Infrastructure Investment: Crowding-In vs Crowding-Out

Policy Controls

Public infrastructure spending 5.0% of GDP

Crowding-out: rate sensitivity to borrowing (β) 0.80

Crowding-in: infrastructure productivity (φ) 0.25

Private investment rate-sensitivity (χ) 1.50

Live Readouts

GDP (Y)

$100.0B

Interest rate (r)

3.00%

Private investment vs. no-public-investment baseline

+0.0B (t = 0.0y)

Public capital stock (Kg) Private capital stock (Kp) — actual Private capital — counterfactual (no public investment) GDP sphere · Interest-rate needle

How it works

Output is Cobb-Douglas in public and private capital, so public infrastructure directly raises the marginal product of private capital — the crowding-in channel:

Y = A · Kg^φ · Kp^(1-φ)

Financing that spending pushes interest rates up with the size of government borrowing relative to GDP — the crowding-out channel:

r = r0 + β · (Ig / Y)
Ig = ig_rate · Y

Private investment responds positively to income and negatively to the rate gap:

Ip = sp·Y − χ·(r − r0)·Y   (floored at 0)

Both capital stocks accumulate net of depreciation δ each quarter:

dKg/dt = Ig − δ·Kg
dKp/dt = Ip − δ·Kp

A second, "counterfactual" economy runs alongside the real one with government investment permanently at zero (public capital frozen, rate fixed at r0). The readout Private investment vs. baseline is the actual private-capital stock minus that counterfactual one — positive means the productivity spillover from φ is outweighing the interest-rate drag from β (net crowding-in); negative means the borrowing-driven rate rise is winning (net crowding-out).

ig_rate — how much of GDP the government channels into infrastructure each period.
β — how aggressively interest rates react to that borrowing.
φ — how productive public capital is as an input to private output (higher = stronger crowding-in).
χ — how sensitive private investment is to interest-rate changes (higher = stronger crowding-out).

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