Causal ordering and inference on acyclic networks

Abstract

This paper develops a new identification result for the causal ordering of observation units in a recursive network or directed acyclic graph. Inferences are developed for an unknown spatial weights matrix in a spatial lag model under the assumption of recursive ordering. The performance of the methods in finite sample settings is very good. Application to data on portfolio returns produces interesting new evidences on the contemporaneous lead-lag relationships between the portfolios and generates superior predictions.Keywords Spatial weights matrix · Directed acyclic graphs · Recursive ordering · M-estimation · Portfolio returns · Partial identificationWe thank the Editors for their encouragement and invitation to contribute towards this Special Issue in honour of Ingmar Prucha. We are especially thankful to two anonymous reviewers for making many helpful suggestions that helped us revise and substantially improve upon this paper. Thanks also due to Nidhan Choudhuri, Atanas Christev and Rod McCrorie for helpful discussions. The usual disclaimer applies.

Abnormal Returns or Mismeasured Risk? Network Effects and Risk Spillover in Stock Returns

“…One such admissible assumption is recursive structure under which information flows are sequential (but contemporaneous) through different segments of the market. Based on 25 portfolios formed on size and book-to-market (Fama and French 1996;French 2017), Basak et al (2018) find substantial explanation for risk spillovers and abnormal returns, and the model outperforms reduced form VAR (vector autoregressive) factor models. Suppose risk neutral traders arrive sequentially and repeatedly at the market taking positions on preferred risk/return FF portfolios.…”

“…Obviously, there are competing structural models where stocks belonging to different groups would be correlated, and we also discussed two such models: First, we refer to Basak et al (2018), who developed a model where limit or market order mechanisms generate recursive ordering of the portfolios in terms of information flow, in turn leading to cross-portfolio correlations. This may be viewed as a model diametrically in opposition to the model developed in this paper.…”

“…To address such misspecifications, we propose modeling cross-correlations using a suitable structural model. Motivated by the recent clustering model (Nagy and Ormos 2018) and recursive model (Basak et al 2018), we propose a social network dependence structure. Applied to data on stock returns for the 30 current DJIA stocks, we find evidence of network effects, the careful 1 Abnormal return is defined in the event study finance literature as the difference between the actual return of a security (in our case, over a one week time horizon) and the expected return as calculated using a model; see, for example, Brown and Warner (1985).…”

Applied Econometrics

“…where the effect of additional FF firm-specific factors is not included. The above CAPM model (2) can imply a specific form of network architecture, known in the spatial econometrics literature as a social interactions model (Lee et al 2010;Hsieh and Lee 2016;Bhattacharjee et al 2018;Cohen-Cole et al 2018;Do gan et al 2018) or a farmer-district model (Case 1992;Robinson 2003;Gupta and Robinson 2015), whereby the units (here, stocks) are classified into several groups or social networks. Stocks in the same social network are related to each other, but not to stocks in the other networks.…”

“…To address such misspecifications, we propose modeling cross-correlations using a suitable structural model. Motivated by the recent clustering model (Nagy and Ormos 2018) and recursive model (Basak et al 2018), we propose a social network dependence structure. Applied to data on stock returns for the 30 current DJIA stocks, we find evidence of network effects, the careful modeling of which addresses misspecification of the underlying factor model.…”