Stephen Richards and Dr. Eric Eide, Department of Economics

The humorist Dave Barry has said, “The one thing that unites all human beings, regardless of age, gender, religion, economic status or ethnic background, is that, deep down inside, we ALL believe that we are above-average drivers.”

I think he’s right, but I presume to add a considerably less funny addendum: We are also united in our certainty that we know just how to “fix” public education. For some, the solution seems to be merit-based pay; for others, revolutionary standardized testing will do the trick. For others, class sizes are key.

Of course, public education is certainly far too complex to have a single, simple solution. Efforts to improve outcomes in public education, therefore, should begin by identifying what is associated with those outcomes and then moving forward to identifiable solutions. In my Honors thesis, funded by an ORCA grant, I apply four models of regression analysis to data from approximately 100 Utah high schools to identify and describe the relationship between graduation rates and minority rates. I ask whether the two are associated, what the magnitude of that association is, and whether that association is stronger at one end of the distribution of either minority rates or graduation rates. To answers these questions, I apply ordinary least squares regression, quantile regression, a random effects model, and a profit model.

Few issues in public education have larger economic implications than high school graduation rates. The Census Bureau estimates that students who graduate with a high school diploma but who do not pursue a college education will over the course of their lifetimes earn $200,000 more than students who drop out of high school. This figure rises after accounting for the likelihood of students attending an institution of higher learning.

However, despite broad agreement that the returns to education are high, experts are divided on how exactly to expose more students to those returns. That is to say that there is not a clear policy path to improving high school graduation rates. Many exogenous changes to graduation requirements and funding do not seem to have the desired effects. In this research, rather than identify the effects of exogenous changes, I describe the relationship between a demographic characteristic of my data (minority rates) and an outcome (graduation rates).

What do four types of regression analysis reveal about the interaction between minority rates and graduation rates in Utah high schools? I state my original research questions to discuss the results of my regression analysis.

8.1 Are changes in the minority rate at a given school associated with changes in that school’s graduation rate? If so, what is the magnitude of those changes, and does the relationship differ significantly across years?

Increases in a school’s minority are highly associated with decreases in that school’s graduation rate. OLS regression estimate the coefficient on minrate to be -.533, -.34, and -.353 across all schools in 2007-2008, 2008-2009, and 2009-2010, respectively. That is, increases in the minority rate of 10 percentage points would be associated with decreases in the graduation rate of 5.3, 3.4, and 3.5 percentage points, respectively. These coefficients increase dramatically when alternative schools are included, but it is worth noting that the lower coefficients (traditional schools only) were still significant in 2007-2008 and 2009-2010.

In almost every sense, 2008-2009 is an odd year. It produces less significant and smaller (in absolute terms) coefficients in OLS, no significant coefficients in quantile regression analysis, and a very different set of probabilities in the profit analysis. The reasons for these differences are unclear.

8.1a Is the relationship between graduation rates and minority rates different at different places along the distribution of graduation rates, or alternatively, along the distribution of minority rates?

Quantile regression specified to the first and third quartiles tells three very different stories. In 2007-2008, the coefficient on minrate is highly significant—and very, very large—at the first quartile (for both datasets—traditional only and traditional + alternative), but significant at the third quartile only when alternative schools are in the dataset. Conversely, in 2009-2010, the coefficient on minrate is significant only at the third quartile. Further, in 2008-2009, the coefficient on minrate is never significant at the first or third quartiles, even when alternative schools are included. That is, looking at the 2007-2008 data, schools with low graduation rates seem to be most affected by high minority rates. In 2009-2010, schools with high graduation rates are most affected. And in 2008-2009, schools at the conditional mean are most affected.

The story becomes even less clear when I divide the dataset at the mean of minrate to try to tease out significant coefficients at either end of the distribution of minority rates. It doesn’t work, though—the only significant coefficient is for schools below the mean of minrate in 2007-2008.

The magnitude of my coefficient of interest varies wildly as well. It climbs as high as -.75 when measured at the first quartile of all schools in 2007-2008, but falls as low as -.129 when measured at the third quartile of all schools in 2009-2010 (both of the above results were significant at the 1% level).

The reasons for these variations are unclear: most likely, the dataset is simply too small to correctly describe the underlying relationships. Alternatively, the relationships may simply vary over time.

8.1b Does the magnitude of the relationship change if the data are treated as a panel?

The statistically significant relationship between graduation rates and minority rates holds when the data are considered a panel in a random effects model. The coefficient of interest is -.287 and is significant at the 1% level.

8.1c Given a level of minority rate, what is the probability that a school has a high graduation rate?

A profit model shows, unsurprisingly, that schools with low minority rates are the most likely to have high graduation rates. The decrease in this probability as minrate increases accelerates, then decelerates in 2007-2008 and 2009-2010, but remains relatively constant in 2008-2009.