D-SOCIAL-KLD

Dynamic IRT scores for corporate social responsibility · 1991–2018 · with David Primo and Brian Kelleher Richter

Overview

KLD STATS (now MSCI ESG) codes publicly traded U.S. firms on dozens of binary indicators each year — strengths and concerns across categories like environment, labor, governance, and community relations. The standard approach in the management literature is the KLD Index: sum the strengths and subtract the concerns. This treats every indicator as equally informative, which is a strong and usually implausible assumption.

D-SOCIAL-KLD replaces the additive index with a dynamic two-parameter IRT model. The model treats firms as examinees and KLD indicators as test items. A discrimination parameter for each item lets the data decide how informative each indicator is; a difficulty parameter captures how demanding each indicator is at the population level. A firm-specific random walk prior links scores across years, encoding the intuition that a firm’s CSR position in 2006 is strongly predicted by its position in 2005.

The result is a posterior distribution over a latent CSR score \(\theta_{it}\) for each firm-year — with uncertainty quantified, discrimination weights estimated from the data, and year-to-year dynamics modeled explicitly.

The model

\[ y_{ijt} \sim \text{Bernoulli}\bigl(\Phi(\beta_{jt} \cdot \theta_{it} - \alpha_{jt})\bigr) \]

  • \(\theta_{it}\): latent CSR score for firm \(i\) in year \(t\)
  • \(\alpha_{jt}\): difficulty of indicator \(j\) in year \(t\)
  • \(\beta_{jt}\): discrimination of indicator \(j\) in year \(t\)
  • Year-to-year dynamics: \(\theta_{i,t} = \theta_{i,t-1} + \sigma_{\text{firm},i} \cdot \varepsilon\)

Estimation uses Stan’s No-U-Turn Sampler with a non-centered parameterization for the dynamic prior, which resolves the funnel geometry that the centered form creates in the joint posterior.

Data

  • Source: KLD STATS, 1991–2018, via Wharton Research Data Services
  • Coverage: ~6,300 unique firms; 2,000+ indicator-year items; ~1.5M non-missing observations
  • Universe: firms present in the KLD database by 2012 (for comparability with published scores)

Outputs

The estimation pipeline produces posterior means, standard deviations, and percentiles for:

  • Firm-year scores (\(\theta_{it}\)): the primary quantity of interest
  • Item parameters (\(\alpha_{jt}\), \(\beta_{jt}\)): difficulty and discrimination for each indicator-year

Scores are interval-scaled and centered near zero in each year. Posterior uncertainty is reported explicitly and should be propagated into downstream analyses.

Resources

Code and data available on request. Full draws will be made available at socialscores.org.