Essays in econometric theory

Nowakowicz, Kamila (2025) Essays in econometric theory. PhD thesis, London School of Economics and Political Science.

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Abstract

We design and analyse nonparametric techniques for understanding the structure of network data, inference on network statistics, and testing for shape constraints. In the first chapter, I look at symmetric binary exchangeable networks. Any such network can be characterised by a distribution over characteristics of nodes and a linking (graphon) function which gives the probability of link between any two nodes. To learn about the network structure, I propose a nonparametric estimator of the linking function. I provide conditions under which the estimator is uniformly consistent and a numerical procedure for choosing a tuning parameter. My procedure makes minimal assumptions and allows for moderate sparsity levels. In the second chapter, I propose a bootstrap procedure which allows for valid inference on network statistics. It uses my nonparametric linking function estimator from Chapter 1 to generate bootstrap networks with a similar dependence structure to the original network. I prove that the distribution of the bootstrap network is consistent for the distribution of the original network, and I provide conditions under which bootstrap consistently recovers distributions of a class of functions related to U-statistics. I find good performance in Monte Carlo simulations and apply my procedure to the data from Banerjee, Chandrasekhar, Duflo, and Jackson (2013). In the third chapter, we propose a test for whether a nonparametric regression mean satisfies a shape restriction that varies within the domain of the regressor (e.g. (inverted) U-shaped, S-shaped). Our procedure extends the methodology of Komarova and Hidalgo (2023) to the setting where the points at which the shape changes are unknown and must be estimated, and the shapes may only appear after controlling for covariates. We provide a generalised transformation which achieves the same asymptotic distribution but adds robustness to the test and credibility to the conclusions.

Item Type:	Thesis (PhD)
Additional Information:	© 2025 Kamila Nowakowicz
Library of Congress subject classification:	H Social Sciences > HB Economic Theory
Sets:	Departments > Economics
Supervisor:	Hidalgo, Javier and Otsu, Taisuke
URI:	http://etheses.lse.ac.uk/id/eprint/4866

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