Are estimated departures from the law of one price exaggerated by the bundling of non-traded and traded inputs into observed prices?

Two celebrated facts are these: that fluctuations in the terms of trade are long-lasting. And that fluctuations in the terms of trade account for large portions of the variation in the overall real exchange rate, even at long horizons. Our paper explores one simple argument: if observed traded goods prices are really a weighted sum of traded and non-traded goods, and fluctuations in the relative price of non-traded goods are (perhaps because of the absence of arbitrage pressures) larger and longer lasting, then estimates of these two facts will be exaggerated. True fluctuations in the terms of trade will be smaller and shorter-lived than estimated, and the true contribution to the variation in the real exchange rate will be over-estimated. We show how plausible guesses at the non-traded component in traded goods prices can lead to significant biases of this sort.