Analysis of Structural Economic Models: Misspecification and Flexible Estimation

Project Information

NPSkills

Grant agreement ID: 949319

DOI

10.3030/949319

EC signature date 3 November 2020

Start date 1 December 2020

End date 31 August 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 050 161,00

EU contribution

€ 1 050 161,00

Coordinated by

RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN
Germany

Periodic Reporting for period 3 - NPSkills (Analysis of Structural Economic Models: Misspecification and Flexible Estimation)

Reporting period: 2023-12-01 to 2025-05-31

Summary of the context and overall objectives of the project

Structural models are key tools of economists to evaluate and design policies. These models specify economic environments, estimate mechanisms that determine outcomes, and can be used for counterfactual predictions. One important class of models deals with skill and human capital formation, which is an important driver of economic growth and inequality. These models study the determinants of skill formation and the timing of optimal investments in children. Since structural models require simplifying assumptions, they are also prone to misspecification.

The research of this project shows that existing skill formation models rely on seemingly innocuous normalizations, which can severely impact counterfactual predictions. For example, simply changing the units of measurements of observed variables can yield ineffective investment strategies and misleading policy recommendations. The project tackles these problems by providing a new comprehensive identification analysis and by focusing on a novel set of important policy-relevant parameters that yield robust conclusions. These issues and solutions extend to many other structural models with latent variables. In addition, the project provides a new flexible estimator for the policy-relevant features and analyzes various data sets to reevaluate policy recommendations with potentially large impacts on costs and benefits of large public investments in children, economic growth, and inequality.

Estimation is facilitated by new econometric tools that are developed in this project. These tools are important contributions on their own rights and are applicable in a wide range of settings. They allow researchers to obtain more precise nonparametric estimators and more reliable conclusions by using shape restrictions implied by economic theory and data-driven dimension reduction techniques. By also providing guidance on which estimation method to use in practice, these results can have a large impact on empirical research.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The PI completed a paper that provides new identification results for skill formation models and investigates the effects of seemingly innocuous scale and location restrictions on parameters of interest. The results show, among other, that commonly used models are missspecified, and consequently, simply changing the units of measurements of observed variables might yield ineffective investment strategies and misleading policy recommendations. These serious misspecification issues can be illustrated using data sets from recently published studies. The paper also provides a new set of restrictions and policy relevant parameters that do not suffer from these issues.

The project team also worked on a new way to estimate skill formation models because popular existing estimators are generally not consistent and can therefore yield misleading conclusion, even once the misspecification issues are fixed. The new estimator uses an iterative approach to reduce the computational burden and leverages recent results from the numerical mathematics literature to achieve an efficient and accurate implementation.

Using the new estimation method, the team performed preliminary analyses of different data sets. For example, it started applying the new methodology to study the evolution and the determinants of mental and physical health. Just like skills, mental and physical health are not perfectly observed, but questionnaires can provide multiple measures of them. Moreover, they evolve over time, depend on treatments, and they might interact with each other. Hence, health formation also fits into the framework provided.

The team also made process on optimal estimation under shape restrictions, which are often reasonable assumptions in economic applications, as well as estimation in high-dimensional models. The newly proposed estimators perform well in preliminary Monte Carlo simulations.

The research has been presented at various invited seminars at renowned universities and international academic conferences.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Previous empirical studies using skills formation models have been quite influential, for example in literature on early childhood education. This project shows that many previously used models are misspecified. Consequently, they might provide misleading policy recommendations, the results are very dependent on the units of measurements of the data, and the results are not comparable across different studies. The project contributes to this literature by provide a new set of restrictions and policy relevant parameters that do not suffer from these issues and yield robust conclusions. In addition, the new estimator solves implementation problems of existing approaches by using a new and accurate computational approach. The research advances the literature significantly beyond the state of the art because some of the main conclusions in recent existing studies are not robust to simple changes in the units of measurements of observed variables. The new results in this project provide researchers with tools to analyze models with latent variables and to obtain reliable conclusions.

The expected results of the projects are academic papers on identification and estimation of skill formation models. These papers explain how these models can be specified, which restrictions need to be imposed, how the models can be implemented using data, and how the results can be interpreted. In addition, the project will produce empirical application that applies the newly developed methods and illustrates the practical relevance of the project. The project will also develop well-documented computer programs, which will allow researchers to replicate simulations and empirical applications of the project and to easily apply the methodology to their own data. Finally, the project aims to develop new econometric tools for estimation with shape constraints and high-dimensional covariates, which are important contributions on their own rights and are applicable in a wide range of settings.