# Is there really a school-to-prison pipeline?

**1. Can we really say there is a school-to-prison pipeline? And if so, what’s “pumping” it?**

The notion of a [school-to-prison pipeline][1] is increasingly popular in the discourse of a wide coalition of U.S. activists fighting mass incarceration and defending public education. The concept is invoked by groups such as the [American Civil Liberties Union][2], the Justice Policy Center, and the [New York Civil Liberties Union][3] (NYCLU). Here in Pennsylvania, [DecarceratePA][4] and friends in Occupy Philly invoke this image especially in protest of Governor Corbett’s budget priorities, arguing that state spending favors the prison system at the cost of public education.

Despite the popularity of this pipeline imagery, it remains only a hypothesis. [Skiba et al. 2003][5] find some evidence that higher school suspension rates are correlated with higher juvenile incarceration rates, but the data is cross-sectional and limited in other ways that preclude confidence in a particular causal story. In a 2009 study, [Hood and Lopez][6] 2009 find that racial composition of school discipline is not related to the racial composition of juvenile incarceration. In any event, confidence in the argument seems far greater than current research allows, and at worst this could be an erroneous and merely rhetorical hook. Given that the American prison system is probably nothing short of our era’s very own[ Jim Crow][7] regime, the school-to-prison pipeline hypothesis is worth analyzing more scrupulously.

**2. A simple model: Is rising inequality “pumping” resources from education to incarceration?**

****The question of whether there is a school-to-prison pipeline begs the question of why there would be a school-to-prison pipeline. Lacking is a specifiable political explanation. One possible explanation is that_ rising income inequality in the United States encourages policymakers to divert funding from education to incarceration_. Why? Classic political economy models of redistribution suggest that as income inequality increases, the median voter increasingly prefers higher taxation and public spending. Because elected policymakers aim to satisfy the pivotal median voter, redistribution should be positively associated with inequality. However, it’s also well known that many factors often neutralize or reverse the link between inequality and redistribution. For instance, income inequality can enable the rich to simply capture the government. A combination of these two models can explain how there could be a systematic spending dynamic between education and incarceration. As income inequality increases and the rich gain political power relative to the poor, policymakers have much to gain from the rich, and little to lose from the poor, by cutting taxes and social spending. Although the poor face decreasing political power, we might expect that beyond some threshold, where the poor “have nothing to lose but their chains,” cuts to essential social services would indeed be severely punished–by, say, revolutionary upheaval. Therefore, as policymakers cut essential social spending, they should also alter the_ composition_ of social spending in a way that also pacifies a rising threat of rebellion.

In summary, perhaps rising income inequality (government capture by the rich and the political alienation of the poor) leads policymakers to divert spending from redistributive programs (public education) to programs of outright and coercive pacification (incarceration), not only further excluding the poor from political participation (the formal disenfranchisement of felons) but also literally, forcibly containing the threat of rebellion against the political system itself.

**3. Data**

****I’ve collected time-series data from the United States for the past 60 years to examine whether there is, or has been, some sort of systematic relationship between education and incarceration. Most of the data is culled from the [Census Bureau historical abstract][8] and usgovernmentspending.com. To extend the Census Bureau historical data past 2001 or so, I do some simple linear interpolations using more up-to-date Census Bureau time series (which go up to 2009 but extend back and overlap the early 2000s cutoff of the historical abstract). In any event, I’ve uploaded all of the data to Google Fusion Tables for [download][9] lest anyone wants to investigate further. The inequality variable is share of income going to the top 5% percent minus the share of income going to the bottom 5%; education spending per capita is total public spending per capita on elementary, secondary, and tertiary education; the incarceration variable is the number of people incarcerated per 1000 people (interpolated for some years with a slightly different measure, that of the total number under some form of supervision; this is a little awkward but it’s a blog post, not a journal article, right?) The final variables used here are found in the last few columns of the Google Fusion table.

The timespan analyzed here implies a much stronger version of the argument than is popularly articulated: evidence that a school-to-prison pipeline has not existed for several decades would not disprove many more limited versions of the argument. However, evidence of the harder-to-prove, stronger claim of a pipeline dynamic that holds across the past half-century would be even stronger support for today’s more limited claims.

caption id=”attachment_74” align=”alignnone” width=”600”(http://justinmurphy.wordpress.com/2012/05/26/67/school_prison_inequality-5/) The first graph illustrates the puzzle of increasing incarceration and decreasing crime. The second graph shows that inequality appears to track incarceration./caption

**Evidence**

The concept of a “pipeline” poses an interesting challenge for how we think about causality and statistical modeling. At a minimum, it seems to imply a negative relationship between two variables, an egress from a source and a flow into a sink, possibly driven by some third quantity representing the pressure or energy pumping the pipeline. There are certainly several ways one could approach modeling such pipeline between education and incarceration, but as a first cut, I test and find some evidence of relationships that together suggest the possibility of something that could reasonably be called a school-to-prison pipeline. The claims are followed by some fairly technical statistical output but with some non-technical notes for interpreting them.

**Year-to-year increases in the incarceration rate are correlated with year-to-year decreases in education spending per capita**, even after controlling for economic growth (GDP per capita) and any simple, secular trend over time. A common problem from modeling time-series data is that the variable one wants to explain is often so much a function of its previous years’ values that it’s easy to find spurious relationships with other explanatory variables. So all of the models below include a combination of lagged dependent variables or transformed variables (and pass traditional tests of significant serial correlation in the dependent variable).

2. **Year-to year increases in inequality are also correlated with year-to-year decreases in education spending per capita, although it is not clear if inequality itself correlates with decreases in education spending beyond its correlation with the incarceration rate. **This is because when both inequality and incarceration rates are included in the same model (not displayed), Inequality drops out of statistical significance and Incarceration_Rate remains significant. It’s possible that both have independent and separate negative effects on education spending but a full model can’t sort out independent effects from two explanatory variables that are themselves highly correlated (high collinearity). Nonetheless, changes in the incarceration rate seem directly correlated with decreases in education spending. Inequality may or may not

- If rising inequality is the pump of the pipeline, it would make sense that inequality itself is not directly, independently correlated with education spending. If increases in incarceration are associated with decreases in education, the model sketched above suggests rising inequality might very well explain most directly changes in the incarceration rate.
**Inequality is positively associated with increased incarceration, controlling for the crime rate, previous incarceration rates, and secular trend.**This is true whether or not one looks at levels or year-to-year changes. The interaction of crime and inequality (crime rate multiplied by inequality) also appears to have a systematic relationship to the incarceration rate, suggesting that neither inequality nor crime alone drive incarceration but that perhaps crime is a trigger for incarceration that is conditional on the degree of inequality–also consistent with the model sketched above.

- Conservatives might claim that the notion of a school-to-prison pipeline is a misleading interpretation of the culture of poverty, in which the poor are thought to simply opt for crime over educational aspirations, requiring greater incarceration and less spending on education, which in turn leads the rich to get richer compared to an increasingly incarcerated poor. But there’s no evidence for these claims: when all these variables are considered in one system of equations (vector autoregression or VAR), effectively allowing each to cause each controlling for the effects of the others,
**there remains evidence that inequality drives the incarceration rate and no evidence that crime or incarceration is driving inequality.**It could be that crime and incarceration have an immediate effect on inequality or are highly collinear, and that either of these facts make its effect on inequality statistically indistinguishable–and for this reason it’s no surprise the relationship between incarceration and education spending drops out–the key point of the table below is simply that inequality’s effect on incarceration is robust against the conservative arguments to the effect that inequality is a fair outcome rather than a driver of unfair outcomes.

Below are overlaid impulse-response functions. The first graph displays the predicted effect that some exogenous shock on inequality has on education spending, compared to its effect on the incarceration rate. Moving from left to right across the x-axis charts the decay of the effect over time. Of course, this assumes that our VAR was a fully and correctly specified model, which is unlikely. Nonetheless, as a back of the e-napkin analysis, it’s interesting to note that an exogenous shock to inequality has a positive and statistically significant effect on incarceration.

The second graph shows that an exogenous shock to inequality has a far larger effect on the incarceration rate than an exogenous shock to the crime rate.

[1]: http://en.wikipedia.org/wiki/School-to-prison_pipeline [2]: http://en.wikipedia.org/wiki/American_Civil_Liberties_Union [3]: http://en.wikipedia.org/wiki/New_York_Civil_Liberties_Union [4]: http://decarceratepa.info/ [5]: http://www.zerotolerancereform.com/wpblog/wp-content/uploads/2010/12/Harvard-Civil-Rights-Project.pdf [6]: http://healthpolicy.unm.edu/sites/default/files/documents/Untangling%20the%20School%20Segment%20of%20The%20School-to-Prison%20Pipeline.pdf [7]: http://www.amazon.com/The-New-Crow-Michelle-Alexander/dp/1595586431/ref=sr_1_1?ie=UTF8&qid=1337506101&sr=8-1 [8]: http://www.census.gov/compendia/statab/hist_stats.html [9]: https://www.google.com/fusiontables/DataSource?docid=1TsYrSeGBV-mZSvJy0hRRHbUx4aEZoxrZgrymXTI

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Murphy, Justin. 2012. "Is there really a school-to-prison pipeline?," https://jmrphy.net/blog/2012/06/10/67/ (September 9, 2018).