arXiv subjects

Maximilian Osterhaus

Publications and source records attributed to Maximilian Osterhaus.

4 recordsLinked to original sources

arXiv2026

From dense grids to valid inference: Accounting for regularization bias in nonparametric random coefficient models

This paper develops an inference procedure for average functionals of random-coefficient distributions, such as mean willingness-to-pay and average elasticities, when the distribution is estimated nonparametrically using the penalized fixed-grid estimator of Heiss, Hetzenecker, and Osterhaus (2022). We establish asymptotic normality of the corresponding penalized plug-in estimator centered at the functional evaluated at the penalized pseudo-true value and propose a confidence interval that accounts for the regularization bias. Our method applies to a broad class of linear and nonlinear functionals and allows researchers to use dense grids to reduce approximation bias while maintaining valid inference. Monte Carlo simulations show that the proposed intervals achieve coverage close to the nominal level while remaining informative in finite samples. An empirical application to travel mode demand illustrates that flexible nonparametric specifications can yield economically meaningful differences relative to standard parametric models.

econ.EM↗

arXiv2024

Deep Learning for the Estimation of Heterogeneous Parameters in Discrete Choice Models

This paper studies the finite sample performance of the flexible estimation approach of Farrell, Liang, and Misra (2021a), who propose to use deep learning for the estimation of heterogeneous parameters in economic models, in the context of discrete choice models. The approach combines the structure imposed by economic models with the flexibility of deep learning, which assures the interpretebility of results on the one hand, and allows estimating flexible functional forms of observed heterogeneity on the other hand. For inference after the estimation with deep learning, Farrell et al. (2021a) derive an influence function that can be applied to many quantities of interest. We conduct a series of Monte Carlo experiments that investigate the impact of regularization on the proposed estimation and inference procedure in the context of discrete choice models. The results show that the deep learning approach generally leads to precise estimates of the true average parameters and that regular robust standard errors lead to invalid inference results, showing the need for the influence function approach for inference. Without regularization, the influence function approach can lead to substantial bias and large estimated standard errors caused by extreme outliers. Regularization reduces this property and stabilizes the estimation procedure, but at the expense of inducing an additional bias. The bias in combination with decreasing variance associated with increasing regularization leads to the construction of invalid inferential statements in our experiments. Repeated sample splitting, unlike regularization, stabilizes the estimation approach without introducing an additional bias, thereby allowing for the construction of valid inferential statements.

econ.EM↗

arXiv2024

A Sparse Grid Approach for the Nonparametric Estimation of High-Dimensional Random Coefficient Models

A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of dimensionality, restricts the application of such estimators to models with moderately few random coefficients. This paper proposes a scalable nonparametric estimator for high-dimensional random coefficient models. The estimator uses a truncated tensor product of one-dimensional hierarchical basis functions to approximate the underlying random coefficients' distribution. Due to the truncation, the number of parameters increases at a much slower rate than in the regular tensor product basis, rendering the nonparametric estimation of high-dimensional random coefficient models feasible. The derived estimator allows estimating the underlying distribution with constrained least squares, making the approach computationally simple and fast. Monte Carlo experiments and an application to data on the regulation of air pollution illustrate the good performance of the estimator.

econ.EM↗

arXiv2019

Nonparametric Estimation of the Random Coefficients Model: An Elastic Net Approach

This paper investigates and extends the computationally attractive nonparametric random coefficients estimator of Fox, Kim, Ryan, and Bajari (2011). We show that their estimator is a special case of the nonnegative LASSO, explaining its sparse nature observed in many applications. Recognizing this link, we extend the estimator, transforming it to a special case of the nonnegative elastic net. The extension improves the estimator's recovery of the true support and allows for more accurate estimates of the random coefficients' distribution. Our estimator is a generalization of the original estimator and therefore, is guaranteed to have a model fit at least as good as the original one. A theoretical analysis of both estimators' properties shows that, under conditions, our generalized estimator approximates the true distribution more accurately. Two Monte Carlo experiments and an application to a travel mode data set illustrate the improved performance of the generalized estimator.

econ.EM↗