How Much of a Rupee Depreciation Reaches Indian Consumer Prices? Distributed Lags, Local Projections and an Exact Mapping, 1995-2025

I estimate how much of a change in the rupee-dollar exchange rate passes into India's consumer price index, using 363 monthly observations from January 1995 to March 2025 (FRED series for the OECD CPI of India, the INR/USD rate and Brent crude). A distributed-lag regression of monthly CPI inflation on the current and twelve lagged changes in the exchange rate, with oil-price lags and month dummies, gives a cumulative pass-through of 0.027 on impact and 0.145 (Newey-West standard error 0.069) after twelve months: a 10% depreciation raises consumer prices by about 1.5% within a year. I prove that, in population, the local-projection coefficient without controls equals the double sum of the distributed-lag coefficients weighted by the autocorrelations of exchange-rate changes, which explains why the two methods differ when the rupee's changes are persistent (first-order autocorrelation 0.277); in the sample the implied and direct values at twelve months are 0.243 and 0.247. Before inflation targeting (1995-2015) the twelve-month pass-through is 0.133 (0.073); from 2016 it is 0.039 (0.092), but the difference, minus 0.095, has a standard error of 0.117 and is not statistically significant. Pass-through from depreciations (0.262) exceeds that from appreciations, whose estimated sign is implausible, so the asymmetry result should be read with caution. Rolling ten-year estimates range from minus 0.140 to 0.458 and are uncorrelated with mean inflation in the window (correlation minus 0.02).