Core Concepts and Econometrics in Labor Market Analysis

Posted on Nov 14, 2025 in Economics

Section 1: Labor Demand Basics

  • Firms hire workers up to the point where the wage equals the Value of Marginal Product (VMP).
    • VMP = P × MP (where P = price of output, MP = marginal product of labor)
  • Downward-sloping labor demand due to diminishing marginal returns to labor.

Section 2: Labor Supply and Elasticity

  • Labor supply reflects the tradeoff between leisure and work.
  • Reservation wage: the minimum wage a person is willing to accept for a job.
  • Effects of wage increase:
    • Substitution effect: work is more rewarding, leading to more hours worked.
    • Income effect: You can afford more leisure, leading to fewer hours worked.
  • Effects of non-labor income increase: shifts labor supply left.
  • Labor supply elasticity = % change in hours worked / % change in wage.
  • Econometric issue: difficult to isolate wage variation from other correlated variables.
  • Best empirical estimates:
    • Long-run labor demand elasticity: -1
    • Short-run labor demand elasticity: -0.5

Section 3: Labor Market Equilibrium

  • Intersection of labor demand and labor supply determines equilibrium wage and employment.
  • Comparative statics: shifts in demand (e.g., due to technology) or supply (e.g., due to demographics).

Section 4: Labor Market Policies

  • Minimum wage:
    • Theory: could reduce employment in competitive markets, but not necessarily in monopsony.
    • Card & Krueger study: found minimum wage increases did not reduce employment in NJ fast food; possibly due to monopsonistic conditions.
    • Considerations:
      • Pass-through to prices (may increase labor demand)
      • Elasticity of labor demand
      • Fringe benefits reduced
      • Worker effort/injury effects

Section 5: Technology and Labor Demand (Elasticity & Substitution)

  • In Cobb-Douglas: Y = A * K^(1/3) * L^(2/3), rising A raises MPL and wages.
  • In CES production:
    • Low elasticity of substitution: harder to substitute capital for labor; technology may reduce MPL and wages.
    • High elasticity: easier substitution; fewer workers, but those who stay are more productive.
    • High elasticity: capital replaces labor; wages fall but output may rise.
    • Low elasticity: labor remains essential; technology raises wages and employment.

Section 6: Task-Based Framework – Automation vs. New Tasks

  • Automation:
    • Productivity effect: capital takes over existing tasks, boosting output.
    • Displacement effect: fewer tasks for labor; labor share falls.
    • Labor could lose if tasks lost are not replaced.
  • New Tasks:
    • Productivity effect: new tasks increase total output.
    • Reinstatement effect: labor performs new valuable tasks; labor share rises.
    • Net effect positive: more output and more income share for labor.

Section 7: Immigration

  • Basic model: immigration increases labor supply, causing wages to fall.
  • Immigration surplus: Triangle = (1/2) × Δw × M
    • M = number of immigrants, Δw = wage drop.
  • With positive spillovers:
    • Native workers become more productive (e.g., skilled immigrants help firms).
    • Native surplus = immigration surplus + extra surplus from productivity.

Section 8: Trade (China Shock)

  • Autor, Dorn & Hanson: trade with China caused job loss and wage pressure in import-exposed U.S. regions.
  • Important because it showed permanent displacement rather than simple reallocation.

Section 9: Monopsony and Minimum Wage

  • Monopsonistic firms hire fewer workers and pay lower wages than competitive firms.
  • Minimum wage can increase both wage and employment in monopsony.
  • Pass-through, worker behavior, and monopsony power matter.

Section 10: Instrumental Variables (IV)

  • Used to isolate causal effects of wages, education, etc.
  • Example: Angrist & Krueger used quarter of birth to estimate return to schooling.
  • Example: Autor, Lyle, Acemoglu used WWII men mobilization to study women’s labor supply.
  • Card: proximity to college as IV (high school validity concerns).

Section 11: Education and Human Capital

  • Returns to education: OLS can be biased due to ability.
  • IV strategies: quarter of birth (Angrist & Krueger), school construction (Indonesia), Maimonides rule (Angrist & Lavy).
  • LATE = Local Average Treatment Effect (effect for compliers).
  • Estimating Present Value (PV) of education:
    • PVhs = Whs + Whs/(1+r) + Whs/(1+r)^2 + …
    • PVcol = -H – H/(1+r) – H/(1+r)^2 – H/(1+r)^3 + Wcol/(1+r)^4 + …
    • Choose schooling where PV(earnings with school) > PV(earnings without).
  • Schooling decision:
    • Lower discount rate r → more school (r=MRR).
  • Different ability students:
    • High-ability: steeper earnings-schooling slope → more school.
  • Rate of return to schooling formula:
    • ln(wᵢ) = a + b ⋅ sᵢ + controls
  • Alternative estimation strategies:
    • Twins: problematic due to non-random differences.
    • Angrist & Krueger: quarter of birth.
    • Card: proximity to college.

Section 12: Signaling and GED

  • Spence signaling model:
    • Education may not raise productivity but signals ability.
    • High-types (H-types) find school less costly → choose s ≥ s̄.
    • Low-types (L-types) find school too costly.
    • Separating equilibrium: school serves as a signal.
  • GED study (Tyler, Murnane, Willett):
    • Difference-in-Differences (DiD) shows greater signaling value in states where GED is hard to earn.

Section 13: Difference-in-Differences (DiD)

  • Measures treatment effect using before/after and treatment/control:
    • (Y₁ᵀ – Y₀ᵀ) – (Y₁ᶜ – Y₀ᶜ)

Section 14: World War II Studies on Labor

  • Goldin & Olivetti: women’s wartime employment had long-run labor force impacts.
  • Acemoglu, Autor, Lyle: used WWII mobilization rates to estimate female labor supply elasticity.
    • States with higher male mobilization → more female labor → affected long-term female wages due to oversupply of workers when men returned from war and women reallocated to lower wage jobs.

Section 15: Unions and Wage Determination

  • Union wage premium: hard to estimate due to selection.
  • Wage compression: unions raise low wages more, reducing inequality.
  • Decline in unions → rise in inequality (1980–2020).
  • Oaxaca–Blinder decomposition used to isolate union effect.

Section 16: Monopoly Union Model

  • Union sets wage w_M; firm hires off demand curve at E_M.
  • Optimal wage: where union indifference = firm’s labor demand slope.
  • Example from Borjas 10-1:
    • Labor demand: w = 20 – 0.01E
    • MUe/MUw = w/E
    • Union utility: U = w × E
    • Slope condition: w / E = 0.01
    • Solve to get: w = 10, E = 1000

Section 17: Efficient Contracts and Bargaining

  • Contract curve: set of points where firm isoprofit and union indifference curves are tangent.
  • Final deal must be on or above the threat point (firm’s profit ≥ threat point, union utility ≥ threat point).
  • Contract curve: between Points P and Z; if threat point is M, the deal is on QR.

🎯 The final deal should be on the contract curve where:

  • The firm’s profit is at least as high as the threat point (e.g., Point M).
  • The union’s utility is at least as high as the threat point.

Section 18: Hedonic Wage Function

  • Explains wage differences based on job characteristics (e.g., risk).
  • Graphs show:
    • Red line: hedonic wage function (market)
    • U-curves: worker indifference curves (preferences)
    • π-curves: firm isoprofit curves
  • Steeper U = more risk-averse, requiring higher compensation.

Section 19: Statistical Discrimination

  • Firms use group averages when individual information is noisy.
  • Test scores predict wages better for whites than for Blacks, affecting wage offers.
  • Wages depend partly on perceived group ability.
  • Wage prediction: w = a + b × test_score + c × Black

Section 20: Arrow’s Critique of Becker

  • Becker: employers who discriminate pay a cost (discrimination coefficient).
  • Arrow: statistical discrimination can persist even without animus.

Section 21: Household Production and Intertemporal Decisions

  • Household production: combines market goods + time to produce commodities (e.g., clean clothes).
  • Intertemporal labor supply:
    • Percentage change in labor supply associated with 1% increase in wage.
    • σ = % ΔLS / % Δw

Section 22: Long-Run Cost Minimization

  • Cost = wL + rK
  • Minimize cost subject to f(L, K) = Q
  • Optimality condition: MPL/MPK = w/r

Section 23: Labor Market Flows and Steady State

  • Workers flow between employment, unemployment, and out of the labor force.
  • Steady-state unemployment:
    • u* = s / (s + a)
  • Flows model:
    • s = job loss probability
    • a = job finding probability
    • Average unemployment duration = 1 / a

Section 24: DMP Matching Model

  • Endogenizes a = a(θ), where θ = V / U (V=Vacancies, U=Unemployed).
  • Firms create vacancies if surplus is high enough: (1 – β)(p – z)/c
  • Equilibrium condition: (r + s)/q(θ) + βθ = (1 – β)(p – z)/c
  • Higher p – z → more vacancies → higher θ → higher a → lower u.

Section 25: Strikes and Bargaining

  • Hicks paradox:
    • Strikes are inefficient; both sides would prefer a pre-strike deal.
    • Strike wastes surplus; settlement is inside the original Pareto frontier.
  • Optimal strike duration:
    • Union resistance curve: as strike goes on, wage demands fall.
    • Firm picks point on lowest isoprofit curve tangent to the resistance curve.

Section 26: Tax Incidence and Elasticity

  • Statutory burden ≠ economic burden.
  • The more elastic side of the market bears less tax burden.

Section 27: Compensating Differentials

  • Wage differences due to non-wage job attributes (e.g., risk, amenities).
  • Used to estimate Value of Statistical Life (VSL):
    • VSL = Δw / Δrisk

Section 28: Class Size and Instrumental Variables

  • Equation for estimating class size effects:
    • ō_sc = βX_s + αn_sc + η_s + μ_c
    • ō_sc: average test score, n_sc: class size, X_s: school controls.
  • Maimonides Rule: splits classes when student count exceeds 40.
  • Instrument: f_sc = e_s / [int((e_s – 1)/40) + 1]
    • Must affect class size but not test scores directly (exclusion restriction).

Section 29: Discrimination in Hiring

  • Nondiscriminatory firm: hires until VMP = wage.
  • Discriminatory firm: VMP = (1 + d) × wage (d = discrimination coefficient).

Section 30: Summary of Econometric Issues

  • Endogeneity: problem when a regressor is correlated with the error term.
  • Sources of bias: Omitted variable bias, simultaneity, measurement error.
  • IVs solve endogeneity if relevance and exclusion hold.
  • DiD helps account for time trends.
  • Measurement error biases OLS coefficients toward zero.