arXiv subjects

Kyungchul Song

Publications and source records attributed to Kyungchul Song.

At least 19 recordsLinked to original sources

arXiv2026

Existence of Bayesian Equilibria in Incomplete Information Games without Common Priors

This paper focuses on finite-player incomplete information games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolute continuity of information in Milgrom and Weber (1985), and prove that Bayesian equilibria exist in a broad class of games, including those with discontinuous payoffs. Examples illustrate the scope and implications of our findings.

econ.TH↗

arXiv2026

Causal Inference with Groupwise Matching

This paper examines methods of causal inference based on groupwise matching when we observe multiple large groups of individuals over several periods. We formulate causal inference validity through a generalized matching condition, generalizing the parallel trend assumption in difference-in-differences designs. We show that difference-in-differences, synthetic control, and synthetic difference-in-differences designs are distinguished by the specific matching conditions that they invoke. Through regret analysis, we demonstrate that difference-in-differences and synthetic control with differencing are complementary; the former dominates the latter if and only if the latter's extrapolation error exceeds the former's matching error up to a term vanishing at the parametric rate. The analysis also reveals that synthetic control with differencing is equivalent to difference-in-differences when the parallel trend assumption holds for both the pre-treatment and post-treatment periods. We develop a statistical inference procedure based on synthetic control with differencing and present an empirical application demonstrating its usefulness.

econ.EM↗

arXiv2026

Simple Inference on a Simplex-Valued Weight

In many applications, the parameter of interest involves a simplex-valued weight which is identified as a solution to an optimization problem. Examples include synthetic control methods with group-level weights and various methods of model averaging and forecast combinations. The simplex constraint on the weight poses a challenge in statistical inference due to the constraint potentially binding. In this paper, we propose a simple method of constructing a confidence set for the weight using an adaptive test based on the projection on a polyhedral cone and prove that the method is asymptotically uniformly valid. The procedure does not require tuning parameters or simulations to compute critical values. The confidence set accommodates both the cases of point-identification or set-identification of the weight. We illustrate the method with an empirical example.

econ.EM↗

arXiv2025

Synthetic Decomposition for Counterfactual Predictions

Counterfactual predictions are challenging when the policy variable goes beyond its pre-policy support. However, in many cases, information about the policy of interest is available from different ("source") regions where a similar policy has already been implemented. In this paper, we propose a novel method of using such data from source regions to predict a new policy in a target region. Instead of relying on extrapolation of a structural relationship using a parametric specification, we formulate a transferability condition and construct a synthetic outcome-policy relationship such that it is as close as possible to meeting the condition. The synthetic relationship weighs both the similarity in distributions of observables and in structural relationships. We develop a general procedure to construct asymptotic confidence intervals for counterfactual predictions and prove its asymptotic validity. We then apply our proposal to predict average teenage employment in Texas following a counterfactual increase in the minimum wage.

econ.EM↗

arXiv2024

A Decomposition Approach to Counterfactual Analysis in Game-Theoretic Models

Decomposition methods are often used for producing counterfactual predictions in non-strategic settings. When the outcome of interest arises from a game-theoretic setting where agents are better off by deviating from their strategies after a new policy, such predictions, despite their practical simplicity, are hard to justify. We present conditions in Bayesian games under which the decomposition-based predictions coincide with the equilibrium-based ones. In many games, such coincidence follows from an invariance condition for equilibrium selection rules. To illustrate our message, we revisit an empirical analysis in Ciliberto and Tamer (2009) on firms' entry decisions in the airline industry.

econ.EM↗

arXiv2024

The Law of Large Numbers for Large Stable Matchings

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong correlation among the colleges' preferences while allowing students' preferences to be fully heterogeneous. Our concentration inequality yields laws of large numbers for the empirical matching probabilities and other statistics commonly used in empirical analyses of a large matching market. To illustrate the usefulness of our concentration inequality, we prove consistency for estimators of conditional matching probabilities and measures of positive assortative matching.

econ.EM↗

arXiv2023

Some Impossibility Results for Inference With Cluster Dependence with Large Clusters

This paper focuses on a setting with observations having a cluster dependence structure and presents two main impossibility results. First, we show that when there is only one large cluster, i.e., the researcher does not have any knowledge on the dependence structure of the observations, it is not possible to consistently discriminate the mean. When within-cluster observations satisfy the uniform central limit theorem, we also show that a sufficient condition for consistent $\sqrt{n}$-discrimination of the mean is that we have at least two large clusters. This result shows some limitations for inference when we lack information on the dependence structure of observations. Our second result provides a necessary and sufficient condition for the cluster structure that the long run variance is consistently estimable. Our result implies that when there is at least one large cluster, the long run variance is not consistently estimable.

econ.EM↗

arXiv2023

Econometric Inference on a Large Bayesian Game with Heterogeneous Beliefs

Econometric models of strategic interactions among people or firms have received a great deal of attention in the literature. Less attention has been paid to the role of the underlying assumptions about the way agents form beliefs about other agents. We focus on a single large Bayesian game with idiosyncratic strategic neighborhoods and develop an approach of empirical modeling that relaxes the assumption of rational expectations and allows the players to form beliefs differently. By drawing on the main intuition of Kalai (2004), we introduce the notion of hindsight regret, which measures each player's ex-post value of other players' type information, and obtain the belief-free bound for the hindsight regret. Using this bound, we derive testable implications and develop a bootstrap inference procedure for the structural parameters. Our inference method is uniformly valid regardless of the size of strategic neighborhoods and tends to exhibit high power when the neighborhoods are large. We demonstrate the finite sample performance of the method through Monte Carlo simulations.

stat.AP↗

arXiv2023

Measuring Diffusion over a Large Network

This paper introduces a measure of the diffusion of binary outcomes over a large, sparse network, when the diffusion is observed in two time periods. The measure captures the aggregated spillover effect of the state-switches in the initial period on their neighbors' outcomes in the second period. This paper introduces a causal network that captures the causal connections among the cross-sectional units over the two periods. It shows that when the researcher's observed network contains the causal network as a subgraph, the measure of diffusion is identified as a simple, spatio-temporal dependence measure of observed outcomes. When the observed network does not satisfy this condition, but the spillover effect is nonnegative, the spatio-temporal dependence measure serves as a lower bound for diffusion. Using this, a lower confidence bound for diffusion is proposed and its asymptotic validity is established. The Monte Carlo simulation studies demonstrate the finite sample stability of the inference across a range of network configurations. The paper applies the method to data on Indian villages to measure the diffusion of microfinancing decisions over households' social networks.

stat.ME↗

arXiv2022

Estimating Dynamic Spillover Effects along Multiple Networks in a Linear Panel Model

Spillover of economic outcomes often arises over multiple networks, and distinguishing their separate roles is important in empirical research. For example, the direction of spillover between two groups (such as banks and industrial sectors linked in a bipartite graph) has important economic implications, and a researcher may want to learn which direction is supported in the data. For this, we need to have an empirical methodology that allows for both directions of spillover simultaneously. In this paper, we develop a dynamic linear panel model and asymptotic inference with large $n$ and small $T$, where both directions of spillover are accommodated through multiple networks. Using the methodology developed here, we perform an empirical study of spillovers between bank weakness and zombie-firm congestion in industrial sectors, using firm-bank matched data from Spain between 2005 and 2012. Overall, we find that there is positive spillover in both directions between banks and sectors.

econ.EM↗

arXiv2022

A Decomposition Analysis of Diffusion Over a Large Network

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion proposed by He and Song (2022), provides a method of decomposition analysis to measure the role of the covariates on the estimated diffusion, and develops an asymptotic inference procedure for the decomposition analysis in such a situation. This paper also presents results from a Monte Carlo study on the small sample performance of the inference procedure.

stat.ME↗

arXiv2022

A Berry-Esseen Bound for Vector-valued Martingales

This note provides a conditional Berry-Esseen bound for the sum of a martingale difference sequence $\{X_i\}_{i=1}^n$ in $\mathbb{R}^d$, $d\ge 1$, adapted to a filtration $\{\mathcal{F}_i\}_{i=1}^n$. We approximate the conditional distribution of $S=\sum_{i=1}^n X_i$ given some $σ$-field $\mathcal{F}_0\subset \mathcal{F}_1$ by that of a mean-zero normal random vector having the same conditional variance given $\mathcal{F}_0 $ as the vector $S$. Assuming that the conditional variances $\mathsf{E}[X_iX_i^{\top}\mid\mathcal{F}_{i-1}]$, $i\ge 1$, are $\mathcal{F}_0$-measurable and non-singular, and the third conditional moments of $\|X_i\|$, $ i\ge 1 $, given $\mathcal{F}_0$ are uniformly bounded, we present a simple bound on the conditional Kolmogorov distance between $S$ and its approximation given $\mathcal{F}_0$ which is of order $O_{a.s.}([\ln(ed)]^{5/4}n^{-1/4})$.

math.PR↗

arXiv2022

Local Asymptotic Minimax Estimation of Nonregular Parameters with Translation-Scale Equivariant Maps

When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable. However, when the nondifferentiable transform is a known composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map, this paper demonstrates that it is possible to define a notion of asymptotic optimality of an estimator as an extension of the classical local asymptotic minimax estimation. This paper establishes a local asymptotic risk bound and proposes a general method to construct a local asymptotic minimax decision.

math.ST↗

arXiv2021

Estimation and Inference on Treatment Effects Under Treatment-Based Sampling

Causal inference in a program evaluation setting faces the problem of external validity when the treatment effect in the target population is different from the treatment effect identified from the population of which the sample is representative. This paper focuses on a situation where such discrepancy arises by a stratified sampling design based on the individual treatment status and other characteristics. In such settings, the design probability is known from the sampling design but the target population depends on the underlying population share vector which is often unknown, and except for special cases, the treatment effect parameters are not identified. In this paper, we propose a method of constructing confidence sets that are valid for a given range of population shares. When a benchmark population share vector and a corresponding estimator of a treatment effect parameter are given, we develop a method to discover the scope of external validity with familywise error rate control. Finally, we derive an optimal sampling design which minimizes the semiparametric efficiency bound given a population share associated with a target population. We provide Monte Carlo simulation results and an empirical application to demonstrate the usefulness of our proposals.

stat.ME↗

arXiv2021

Limit Theorems for Network Dependent Random Variables

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations.

econ.EM↗

arXiv2021

Counterfactual Analysis under Partial Identification Using Locally Robust Refinement

Structural models that admit multiple reduced forms, such as game-theoretic models with multiple equilibria, pose challenges in practice, especially when parameters are set-identified and the identified set is large. In such cases, researchers often choose to focus on a particular subset of equilibria for counterfactual analysis, but this choice can be hard to justify. This paper shows that some parameter values can be more "desirable" than others for counterfactual analysis, even if they are empirically equivalent given the data. In particular, within the identified set, some counterfactual predictions can exhibit more robustness than others, against local perturbations of the reduced forms (e.g. the equilibrium selection rule). We provide a representation of this subset which can be used to simplify the implementation. We illustrate our message using moment inequality models, and provide an empirical application based on a model with top-coded data.

econ.EM↗

arXiv2020

Estimating Unobserved Individual Heterogeneity Using Pairwise Comparisons

We propose a new method for studying environments with unobserved individual heterogeneity. Based on model-implied pairwise inequalities, the method classifies individuals in the sample into groups defined by discrete unobserved heterogeneity with unknown support. We establish conditions under which the groups are identified and consistently estimated through our method. We show that the method performs well in finite samples through Monte Carlo simulation. We then apply the method to estimate a model of lowest-price procurement auctions with unobserved bidder heterogeneity, using data from the California highway procurement market.

econ.EM↗

arXiv2019

Estimating Local Interactions Among Many Agents Who Observe Their Neighbors

In various economic environments, people observe other people with whom they strategically interact. We can model such information-sharing relations as an information network, and the strategic interactions as a game on the network. When any two agents in the network are connected either directly or indirectly in a large network, empirical modeling using an equilibrium approach can be cumbersome, since the testable implications from an equilibrium generally involve all the players of the game, whereas a researcher's data set may contain only a fraction of these players in practice. This paper develops a tractable empirical model of linear interactions where each agent, after observing part of his neighbors' types, not knowing the full information network, uses best responses that are linear in his and other players' types that he observes, based on simple beliefs about the other players' strategies. We provide conditions on information networks and beliefs such that the best responses take an explicit form with multiple intuitive features. Furthermore, the best responses reveal how local payoff interdependence among agents is translated into local stochastic dependence of their actions, allowing the econometrician to perform asymptotic inference without having to observe all the players in the game or having to know the precise sampling process.

stat.ME↗