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Adventures with Price Indexes

March 18, 2011

Rather than bore you with the details of our recent report highlighting problems with the Higher Education Price Index (HEPI) and the Higher Education Cost Adjustment (HECA), we thought we’d tell you about recent developments concerning lunch at the Center for College Affordability and Productivity (CCAP).

Contract negotiations at CCAP typically involve plenty of Janx Spirits and closely resemble Ford Prefect’s favorite drinking game. After winning the previous round against our boss, we insisted on a lunch per diem. We decided that we would construct the Lunchtime Cost Index (LCI) so that we would know how much the per diem should be each week.

Everything was going smoothly, until one day, while eating our now routine steak and scotch lunch at Smith and Wollensky, we realized that CCAP was in dire financial straits. We conducted a thorough analysis to determine the cause of this unexpected turn of events. It turned out we were spending an inordinate amount of money on the newly established lunch per diems. We studied charts showing that the per diems, adjusted by the LCI, were relatively stable. And yet here we were, running out of money.

With little else to be done, we brought in consultants to get to the bottom of things. The final ValueLandShackWoodenShowerRepair, LLC report (we couldn’t afford the better-known PricewaterhouseCoopers) pointed out that when determining the cost of the per diems to CCAP, it was inappropriate to adjust them by the LCI. Doing so indicated the cost of the per diems relative to the cost of lunch (assuming the LCI accurately gauged the cost of lunch), but what we wanted to know was the cost of the per diems relative to everything else in the budget – something that a lunch-specific price index could not reveal.

Moreover, it turns out that the LCI was not even a good measure of the cost of lunch, because it was biased whenever there was a change in productivity, whenever substitution occurred, whenever quality changed, and because it was self-referential.

Prior to the lunch per diem, Andrew and Jonathan would trek to Subway and order an a la carte meatball sub every day ($5.00). The LCI was supposed to tell us the cost of maintaining a meatball sub’s worth of lunch. However, shortly after CCAP introduced the per diem, Subway introduced value meals. Now, we could get chips and a drink with our sub for the same $5.00. Theoretically, the LCI should have registered this as a decline in the cost of a meatball sub’s worth of lunch. But since we were still spending $5.00 at lunch, and the LCI was determined by asking how much the standard meatball sub option at Subway costs, the LCI reported that the cost of lunch was unchanged. Economists would say that the LCI missed the productivity increase -- more output (lunch) for the same input ($5) - and was therefore biased upward.

The following month, Subway raised the price of their meatball sub meal to $6.00. Quizno’s, however, did not. The price of their meatball sub meal remained at $5.00. Jonathan and Andrew started buying Quizno’s subs instead. However, the LCI continued to ask how much a meatball sub at Subway costs. By failing to account for the substitution from Subway to Quizno’s when their relative prices changed, the LCI was again biased upwards (reporting an increase when actual spending was unchanged).

The astute staff at CCAP quickly diagnosed this particular problem, and changed the methodology of the LCI from just the cost of a meatball sub at Subway to tabulating lunch costs wherever they were spent. In retrospect, this merely caused other problems.

Since Jonathan and Andrew were used to spending $5 out of pocket prior to the per diem, after they started receiving the per diem, it wasn’t long before they started to buy higher-quality meals. They were still willing to spend $5 out of pocket on lunch, which with the per diem meant that they could now spend $10. They started off upgrading to chicken subs at Subway and Quizno’s. These higher-cost subs would then drive up the LCI, and as the LCI grew, the per diem grew.

Of course, the cost of a meatball sub's worth of lunch hadn’t changed, but as higher-quality subs were ordered, the LCI was unable to disentangle the different effects. Because the LCI did not hold the quality of lunch constant, it was unable to distinguish between (1) cost increases due to changes in the quality of lunch and (2) cost increases due to higher prices for a given lunch.

The last problem we discovered was that our actions affected the LCI. As the per diem increased, it wasn’t long before Jonathan and Andrew began venturing beyond Subway and Quizno’s. Each move resulted in higher spending, which led to a higher LCI, which led to a higher per diem, which then spurred us to go to a better restaurant, starting the cycle again. The LCI kept increasing, not because the cost of lunch kept increasing, but simply because we spent more. In other words, the LCI was self-referential. It wasn’t long before we were eating a steak and scotch lunch at Smith and Wollensky every day.

Our consultants suggested that rather than creating a highly specific price index with all these problems, we should just use what everyone else uses 90 percent of the time, the Consumer Price Index (CPI). While the LCI was useful in answering some questions that were specific to CCAP lunch patterns, it was not at all appropriate to rely on it as a gauge of how much lunch should cost.

Sadly, before this sensible change could be implemented, Jonathan and Andrew lost the next round of contract negotiations, and with it, their lunch per diem. In fact, as punishment for the lost revenue, Jonathan and Andrew are required to write more op-eds. Fortunately, they’ve discovered that fiction can at times be easier to write than nonfiction.

Ridiculous as this may seem, our lunchtime escapades are not too far off from what has been occurring with HEPI and HECA in the higher education industry. In addition to both of them suffering from quality, productivity, and substitution biases, the HEPI is self-referential. Even more importantly, because of what they measure and how they measure it, their actual usage deviates substantially from their appropriate usage.

For more details, see our recent study.

Bio

Andrew Gillen and Jonathan Robe are underfed, and conduct research at the Center for College Affordability and Productivity

 

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