## Estimation and Selection of Spatial Weight Matrix in a Spatial Lag Model

## with Clifford lam (LSE)

## accepted at journal of business and economic statistics, 2019

Spatial econometric models allow for interactions among variables through the specification of a spatial weight matrix. Practitioners often face the risk of misspecification of such a matrix. In many problems a number of potential specifications exist, such as geographic distances, or various economic quantities among variables. We propose estimating the best linear combination of these specifications, added with a potentially sparse adjustment matrix. The coefficients in the linear combination, together with the sparse adjustment matrix, are subjected to variable selection through the adaptive Least Absolute Shrinkage and Selection Operator (LASSO). As a special case, if no spatial weight matrices are specified, the sparse adjustment matrix becomes a sparse spatial weight matrix estimator of our model. Our method can therefore be seen as a unified framework for the estimation and selection of a spatial weight matrix. The rate of convergence of all proposed estimators are determined when the number of time series variables can grow faster than the number of time points for data, while Oracle properties for all penalized estimators are presented. Simulations and an application to stocks data confirms the good performance of our procedure.

## A test for weak stationarity in the spectral domain

## with javier hidalgo (LSE)

## accepted at econometric theory, 2018

We examine tests for stability of the dynamics of a time series against alternatives that cover both local-stationarity and break points. One key feature of the tests is that the asymptotic distribution are functionals of the standard Brownian Bridge sheet in [0,1]^2 and do not depend on unknown parameters. The tests have nontrivial power against local alternatives converging to the null hypothesis at a T^{−1/2} rate, where T is the sample size. We examine an easy-to-implement bootstrap analogue and confirm the finite-sample performance in Monte-Carlo experiment. Finally, we implement the methodology to assess the stability of the inflation dynamics in the United States and on a set of neuroscience tremor data. Full paper.

## Detection and estimation of block structure in spatial weight matrix

## with clifford lam (LSE)

## Econometric Reviews, Vol. 35, Issue 8-10, pp. 1347-1376, 2016

In many economic applications, it is often of interest to categorize, classify or label individuals by groups based on similarity of observed behavior. We propose a method that captures group affiliation or, equivalently, estimates the block structure of a neighboring matrix embedded in a Spatial Econometric model. The main results of the LASSO estimator shows that off-diagonal block elements are estimated as zeros with high probability, property defined as “zero-block consistency”. Furthermore, we present and prove zero-block consistency for the estimated spatial weight matrix even under a thin margin of interaction between groups. The tool developed in this paper can be used as a verification of block structure by applied researchers, or as an exploration tool for estimating unknown block structures. We analyzed the US Senate voting data and correctly identified blocks based on party affiliations. Simulations also show that the method performs well. Full paper.

## Recovering Social Networks from Panel Data: Identification, Simulations and an Application

## with aureo de paula and imran rasul (UCL)

## working paper

It is almost self-evident that social interactions can determine economic behavior and outcomes. Yet, information on social ties does not exist in most publicly available and widely used datasets. We present methods to recover information on the entire structure of social networks from observational panel data that contains no information on social ties between individuals. In the context of a canonical social interactions model, we provide sufficient conditions under which the social interactions matrix, endogenous and exogenous social effect parameters are all globally identified. We describe how high-dimensional estimation techniques can be used to estimate the model based on the Adaptive Elastic Net GMM method. We showcase our method in Monte Carlo simulations using two stylized and two real world network structures. Finally, we employ our method to study tax competition across US states. We find the identified network structure of tax competition differs markedly from the common assumption of tax competition between geographically neighboring states. We analyze the identified social interactions matrix to provide novel insights into the long-standing debate on the relative roles of factor mobility and yardstick competition in driving tax setting behavior across states. Most broadly, our method shows how the analysis of social interactions can be usefully extended to economic realms where no network data exists. Full paper.

## Internet Access, Social Media, and the Behavior of Politicians: evidence from Brazil

## with F. Campante (HARVARD), C. Ferraz (PUC-Rio) and P. tepedino (MIT)

## working paper

Spatial econometric models allow for interactions among variables through the specification of a spatial weight matrix. Practitioners often face the risk of misspecification of such a matrix. In many problems a number of potential specifications exist, such as geographic distances, or various economic quantities among variables. We propose estimating the best linear combination of these specifications, added with a potentially sparse adjustment matrix. The coefficients in the linear combination, together with the sparse adjustment matrix, are subjected to variable selection through the adaptive Least Absolute Shrinkage and Selection Operator (LASSO). As a special case, if no spatial weight matrices are specified, the sparse adjustment matrix becomes a sparse spatial weight matrix estimator of our model. Our method can therefore be seen as a unified framework for the estimation and selection of a spatial weight matrix. The rate of convergence of all proposed estimators are determined when the number of time series variables can grow faster than the number of time points for data, while Oracle properties for all penalized estimators are presented. Simulations and an applications to stock data confirms the good performance of our procedure. [revised version soon]

## Estimating Network Effects From many groups

## working paper

[Former job market paper]

[revised version soon]