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. The full model (~120K parameters) runs 4 chains for 3,500 iterations each, completing in approximately 3 days with zero divergent transitions and R-hat \(\leq\) 1.004 across all spot-checked parameters.

Data

  • Source: KLD STATS, 1991–2018, via Wharton Research Data Services
  • Coverage: 6,324 unique firms; 2,068 indicator-year items; 3,273,013 non-missing observations across 51,586 firm-years
  • 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

Full draws will be made available at socialscores.org.