Case of the Day: Elasticity of Demand for Higher Education
Elasticity of demand attempts to measure how sensitive the quantity of a product demanded is to the main variables that affect it: the price of the product, consumers' incomes, and the prices of other related products. One of the most significant products that all of your families have in one way or another recently purchased is a year of Reed education. Having just made this decision as a consumer, you may be more familiar with the process of choosing to purchase this product than some others we might consider as examples.
Peculiarities of higher-education demand
Before we examine some elasticity estimates, we need to consider some aspects of higher education that make it a unique product. First, the process of buying higher education involves multiple steps and decisions of both sellers and buyers. Unlike prospective buyers of Spicy Anasazi Bean Burgers at Burgerville, prospective students at selective colleges and universities must apply for admission to their institutions of interest and, depending on their academic credentials, may or may not be granted the privilege of purchasing the product.
Second, colleges and universities often offer price discounts to a large share of their admitted applicants through financial aid. These discounts can be based on measured ability to pay ("need," as at Reed) or on the basis of perceived academic "merit" (as at many other colleges). Subsidies and subsidized loans are offered by federal and some state governments for purchase of this good as well. These "financial aid" factors make it very difficult for someone studying the demand for higher education to measure the appropriate "price."
Finally, a college education is purchased over a period of (more or less) four years. While it is easiest to examine the demand decisions of new freshmen, the "persistence" of these new students at the college over the remainder of their four-year college career is equally important for the overall demand for the higher-education product.
Approaches to estimating higher-education demand functions
All of these factors make estimation of the demand elasticities for colleges difficult. Nonetheless, some investigators have attempted to try to put numbers on some of the important elasticities. There is great variation in the approaches that different economists have used to estimate demand functions.
Some studies have looked at the overall demand for higher education in general; some have examined the demand for specific sectors (public, four-year colleges and universities, for example); and some have considered demand at the level of the individual institution. Obviously, we would expect the elasticities to be quite different depending on the level of the analysis. The only substitute for attending higher education is not attending (and presumably working). At the other extreme, there are many other colleges (in addition to not attending college at all) that are (imperfect) substitutes for attending Reed.
Some studies have used cross-sectional data at the level of the individual student, estimating how the probability of attending a school (or a category of schools, or any college at all) is affected by prices, family income, student characteristics, and other variables. Others have looked at variation in aggregate data over time to assess how changes in prices and aggregate income measures (such as GDP or personal disposable income) affect enrollments.
Some studies have compressed the entire process of application, admission, and matriculation into a single step by using total enrollment as the quantity variable. Others have focused on the last step, examining colleges' "yield" rates (new matriculants divided by admitted applicants) to focus only on the last stage at which those who are admitted decide whether or not to attend.
Selected results
[Note: You are not expected to read the primary sources. Links are provided in case you want more information or want to see what the original studies look like.] William Becker ("The Demand for Higher Education," in The Economics of American Universities, ed. by S. A. Hoenack and E. L. Collins, Albany, N.Y.: SUNY Press, 1990) summarizes a variety of estimates for the demand for higher education. One of the earliest studies (by Campbell and Siegel (1967), see Becker for detailed citations) estimated the overall demand for four-year colleges and universities. This is an example of a highly aggregated study using time-series data. They estimated an own-price elasticity of demand of -0.44 and an income elasticity of 1.20. A later study by Hight (1970) broke the results down by private and public institutions, finding own-price elasticities of -1.058 for publics and -0.6414 for privates and income elasticities of 0.977 for publics and 1.701 for privates.
An early study of demand at the level of individual institutions was Hoenack (1967). He used cross-sectional data for California to estimate the demand for education at University of California campuses. He found a price elasticity of -0.85 and income elasticity of 0.7.
More recently, in a study based on a Reed senior thesis, Buss, Parker, and Rivenburg (2004) (BPR) examine a cross-section of selective liberal-arts colleges to estimate demand functions at the individual college level. They looked separately at the yield for full-paying students and financial-aid students. For full-paying students, they found an own-price elasticity of -0.76. BPR also estimated cross-price elasticities of demand by looking at the effects of the prices of two substitutes: the average price of other liberal-arts colleges and the price of flagship state universities in the same region as the college. Neither of these cross-price elasticities were statistically different from zero. Their estimate of income elasticity was very crude, relying on fluctuations in aggregate income over a short sample. Although the estimated elasticity of 1.21 is consistent with other studies, it has a large standard error and has very low statistical precision.
For financial-aid students, BPR find a larger own-price elasticity of -1.18 (when own price is defined as gross tuition ignoring aid) and strong positive elasticities with respect to grant and loan components of financial aid (+0.31 and +0.12, respectively). As suggested by these results, they find that an increase in tuition accompanied by an equal percentage increase in financial aid would lower quantity demanded, which refutes a commonly held hypothesis that only "net tuition" (full price minus financial aid) matters to students.
One difficulty of BPR's cross-college approach to modeling demand is that each individual financial-aid student faces a different price, depending on his or her individual financial aid package. By aggregating together all students at each college, only the average financial-aid award can be observed. A more effective approach to estimating the effect of financial aid on demand is to look at individual students. Moore, Studenmund, and Slobko (Economics of Education Review 10(4), 1991) (hereafter, MSS) looked at the choices of individual admitted applicants to Occidental College to examine the effect of the student's financial-aid offer at Occidental and the student's competing financial aid offer from an alternative institution on the probability of enrolling. MSS find an own-price elasticity with respect to the net cost of enrollment of -0.72. They also find a positive cross-elasticity of the net cost of the alternative school with a slightly smaller absolute magnitude.
One weakness of the MSS approach is that it considers only a single institution. Avery and Hoxby (2004) constructed a remarkable data set by surveying high-achieving graduates of 500+ top high schools to ask about their college applications, admissions, financial-aid offers, and decisions. For a sample of over 3200 students they were able to get detailed information about the choices available to the individual students and which they chose. Although their results are not reported in elasticity form, Avery and Hoxby estimated that an increase of $1000 in a college's tuition level would lower the probability of a student enrolling at that college by about 2%. (That's 2 percent of the prior probability, not 2 percentage points. This is an important difference: If the prior probability of you choosing Reed is 20%, then a 2 percent decrease in that probability is 0.02 x 20% or 0.4%, lowering the probability of attending to 19.6%. A 2 percentage point decrease in probability would be a decline from 20% to 18%.) Remarkably, an increase of $1000 in room and board would lower the probability of enrollment by 10%!
Avery and Hoxby are particularly interested in the effects of the size and composition of financial-aid packages on enrollment probability. They find that a $1,000 increase in grants raises the probability by about 11% and an extra $1,000 in loans increases it by about 7%. They also look at specific details of financial-aid awards and find some surprising and (from an economist's point of view) anomalous results. Among other results, they find that students receiving grants in the form of "named scholarships" respond much more strongly than students being offered the same amount of money as simple financial-aid grants. They also find that front-loading the grant (more money in the freshman year relative to later years) significantly increases the effect on enrollment.
Questions
1. Would you expect the own-price elasticity of demand to be higher at the level of an individual school (e.g., Reed) or at the aggregate level (e.g., all 4-year colleges and universities)? Why?
2. Despite the empirical evidence to the contrary, college administrators often believe that their own-price elasticity of demand is essentially zero. Who do you think is right? How important were price considerations in making your own college decision? Would a change of a few thousand dollars in Reed's tuition level have mattered?
3. Would you expect the own-price elasticity of demand to be higher for financial-aid students or for non-aid students (and does it depend on whether "own price" is gross tuition or net tuition?)? Why? What about the income elasticity?
4. The elite colleges that charge the highest tuition often also have the highest yield rates (number attending divided by number admitted). If you simply plotted yield against tuition and called that a demand curve, would it slope upward or downward? Buss, Parker, and Rivenburg are careful to control for "institutional quality" and by doing so they estimate a negatively sloped demand curve. Explain why controlling for quality is important in order to generate this result.
5. How much should a dollar's worth of loans or work study be worth, relative to a dollar's worth of grant? Full value? Nothing? Why do you think Avery and Hoxby (also MSS and BPR) found that loans have an effect almost as large as grants? Why do you think they found that named scholarships affect enrollment decisions more than simple dollar awards? Is this rational? What strategy should Reed follow if this result is true for Reed applicants?