The use of formal education in Denmark 1980-1992

Education of the labour force is often seen as one of the most important factors for the development of affluent economies. Denmark is such an economy with a GDP per capita above those of Germany and the US. Furthermore inequality is low. Denmark has only 5.1 million inhabitants and is closely interconnected to Cental Europe, both in infrastructure (Border to Germany, and ferry lines to Scandinavia, UK , Germany and Poland) and economically (EU-member since 1973). The Danish economy has been open to im- and export of all kinds of goods for decades. This article analyses the role of formal education for the development of the Danish economy. It uses input-output tables and is based on the Heckscher-Ohlin-Vanek model for trade and factor endowment.

Smart City Analytics: Ensemble-Learned Prediction of Citizen Home Care

We present an ensemble learning method that predicts large increases in the hours of home care received by citizens. The method is supervised, and uses different ensembles of either linear (logistic regression) or non-linear (random forests) classifiers. Experiments with data available from 2013 to 2017 for every citizen in Copenhagen receiving home care (27,775 citizens) show that prediction can achieve state of the art performance as reported in similar health related domains (AUC=0.715). We further find that competitive results can be obtained by using limited information for training, which is very useful when full records are not accessible or available. Smart city analytics does not necessarily require full city records. To our knowledge this preliminary study is the first to predict large increases in home care for smart city analytics

Sequence Modelling For Analysing Student Interaction with Educational Systems

The analysis of log data generated by online educational systems is an important task for improving the systems, and furthering our knowledge of how students learn. This paper uses previously unseen log data from Edulab, the largest provider of digital learning for mathematics in Denmark, to analyse the sessions of its users, where 1.08 million student sessions are extracted from a subset of their data. We propose to model students as a distribution of different underlying student behaviours, where the sequence of actions from each session belongs to an underlying student behaviour. We model student behaviour as Markov chains, such that a student is modelled as a distribution of Markov chains, which are estimated using a modified k-means clustering algorithm. The resulting Markov chains are readily interpretable, and in a qualitative analysis around 125,000 student sessions are identified as exhibiting unproductive student behaviour. Based on our results this student representation is promising, especially for educational systems offering many different learning usages, and offers an alternative to common approaches like modelling student behaviour as a single Markov chain often done in the literature.Comment: The 10th International Conference on Educational Data Mining 201

Unobserved Ability and the Return to Schooling

We estimate a structural dynamic programming model of schooling decisions with unobserved heterogeneity in school ability and market ability on a sample taken from the National Longitudinal Survey of Youth (NLSY). Both the instantaneous utility of attending school and the wage regression function are estimated flexibly. The null hypothesis that the local returns to schooling are constant is strongly rejected in favor of a convex wage regression function composed of 8 spline segments. The local returns are very low until grade 11 (1% per year or less), increase to 3.7% in grade 12 and exceed 10% only from grade 14 to grade 16. The average return increases smoothly from 0.4% (grade 7) to 4.6% (grade 16). The convexity of the log wage regression function implies that those who obtain more schooling also experience higher average returns. We strongly reject the null hypothesis that unobserved market ability is uncorrelated with realized schooling attainments, which underlies many previous studies that have used OLS to estimate the return to schooling. The correlation between realized schooling and market ability is found to be positive and is consistent with the existence of a positive "Ability Bias". À partir d'un échantillon tiré du National Longitudinal Survey of Youth (NLSY), nous estimons un modèle de programmation dynamique des choix d'éducation en présence d'hétérogénéité non observée dans les capacités scolaires et aptitudes sur le marché de l'emploi. L'utilité instantanée de la fréquentation scolaire ainsi que la fonction de salaire sont évaluées de façon flexible. L'hypothèse nulle que les rendements marginaux de l'éducation sont constants est catégoriquement rejetée en faveur d'une fonction de salaire convexe composée de huit segments de fonction d'approximation spline. Les rendements marginaux s'avèrent être très faibles jusqu'à la onzième année (1 % ou moins par an), augmentent jusqu'à 3,7 % pour la douzième année et dépassent les 10 % pour les années 14 à 16. Le rendement moyen augmente uniformément de 0,4 % (7ème année) à 4,6 % (16ème année). La convexité de la fonction de régression logarithmique du salaire implique que ceux qui atteignent un plus haut niveau de scolarisation obtiennent également de meilleurs rendements moyens sur le marché de l'emploi. Nous rejetons l'hypothèse nulle selon laquelle les aptitudes non observées sur le marché du travail ne sont pas corrélées avec les niveaux d'éducation atteints. Ce résultat va à l'encontre de ceux obtenus dans plusieurs études antérieures qui estimaient le rendement de l'éducation par la méthode des MCO. Nous trouvons une corrélation positive entre le niveau de scolarité atteint et les aptitudes sur le marché de l'emploi, confirmant ainsi l'existence d'un «Biais d'aptitude» positif.Return to Schooling, Dynamic Programming, Ability Bias, Discount Rate Bias, Rendements de l'éducation, Programmation dynamique, Biais d'aptitude, Biais de taux d'escompte

Calibration and IV Estimation of a Wage Outcome Equation in a Dynamic Environment

We consider an artificial population of forward looking heterogeneous agents making decisions between schooling, employment, employment with training and household production, according to a behavioral model calibrated to a large set of stylized facts. Some of these agents are subject to policy interventions (a higher education subsidy) that vary according to their generosity. We evaluate the capacity of Instrumental Variable (IV) methods to recover the population Local Average Treatment Effect (LATE) and analyze the economic implications of using a strong instrument within a dynamic economic model. We also examine the performances of two sampling designs that may be used to improve classical linear IV; a Regression-Discontinuity (RD) design and an age-based sampling design targeting early career wages. Finally, we investigate the capacity of IV to estimate alternative "causal" parameters. The failure of classical linear IV is spectacular. IV fails to recover the true LATE, even in the static version of the model. In some cases, the estimates lie outside the support of the population distribution of returns to schooling and are nearly twice as large as the population LATE. The trade-off between the statistical power of the instrument and dynamic self-selection caused by the policy shock implies that access to a "strong instrument" is not necessarily desirable. There appears to be no obvious realistic sampling design that can guarantee IV accuracy. Finally, IV also fails to estimate the reduced-form marginal effect of schooling on wages of those affected by the experiment. Within a dynamic setting, IV is deprived of any “causal” substance.dynamic discrete choice, dynamic programming, treatment effects, weak instruments, instrumental variable, returns to schooling

Earnings Dispersion, Risk Aversion and Education

We estimate a dynamic programming model of schooling decisions in which the degree of risk aversion can be inferred from schooling decisions. In our model, individuals are heterogeneous with respect to school and market abilities but homogeneous with respect to the degree of risk aversion. We allow endogenous schooling attainments to affect the level of risk experienced in labor market earnings through wage dispersion and employment rate dispersion. We find a low degree of relative risk aversion (0.9282) and the estimates indicate that both wage and employment rate dispersions decrease significantly with schooling attainments. We find that a counterfactual increase in risk aversion will increase schooling attainments. Finally, the low degree of risk aversion implies that an increase in earnings dispersion would have little effect on schooling attainments. Nous estimons un modèle de programmation dynamique des choix d'éducation dans lequel le degré d'aversion au risque peut être estimé à partir des choix de scolarisation. Dans notre modèle, les individus sont hétérogènes quant à leurs capacités scolaires et aptitudes sur le marché de l'emploi, mais homogènes en ce qui concerne le degré d'aversion au risque. Nous laissons les niveaux scolaires endogènes influencer le niveau de risque concernant les revenus d'emploi, et ce, à travers la dispersion des salaires et la dispersion du taux d'emploi. Nous trouvons un faible degré d'aversion relative au risque (0,9282) et nos résultats indiquent que les taux de dispersion, aussi bien pour le salaire que pour le taux d'emploi, diminuent de façon significative avec le niveau de scolarisation. Nous trouvons qu'une augmentation contrefactuelle de l'aversion au risque va faire augmenter le niveau de scolarité atteint. Finalement, un niveau faible d'aversion au risque implique qu'une augmentation de la dispersion des revenus aurait peu d'impact sur le niveau de scolarisation.Dynamic Programming, Returns to Education, Risk Aversion, Human Capital, Earnings Dispersion, Programmation dynamique, Rendements de l'éducation, Aversion au risque, Capital humain, Dispersion des revenus

Earnings Dispersion, Risk Aversion and Education

We estimate a dynamic programming model of schooling decisions in which the degree of risk aversion can be inferred from schooling decisions. In our model, individuals are heterogeneous with respect to school and market abilities but homogeneous with respect to the degree of risk aversion. We allow endogenous schooling attainments to affect the level of risk experienced in labor market earnings through wage dispersion and employment rate dispersion. We find a low degree of relative risk aversion (0.93) and the estimates indicate that both wage and employment rate dispersions decrease significantly with schooling attainments. We find that a counterfactual increase in risk aversion will increase schooling attainments. Finally, the low degree of risk aversion implies that an increase in earnings dispersion would have little effect on schooling attainments.dynamic programming; earnings dispersion; human capital; returns to education; risk aversion

The distinction between dictatorial and incentive policy interventions and its implication for IV estimation

We investigate if, and under which conditions, the distinction between dictatorial and incentive-based policy interventions, affects the capacity of Instrument Variable (IV) methods to estimate the relevant treatment effect parameter of an outcome equation. The analysis is set in a non-trivial framework, in which the right-hand side variable of interest is affected by selectivity, and the error term is driven by a sequence of unobserved life-cycle endogenous choices. We show that, for a wide class of outcome equations, incentive-based policies may be designed so to generate a sufficient degree of post-intervention randomization (a lesser degree of selection on individual endowments among the sub-population affected). This helps the instrument to fulfill the orthogonality condition. However, for a same class of outcome equation, dictatorial policies that enforce minimum consumption cannot meet this condition. We illustrate these concepts within a calibrated dynamic life cycle model of human capital accumulation, and focus on the estimation of the returns to schooling using instruments generated from mandatory schooling reforms and education subsidies. We show how the nature of the skill accumulation process (substitutability vs complementarity) may play a fundamental role in interpreting IV estimates of the returns to schooling.Returns to schooling, Instrumental Variable methods, Dynamic Discrete Choice, Dynamic Programming, Local Average Treatment Effects .

A Structural Analysis of the Correlated Random Coefficient Wage Regression Model

We estimate a finite mixture dynamic programming model of schooling decisions in which the log wage regression function is set in a random coefficient framework. We also analyze the determinants of 3 counterfactual experiments (a college attendance subsidy, a high school graduation subsidy and an overall decrease in the rate of time preference) and examine a proposition often claimed in the "Average Treatment Effects" literature; that the discrepancy between OLS and IV estimates of the returns to schooling may be explained by the relatively higher returns experienced by those affected by exogenous policy changes. We find that the average return to experience upon entering the labor market (0.0863) exceeds the average return to schooling (0.0576) and we find more cross-sectional variability in the returns to experience than in the returns to schooling. Labor market skills (as opposed to taste for schooling) appear to be the prime factor explaining schooling attainments. We find little evidence in favor of a positive correlation between reactions induced by an exogenous experiment and the individual specific returns to schooling.Random Coefficient; Returns to Schooling; Comparative Advantages; Dynamic Programming; Dynamic Self-Selection