The Two Factors That Explain The Popularity of Private Schools

The topic of private school enrollment provokes strong emotions. The decision to go private is seen as an assessment of the quality of the local school district (the schools are not challenging enough or they are unsafe) or an insight into the character of the parents who go private (they’re either selfish or racist). There may be instances where these negative assessments are valid but, in general, going private should be seen unemotionally as a standard consumption decision made by people who can afford to do so.

The last post was in response to a KQED story in which it was claimed that San Francisco’s high rate of private school enrollment was a legacy of desegregation efforts in the 1970s. I pointed out that San Francisco had a lower rate of private school enrollment in 1990 than it had in 1960. That was straightforward because I had run the numbers years ago. I then rather too casually asserted that high private school enrollment rates in the Bay Area were due to the high income levels here. One reader pointed out a problem: my theory didn’t explain why San Francisco had high rates of private school enrollment back in 1960 even when its family income level was closer to the state average. It was time to dig a little deeper and produce a more persuasive theory that can account for what we see today and what we saw back in 1960.

How Many Private School Students Are There?

The California Department of Education (CDE) tracks enrollment in individual public and private schools which are summed to produce totals by county. The Census Bureau publishes its own estimates for the total number of students in public and private schools in each county. The Census Bureau and the CDE are in rough agreement on the number of public school students but the Census Bureau thinks there are 627,000 private school students while the CDE counts only 500,000. The counties where the estimates diverge most include Riverside, Kern, Tulare, and Placer. In the absence of evidence that private schools in the Central Valley are systematically failing to report their enrollments to CDE, I’m going to trust the CDE’s numbers.

Using the CDE numbers, the percentage of K-12 students in private school statewide is 7.9%. Most of the inland counties are under 4% with Madera the lowest at 1.3%. Sacramento is at 7%. The coastal neighbors of Los Angeles, Orange, and Ventura are all around 10%. In the Bay Area, Contra Costa is at 8%, Alameda at 10%, Santa Clara and San Mateo at 16%, Marin at 19% and San Francisco at 30%. Unless you believe that the Central Valley counties have the best public schools, the argument that private school enrollment is a referendum on the local public schools is looking weak.

The Demand for Private Schools

Imagine you want to launch a business that requires your customers to visit your physical premises every day and that you want to charge a premium price for your product. Two factors are going to affect your choice of where to locate your business:

• how many people live near your proposed location

• whether those people can afford your product

Private schools are no different. We can predict private school enrollment by county using just two variables:

• Mean Family Income (i.e. the average income of households with children)

• Population Density (i.e. the number of people per square mile in the county)

The chart below compares the prediction derived from a linear regression of these two variables with actual private school enrollment rates from the CDE. R-squared is a statistical term that measures how well the regression models fits the actual data. An R-squared of 0.871 is astonishingly high considering that there’s no obvious relationship between income, density and private schools.

A few notes for the statistically minded:

• Both variables are statistically significant at a 99.99% confidence level.

• The enrollment numbers for public and private schools are based on where the schools are located. The enrollment rate calculation assumes that students attend school in the county where they live. That’s true for regular public schools but not necessarily for charter schools¹ (particularly online schools) or private schools. If a county has a large number of students in online schools, its public school enrollment would be overstated and the percentage in private schools would be understated. If one county’s private schools attract students from a neighboring county, this might distort the calculated private school enrollment rates for both counties.

• I’m using the density of the total population. Conceptually, there’s a good argument for using the density of K-12 students instead but this would not change the result very much (the R-squared would drop from 0.871 to 0.862).

• San Francisco’s population density is four times greater than that of Orange which is the second most densely populated county. If San Francisco mysteriously vanished, density wouldn’t be as significant a variable.

• As alternatives to Mean Family Income, I experimented with other measures of income such as Median Family Income or Mean Household Income or Mean Married Family Income or the percentage of families with incomes over $200,000. All would be statistically significant if used by themselves but Mean Family Income gives the best result.

• Mean Family Income is based on a sample of the population. As with any sample, there’s a margin of error and the margin is greater for counties with smaller populations. For Los Angeles, it’s $783; for Alameda, it’s $1731; for San Francisco, it’s $4,579; for Marin, it’s $8,494; for Tehama, it’s $21,149.

• I’m including all counties with at least 5,000 K-12 students. Since mean family income has a bigger margin of error in less populated counties, the more of those less populated counties we exclude, the stronger the relationship appears. If we focus on the 26 counties with at least 35,000 K-12 students, Marin becomes the smallest county, the counties we’re including still cover 93.4% of all students, and the R-squared rises to 0.93!

Does this work back in 1960?

1960 was 65 years ago. A lot has changed since then. The population has grown from 17 million to 39 million and is a lot more diverse than it used to be. Funding for public schools suffered long-term damage after the 1979 passage of Proposition 13. Some school districts endured years of upheaval as they implemented various desegregation strategies.

What do you think the private school enrollment rate was back in 1960? Well, the CDE does not have private school enrollment data that far back so we have to rely on the Census Bureau’s figures for each county. The 1960 Census showed the statewide private school enrollment rate at 9.6%, which is higher than the 7.8% that CDE calculates today (but exactly the same as the Census Bureau estimates today).

The counties with the highest private school enrollment rates back then were San Francisco (23.7%), Marin (13.7%), San Mateo (12.5%), and Los Angeles (12.4%). The first three were the highest in 1960 and remain the highest today. The counties under 3% in 1960 included Madera, Placer, Shasta, Siskiyou, and Tehama, which all still have very low rates today.

I ran a new regression using the 1960 private school data and the following independent variables:

• the population density of the county;

• the percentage of families with an income over $10,000 (Mean Family Income was not available).

To give a sense of scale, the Median Family Income in the state was $6,726 and 21.8% of families had an income over $10,000. There was no special significance to the $10,000 number: the census only published two income thresholds: below $3,000 and above $10,000.

This time, these two variables explained 78% of the variation in private school enrollment which is down on today’s 87% but is still very high. Notably, they predicted San Francisco’s extremely high private school enrollment rate almost exactly. I tried adding other variables, such as the percentage who live in urban areas, or the non-White share of the population, but these were not statistically significant.

The strongest evidence for the explanatory power of income and density is that they work in two such different time periods as today and 1960.

Conclusions

In economics, there is a distinction between microeconomics, which focuses on the decision-making of individuals and firms, and macroeconomics, which focuses on the economy in aggregate. Individuals make decisions in response to their particular circumstances and incentives. But if we’re analyzing the health of the economy, we pay attention to different variables such as inflation-adjusted interest rates or changes to investment rates.

Individual families send their children to private schools for many different reasons. They may attracted by smaller classes or different pedagogical approaches or more compatible parent communities. They may be reacting against decisions made by their local school district or be motivated by fears about the environment in their local schools. But if we want to know why overall rates of private school enrollment are what they are, we can zoom out from all that individual decision-making and just look at income and density.

Note

If you can think of a variable that might explain private school enrollment that I have not included, please let me know. I’d be happy to run the numbers. For example, keen eyes will note that Marin and Napa had higher private school enrollment rates than predicted in both 1960 and today while Contra Costa was lower than predicted both times. Why are they outliers?

More generally, this is the 3rd post in a row that was directly inspired by a reader email or comment. If you come across some education-related issue that might be addressable with data, please let me know. Fresh ideas are always welcome.

1. For example, Five Keys Independence High is a charter school notionally located in San Francisco most of whose students are adults in Los Angeles jails.