Machine Learning for Set-Identified Linear Models

This paper provides estimation and inference methods for an identified set where the selection among a very large number of covariates is based on modern machine learning tools. I characterize the boundary of the identified set (i.e., support function) using a semiparametric moment condition. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the support function and propose a weighted bootstrap procedure to conduct inference about the identified set. I provide a general method to construct a Neyman-orthogonal moment condition for the support function. Applying my method to Lee (2008)'s endogenous selection model, I provide the asymptotic theory for the sharp (i.e., the tightest possible) bounds on the Average Treatment Effect in the presence of high-dimensional covariates. Furthermore, I relax the conventional monotonicity assumption and allow the sign of the treatment effect on the selection (e.g., employment) to be determined by covariates. Using JobCorps data set with very rich baseline characteristics, I substantially tighten the bounds on the JobCorps effect on wages under weakened monotonicity assumption

Information sharing in credit markets: incentives for incorrect information reporting

The introduction of institutions of credit information sharing - private credit bureaus and public credit registries - in the market for bank loans represent one of the possible solutions of information asymmetry problem, - the problem which the creditors tend to face. However the possibility of information sharing influences the bank's incentives in two different ways. While it disciplines the borrowers and, therefore, reduces the share of bad loans, a bank loses the competitive advantage, namely the monopolistic knowledge about the data in its clients' credit histories. Does the bank have an opportunity at its disposal to use the benefits of information sharing without losing its competitive advantage and its clientele? One way to do so is to report false data on borrowers. This paper analyses the bank's incentives for such opportunistic behavior and describes the impact of false information reporting on the characteristics of market equilibrium. The opportunity to get extra profit and to offer less expensive credit to new clients explains why banks prefer the strategy of dishonest behavior. This paper outlines the role of the informational intermediary in quality control for the data, contained in credit reports. Also, it describes the conditions under which verification of a certain share of reports provides that the parameters characterizing the equilibrium are equal to those in no information asymmetry situation.

Corporate Environmental Performance: Consistency of Metrics and Identification of Drivers

This study is among the first to provide insight into the assessment of the convergent validity of widely used environmental performance ratings. Using a set of environmental dimensions in KLD, GES, and ASSET4 ratings, this study demonstrates that the different environmental performance aggregated metrics sufficiently correlate and provide consistent information when comparing companies. The KLD environmental concerns measure provides a summary of the environmental impact of industrial activities in contrast to the KLD measure of strengths that is a proxy for environmental performance. The observed different patterns in KLD environmental dimensions suggest that they are distinct constructs and should not be combined in future research. This study demonstrates that GES environmental industry risk and KLD concerns are impact factors that drive corporate environmental performance. Companies in high impact sectors are on average rated with high environmental performance. The contribution of this paper is, therefore, a validation of environmental ratings and a sharper focus upon impact factors that are associated with high levels of environmental performance. In addition, this study discusses the implications of findings for advocates and sceptics of environmental ratings, as well as for academics and practitioners in the realm of SRI and CSR.Environmental performance; Ratings; Convergent validity; Industry risk

Linear representations of regular rings and complemented modular lattices with involution

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between classes of spaces and classes of representables is analyzed; for a class of spaces which is closed under ultraproducts and non-degenerate finite dimensional subspaces, the latter are shown to be closed under complemented [regular] subalgebras, homomorphic images, and ultraproducts and being generated by those members which are associated with finite dimensional spaces. Under natural restrictions, this is refined to a $1$-$1$-correspondence between the two types of classes

Sublattices of lattices of convex subsets of vector spaces

For a left vector space V over a totally ordered division ring F, let Co(V) denote the lattice of convex subsets of V. We prove that every lattice L can be embedded into Co(V) for some left F-vector space V. Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form $Co(V,Z)=\{X\cap Z | X\in Co(V)\}$, for some finite subset $Z$ of $V$. In particular, we obtain a new universal class for finite lower bounded lattices

Sublattices of lattices of order-convex sets, I. The main representation theorem

For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some lattice of the form Co(P) iff L satisfies (S), (U), and (B). Furthermore, if L has an embedding into some Co(P), then it has such an embedding that preserves the existing bounds. If L is finite, then one can take P finite, of cardinality at most $2n^2-5n+4$, where n is the number of join-irreducible elements of L. On the other hand, the partially ordered set P can be chosen in such a way that there are no infinite bounded chains in P and the undirected graph of the predecessor relation of P is a tree