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Identifying Causal Effects in Information Provision Experiments

Dylan Balla-Elliott

TL;DR

This paper tackles the problem that standard estimators in information provision experiments overweight individuals who update beliefs the most, yet these individuals often exhibit weaker causal effects of beliefs on outcomes. It introduces the Local Least Squares (LLS) estimator, which yields an equally weighted average of individual slopes, $\mathbb{E}[\beta_i]$, even when belief updating is correlated with the causal effect, and it extends to panel, active, and passive designs under a broad class of learning-rate models. Applying LLS to six replications from leading journals, the author finds that in five studies the LLS estimates are meaningfully larger than conventional panel/TSLS estimates, with two cases more than doubling, and demonstrates how belief effects vary with learning rates. The method provides a more representative summary of heterogeneous effects and offers a tractable way to analyze endogenous information acquisition, with broad practical implications for evaluating how information provision changes behavior via beliefs.

Abstract

Standard estimators in information provision experiments place more weight on individuals who update their beliefs more in response to new information. This paper shows that, in practice, these individuals who update the most have the weakest causal effects of beliefs on outcomes. Standard estimators therefore understate these causal effects. I propose an alternative local least squares (LLS) estimator that recovers a representative unweighted average effect in a broad class of learning rate models that generalize Bayesian updating. I reanalyze six published studies. In five, estimates of the causal effects of beliefs on outcomes increase; in two, they more than double.

Identifying Causal Effects in Information Provision Experiments

TL;DR

This paper tackles the problem that standard estimators in information provision experiments overweight individuals who update beliefs the most, yet these individuals often exhibit weaker causal effects of beliefs on outcomes. It introduces the Local Least Squares (LLS) estimator, which yields an equally weighted average of individual slopes, , even when belief updating is correlated with the causal effect, and it extends to panel, active, and passive designs under a broad class of learning-rate models. Applying LLS to six replications from leading journals, the author finds that in five studies the LLS estimates are meaningfully larger than conventional panel/TSLS estimates, with two cases more than doubling, and demonstrates how belief effects vary with learning rates. The method provides a more representative summary of heterogeneous effects and offers a tractable way to analyze endogenous information acquisition, with broad practical implications for evaluating how information provision changes behavior via beliefs.

Abstract

Standard estimators in information provision experiments place more weight on individuals who update their beliefs more in response to new information. This paper shows that, in practice, these individuals who update the most have the weakest causal effects of beliefs on outcomes. Standard estimators therefore understate these causal effects. I propose an alternative local least squares (LLS) estimator that recovers a representative unweighted average effect in a broad class of learning rate models that generalize Bayesian updating. I reanalyze six published studies. In five, estimates of the causal effects of beliefs on outcomes increase; in two, they more than double.
Paper Structure (111 sections, 6 theorems, 75 equations, 8 figures, 3 tables)

This paper contains 111 sections, 6 theorems, 75 equations, 8 figures, 3 tables.

Table of Contents

  1. Conceptual Framework and Identifying Assumptions
  2. Potential Outcomes
  3. Experimental Designs
  4. Panel Identifying Assumption
  5. Active and Passive Control Identifying Assumption
  6. Learning Rate Belief Updating
  7. Randomization and Potential Beliefs
  8. Standard Panel and TSLS Estimators
  9. Individual Slopes: The Causal Building Block
  10. Standard Panel and TSLS Specifications
  11. A Representative Panel Specification
  12. Heterogeneity Bias Causes Negative Weights in Panel Regressions
  13. A Representative Active Control Specification
  14. A Representative Passive Control Specification
  15. Discussion
  16. ...and 96 more sections

Key Result

proposition A1

Consider a linear regression of $Y$ on $X$ where $X$ takes only two values, $x_1$ and $x_2$. Then the regression coefficient $\beta$ equals:

Figures (8)

  • Figure A1: Dependence between Belief Updating and Belief Effects in Six Studies
  • Figure D.1: Conditional Average Partial Effects in wiswallDeterminantsCollege15, Several Bandwidths
  • Figure D.2: Conditional Average Partial Effects in armonaHomePrice19, Several Bandwidths
  • Figure D.3: Conditional Average Partial Effects in setteleHowBeliefs22, Several Bandwidths
  • Figure D.4: Conditional Average Partial Effects in rothRiskExposure22, Several Bandwidths
  • ...and 3 more figures

Theorems & Definitions (12)

  • proposition A1: Binary Regression Property
  • proof
  • proposition A2: Panel Identification
  • proof
  • proposition A3: Necessity
  • proof
  • proposition A4: Active Control Identification
  • proof
  • proposition A5: Passive Control Identification
  • proof
  • ...and 2 more