2026-04-19

Method

  • Interrupted time series (ITS) model
  • Data observed every 3 years, 1989–2016
  • 2010 treated as first post-crisis observation
  • Chow test uses 2007 as the final pre-crisis breakpoint

\[\text{outcome}_t = \beta_0 + \beta_1 \text{time} + \beta_2 \text{post\_crisis} + \beta_3 \text{time\_post} + \varepsilon_t\]

Main Findings

ITS Model Coefficients
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1049 0.0173 6.0650 0.0009
time_index 0.0136 0.0016 8.5087 0.0001
post_crisis -0.2578 0.0316 -8.1644 0.0002
time_post 0.0096 0.0062 1.5478 0.1726
  • Positive pre-crisis trend (\(\hat{\beta}_1 > 0\))
  • Large, significant post-crisis level drop (\(\hat{\beta}_2\))
  • Post-crisis slope change not statistically significant (\(\hat{\beta}_3\))
  • Chow test confirms structural break at 2007

Chow Test

Chow Test at 2007 Breakpoint
F F-statistic 34.946
p-value 0.000494
  • Breakpoint: 2007 (final pre-crisis observation)
  • F = 34.946, p < 0.001
  • Strong evidence of a structural break in the outcome series

Interpretation

  • The 2008 financial crisis interrupted prior gains in Black economic well-being
  • The dominant effect is a persistent level loss — outcomes dropped sharply after 2009
  • The post-crisis slope (\(\hat{\beta}_3\)) is not significant: recovery did not offset the shock
  • Evidence supports lasting structural harm consistent with a Chow-identified break

Time Series Plot

Observed vs. Counterfactual Trend