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The Grade Multiplier :

Applying Gresham's law to grade inflation

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PRELIMINARY DRAFT

07 April 2021

*Please do not reuse or recirculate any portion of this article and research report without express written permission.

When “A” is for average and Gresham’s law (of grade inflation) posits that “bad grades drive out good grades”

An “A” today is not worth the same as an “A” a few decades ago. Apparently, GPAs are among the list of highly depreciable intangibles.

 

            In inquiring about Harvard College’s grade distribution, professor Harvey Mansfield said to the Dean of Undergraduate Education: "A little bird has told me that the most frequently given grade at Harvard College right now is an A-."

 

            The Dean’s apparent correction

"The median grade in Harvard College is indeed an A-. The most frequently awarded grade in Harvard College is actually a straight-A."

            There is clearly some major misalignment behind the scenes when your professor gives you a less-flattering grade (as a genuine benchmark of your progress) and a very attractive (inflated) grade (for official transcript purposes). In fact, Mansfield himself has resorted to the dual-grade system.

IN SEARCH OF THE GRADE MULTIPLIER

In Keynesian economics, the government multiplier (or commonly the “multiplier”) - refers to the concept of when the government increases expenditures (i.e., public spending, such as infrastructure) by ΔG, the overall economy expands by ΔY, given by the formula ΔY = gΔT, where g is the government multiplier. If you claim that g is greater than 1, you’re saying that more government spending means more national income, whereas if you state that g is less than 1, you believe that increased government expenditure reduces overall economic output. 

            You may have met some of g’s brothers and sisters too, including the tax (commonly denoted by t) and open economy (m) multipliers. Most of these in essence state that for a ΔG increase in government spending, there is an increase in overall economic output given by ΔG times the respective multiplier.

            In the context of the educational market, the grade multiplier would represent a similar phenomenon: an increase in average grade point by a point increase triggering an increase in the overall economic output of the increase multiplied by a factor. The translation may be interpreted as increasing grades indicate better jobs obtained (where high-skilled jobs imply market efficiency and thus economic output expansion). However, it turns out that the grade multiplier may, in actuality, be negative: grade increases (or “inflation”) may be dampening the job market with worse jobs and, au contraire, contractionary

THE STAKES

Theoretically, if grades were to inflate indefinitely, meaning that an A+ today becomes A++ tomorrow, and continuously moves from Aⁿ on day n to Aⁿ⁺¹ on the next, admissions offices could just bump up GPA thresholds to 6.243 - or hire some economists to deflate grades to prior-period levels - no harm done. 

            The latter treatment would be on par with that of monetary currency inflation. After all, both operate similarly - the USD is a currency carrying monetary value and grades are the currency in the educational market: the more in circulation, the less in valuation. As with all other market goods in our traditional neoclassical model, there’s an inevitable inverse relationship between supply (by schools in the educational market) and demand (by firms).

            But there is one major distinction: the type of value contained in the currency. Fundamentally, grades reveal the underlying academic value (e.g., achievement, soft skills, etc.) of a student to employers, parents, admissions officers, the students themselves, among others. In other words, grades carry signalling value - which indicates essential factors that cannot be observed by the principal (i.e., the hiring party in this case) in a principal-agent game in economic game theory. Another way to understand this is that grades are an attribute upon which employers rely in determining whether to hire a student or not, since employers view grades as reflective of a student’s innate ability (an unobservable trait).

            The critical question here is whether grade inflation has significantly reduced the signalling power of grades of incoming employees from the perspective of employers.

GRADES ON THE RISE

In case you’re not convinced grades are on the rise, however, take a look at some average GPAs (including both lower and upper division courses) across time at University of California, Los Angeles.

UCLA GPA
Figure 1: UCLA GPA trend, 1927-2015

            GPAs over time measured against standardised test scores - predictors of student achievement - puts the phenomenon in better perspective; we can now clearly see whether grades, which supposedly signify student achievement, indeed correlate positively with other reputable indicators of achievement.

            One can employ various methodologies to tease out this trend, one of which utilises a set of standardised test scores corresponding to a period of rising grades. Two sets of data can attest to an increase in grades alongside a decrease in student achievement: (1) the Graduate Record Examination (GRE) and (2) the Scholastic Aptitude Test (SAT) and American College Training (ACT). The former study tracks an inverse relationship between the two in the period of 1965-1980, while the latter measures decreased college preparedness from 1963-1980 as grades inflated most rapidly. 

            Another (perhaps more reflective) indicator is the threshold for Latin honours eligibility over multiple years. Data extracted from the College of Letters and Sciences at University of California, Los Angeles between the 1994-1995 and 2020-2021 academic years indeed tell an interesting story: the minimum GPA required for cum laude, the top 20% of a graduating class, rose from 3.500 to 3.782, while the minimum threshold for summa cum laude, the top 5%, only increased from 3.850 to 3.936 - 8.057% and 2.234% increases, respectively. The following (original) plot illustrates this statistically significant increase in all three thresholds.

College of L&S Latin Honours Eligibility over time
Figure 2: UCLA L&S Latin Honours Eligibility, 1995-2021

            Even more significant is the convergence of all three honours towards the upper limit of the 4.0 GPA cap, and that cum laude - the honor with the lowest threshold - is increasing at the greatest rate while the threshold for summa cum laude is hardly increasing. The mathematical interpretation is available for those interested, but the point is that the above plot precisely illustrates the case of grade compression - our next guest.

NOT ALL INFLATION IS CREATED EQUAL: INFLATION VS. COMPRESSION

Rampant rising, for many, is interpreted as inflation. But consider the case where the price of your favourite cereal can only increase up to a ceiling of, say, $5 per box. So how would this pan out? Well, evidently, eventually all brands will be selling their cereal for $5 per box - the utmost price possible (assuming our cereal selling agents are rational and thus aim to maximize profits). In most economics textbooks, this phenomenon of an artificially-induced perfectly competitive equilibrium would not be your ideal inflation illustration. 

            Apply the same principle to another beloved commodity - grades - and a mirrored transformation occurs; your best friend, your worst enemy, the kid who sits there and just twiddles his thumbs the whole lecture, and virtually everyone else all magically wind up with an A. At long last, a keen observer laments a long-lost past when an A did not mean “average.”

            Of course, in actuality prices cannot be capped the way As are under capitalistic operations. Prices can rise indefinitely and arbitrarily, per laissez-faire principles. Indeed, not all nominal inflation is created equally: rising grades and rising prices yield divergent issues. Here we introduce the more precise descriptor of grade compression to depict the true nature of what is commonly phrased as grade inflation.

GRADES AND CURVES: TO CURVE OR CURB?

At current, various studies within the existing grade compression literature seem to contradict each other. Chan, Li, and Suen (2005) and Ostrovsky and Schwarz (2003) suggest that compression attenuates the signalling value of grades, benefiting lower-ability students at the expense of higher-ability students. Others, however, contend that no such risk is involved and that employers are still able to draw upon cumulative GPAs to offset whatever benefit may be derived from rising grades in individual courses. The more probable (and lower) proportion of students maintaining high cumulative GPAs remains indicative of ability to employers, as demonstrated in a sample of 14.5% of students with 3.75 or greater GPAs in 2000.

            Alternatively, economist Tim Harford introduces the AAAA (i.e., A+++) in order to combat what he identifies as “classic grade distortion” (previously introduced as compression) rather than grade inflation. Rather than capping grades at 100%, grades will rise freely from A to AA to Aⁿ to A ⁿ⁺¹, whereas with grade distortion, the entire universe is rendered average with spotless As. 

            The latter scenario is precisely what we have at present – since grades are capped on the upper bound, effectively resulting in the equalisation and thus devaluation of all grades assigned. Harford’s proposed translation of an Aⁿ grade today to A ⁿ⁺¹ tomorrow would convert grade distortion to true inflation, and employers and admission offices would henceforth deflate grades just as economists periodically deflate prices for the purposes of meaningful comparison. (Man, who knew that working in admissions might warrant a dual economics degree one day?)

“The rating agencies might even find a new line of business here – handing out an AAA for nicely packaged dross is something they should be able to master.”

- TIM HARFORD, economist

            The caveat? Merely mutual understanding.

SIGNALLINIG ASKEW

To turn back to our previously posed critical question, let us model the situation with economics game theory.

            The effect of the grade multiplier may be illustrated through a classic signalling game with three players: students of ability types high (H) and low (L), universities assigning grades of type high (h) and low (l), and firms hiring students for jobs of type good (g) and bad (b). The goal of the firm is to match students of type H to jobs of type g and students of type L to jobs of type b. While this may sound logical and perhaps straightforward, the issue stems from student ability being a hidden type: ability is an unobservable trait, as previously explained regarding the signalling value of grades. Firms hence must turn to grades (g or b) to signal the true type of the student (H or L). (If you're fond of derivatives and Greek letters, here is the original inspiration for modelling grade inflation as a signalling game.)

            The game would remain quite simple if one were to assume that universities truly assign the correct grade type to both respective types of students (i.e., universities serve as the matchmaker, and we trust them to be honest in their matching). 

            The problem thus arises when our matchmakers aren’t so honest in playing the game. Front and center: grade inflation.

            By artificially inflating (or compressing) grades by giving every student a high grade, universities meddle with the game rules and consequently attenuate the ability of grades to reveal the true type of students. Since firms are non-discriminant and rely upon these grades in their hiring decision-making, they thus incorrectly interpret every student to be of high ability and thus fit for a good job. 

            Now we’ll add the resulting job misalignment and thus overall market inefficiency and deadweight loss - arising from unexploited gains - to the melting pot. We arrive at the precise opposite outcome of what firms seek to achieve: matching L-type students with g jobs (which are presumed to necessitate H-type skills).

            This inefficient outcome effectively exemplifies a negative-sum game: while (certain) individual agents may benefit substantially (oftentimes through free-riding), the overall payoffs for all agents collectively are lower.

            Beyond potential revenue losses for firms due to job mismatches, the students - specifically, of type H - largely are also collectively negatively impacted in the negative-sum game: their collective reputation depreciates in value. 

            The collective reputation - which may be modeled as the public good in the game - is determined by the average quality of h-grade students in the job market. If all students - of both type H and L - were assigned h-grades by universities, the public good would be devalued since the collective reputation no longer matches up to its previous value (equating to the abilities of only H-type students). 

            Significantly, market wages for good jobs (i.e., the price of the public good) are set by the value of the collective reputation, analogous to a product’s price reflecting its innate value. When the collective reputation drops in value, its price would correspondingly decrease. Hence, an influx of low-type students into the pool of high-type students altogether reduces the overall value of high-type students to firms, which respond to reduced “product quality” by cutting wages (prices) for previously high-paying good jobs.

            The problem of payment segues into our original posit wherein rampantly rising grades attenuate their signaling value. The collectively lower payoffs - previously presented in the negative-sum game - for both firms and high-type students precisely proves the point. The universities’ objectives of maximising individual payoffs effectively lead to the least favourable outcome: an inefficient market where both high-type students and good jobs are displaced in equilibrium (i.e., high-type students face competition from low types and good jobs no longer pay as well). Arguably, the resulting futile grades deserve Fs for failing to do their due diligence in distinguishing student ability types and preserving both the quality of the higher-skilled labour force and the corresponding compensation for such labour rendered.

            In effect, we can say that “bad” grades drive out the “good” in applying Gresham’s law of inflation (where “bad” money drives out the “good”) to the equilibrium outcome: the inflated, unreliable grades serve no functional purpose and take over the true grades carrying intrinsic value, as no school has an incentive to deviate from the inflation train.

THE INFLATION INCENTIVE

If this dire outcome seems logically inevitable and evident, universities theoretically would ponder prospectively and avoid going down that track - foreseeing an unhappily-ever-after. We seem inherently aware that we are bound to wind up in the square with worse payoffs when we collectively act in individualistic ways. 

            But recall that economics rests upon the presumption that our little agents are self-interested and only care to maximise individual payoffs. Or, turn to psychological egoism for an extensive elaboration on self-interested motives. 

            Thus arises another phenomenon ubiquitous throughout the world of economic theory: the free-rider problem. A quite relatable example would be group projects: no one wants to do the work but everyone wants to get an A, so each person waits for another group member to do the work. After all, no one wants to fail. Someone will step up and turn the darn thing in. Just not me. This occurs wherever there are individual benefits to be sought through skimping on the burden - and may well be the antonym to the benefit-burden principle. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

            Per the self-interested presumption, no school has an incentive to maintain the collective reputation, and instead each chooses to free-ride at the expense of other schools and firms. The additional characteristics of adverse selection (due to an inability to distinguish between hidden types) and non-discrimination (i.e., payment of equivalent wages to students from schools of differing prestige for the same job) on behalf of firms further contribute to the mess. 

            These overall lower payoffs furthermore depict a classic prisoner’s dilemma scenario, where the dominant - or default - strategy for both players is to defect (i.e., throw the other player under the bus) - or to only seek the maximal individual benefit regardless of the other player’s strategy. When both players only care for their own payoff, they inevitably land in the square with suboptimal payoffs, as neither has the incentive to not defect. 

            As schools individually seek to maximize their respective payoffs regardless of other schools, each school’s only incentive is to give high grades, which may be represented by the dominant strategy of defecting in the prisoner’s dilemma game. When each player (school) chooses the dominant strategy of assigning high grades to both high and low type students, all players end up with worse payoffs: the high grade is rendered meaningless in terms of signaling ability and the original objective of obtaining good jobs for students is defeated. The attenuation of signaling power thus manifests as a reduction in both labor quality of the high-ability group and price for high-type labor (i.e., market wages). 

            The incentive may perhaps be alternatively explained as a flawed fantasy on behalf of universities: in a perfect world, even the low-type students will land high-paying good jobs. The flaw lies in the bitter reality that there are not enough high-paying jobs to go around: trying to squeeze more students through the door simply shuts the door for everyone. At the end of the day, all that is left to be shared are lower-paying jobs.

            To add a few more realistic predictors back into our simplified model, we can examine the motives of individual professors. The tenure track is largely cited: commonly, the incentive comes from untenured professors, whose tenure statuses partially depend upon student evaluations. 

            For others, inflation serves as an effective means of conflict resolution (with grade-driven students): namely, by avoiding conflict. After all, why not save the bickering time for research, counseling, or perhaps a good old nap? It’s about on par with taking the sugar pill instead of the bitter medication for treating a debilitating disease: your taste buds will surely love you at the moment, but the rest of your body will come back for you later once your system starts refusing to cooperate.

free rider

The conditions for the free-rider problem are not so difficult to meet. Individual schools can maximize their own respective payoffs (i.e., individual reputation) through doling out h grades, which theoretically convert to g jobs for their students. But this otherwise-ideal arrangement throws the collective reputation of all schools out the window, in addition to tainting the collective reputation of high-type students as discussed above. 

Why do group projects oftentimes feel like a stress-free stroll down the street?

THE SEARCH REVISITED

To retrace our steps back to the grade multiplier: is it less than or greater than one?

            A question of more interest may be whether it is less than or greater than zero. After all, if the signalling value of grades is attenuating and thus decreasing overall market output, a logical analysis (consistent with aforementioned examples, theories, and deductions) would indicate a negative value.

            Of course, contrary literature exists alongside concurring data. You can argue for 1.5, just as you can go on either side of the balance with the government or tax multiplier. 

            A common counterargument is that employers do not value grades at all, so inflation (or compression) would not matter anyhow. The multiplier would effectively be wiped out in this case. This may be true for graduate students: with a 50/50 A and B curve¹, grades indeed do not seem to carry much signalling value in the first place.

            Or perhaps instead of searching for the grade multiplier, we should instead allocate our resources to a search for Lake Wobegon² - as this seems to be the destination that higher education is set for.

 

1. The standard curve for masters of business administration (MBA) graduate students at the Anderson School of Management at University of California, Los Angeles. 

2. The place where all children are beyond exceptional, from the 1985 novel Lake Wobegon Days.