivariate Calculus, Matrix Theory/Linear Algebra, Differential Equations, Statistics 1, Statistics 2, Econometrics 1, Econometrics 2, Real Analysis, and Stochastic Processes. In this article, we analyze the number of mathematics courses that PhD programs are likely to require or recommend. We then group the doctoral programs into quality tiers to determine whether the number of courses required or recommended varies across programs according to the respective department’s level of research activity.
Number of Mathematics Courses
Many economics PhD programs require or recommend certain mathematics courses as part of their requirements for admission. A “requirement” for a specific mathematics course typically means that the absence of the course on an applicant’s academic transcript will significantly reduce, or eliminate, the probability of acceptance into the program. However, a “recommendation” for a certain mathematics course typically means that an absence of such a course will not disqualify an application from consideration. An economics PhD program may recommend a mathematics course because it will help students to succeed in their doctoral course of study. Completion of such courses may also strengthen an application to the program.
We performed a frequency analysis by counting how many mathematics courses are required for admission consideration by each program in our sample of 134 doctoral programs. Then, we looked at the frequency of programs that require a certain number (minimum of 0 and maximum of 9) of mathematics courses. The results are presented in Table 1. We also counted how many mathematics courses each program “requires or recommends” and performed the same frequency analysis. These results appear in Table 2.
Number of Mathematics Courses Required.
Number of Mathematics Courses Required or Recommended.
Table 1 shows that 10.45% (7.46% + 2.24% + 0.75%) of the PhD programs require seven or more mathematics courses. The median number of mathematics courses required is four. It is interesting to note that nine out of the 13 programs that do not require any mathematics courses are ranked in the top 15 economics PhD programs in the United States (see Milkman & Marjadi, 2017; National Research Council [NRC], 2011). Perhaps these top tier programs simply expect that their applicants have sufficient mathematics backgrounds. Examination of Table 2 reveals that 54.48% of the PhD programs require or recommend seven or more mathematics courses. The median number of mathematics courses required or recommended is seven.
Rankings
NRC
We also examined whether program “quality tiers” make a difference in the mathematics requirements for admission. We define quality as the level of academic research activity produced by each program’s faculty. To determine quality tiers, we followed Hansen’s (1991, p. 1055) method that groups economics PhD programs into five different tiers: the top 6, the next 9, the next 15, the next 18, and, the remaining departments.
The NRC develops and publishes rankings of the graduate faculty across PhD programs in various fields (see NRC, 1982, for an explanation of their methodology.) For our analysis, we use the latest NRC rankings based on data collected for the academic year 2005-2006 (NRC, 2011). Although the NRC data provide several characteristics of PhD programs in the United States, we use the ranking of economics PhD programs based on research activity. Hansen’s tier definitions were adapted to suit the number of economics PhD programs in 2016 (The number of schools in the lowest tier rises from 43 to 86 due to the growth in the number of doctoral programs ranked since Hansen [1991] wrote his paper.). The resulting tiers and their associated mathematics requirements (required, recommended, and neither) are used to construct two-way tables for each course. Since we do not have sufficient data to run a chi-square test of independence, we use Fisher’s exact test to see whether quality tier and requirements are independent. Table 3 summarizes the test results for all 11 courses in our study.
Summary of Fisher’s Exact Test Across Five Quality Tiers Using NRC 2005-2006 Data.
Note. NRC = National Research Council.
As shown in Table 3, Statistics 1, Real Analysis, and Stochastic Processes show statistically significant differences by tier, with p values less than .05. This implies that the quality tiers affect whether the programs require, recommend, or neither require nor recommend those mathematics courses. Seventy-six out of the total 134 programs require Statistics 1. It is important to note that 66 of 76 are programs in Tiers 4 and 5. Perhaps higher tier programs implicitly expect applicants to have completed Statistics 1 based on the data for requirements that would have included Statistics 1 as a prerequisite. If we consider that, the variable might not be as statistically significant as the p value indicates. Only seven programs require Real Analysis. There is one program in each of Tier 1, 4, and 5. There are two programs in each of Tier 2 and 3. Only two programs require Stochastic Processes, one program is in Tier 1 and the other is in Tier 5.
Top 30 Programs
We performed a similar analysis while dividing our sample into only two groups. The first group includes the 30 programs in Tiers 1, 2, and 3. The other group comprised the remaining 104 programs. We summarize the Fisher’s exact test results in Table 4.
Summary of Fisher’s Exact Test Between Upper Thirty and Other Programs Using NRC 2005-2006 Data.
Note. NRC = National Research Council.
The test reveals that three courses—Statistics 1, Real Analysis, and Multivariate Calculus—have different requirements for the top 30 economics PhD programs compared with the other economics PhD programs. Similar to the earlier analysis for five different quality tiers, fewer top 30 programs require Statistics 1 compared with lower ranked programs. Ten out of 30 programs (33.33%) require Statistics 1 compared with 66 out of 104 (63.46%) for the lower ranked programs. For Real Analysis, five programs (16.67%) in the top 30 require the course, while there are only two programs (1.92%) in the lower ranked group. Sixty-one economics PhD programs require Multivariate Calculus, 20 of them (66.67%) are in the top-30 programs compared with 41 (39.42%) in the lower ranked group.
Conclusion
We find that a vast majority of economics PhD programs require or recommend mathematics courses for admission to doctoral study. Students who aspire to enter a PhD program in economics can examine our previous article (Milkman & Marjadi, 2017) to determine which mathematics courses each American PhD program in economics requires or recommends for admission. It is important to note that admission committees also consider other factors such as grades in an applicant’s mathematics courses and quantitative GRE scores. Furthermore, some prospective economics PhD students may not meet all the mathematics admissions requirements but are admitted based on combinations of factors such as GRE scores, previous experience, or strong recommendations. This, of course, raises the question of whether those admitted students with weaker mathematics background succeed and earn their intended PhDs in economics at the same rate as those who meet the mathematics course requirements and recommendations. Additional research is needed to answer this question.
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.