Jeff Naecker In data we trust.           Research     Teaching     Blog     CV

States spend on average nearly 3 times as much per prisoner as they do per K-12 student

Inspired by this tweet, I went looking for a graph of state spending on students and on prisoners. I found a couple graphics which I felt could have been done better, so I made my own version.

I found state-by-state data on correctional department spending per prison inmate from vera.org (see figure 4). I found roughly corresponding data on per-pupil K-12 education department spending from the U.S. Census (see table 8).

It is important to note that the prison spending data is from 2010 but the education spending data is from 2013. Comparing across years like this is somewhat dangerous, because the economic and political climates in each state might be very different in those time periods. However, this is the best I could find. Also, there is complete data for only 40 states.

Here is the resulting graph:

Here’s how to interpret the graphs: Each data point is one state. The x-axis is the state’s corrections department spending per prisoner, while the y-axis is the state’s education departments spending per student. If you hover over the state’s data point, you can see the exact numbers for per-prisoner and per-pupil spending, as well as the ratio.

The grey dashed lines indicate where the ratio of per-prisoner to per-student spending would be 1:1, 2:1, 3:1, and 4:1. Note that every state spends more per prisoner than they spend per K-12 student. The highest ratio actually belongs to California, at 5.14:1. The average ratio across the 40 states with complete data is 2.9:1.

The code and data for this graph can be found here.

New Working Paper: Observability Increases the Demand for Commitment Devices

I recently completed a new paper with my friend and classmate Christine Exley. The paper addresses an issue that has gotten much attention in the experimental economics literature: commitment devices.

To understand what I mean by a commitment device, let’s take a step back and talk about time preferences more generally. Suppose you are planning your activities for the coming day or week. It would be strange to limit your options of activities without some form of compensation. Yet that is exactly what we see people do in a variety of settings: They voluntarily open savings accounts with restricted access to their own cash. They choose wage contracts that are strictly dominated. They choose to set early deadlines for classroom assignments.

One possible explanation has been very popular in recent literature: people suffer from present-bias, which essentially means they lack perfect self control. That is, they have trouble following through on activities in future that they know are good for them in the long run. A widely-used model of this problem imagines that you are playing a game with your future selves: you all agree what the best outcome is, but each version of yourself would prefer to push off the hard work to tomorrow’s version. So, it then makes sense for today’s version to force tomorrow’s version to take the action. Thus people put money in lockbox account to force their future self to save. They choose a goal-oriented wage contract or early deadlines to prevent tomorrow’s self from shirking. These are all examples of commitment devices.

The plethora of lab, field, and theoretical work on this model leaves little doubt that present bias is a real phenomena, or that it is driving commitment demand in many settings. In our paper, Christine and I note an interesting phenomenon in a field experiment: increasing observability of the commitment choice leads to greater demand for that device. If demand for commitment devices were driven by present bias alone, the observability of the level of commitment should have no effect on the choice itself.

In our experiment, students signed up for workshops at a campus center through a website that we set up. After indicating which workshop they wanted to go to, our website offered them the following prospect: If they attended the workshop they had selected, they would receive a gift card for \$15.00. If they did not attend, they would receive an amount of their choosing between \$0 and \$15.00. If they wanted to commit themselves to going (at least partially), they could choose to receive less than the full amount. And many students did, putting about \$5.00 on the line on average. This was our private treatment.

For a second treatment group, we then made a very simple change: The amount they choose to forgo would be made public to the people running the workshop. This small change increased the average commitment choice to almost \$9.00 on average. Our hypothesis is that at least some of the students in our experiment chose to commit themselves in order to signal something about themselves: they were interested in the center’s mission, or that they knew that failing to follow through with their actions was a bad thing.

The takeaway message from this field experiment is simple: We may be looking for present bias when there are other mechanisms at play. Returning to the examples I cited earlier: People may choose lockbox accounts to show others that they value saving. They may choose restrictive deadlines or goals to signal to their boss or teacher than their are dedicated and conscientious workers. When running experiments such as these, we need to be cautious about inferring that these actions are driven necessarily by time preference issues. If we are not careful, our estimates about the prevalence of present bias or the parameters of time preferences may be biased.

The Making Of

When I set out to make this site, I was interested in a minimal structure that used tools I was already familiar with. I settled on Jekyll, because I could write pages and posts in Markdown and use Github for hosting.

I started by building a very basic site following the documentation on Jekyll. However, I soon found this tutorial from Joshua Lande, and found it incredibly helpful. It walked me through setting up the site with Poole, a very clean and beautiful fork of Jekyll. I recommend this tutorial to anyone looking to build a similar site to mine. Below I’ve noted a couple small details to supplement Josh’s extensive walkthrough.

MathJax support

MathJax is a Javascript library that allows for live rendering of LaTeX-like equations. I wanted this feature to be able to include nicely formatted equations in my posts, like this:

To add MathJax support, I put the following in _includes/head.html :

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js"></script>
<script>
MathJax.Hub.Config({
            config: ["MMLorHTML.js"],
            extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
            jax: ["input/TeX"],
            tex2jax: {
                inlineMath: [ ['$','$'], ["\\(","\\)"] ],
                displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
                processEscapes: false
            },
            TeX: {
                TagSide: "right",
                TagIndent: ".8em",
                MultLineWidth: "85%",
                equationNumbers: {
                   autoNumber: "AMS",
                },
                unicode: {
                   fonts: "STIXGeneral,'Arial Unicode MS'" 
                }
            },
            showProcessingMessages: false
        });
</script>

The configuration script is not necessary, but it make the typesetting a little prettier, and allows me to typeset inline equations (ike this one: $y = f(x) + z_0$) by surrounding the LaTeX code with single dollar signs.

Domain name hosting

Perhaps the single best feature of Jekyll is that you can host your site for free on Github pages. So, my site is hosted on Github at jnaecker.github.io, simply by virtue of having my site’s repository pushed to Github. I got the domain name jeffnaecker.com from Namecheap. Here are directions on setting up your custom domain with Github pages.

You might notice that the url of this page is jeffnaecker.com/blog/the-making-of, not jeffnaecker.com/blog/2014/09/07/the-making-of. To get the simpler URL, I set the permalink entry in _config.yml to /blog/:title. For more details, see the comments on Josh’s post on this issue.