Expectations, Consumption & Investment

Permanent Income Hypothesis

coreExam · medium

The PIH says consumption depends on permanent (expected lifetime average) income, not transitory income. Ct ≈ (r/(1+r))·(Wealth + Human Capital). Temporary shocks to Y move consumption only by their annuity value; permanent shocks move C one-for-one. Implies smooth consumption and sharp predictions — tax rebates have small effects on C if perceived as transitory.

Derivation

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Permanent Income

Permanent income is the annuity value of lifetime wealth:

Y^P = r \cdot \text{Lifetime Wealth} = r \cdot (W_0 + H)

where $H$ = human capital = PDV of all future labour income.

Consumption Rule

C_t = Y^P_t

Consumption tracks permanent income, not current income. This is why PIH predicts smooth consumption even when $Y^d_t$ is volatile.

Two MPCs

| Shock type | MPC | |------------|-----| | Temporary (one-year bonus) | $r/(1+r) \approx 5\%$ | | Permanent (lifelong raise) | $\approx 100\%$ |

Implications for Policy

Transitory tax rebates (US 2001, 2008): small $C$ response. Most is saved.
Permanent tax changes: large $C$ response, closer to Keynesian predictions.
Anticipated taxes: near-zero response at announcement if already priced in (Ricardian).

Empirical Qualifications

PIH in pure form is too strong. Real-world data show:

Excess sensitivity to transitory income (credit constraints, rules of thumb).
Excess smoothness to permanent income news (slow belief updating).
Hand-to-mouth behaviour by ~30% of households.

A richer model blends PIH households and liquidity-constrained (Keynesian) households.

Worked Example

Household has wealth 100,000, expected lifetime earnings PDV = 900,000. r = 5%. One-time bonus = 20,000.

Permanent income = r · Wealth = 0.05 · (100,000 + 900,000) = 50,000 per year.
After one-time bonus: new wealth = 120,000 + 900,000 = 1,020,000. New Y^P = 0.05 · 1,020,000 = 51,000.
ΔC = 1,000 per year from the bonus — a permanent addition to annual consumption.
Keynesian c₁ = 0.6 would give ΔC = 12,000 this year alone — 12× more than PIH.

PIH says ΔC = 1,000 per year permanently. Keynesian says ΔC = 12,000 this year. Massive difference in predicted response to transitory income.

Common Mistakes

—Confusing permanent income with current income — the whole point is they differ for transitory shocks.
—Assuming PIH implies smooth consumption always — only if credit markets are complete and expectations are correct.
—Using r/(1+r) for finite horizons without correction — the annuity formula depends on T.
—Forgetting human capital: a recent graduate with low current income but high expected future income has high Y^P.

Exam Cues

→Permanent income: Y^P = r · Lifetime Wealth. Consumption equals Y^P.
→MPC from temporary income: r/(1+r) (small). From permanent: 1 (full pass-through).
→Tax-rebate policy: transitory → small C effect (most saved). Permanent → large effect.
→Explains: lottery winners, smoothing behaviour, why Keynesian MPCs overestimate stimulus effects.