Effect of Any PBF Program

model to help deal with the endogeneity problem due to potential non-random adoption. I account for two possible sources of endogeneity, one relating to trends among all public colleges and another relating to trends in states who adopt performance funding.

The first source of endogeneity arises because PBF could potentially be adopted in re- sponse to an overall decrease in public college performance. However, this decrease could be due to nationwide trends. Changing tastes of students could change the composition of students who decide to attend public colleges. If nationwide, public college outcomes started to deteriorate and then subsequently improved, passage of PBF when outcomes are at their worst could result in the improvement incorrectly being attributed to PBF. To deal with this issue, I account for nationwide public college trends by comparing the effect of PBF on public colleges in states with PBF to states that have not adopted PBF.

The second source of endogeneity arises if state-level trends affect the adoption of PBF. Suppose colleges in a state had unusually bad outcomes for a few years and then returned to normal levels a few years later. If the government of this state reacted to the bad outcomes by implementing PBF, it would appear that PBF had a large effect on outcomes. However, if the real reason these outcomes changed was due to cohort effects, it would be wrong to attribute the improvement to PBF. To deal with this issue, I account for state specific trends common among states who adopt PBF by comparing the effect of PBF on public colleges to private colleges in the same state. According to Hillman and Weichman[2016], the median four-year public college student attends a college located 18 miles from their home and the median four-year private college student attends a college located 46 miles from their home. This suggests that the majority of students in both public and private colleges are in-state students, hence both types of colleges are subject to the same cohort effects and other statewide trends. When contrasting the improvements in public colleges to that of private colleges, private colleges act as a control. Using private colleges in this way is possible since PBF changes do not affect the funding that private colleges receive from the government. Therefore, differential improvements to outcomes seen in public colleges can be attributed to PBF.

following form:

Y_i,s,t =β0+β1Gi·Es,t+β2Es,t+Gi·δtG+δi+δt+β3Xi,t+εi,s,t, (2.1)

whereY_i,s,t denotes the outcome of interest for collegei, located in states, in yeart. E_s,t

is an indicator which takes on a value of 1 if PBF is in effect in state s at timet and 0 otherwise. G_i is an indicator equal to 1 if college i is public. The vector of covariates introduced in Section2.3is denoted by Xi,t. δiare college-level fixed effects,δt are year fixed effects, andδ_tGare public college specific year fixed effects. εi,t is the error term.

The triple-difference setup utilizes three layers of difference: difference between pu- blic and private colleges, difference between states who adopt PBF and states who do not, and difference before and after PBF is adopted. Because the performance funding pro- grams are enacted at different time periods, the variableE_s,t is used to indicate when PBF is in effect at timet for state s. This term is identical to the interaction term of post and treatment that is traditionally included. The inclusion of college-level fixed effects account for the public-private term,G_i, and the treatment indicator. The time fixed effects account for the post indicator.

College-level fixed effects are included to control for time invariant college level dif- ferences which may impact outcomes, such as location, public status, and Carnegie Clas- sification of Institutions of Higher Education.9 Year fixed effects are included to control for time variant factors which affect all colleges, such as yearly changes in federal college aid programs. In addition to the overall year fixed effects, the regression includes separate year fixed effects for public colleges. Inclusion of two types of year fixed effects cont- rol for any separate nationwide trends that may be occurring in either public or private colleges.

9_{Carnegie Classification of Institutions of Higher Education sorts colleges into categories of roughly}

comparable institutions.

The coefficient of interest,β1, estimates the impact of performance funding on public

colleges. In addition to controlling for public-college trends, endogeneity is controlled for by accounting for state-level trends common among states that adopt PBF. State-level trends occurring after the adoption of PBF that affect both public and private colleges are controlled for through inclusion of the termEs,t. Due to this term, effects common to both types of college do not effect the estimate ofβ1and instead are seen in the coefficientβ2.

The identification of β1 does not solely come from the adoption of PBF programs.

In practice, some states see multiple funding transitions, from non-performance-based funding to performance-based funding and from performance-based funding to back to non-performance-based funding. This meansβ1is identified by changes in outcomes that

occur following states’ adoption of PBF and also through states’ abolishment of PBF. In my sample, there are 14 adoptions and 8 terminations of PBF. In the next estimation strategy, I analyze the differential effect of funding amount. Since the funding amount associated with each PBF program changes often, concerns about limited variation are addressed by including performance funding amount.

To support the usage of a triple-difference model, Figure2.1shows four parallel trend graphs. These graphs provide an opportunity to test the validity of the assumption of similar trends in advance of PBF adoption. The variable on the x-axis is the number of years relative to the year PBF was adopted. Year 0 is normalized to be the year PBF first went into effect. On the y-axis the graphs plot the average residual, obtained from running the regression specified in Equation (2.1) without the termGi·Es,t, for each of the four incentivized outcomes. Before enactment of PBF, the movements of the public and private lines for completion, research, and progression mirror each other. The year- to-year movements for efficiency are not as close as the other three outcome variables, but the overall trends before enactment are similar. These similar patterns suggest that the parallel trend assumption is valid in this situation. Once the performance funding program

Figure 2.1: College Trend In Incentivized Outcomes Relative to PBF Adoption

Notes: Year 0 is normalized to be the year PBF first went into effect. Other years values are in reference to this adoption year. The y-axis refers to the average residual, obtained from running the regression specified in Equation (2.1) without the termGi·Es,t, for each of the four incentivized outcomes.

is enacted, public colleges see a large increase in completion and progression. These differences disappear as time passes. The temporary nature of these effects may be due to the fact that some states abolish PBF and return to other funding methods. In addition, since some PBF implementations occurred relatively recently there is not information on the effect of outcomes many years after PBF was implemented. The compositional change that occurs when these states drop out of the sample may also contribute to the decrease

observed a couple of years after PBF is adopted. The gap in amount of research spending grows following PBF adoption, with public college spending decreasing while private college spending increases. The public college efficiency measure does not change much following the PBF adoption.

As a robustness check, I run the following regression separately for private and public colleges:

Y_i,t =β0+β1Es,t+β3Xi,t+δi+δt+εi,t. (2.2) Private colleges receive relatively little state funding and are not directly affected by fun- ding changes. In Equation (2.2), the coefficientβ1 reveals the average effect of PBF in

reference to colleges in states without PBF. Identification in this model comes from the differential timing of performance funding adoption and termination. If the change in out- comes is actually due to the change in public college funding, then in a regression run on a sample of only on private colleges the estimate ofβ1 should not be significant. On the

other hand since public colleges are affected, then in a regression run on a sample of only public colleges the estimate ofβ1should be significant.

2.4.1.2 Performance Funding Amount The amount of state college appropriations