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The Econometrics of Networks

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ADVANCES IN ECONOMETRICS

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Advances in Econometrics Volume 42

Title Page

The Econometrics of Networks

Edited by

ÁUREO DE PAULA

University College London, UK

Elie Tamer

Harvard University, USA

Marcel-Cristian Voia

University of Orléans, France

United Kingdom – North America – Japan – India – Malaysia – China

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Emerald Publishing Limited

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First edition 2020

Copyright © Chapter 9. ‘Survival Analysis of Banknote Circulation: Fitness, Network Structure, and Machine Learning’, © 2020 Bank of Canada. Published under exclusive licence by Emerald Publishing Limited. All other chapters © 2020 Emerald Publishing Limited.

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ISBN: 978-1-83867-576-9 (Print)

ISBN: 978-1-83867-575-2 (Online)

ISBN: 978-1-83867-577-6 (Epub)

ISSN: 0731-9053 (Series)

Contents

Introduction

Econometrics of Networks

Áureo de Paula, Elie Tamer and Marcel Voia

The Econometrics of Networks. Volume 42 of the series Advances in Econometrics (AiE) aims at providing novel methodological and empirical research on the econometrics of networks. The volume includes both theoretical and empirical/policy papers with the specific purpose of providing an opportunity for a dialogue between academics and practitioners to better understand this new and important area of research and its role in policy discussions.

The volume is a good resource for graduate students and researchers. It includes 13 chapters covering various topics such as identification of network models, network formation, networks and spatial econometrics and applications of financial networks. One can also learn about network models with different types of interactions, sample selection in social networks, trade networks, stochastic dynamic programing in space, spatial panels, survival and networks, financial contagion, spillover effects, interconnectedness on consumer credit markets and a financial risk meter.

The book can be also a resource for data scientists and professionals from the industry as it provides a useful resource for applications, such as, for example, offering theoretical discussions about within and between groups interactions, the role unknown networks play in social interactions and the role of strong ties on trade networks.

A brief description of the chapters of the book which are grouped in four sections is presented below.

Section 1: Identification of Network Models

This section comprises of three chapters. The chapter by Tiziano Arduini, Eleonora Patacchini and Edoardo Rainone, “Identification and Estimation of Network Models with Heterogeneous Interactions,” generalizes the standard linear-in-means model to allow for multiple types of between and within-type interactions. It extends the Bramoulle, Djebbari, and Fortin’s (2009) and Calvo-Armengol, Patacchini, and Zenou’s (2009) identification conditions and Liu and Lee’s (2010) estimation approach when network data are available and peer effects are heterogeneous by peer-type. The proposed methodology is inspired by Liu and Lee (2010) and Liu (2014) where the many instruments are derived from many networks (groups) observed in the sample. Differently, in the model proposed by the authors the many instruments derive from the multiple subnetwork framework. A multiple subnetwork framework does not only result in a larger number of instruments but also yields multiple approximations of the optimal instruments. The bias arising when interactions are ignored is analytically derived and evaluated in finite samples using simulation experiments. The authors show that the form of the many-instrument bias differs, though the leading order remains unchanged.

The chapter by Hon Ho Kwok, “Identification Methods for Social Interactions Models with Unknown Networks,” develops a two-step identification method for social interaction models with unknown networks and discusses how the proposed methods are connected to the identification methods for models with known networks. In the first step, a linear regression is used to identify the reduced forms, while the second step decomposes the reduced forms to identify the primitive parameters. The proposed methods use panel data to identify networks. Two cases are considered: the sample exogenous vectors span Rn (long panels), and the sample exogenous vectors span a proper subspace of Rn (short panels). For the short panel case, in order to solve the sample covariance matrices’ non-invertibility problem, the chapter proposes to represent the sample vectors with respect to a basis of a lower-dimensional space so that fewer regression coefficients are needed in the first step. This allows for the identification of some reduced form submatrices, which provide the equations necessary for identifying the primitive parameters.

The chapter by TszKin Julian Chan, “Snowball Sampling and Sample Selection in a Social Network,” studies a snowball sampling method for social networks with endogenous peer selection. Snowball sampling is a sampling design which preserves the dependence structure of the network. It sequentially collects the information of vertices linked to the vertices collected in the previous iteration. The snowball samples suffer from a sample selection problem because of the endogenous peer selection. The chapter proposes a new estimation method that uses the relationship between samples in different iterations to correct for selection. In the application, the snowball samples collected from Facebook is used to estimate the proportion of users who support the Umbrella Movement in Hong Kong.

Section 2: Network Formation

This section has two chapters. The chapter by Áureo de Paula, “Trade Networks and the Strength of Strong Ties,” surveys the relevant literature on strategic formation of networks and uses it to motivate looking at questions related to the behavior of individuals in the presence of imperfect market institutions. In particular, the chapter is interested in how individuals devote resources to the establishment of reliable connections in order to attenuate the frictions that reduce trading and insurance opportunities by looking to answer questions such as: When should we expect to see the appearance of such interpersonal networks as a stable support of economic transactions? Having been established as a stable phenomenon, does voluntary networking improve upon the situation in which no such connections can be established?

To answer these questions de Paula extends a trade network first suggested by an example in Jackson and Watts (2002) and builds a model which shows that the investment in strong ties often, though not always, produces stable configurations that manage to improve upon the imperfections of market institutions.

The author finds that such voluntary networks of “strong ties” can usually be sustained as a stable outcome, though examples are not hard to achieve in which no equilibrium configuration occurs.

Additionally, he finds that whenever such a structure exists, it improves general well-being over a situation in which only formal unreliable markets existed. And finally, the analysis suggests that though voluntary networking efforts are no substitute for an improvement in the reliability of formal institutions, emergence of informal insurance networks or extensive investment in connections should come as no surprise in the presence of “noisy” market institutions.

The chapter by Seth Richards-Shubik, “Application and Computation of a Flexible Class of Network Formation Models,” discusses the empirical application of a class of strategic network formation models, using the approach to identification introduced by de Paula, Richards-Shubik and Tamer (2018). The chapter emphasizes the interplay between model specification and computational complexity and suggests approaches that help in improving empirical/computational tractability. Two detailed examples, one on friendship networks and another on coauthorship networks, are used to illustrate these issues and to demonstrate the performance of the approach with both simulation and empirical evidence.

The analysis shows how the utility specification impacts dimensionality. Additionally, the author shows how machine learning techniques can be used for dimension reduction in the coauthorship model to make the model computationally feasible while including a rich set of covariates. The chapter presents a more general estimation method, which expands the potential range of applications. Also, a statistical inference is provided with minimal computational burden.

Section 3: Networks and Spatial Econometrics

This section comprises of four chapters.

The chapter by Harry J. Paarsch and John Rust, “Implementing Faustmann–Marshall–Pressler at Scale: Stochastic Dynamic Programming in Space,” constructs an intertemporal model of rent-maximizing behavior on the part of a timber harvester under potentially multi-dimensional risk as well as geographical heterogeneity. Subsequently, the authors use recursive methods (the method of stochastic dynamic programing) to characterize the optimal policy function which is the rent-maximizing timber-harvesting profile.

One feature of their application to forestry in the province of British Columbia is the unique and detailed information that is organized in the form of a dynamic geographical information system which helps to account for site-specific cost heterogeneity in harvesting and transportation, as well as an uneven-aged stand dynamics in timber growth and yield across space and time in the presence of stochastic lumber prices.

Their framework is a powerful tool, and by using it one can conduct a variety of different policy experiments. First, the authors use geography both in the planar sense and in the three-dimensional sense. Second, they consider site-specific heterogeneity both on the cost side in terms of harvesting and transportation and on the growth and yield side in terms of heterogeneous stands of timber. Third, they use best-practice biological methods to model the dynamics of uneven-aged forest growth and yield. Fourth, in the past, economists have typically demonstrated their methods by solving simple, prototypical examples in closed-form or they have imposed conditions sufficient to sign comparative static predictions. Alternatively, in this chapter the authors use recent developments in computational methods to solve numerically for the optimal policy function. Finally, they compared their optimal harvesting policy with the harvests that have occurred during the past eight years, or so, finding striking and significant differences.

The chapter by Heng Chen and Matthew Strathearn, “A Spatial Panel Model of Bank Branches in Canada,” empirically analyzes the spatial bank branch network in Canada. The authors study the market structure (both industrial and geographic concentrations) via its own or adjacent postal areas. The empirical framework considers branch density (the ratio of the total number of branches to area size) by employing a spatial two-way fixed effects model.

The addition of geographic concentration, as measured by the average distance to the closest bank branch, allows the authors to reflect on the degree of spatial clustering among bank branches in a given postal area. By controlling for both industrial and geographic concentrations the authors can capture not only the degree of competitiveness in a given area, but also how well the area is serviced in terms of travel distance to the nearest branch.

The chapter finds that there are no effects associated with market structure but that there are strong spatial within and nearby effects associated with the socioeconomic variables. In addition, the chapter studies the effect of spatial competition from rival banks and finds that large and small banks tend to avoid markets dominated by their competitors.

The chapter by Sophia Ding and Peter H. Egger, “Full-information Bayesian Estimation of Cross-sectional Sample Selection Models,” proposes an approach to estimate cross-sectional sample selection models, where the shocks on the units of observation feature some interdependence through spatial or network autocorrelation.

There is research that aims at addressing these two issues in conjunction. The authors are showing that previous Bayesian algorithms such as the ones developed by Dogan and Taspinar (2018) do not allow for the latent variables (and the associated random shocks) to affect the latent outcome of the units whose outcome is observed. This may lead to biased parameters, in particular, of the covariances of the disturbances between the equations. This chapter improves on the prior Bayesian work on this subject by proposing a modified approach toward sampling using the multivariate-truncated, cross-sectionally dependent latent variable of the selection equation. The chapter outlines the model and implementation approach and provides simulation results documenting improved performance.

The chapter by Diego Rojas, Juan Estrada, Kim P. Huynh and David T. Jacho-Chavez, “Survival Analysis of Banknote Circulation: Fitness, Network Structure, and Machine Learning,” utilizes machine learning techniques to study the distribution network patterns of over 900 million banknotes using an administrative data set from the Bank of Canada’s Currency Information Management System. The data contain information regarding the printing date, physical fitness and where and when these banknotes return to the Bank of Canada’s distribution centers. Having constructed networks at the region and at the financial institution (those requesting as well as depositing banknotes) level, the authors use a K-prototypes clustering unsupervised machine learning algorithm to classify notes into different types. This information is then used when fitting a hazard model to explain how long a banknote stays in circulation. The results show that their denominations, and not fitness measures, are the main determinants of a banknote duration in circulation after controlling for the network structure.

Section 4: Applications of Financial Networks

The last section comprises of four chapters and provides applications to financial networks.

The chapter by Pablo Estrada and Leonardo Sánchez-Aragón, “Financial Contagion in Cross-holdings Networks: the case of Ecuador,” applies a financial contagion model proposed by Elliott, Golub, and Jackson (2014) to a cross-shareholding network of firms in Ecuador where the nodes are the firms and the links are the cross-shareholdings among firms. A novel data set provided by SUPERCIAS is used in the analysis.

The financial contagion model uses a network of financial interdependencies among firms in a dependency matrix where each element represents the cross-shareholding. The authors study how a negative shock that affects one firm propagates through the network and generates a cascade of failures. The results show that the Ecuadorian market exhibits low levels of diversification and integration, which means that the effects of cascades cannot be amplified throughout the network. Low integration implies the presence of weak links in the network. Results also show the presence of a giant weakly connected component (40% of the total firms) because diversification is moderate suggesting that cascade effects are still weak.

Furthermore, a sensitivity analysis is conducted to determine which parameters contribute to firm’s failure. When allowed the threshold, the failure cost, and the drop market value to vary, only two waves of contagion are noticeable. It was also found that two firms coming from the finance and trade industry cause the highest contagion and when a shock affects an entire industry there are more firm failures from trade and manufacturing industries than other industries. The results can be relevant for policymakers as they are better able to monitor the market and anticipate future losses.

The chapter by Edoardo Rainone, “Estimating Spillover Effects with Bilateral Outcomes,” is concerned with the estimation of spillover effects when outcomes arise as a consequence of bilateral interactions instead from individual actions, in other words the analysis refers to network effects when outcomes are generated on links and not on nodes.

With the diffusion of over-the-counter (OTC) platforms and the advances in the economic theory related to networks, the chapter emphasizes the importance of assessing network effects with link-based outcomes. A link-based spatial autoregressive (SAR) model is proposed together with identification conditions and a two step least square (2SLS) estimation procedure. The author shows analytically and with Monte Carlo simulations that using a standard node-based SAR, which models nodes’ instead of links’ outcomes, produces misleading results when the data generating process (DGP) is link-based. The methodology is illustrated using real data from an interbank network. The results highlight that under conditions that are often met in OTC markets, modeling nodes’ outcomes can lead to biased results and misleading policy implications.

The chapter by Anson T. Y. Ho, “Interconnectedness through the Lens of Consumer Credit Markets,” looks at the interconnectedness between financial institutions (FIs) through the lens of consumer credits. Financial systemic risk is often assessed by the interconnectedness of FIs in terms of cross ownership, overlapping investment portfolios, interbank credit exposures and other factors. Using detailed consumer credit data in Canada, this chapter constructs a novel banking network to measure FIs’ interconnectedness in consumer credit markets. Results show that FIs on average are more connected to each other over the sample period, when the interconnectedness measure increases by 21% from 2014 to 2019.

The FIs with more diversified portfolios are also more connected in the network. Participation in mortgage markets has strong positive influence on FIs’ connectedness, because FIs with mortgage operations have more similar portfolios to the large FIs. Findings in this chapter highlight the importance of FIs exposure to the household sector, which may have important implications on systemic risk and the risk of multiple stress incidences across FIs. Measuring the connectedness in consumer lending networks is the first step in quantifying the potential systemic risk generated by FIs’ consumer lending operations. Deeper understanding on how FIs finance their consumer lending is required to further translate the connectedness in consumer lending network into systemic risk measures.

Finally, the chapter by Andrija Mihoci, Michael Althof, Cathy Yi-Hsuan Chen and Wolfgang Karl Härdle, “FRM Financial Risk Meter,” proposes a systemic risk measure that accounts for links and mutual dependencies between financial institutions utilizing tail event information. The proposed Financial Risk Meter (FRM) is based on a Lasso quantile regression and it is designed to capture tail event co-movements. The FRM focus lies on understanding active data sets characteristics and the interdependencies in a network topology.

The focus of the chapter is on two selected FRM indices, namely FRM@Americas and FRM@Europe for the equity markets, and SRM@EuroArea as an application to the asset class of government bonds. Augmenting them, for example, by simultaneously checking varieties of quantiles of FRM components, one can monitor economic activity and network dynamics, and suggest further improvements in portfolio risk management.

The chapter’s findings are: first, FRM correlates positively with other measures of systemic risk and peaks around crises; second, a detailed inspection of the active set across time allows to detect the network’s nodes presenting the highest risk of spillover and third, FRM is shown to predict upcoming recession periods and serves as a leading indicator for systemic risk in a variety of world regions, the US and the EU market.

Therefore, the FRM can be viewed as an early recession indicator that can help to detect distressed areas in the financial system network consisting of banks and non-banks, and thereby can help prevent spillovers into the wider financial industry. Finally, FRM can measure tail event risk, accounts for network dynamics characteristics and offers a flexible risk measuring platform.

In practice, FRM can be applied to the return time series of selected financial institutions and macroeconomic risk factors.