Does free trade bring lower prices?

Dani Rodrik says not really:

Advocates of globalization love to argue that free trade lowers prices, and the argument seems sensible enough. Think of all the cheap goods from China that we can buy at Wal-Mart.  But anyone who understands comparative advantage knows that free trade affects relative prices, not the price level (the latter being the province of macro and monetary factors).  When a country opens up to trade (or liberalizes its trade), it is the relative price of imports that comes down; by necessity, the relative prices of its exports must go up!  Consumers are better off to the extent that their consumption basket is weighted towards importables, but we cannot always rely on this to be the case.

The intuition is this: if my household suddenly trades with the outside world, bread is cheaper but my wife has superior opportunities than before.  It might be harder for me to bid for her time and I will have no one to play tennis with.  If I enjoy tennis enough, I might be worse off.  If you want a real world example, American ethanol use is bidding up the price of Mexican corn; not every campesino is better off.

Greg Mankiw responds, and Rodrik in turn, then Mankiw again.  I would put it as such.  The real gain from trade is the additional output; it should not be surprising if the pecuniary externalities (higher and lower prices) should prove a wash rather than an additional net gain.  In fact a wash of the pecuniary externalities helps ensure that the output effect dominates the welfare calculus. 

More empirically, having your export prices bid up is a wonderful driver of growth more than it is a distributional or efficiency nightmare.  The net externalities of that process are usually positive rather than negative, even without firm- or industry-level increasing returns in the traditional sense.  The exports help build a middle class and in the long run make democracy and rule of law possible.  The dynamic effects are the key to the benefits of trade, and neither the Ricardian nor the Heckscher-Ohlin model is satisfactory.  The best simple (ha!) model has trade bringing more innovation, new goods with high consumer surplus, greater reason to work hard and get ahead, greater domestic inequality, a growing middle class, and new and usually more liberal political coalitions.

Empirically, the troubled cases of trade typically involve exports of oil or diamonds and subsequent corruption.  The relevant problem with trade is not higher prices for home consumption, in fact home consumption of those commodities is usually quite low.  How much oil does Guinea-Bisseau use?  We're left with Mexico and corn prices as a possible example, but note that Mexico would have much lower corn prices with free trade in corn.  And it is U.S. government subsidy, not the market, bidding up the price of corn in the first place.

Maybe we're left with this as the relevant real world example: outsourcing in India drives up wages and makes life harder for people who want lots of servants.

My Inner Misesian is uncomfortable with Rodrik's strong distinction between relative prices and the absolute price level.  Productivity shocks (which are in critical regards analogous to an expansion of trade) can and do lower most of the prices we face, albeit not all of them.

I don't disagree with Rodrik's claims about positive economics, although they don't quite "shade" as I might wish.  I would have liked to have seen the sentence: "The early 20th century trade theorists discussed by Jacob Viner and Gottfried Haberler knew about these problems, but they also realized they did not, when viewed in a realistic context, weaken the case for free trade."

Addendum: Read this survey paper on trade.