We develop a finite-mixture framework for nonparametric difference-in-difference analysis with unobserved heterogeneity correlating treatment and outcome. Our framework includes an instrumental variable for the treatment, and we demonstrate that our method allows us to relax the no common trend restriction usually required in difference-in-difference analysis. We also show that outcomes can be Markovian provided there are multiple post-treatment observations. Our main theoretical contributions are the substitution of an instrument for the common-trends assumption, and a non-parametric identification proof. Empirically, we apply our framework to evaluate the effect of on-the-job/professional (re)training on wages, using novel French linked employee-employer data. Estimating our model using the EM-algorithm, we find small ATEs and ATTs on hourly wages of between 2% and 3%. However, we find larger effects on hours and annual wages with both ATEs and ATTs of over 5%. A simple extension to our model to include *observed* as well as unobserved heterogeneity produces very similar results..
In this paper we provide a new metric and framework to describe the extent of occupational mismatch in a labor market. We do so by constructing a single dimensional continuous measure of ability for individuals, and two distinct measures of occupational quality. This allows us to examine the extent to which young people mismatch into occupations that are higher or lower ranked than they could achieve and explore whether there are systematic differences in the nature of match by key demographics, including socio-economic status (SES) and gender. We find inefficiencies in the match between young peoples’ achievement ranking and their occupation ranking, and large socio-economic inequalities in education-based and earnings-based match, across the achievement distribution. We also find large gender gaps in earnings-based match, with women working in jobs that are significantly lower ranked than their male counterparts, but similarly ranked in terms of education-based match. While educational routes between compulsory education and occupations at age 25 can explain around 33% of these SES gaps among high achievers, a sizeable difference in undermatch remains for high achieving low SES students (8 percentiles), when taking into account all post-16 activity. The gender gap in mismatch remains stable, suggesting that education choices are not responsible for the large differences observed between men and women. Instead, the type of industry worked in can account for almost 76% of the gender gap among low achievers, although a significant difference still remains between men and women.
A growing body of research has shown large SES gaps in the match between students and their courses, with students from disadvantaged backgrounds more likely to 'undermatch' by attending less selective university courses than their entry grades would permit. In this paper we examine the role of university application behaviour in explaining these gaps. We find that individuals from different schools have very different application profiles, with those from independent schools much more likely to make 'reach' applications. In general, these reach applications are successful, and thus largely explain the why those from independent schools appear to be more likely to enrol in more selective courses, even when their entry grades are similar to those from the state sector.
The university application process is centralised in the UK. Applicants can choose up to 5 institutions to apply to and apply on the basis of their predicted A level grades and a personal statement. The latter is a controversial element of the admissions process, with research showing that the personal statement gives unfair advantage to more privileged applicants (Jones, 2013). However, very little quantitative research has been carried out on the importance of the personal statement in the admissions process, and the extent to which it contains useful information about applicants likeliness to perform well in the course. In this project we will use data from two London institutions for whom personal statements are an important part of the applications process: i) both are highly competitive, so have many applicants with highly similar predicted grades, meaning the personal statement may be a more important factor in assessing candidates ii) both systematically score their personal statements. We will first examine the extent to which personal statement quality (measured by scores) impact who is accepted among applicants. We will then examine the extent to which personal statements contain information about the candidates by asking whether personal statements can predict university attainment, holding constant entry grades. We will also look at the characteristics of high scorers, investigating whether students with different characteristics produce 'better' personal statements. Future work will also examine the impact in changing the format of the personal statement (based on the 2024 reform, in which personal statements will be reformatted into a series of questions).