How Fast Does the Rupee's Real Exchange Rate Return to Parity? Median-Unbiased Half-Lives for India, 1973–2025, with Five Comparators

I estimate how fast deviations of the rupee's real exchange rate against the US dollar die out, using monthly data from FRED (IMF exchange rates and OECD consumer price indices) for January 1973 to March 2025. Least squares on the post-liberalisation sample (March 1993 to March 2025, 385 months) gives an autoregressive coefficient of 0.98948 and a half-life of 5.46 years. Least squares is biased downward in persistent series. Kendall's correction moves the coefficient to 0.99978, and Andrews' exactly median-unbiased estimator, computed by simulation, moves it to 1.0, a unit root. The 90% interval for the half-life runs from 3.49 years to infinity. An augmented Dickey-Fuller test does not reject a unit root (p = 0.375). I prove that the median-unbiased estimator and the inverted interval are exact when the quantiles of the least-squares estimator rise with the true coefficient, derive the autocorrelation of time-averaged data in closed form, and show that annual averaging alone stretches the implied half-life from 5.46 to 8.25 years. Since 1993 the real rupee has appreciated by 25 log points against the dollar, as Indian inflation more than offset nominal depreciation. Of five comparators, only Mexico (2.49 years), Korea (5.60) and Japan (8.04) give finite median-unbiased half-lives. For India, the honest statement is that the data cannot pin the half-life down; any single figure such as five years overstates what is known.