The Econometrics of Networks: Volume 42

The authors generalize the standard linear-in-means model to allow for multiple types with between and within-type interactions. The authors provide a set of identification conditions of peer effects and consider a two-stage least squares estimation approach. Large sample properties of the proposed estimators are derived. Their performance in finite samples is investigated using Monte Carlo simulations.

This chapter develops a set of two-step identification methods for social interactions models with unknown networks, and discusses how the proposed methods are connected to the identification methods for models with known networks. The first step uses linear regression to identify the reduced forms. 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, this chapter proposes to represent the sample vectors with respect to a basis of a lower-dimensional space so that we have fewer regression coefficients in the first step. This allows us to identify some reduced form submatrices, which provide equations for identifying the primitive parameters.

This chapter 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 author proposes a new estimation method that uses the relationship between samples in different iterations to correct selection. The author uses the snowball samples collected from Facebook to estimate the proportion of users who support the Umbrella Movement in Hong Kong.

Evidence suggests that, in the presence of imperfect market institutions, individuals devote resources to the establishment of reliable connections to attenuate the frictions that reduce trading and insurance opportunities. In this chapter, the author surveys the relevant literature on strategic formation of networks and use it to study this particular economic situation. A simple model is built to show that the investment in strong ties often, though not always, produces stable configurations that manage to improve upon the imperfections of market institutions.

This chapter 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 author emphasizes the interplay between model specification and computational complexity, and suggests tactics to make empirically realistic models become tractable. Two detailed examples, on friendship networks and coauthorship networks, are used to illustrate these issues and to demonstrate the performance of the approach with both simulation and empirical evidence. Also, the author presents extensions to the estimation method, which expand the potential range of applications, and which provide statistical inference with minimal computational burden.

The authors construct an intertemporal model of rent-maximizing behavior on the part of a timber harvester under potentially multidimensional risk as well as geographical heterogeneity. Subsequently, the authors use recursive methods (specifically, the method of stochastic dynamic programing) to characterize the optimal policy function – the rent-maximizing timber-harvesting profile. One noteworthy feature of their application to forestry in the province of British Columbia, Canada is the unique and detailed information the authors have organized in the form of a dynamic geographic information system to account for site-specific cost heterogeneity in harvesting and transportation, as well as 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 with which to conduct policy analysis at scale.

This research aims to empirically analyze 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 of this study considers branch density (the ratio of the total number of branches to area size) by employing a spatial two-way fixed effects model. The main finding of this study is that there are no effects associated with market structure, however, there are strong spatial within and nearby effects associated with the socioeconomic variables. In addition, the authors also study the effect of spatial competition from rival banks: they find that large banks and small banks tend to avoid markets dominated by their competitors.

This chapter proposes an approach toward the estimation of cross-sectional sample selection models, where the shocks on the units of observation feature some interdependence through spatial or network autocorrelation. In particular, this chapter improves on prior Bayesian work on this subject by proposing a modified approach toward sampling the multivariate-truncated, cross-sectionally dependent latent variable of the selection equation. This chapter outlines the model and implementation approach and provides simulation results documenting the better performance of the proposed approach relative to existing ones.

The efficient distribution of bank notes is a first-order responsibility of central banks. The authors study the distribution patterns of bank notes with an administrative dataset from the Bank of Canada’s Currency Inventory Management Strategy. The single note inspection procedure generates a sample of 900 million bank notes in which the authors can trace the length of the stay of a bank note in the market. The authors define the duration of the bank note circulation cycle as beginning on the date the bank note is first shipped by the Bank of Canada to a financial institution and ending when it is returned to the Bank of Canada. In addition, the authors provide information regarding where the bank note is shipped and later received, as well as the physical fitness of the bank note upon return to the Bank of Canada’s distribution centers. K–prototype clustering classifies bank notes into types. A hazard model estimates the duration of bank note circulation cycles based on their clusters and characteristics. An adaptive elastic net provides an algorithm for dimension reduction. It is found that while the distribution of the duration is affected by fitness measures, their effects are negligible when compared with the influence exerted by the clusters related to bank note denominations.

Financial contagion refers to the propagation of shocks that can generate widespread failures. The authors apply a financial contagion model proposed by Elliott, Golub, and Jackson (2014) to a cross-shareholding network of firms in Ecuador. The authors use a novel dataset to study the potential channels for contagion. Although diversification is not high, results reveal enough conditions for a contagion event to occur. However, the low level of integration attenuates the effects of shocks. The authors run simulations affecting a particular firm at the time, and find that two firms coming from the finance and trade industry cause the highest contagion. In addition, when an entire industry receives a shock, trade and manufacturing industries contagion more companies than the rest. Finally, the model can assist policymakers to monitor the market and evaluate the fragility of the network in different scenarios.

This chapter is concerned with the estimation of spillover effects when outcomes arise as a consequence of bilateral interactions instead of from individual actions. In this type of environments, outcomes are generated on links instead of on nodes of a network, like bilateral prices in over-the-counter markets. The author proposes a link-based spatial autoregressive (SAR) model and discusses identification conditions and a two step least square estimation procedure. The author shows analytically that using a standard node-based SAR, which models nodes instead of links’ outcomes, produces misleading results when the data generating process is link-based. The methodology is illustrated using Monte Carlo experiments and real data from an interbank network.

Financial systemic risk is often assessed by the interconnectedness of financial institutes (FI) in terms of cross-ownership, overlapping investment portfolios, interbank credit exposures, etc. Less is known about the interconnectedness between FIs through the lens of consumer credits. Using detailed consumer credit data in Canada, this chapter constructs a novel banking network to measure FIs’ interconnectedness in the consumer credit markets. Results show that FIs on average are more connected to each other over the sample period, with the interconnectedness measure increases by 19% from 2013 Q4 to 2019 Q4. FIs with more diversified portfolios are more connected in the network. Among various types of FIs, secondary FIs have the notable increase in interconnectedness. Domestic Systemically Important Banks and secondary FIs offering a broad range of loan products are more connected to large FIs, while those specialized in single loan types are more connected to their industry peers. FI connectedness is also significantly related to their participation in the mortgage markets.

A systemic risk measure is proposed accounting for links and mutual dependencies between financial institutions utilizing tail event information. Financial Risk Meter (FRM) is based on least absolute shrinkage and selection operator quantile regression designed to capture tail event co-movements. The FRM focus lies on understanding active set data characteristics and the presentation of interdependencies in a network topology. Two FRM indices are presented, namely, FRM@Americas and FRM@Europe. The FRM indices detect systemic risk at selected areas and identify risk factors. In practice, FRM is applied to the return time series of selected financial institutions and macroeconomic risk factors. The authors identify companies exhibiting extreme “co-stress” as well as “activators” of stress. With the SRM@EuroArea, the authors extend to the government bond asset class, and to credit default swaps with FRM@iTraxx. FRM is a good predictor for recession probabilities, constituting the FRM-implied recession probabilities. Thereby, FRM indicates tail event behavior in a network of financial risk factors.