Minimum Wage and Wage Inequality

Definition

The minimum wage affects the distribution of wages primarily by compressing the lower tail: workers who would otherwise earn below or near the statutory floor are pushed up, reducing the 50/10 percentile gap. The extent of this compression — and thus the minimum wage's contribution to changes in wage inequality over time — is an empirical question that depends critically on identification strategy. The minimum wage's contribution to lower-tail inequality is estimated by regressing inequality measures on the "effective minimum" ($\log(\text{min}) - \log(p_{50})$), which captures how binding the minimum is in a given state and year.

Key Ideas

• Effective minimum: The key right-hand-side variable is the effective minimum $= \log(\text{min}) - \log(p_{50})$, measuring how binding the statutory floor is relative to the local wage distribution. A higher effective minimum means the floor is more compressed against the median.
• Lee (1999) bias: Lee's ordinary least squares (OLS) specification suffers from two upward biases that inflate the estimated minimum wage contribution to lower-tail inequality:
  1. Transitory shock bias: State-level shocks to $p_{50}$ appear in both the dependent variable (e.g., $\log p_{50} - \log p_{10}$) and the regressor (effective minimum $= \log(\text{min}) - \log(p_{50})$), creating a spurious negative correlation.
  2. Omitted variable bias: High-wage states tend to have more latent inequality (larger 60/40 gap) but lower effective minima; this generates a positive correlation between low effective minima and high inequality that is not causal.
• Instrumental variables (IV) correction: Autor, Manning, and Smith (2016) instrument the effective minimum and its square with the statutory minimum, its square, and statutory minimum $\times$ average log state median. This purges both biases because the statutory minimum is set by law (exogenous to local shocks) and the interaction soaks up the omitted-variable correlation with state wage levels. First-stage F-statistics range from $251$ to $684$.
• Revised estimates: After IV correction, the minimum wage explains $40$–$55\%$ of female lower-tail (50/10) inequality growth in the 1980s ($11$–$15$ log points of $24.6$); the male contribution is negligible ($<5\%$). Over 1979–2012, the minimum wage explains roughly $30$–$40\%$ of pooled lower-tail inequality growth.
• State variation and identification: Before 1991, nearly all states paid the federal minimum floor; only post-1991 variation (up to 31 states above federal level by 2008) provides credible IV identification. Lee's 1979–1989 OLS sample had essentially no cross-state variation in statutory minima.

How It Works

The empirical strategy uses a state-year panel from the Current Population Survey (CPS) Merged Outgoing Rotation Groups (MORG) (1979–2012; $N \approx 1{,}700$ observations in levels, $1{,}650$ in first differences). The dependent variable is a wage percentile gap (e.g., $\log p_{50} - \log p_{10}$); the key regressor is the effective minimum. The IV uses the statutory minimum (which is set by legislatures independently of local labor market conditions) to isolate exogenous variation in the effective minimum after absorbing state fixed effects (FE) and trends. In levels, the specification includes state FE; in first differences, it includes year FE. The comparison between Lee's OLS (which implies $\approx 100\%$ of female lower-tail inequality growth is attributable to the minimum wage) and the two-stage least squares (2SLS) (which implies $40$–$55\%$) directly quantifies the magnitude of the two biases.

Why It Matters

• The minimum wage is a first-order policy lever for lower-tail inequality. The corrected estimates show it is significant but not dominant — underlying skill-biased technological change and institutional factors also contributed substantially.

• The bias correction matters for cost-benefit analysis of minimum wage increases: if Lee's estimate were taken at face value, one could argue the minimum wage is the primary driver of distributional outcomes; the corrected estimate implies other policies (Earned Income Tax Credit (EITC), education, labor market regulation) are also essential.

• The measurement error treatment of spillovers provides a methodological caution: apparent effects at percentiles above the statutory floor may not reflect true wage-setting spillovers but rather CPS misreporting.

• Last-place aversion and minimum wage opposition (Kuziemko et al. 2014): Among low-wage workers, those earning just above the current minimum wage ($\$7.26$–$\$8.25$ when the floor is $\$7.25$) oppose a minimum wage increase significantly more than comparable workers. The Last-Place Aversion (LPA) mechanism: raising the floor to their wage level would eliminate the group of worse-off workers from whom they currently distinguish themselves, losing relative-status utility. This is a demand-side behavioral explanation for minimum wage opposition that operates independently of employer lobbying or employment concerns. See Last-Place Aversion.

Open Questions

• Why is the minimum wage's contribution to lower-tail inequality so much larger for women than men? The mechanical explanation (women are more concentrated near the minimum) is partial; taste-based discrimination or sectoral sorting may interact.
• How does the relationship change post-2012, as many states and cities adopted minimum wages well above the federal floor ($\$15{+}$ movements)?
• Are the spillovers truly zero, or do the measurement error confidence intervals simply not have sufficient power to detect moderate true spillovers?
• How do the IV estimates interact with monopsony models, where the minimum wage may have positive employment effects at moderate levels?

Related

• Minimum Wage Spillovers
• Last-Place Aversion
• David Autor
• Alan Manning
• Christopher L. Smith
• Ilyana Kuziemko

Sources

• Autor Manning and Smith 2016 — The Contribution of the Minimum Wage to US Wage Inequality over Three Decades
• Kuziemko et al 2014 — Last-Place Aversion Evidence and Redistributive Implications