The Path to College Education: The Role of Math and Verbal Skills

Abstract

This paper studies the formation of math and verbal skills during compulsory education and their impact on adult outcomes. We introduce a novel method to estimate dynamic, nested CES production functions. Using a rich panel database that follows a cohort of students in England from elementary school to university, we find that the production functions of math and verbal skills are inherently different, where cross-effects are only present in the production of math skills. Results on long-term outcomes indicate that verbal skills play a substantially greater role in explaining university enrollment than math skills. This finding, combined with the large female advantage in verbal skills, has key implications for gender gaps in college enrollment and field of study. Finally, we show that students stuck in low quality schools have lower skill levels at the end of compulsory education compared to students attending high quality schools, with these skill deficits leading to a 30 percentage point gap in college enrollment among these students. Simulation results show that about 15% of this gap is due to differences in skill levels * We thank

A Note on the Importance of Normalizations in Dynamic Latent Factor Models of Skill Formation

“…For the CES, different location and scale normalizations can lead to different estimated treatment effects, all of which can be incorrect. We focus on the CES production function because it is a commonly used specification in the literature on skill formation (Cunha et al , 2010;Attanasio et al , 2019;Aucejo & James, 2019). Additionally, we only consider normalizations that are typically implemented in empirical applications.…”

“…It then follows that changes in the location and scale of the skill distribution (through TFP dynamics and returns to scale production) are identified by changes in the location and scale of the age invariant measure. Many of the most recent dynamic latent factor models employ age-invariant measures Attanasio et al , 2019;Aucejo & James, 2019) to allow for time-varying TFP and free returns to scale.…”

“…We show that these treatment effects can be identified without any location or scale normalization. The fact that we only identify treatment effects is not particularly limiting since most papers in the literature use the estimated production function to examine how changes in a key input, such as household income, impact future child skills or adult outcomes Attanasio et al , 2019;Aucejo & James, 2019).…”

Identification of dynamic latent factor models of skill formation with translog production

“…For example, in the Monte Carlo exercise of Attanasio et al (2020), the initial scale and location of latent skill are set at a value assumed to be the true value, though the authors note that the estimated production parameters and treatment effects can be sensitive to this assumption. A better understanding of the implications of these initial assumptions is important given that many recent dynamic latent factor models employ a CES technology with age invariant measures (Agostinelli et al, 2020; Attanasio et al, 2020; Aucejo & James, 2021) to allow for time‐varying TFP and free returns to scale. As we show here, the translog production function does not suffer the same limitations, and thus provides researchers with a practical alternative.…”

Development Model of College English Education Service Talents Based on Nonlinear Random Matrix

“…With the advent of the era of big data, massive amounts of data have been collected and stored in all walks of life in society, and the characteristics of these data include large number and dimensionality, high value, and fast growth rate, and these characteristics also pose huge challenges for data analysis [1]. e main reason for the explosive growth of data in recent years is the increasingly low cost of data production and storage.…”