Definition
The decomposition of individual or household income changes into a permanent component (persistent shocks that do not mean-revert, analogous to a random walk) and a transitory component (mean-reverting fluctuations around a stable trend). The central question is whether observed rises in cross-sectional income inequality reflect durable structural changes in the wage distribution or temporary volatility that will partially self-correct over time.
Key Ideas
- Error-components model: The standard framework specifies income as yit=αi+μit+εit, where αi is a time-invariant individual fixed effect, μit follows a random walk capturing permanent shocks, and εit is a serially uncorrelated transitory shock. Rising cross-sectional variance of yit can be traced to rising Var(μit) (permanent) or rising Var(εit) (transitory) or both.
- Male earnings inequality: 100% permanent (DeBacker et al. 2013). Using a confidential Internal Revenue Service (IRS) panel (1987–2009), the entire rise in cross-sectional dispersion of male earnings is attributable to the permanent variance component; the transitory variance showed no increase. This means the observed polarization is a structural shift in the wage distribution, not noisy variation.
- Household income: ~75% permanent. Extending the analysis to the household unit, approximately 75% of the household income inequality increase is permanent, with the remaining 25% transitory increase concentrated in spousal earnings and capital income — volatile sources less correlated with primary earner wages.
- Survey vs. administrative data. Prior studies using Current Population Survey (CPS) or Panel Study of Income Dynamics (PSID) data (Moffitt and Gottschalk 1995; Haider 2001) found a roughly equal split between permanent and transitory components. The shift toward predominantly permanent in the DeBacker et al. (2013) IRS data may reflect measurement-error advantages of administrative records (no seam bias, no top-coding at realistic wage levels) or genuine structural change in the character of inequality post-1987.
- Tax system and inequality. The federal income and payroll tax system reduces the level of income inequality by approximately 15% but does not offset the rising trend — redistribution is not keeping pace with structural wage divergence.
How It Works
An error-components model is estimated on an unbalanced panel of tax filers. The cross-sectional variance of log earnings at time t equals the accumulated variance of permanent shocks plus the variance of current transitory shocks. Identifying the split requires panel data: permanent shocks produce covariances that persist across all lags, while transitory shocks produce covariances that die out quickly. The key estimating equations exploit the auto-covariance structure of income residuals (after removing age and cohort effects). With administrative panel data spanning 22 years and millions of observations, DeBacker et al. can estimate the model with much tighter precision than survey-based studies.
Why It Matters
- Disability Insurance (DI) replacement rate channel: A permanently higher dispersion of male earnings means the gap between low-skill wages and the Social Security Administration's (SSA) national wage index (used to compute benefits) is durable. The Autor-Duggan (2003, 2006) mechanism — rising DI replacement rates for low-wage workers driving application growth — requires permanent wage inequality to have sustained incentive effects. DeBacker et al. (2013) provide the direct evidence that this premise holds. See DI Replacement Rate and DI Growth Decomposition.
- Consumption insurance: Whether households can smooth the income shocks matters for welfare. Permanent shocks are harder to insure against; a finding of predominantly permanent inequality implies greater welfare costs than a transitory finding would.
- Policy design: Redistributive policies calibrated on the assumption of mean-reversion (transitory inequality) will undershoot if the underlying process is closer to a random walk. The DeBacker finding that tax policy offsets the level but not the trend of inequality suggests the tax system is not adapting to the permanent character of widening dispersion.
Open Questions
- Whether the result is stable across the full earnings distribution, including the very bottom (where IRS data underrepresent informal workers) and the very top (where top-coding is less of an issue in tax data than surveys).
- Whether the predominance of permanent shocks reflects changing worker-firm match quality, technological skill-biased demand, or globalization — the model identifies magnitudes but not mechanisms.
- Whether the extension to household income (25% transitory) reflects genuine household risk-sharing through spousal labor supply, or compositional changes in household structure.
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