Macroeconomics & Development Finance
Harrod-Domar ICOR Growth & Financing Gap Formula
Calculate Harrod-Domar warranted GDP growth g_w = (s / ICOR) - delta, required gross investment share (g_target + delta) * ICOR, and Chenery-Strout external financing gap.
Audit capital-efficiency ICOR assumptions and avoid forgetting capital depreciation delta!
Developed independently by Roy Harrod (1939) and Evsey Domar (1946) and extended by Hollis Chenery and Alan Strout (1966) into the Two-Gap Development Financing Model, fixed-proportions growth links Gross Domestic Saving Rate s = S / Y, Incremental Capital-Output Ratio ICOR = dK_net / dY (dollars of net capital needed per $1 of extra annual output), and Capital Depreciation Rate delta (as a fraction of capital K, where K / Y = ICOR): Warranted Output Growth is g_w = (s / ICOR) - delta! Conversely, hitting a target real GDP growth rate g_target requires Gross Investment Share i_req = (g_target + delta) * ICOR, leaving External Saving / Financing Gap = MAX(0, i_req - s) * GDP!
Check by hand on Initial_GDP = 250.00 ($B, B2), Domestic_Saving_Rate s = 0.21 (21.0%, B3), ICOR = 3.50 (B4), Capital_Depreciation delta = 0.04 (4.0%/yr, B5), and Target_GDP_Growth g_target = 0.05 (5.0%/yr, B6): Self-Financed Warranted Growth is (0.21 / 3.50) - 0.04 = 0.06 - 0.04 = 0.0200 (2.00%/yr — forgetting delta would falsely claim 6.00%!), Required Gross Investment Share for 5% growth is (0.05 + 0.04) * 3.50 = 0.3150 (31.50% of GDP), and Annual External Financing Gap is (0.3150 - 0.2100) * 250 = 26.25 ($B, or 10.50% of GDP)!
| Macro Financing Metric (GDP=250B, s=21%, ICOR=3.5, delta=4%, g*=5%) | Formula | Verified Output |
|---|---|---|
| Self-Financed Warranted Growth (g_w) | (s / ICOR) - delta | 0.0200 (2.00% / yr) |
| Required Gross Investment Share (i_req) | (g_target + delta) * ICOR | 0.3150 (31.50% of GDP) |
| Saving / Investment Gap (% of GDP) | MAX(0, i_req - s) | 0.1050 (10.50% of GDP) |
| Annual External Financing Shortfall ($B) | GDP * MAX(0, i_req - s) | 26.25 ($B / yr) |
Harrod-Domar Depreciation-Adjusted Warranted Growth Formula
Validate GDP > 0, 0 <= s < 1, ICOR > 0, and 0 <= delta < 1.
=IF(OR(B3 < 0, B3 >= 1, B4 <= 0, B5 < 0, B5 >= 1), "Invalid Macro Input", ROUND((B3 / B4) - B5, 4))Chenery-Strout Annual External Financing Shortfall Formula
Notice Harrod’s Knife-Edge sensitivity: improving capital allocation efficiency from ICOR = 3.50 down to ICOR = 2.3333 cuts required investment from 31.50% to 21.00% and eliminates the entire $26.25B external borrowing gap!
=LET(y_gdp, B2, s_dm, B3, ic_r, B4, dl_k, B5, g_tg, B6, IF(OR(y_gdp <= 0, s_dm < 0, s_dm >= 1, ic_r <= 0, dl_k < 0, dl_k >= 1, g_tg < -0.5), "Invalid Macro Input", LET(i_rq, (g_tg + dl_k) * ic_r, ROUND(y_gdp * MAX(0, i_rq - s_dm), 2))))Try the example
Use the original values or change them to test your understanding.