We study belief accuracy in a centralized higher-education admissions system using Norwegian data that combine a large pre-admission expectations survey with administrative records on offers, enrollment, and completion. Program-specific cutoffs provide a fuzzy regression discontinuity design that identifies objective counterfactual outcomes at the admission margin and allows direct comparison with subjective, state-contingent beliefs (first-choice access versus the relevant second-choice offer state). We find that enrollment forecast errors are driven mainly by mistaken beliefs about offer probabilities, while beliefs about enrollment conditional on an offer are comparatively accurate. For completion, the dominant error is persistence optimism: applicants substantially overestimate completion conditional on enrollment under both access states. Applicants also overstate first-minus-second returns for both enrollment and completion. These errors are economically meaningful for choices: in a partial-equilibrium counterfactual exercise, correcting beliefs implies large declines in the predicted probability of keeping the currently ranked first choice on top.
A first draft of “Getting In and Getting Through: Ex Ante Beliefs and Counterfactual Outcomes in Centralized College Admissions” is now available!
How does college education shape entrepreneurship? We first document striking differences between college fields in the share of students becoming entrepreneurs. We then leverage quasi-random variation in college admissions near GPA-based thresholds to study the causal impact of the college environment on subsequent entrepreneurship. Exposure to more entrepreneurially intensive college programs, measured as a higher share of entrepreneurs among alumni, substantially increases the probability that a student starts their own business.
An extensive revision of “College admission as a screening and sorting device” is now online!
We have added i) a theoretical model to motivate the empirical approach of the paper and interpret the findings, ii) a new reform analysis that validates the model using an alternative design, iii) new heterogeneity analyses, and iv) an updated screening and sorting decomposition.
This is the abstract:
This paper examines how performance-based funding incentives influence college admission decisions in dual-track systems where programs admit students based on either grades or holistic assessment. Using Danish administrative data and regression discontinuity methods, we find that programs respond effectively to funding incentives by equalizing marginal completion rates across admission tracks. A reform removing restrictions on holistic admissions confirms this – previously constrained programs exhibit completion rate gaps across tracks that close once allowed to optimize freely. However, this institutional optimization comes at a broader social cost – rejected holistic applicants are 6.4 percentage points less likely to complete higher education elsewhere. The largest potential social gains from expanding holistic admissions are in selective programs and those currently making least use of this track. The benefits of holistic admissions arise mainly through advantageous self-selection of higher-potential students, with little additional screening benefit.
This paper reconciles different approaches to estimating the labor market effects of children. Combining elements from event study and instrumental variable estimators we find that while both approaches estimate a 15 percent child penalty, they differ in what drives this gap. The standard event study attributes the penalty primarily to reduced maternal earnings, but our results suggest maternal changes account for less than half. We show that women time fertility as their earnings profile flattens, causing the event study to overestimate the maternal penalty. This finding has broader implications for event-study designs, as pre-trends may be uninformative about selection bias.
Propensity score matching implicitly weighs the matched treated observations to compute counterfactual outcomes.
The Stata command -psmatch2- stores these weights in a variable called _weight.
Someone pointed me to an old blog post somewhere on the Internet, which shows that there may be some confusion about what these weights are and where they come from.
K-neighbor matching estimates the counterfactual outcome for a treated observation by averaging the outcomes of its K matches.
This means that every time an untreated observation is matched to a treated observation (and this can happen more than once when matching with replacement), it is used with “weight” 1/K since one is dividing by K when averaging.
If one uses a caliper (i.e. excludes matches that are farther away than a minimum distance called a “caliper”) it can happen that some matches involve less than K neighbors
So more generally the weight is not 1/K but rather 1/nr-of-matches
(-psmatch2- saves the nr of matches for a given treated observation in the variable _nn)
The variable _weight sums these weights every time a control observation is used to construct a counterfactual outcome.
So let’s say that we are matching two treated observations to two neighbors with a caliper.
Then we may have that the first treated has two matches and the second treated only one match as in the following:
_id _treated _n1 _n2 _nn
1 1 3 4 2
2 1 3 . 1
3 0 . . .
4 0 . . .
The matched outcome for the first treated will be averaged across observations 3 and 4 and these have thus each weight 1/2 here.
The matched outcome for the second treated obs will be averaged across observation 3 and which thus has weight 1.
Note that in each case the weights equal 1/_nn.
Putting this together we can compute how often each matched untreated observation is used to construct the overall average counterfactual outcome by summing their weights:
_id _weight
3 1.5
4 0.5
For the example in the blog-post above the following code shows that this indeed gives the weights in the variable _weight:
webuse cattaneo2, clear
set seed 795
g x=uniform()
sort x
psmatch2 mbsmoke prenatal1 fbaby mmarried medu fedu mage fage mrace frace, out(bweight) neighbor(5) caliper(.0295236) logit
tab _weight
rename _n* N* // otherwise reshape complains
reshape long N, i(_id) j(matchnr)
g altweight = 1 / Nn
collapse (sum) altweight, by(N)
tab altweight
The weights in _weight are therefore not specific to -psmatch2-, but they follow directly from the definition of a K-neighbor matching estimator (independently of whether one matches on the propensity score or something else).
We study how GPA-based and holistic admission tracks in a centralized college market affect programs' degree completion through the information (screening) and selection (sorting) they generate. We validate a simple partial equilibrium model of program admissions by exploiting admission cutoffs and a reform that relaxed caps on holistic seats. We find that programs choose cutoffs and quotas so that marginal completion is similar across tracks when holistic quotas are slack but higher in the holistic track when they bind. A sorting–screening decomposi- tion shows that at the admission margin most gains from holistic admissions come from self-selection of higher-potential students into the holistic track, with modest screening gains. Programs do not internalize admission externalities, and marginal applicants rejected from the holistic track are about 5 percentage points less likely to complete a degree elsewhere than comparable GPA-track rejects, with gaps in selective programs with small holistic quotas twice as high. Expanding holis- tic quotas in constrained programs would thus raise total degree completion, and we find that this favors students with weaker academic records and family back- grounds.
College graduates tend to marry each other. We use detailed Norwegian data to show that strong assortativity further arises by institution and field of study, especially among high earners from elite programs. Admission discontinuities reveal that enrollment itself, rather than selection, primarily drives matching by institution and field among the college-educated, and that these matches can be economically consequential. Elite professional programs, in particular, propel marginally admitted women into elite household formation: they earn substantially more themselves and match with higher-earning elite partners, becoming much more likely to join the top percentiles of household earnings while also reducing fertility. Marginal elite admission for men yields no change in partner earnings or fertility. College match-making effects are concentrated among students who attend the same institution at the same time, and are larger when opposite-sex peers are more abundant, indicating search costs in the marriage market.
We have a PhD position under my supervision at the University of Oslo (UiO) in the economics of education starting next fall.
Apply if you are interested, or thanks for spreading the word!
Deadline is February 1st, so soon!
We have a post-doc position at the University of Oslo (UiO) in the economics of education starting next fall.
There are more positions (in other fields) which might be good to know in case candidates are not alone on the market.
Apply if you are interested, or thanks for spreading the word!
Deadline is December 1st.
Bryan Caplan says schooling is mostly a signal and does little for people’s human capital.
His recommendation is that we should stop spending money on it.
I will be in discussion with Bryan on Monday Aug. 20th.
Mari Rege and Odny Solheim are still in denial.
Where before they were claiming that we were using transitory and unpredictable variation in our study to estimate class size effects, this is now off the table.
Now it is something else:
Schools are facing large and unpredictable changes in class sizes from cohort to cohort, and on top of it schools are unable to handle that.
Rege and Solheim forget to mention that these are conjectures.
They also forget to check the data.
If we do that for the period we study (1978-2003), we see that for the large majority of schools class size in our data varies by at most 5 pupils from cohort to cohort.
For a given school these changes are on average zero across cohorts.
Schools therefore have typical class sizes with small variations around the mean.
These changes are predictible (in our data with past changes in enrollment) and are small.
And not unpredictable and large as claimed by Rege and Solheim.
Replying to Mari Rege and Odny Solheim’s claim that quasi-experimental research is not policy relevant because it uses as-if random variation.
Interview in Morgenbladet about my recent paper with Sturla Løkken where we estimate and find no long run effects of class size in compulsory schooling.
To stimulate investment in training by individuals, the Dutch tax system allows a deduction of out-of-pocket training expenditures from taxable income. This paper investigates to what extent the resulting cost reduction encourages training investments. Two different identification strategies are used. The first strategy uses the progressive structure of the income tax scheme and compares groups with taxable income just above or just below kinks. The second strategy takes advantage of the 2001 tax reform, which implied substantial changes in marginal tax rates. These strategies exploit different sources of exogenous variation and are based on different identifying assumptions. Nevertheless, the results point in the same direction: tax incentives increase training participation.
In this paper we investigate how heterogeneous agents choose among tournaments with different prizes. We show that if the number of agents is sufficiently small, multiple equilibria can arise. Depending on how the prize money is split over the tournaments, these may include, for example, a perfect-sorting equilibrium in which high-ability agents compete in the high-prize tournament, while low-ability agents compete for the low prize. However, there are also equilibria in which agents follow a mixed strategy and there can be reverse sorting, i.e. low-ability agents are in the tournament with the high prize, while high-ability agents are in the low-prize tournament. We show that total effort always decreases compared to a single tournament. However, splitting the tournament may increase the effort of low-ability agents.