Wednesday, August 25, 2010

The Littlest Redshirts Sit Out Kindergarten

New York Times article "The Littlest Redshirts Sit Out Kindergarten" (August 20th, 2010) discusses the "redshirting" of kindergarteners, the practice of holding them back a year so they have an age advantage. Corrections is dubious that the practice could become a problem, and that it will wane, despite "the signs."
“Redshirting” of kindergartners — the term comes from the practice of postponing the participation of college athletes in competitive games — became increasingly widespread in the 1990s, and shows no signs of waning.
The Times doesn't articulate the tradeoffs that altruistic parents face when deciding when their children will enter school. Children gain some initial advantage entering Kindergarten later because they are older and more mature, and they may gain a measure of happiness by not entering into school immediately. What they lose is that year of their life that they might have spent working or retiring. There are two important empirical questions the Times should have addressed when discussing this issue. First, whether or not there is an advantage to entering kindergarten late, and if so, the time-profile of this benefit. Second, whether or not the net present value of the time profile for benefits due to entering early is greater than, or less than, the net present value of the time profile for benefits due to not entering early.

What are the benefits to entering class early, assuming there are any? On the one hand, if the "alpha dogs" of a class get a larger share of the resources, confidence, and attention, then we might expect benefits to late enrollment to explode over time. Alternatively, if students enter with a fixed advantage and all students learn equally over time, then the benefits to being a year older than one's peers decays over time. Two prototypical time paths are displayed graphically below (click to enlarge). The plot simply shows an advantage, measured initially at 1, and its decay or growth over time. The black line separates two answers to our second question. If a plot stays above the black line, then benefits grow or stay constant, and below, benefits decay or stay constant.

Evidence indicates that the blue line of decaying benefits is the empirical reality. Elder & Lubotsky find that benefits are relatively short lasting in "Kindergarten Entrance Age and Children's Achievement, Journal of Human Resources" (2009) (gated) (ungated). The authors use exogenous changes in state age cutoffs and consequential differences between predicted and actual entrance ages to produce identification (a counterfactual).

Elder & Lubotsky indicate that there are benefits, however fleeting. What are the costs? Earnings rise as one gets older (falling as one enters retirement age). Inspired by Empirical Age-Earnings Profiles (Kevin M. Murphy and Finis Welch, Journal of Labor Economics, April 1990), Corrections offers a similar treatment, using historical cohort averages of earnings from the Current Population Survey (available at the Census Bureau). We use the data (not plotted) to fit a cubic polynomial of earnings over time or age for cohorts born in 1940 or 1950, displayed graphically below. The first plot has earnings (all earnings in current dollars) by age (click to enlarge) the second plot has earnings by year (click to enlarge). Both plots use median data from males only (all races).

To overcome the cost of putting off one's earnings profile by one year, how much would an individual born in 1940 have to be paid? In this primitive analysis, ceteris paribus, if the net present value of putting off one's education is greater than $8,500, an individual should do it.

Corrections might further add that even if the trend has been increasing, it is likely to find some equilibrium. As the proportion of "alpha-dogs" increase, their allotment of resources above the baseline presumably decreases--the benefits of postponing decrease, while the costs, as discussed above, remain the same. This leads to an interior equilibrium, (the equilibrium proportion of late-entrants is .247, the point of intersection) as displayed below (click to enlarge). In this case, no benefit is gained to waiting, and individuals are indifferent to waiting or not.

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