Balassa-Samuelson Real Exchange Rate Appreciation Formula

Explain the Penn Effect: why fast-growing traded sectors raise nontradable service prices

Even when Purchasing Power Parity holds strictly for tradable goods (manufacturing / commodities), fast productivity growth g_AT in a catching-up economy’s tradable sector bids up economy-wide nominal wages! Because local nontradable services (haircuts, dining, housing, share 1 - gamma_T of the CPI basket) experience much slower productivity growth g_AN, unit labor costs in services rise at rate g_AT - g_AN. Balassa (1964) and Samuelson (1964) proved that trend CPI real exchange rate appreciation relative to a foreign benchmark (* ) equals (1 - gamma_T) * ((g_AT - g_AN) - (g_AT* - g_AN*))!

Verify on an emerging euro-pegged economy with tradable CPI weight gamma_T = 0.40 (B2 -> nontradable weight 0.60), domestic tradable TFP growth g_AT = 0.06 (B3), domestic service TFP growth g_AN = 0.01 (B4 -> internal gap +5.0%), foreign tradable growth g_AT* = 0.02 (B5), foreign service growth g_AN* = 0.01 (B6 -> foreign gap +1.0%), and foreign CPI inflation pi* = 0.02 (B7): relative productivity wedge is 0.05 - 0.01 = 0.0400, equilibrium real appreciation is 0.60 * 0.04 = 0.0240 (+2.40%/yr!), and under a fixed nominal exchange rate domestic CPI inflation settles at 0.02 + 0.024 = 0.0440 (4.40%/yr without loss of tradable competitiveness!).

Balassa-Samuelson Real Exchange Rate Appreciation Rate Formula

Validate CPI tradable weight 0 < gamma_T < 1 (when gamma_T = 1, 100% of goods are tradable and the Balassa-Samuelson wedge vanishes identically to 0).

=LET(gam_t, B2, g_at, B3, g_an, B4, f_at, B5, f_an, B6, IF(OR(gam_t < 0, gam_t > 1), "Invalid Tradable Share (Require 0 <= gamma_T <= 1)", ROUND((1 - gam_t) * ((g_at - g_an) - (f_at - f_an)), 4)))

Equilibrium CPI Inflation Under a Fixed Nominal Exchange Rate Formula

Add structural Balassa-Samuelson real appreciation to foreign benchmark inflation pi* to distinguish benign convergence inflation from overheating.

=IF(ISTEXT(E3), E3, ROUND(B7 + E3, 4))

Further reading

• Arte Sheets Lesson — Purchasing Power Parity (PPP) Implied FX Rate and Valuation
• Microsoft Support — ROUND function