We propose that analysis of purchasing power parity (PPP) and the law of one price (LOOP) should explicitly take into account the possibility of "commodity points" -- thresholds delineating a region of no central tendency among relative prices, possibly due to lack of perfect arbitrage in the presence of transaction costs and uncertainty. More than eighty years ago, Heckscher stressed the importance of such incomplete arbitrage in the empirical application of PPP. We devise an econometric method to identify commodity points. Price adjustment is treated as a nonlinear process, and a threshold autoregression (TAR) offers a parsimonious specification within which both thresholds and adjustment speeds are estimated by maximum likelihood methods. Our model performs well using post-1980 data, and yields parameter estimates that appear quite reasonable: adjustment outside the thresholds might imply half-lives of price deviations measured in months rather than years, and the thresholds correspond to popular rough estimates as to the order of magnitude of actual transport costs. The estimated commodity points appear to be positively related to objective measures of market segmentation, notably nominal exchange rate volatility.