The relation between “free trade” (open borders for goods) and “free immigration” (open borders for people) is interesting and multifaceted. Some points about the relation are noted below:

Similarities

• There is a strong parallel between free trade and free immigration. In one sense, free immigration (open borders for people) is simply free trade in labor and what economists have called “human capital.” The utilitarian/welfare/efficiency arguments that are commonly employed in favor for free trade in goods can also be applied to free trade in labor. Further, given that labor is quantitatively a more significant factor of production than the other factors of production, the economic arguments apply with stronger force to labor than they do to goods. As the double world GDP page documents, the economic literature is largely agreed on the point that removal of barriers to labor mobility would have substantially greater positive impacts on world GDP than removal of barriers to trade and capital flows.
• In a blog post titled Open Borders with Migration Taxes are the Optimal Policy, which covers an eponymous paper, Nathanael Smith adapts the usual economic proofs of the efficiency of free trade to the case of free migration, with suitable use of immigration and emigration taxes to convert a potential Pareto improvement into an actual Pareto improvement.
• Many people have pointed out the similarities between the kinds of arguments given against free trade and free immigration, in particular pointing out to the flawed mercantilist tradition that provides the intellectual underpinning for such analyses. The same holds true in more academic settings. For instance, in his paper Economics and Emigration: Trillion-Dollar Bills on the Sidewalk? (PDF, 24 pages, ungated), Michael Clemens writes:
  

  I am far from the first to claim a link between the mercantilist tradition and economics’ preoccupation with suspected negative, within-country effects from emigration. After Furniss (1920, p. 54), this link has been explicitly made by Nobel laureate Ted Schultz (1978); Charles Kindleberger (1986) when he was president of the American Economic Association; and one of the great scholars of migration and economic growth, Brinley Thomas (1973, pp. 1–6); among many others.

Differences

• One key way the parallel fails is that people carry with them not just their labor, but other aspects of their human existence, including their non-market activities, their culture, and their political and religious beliefs. Some restrictionists concede that from a purely economic perspective, free immigration makes great sense, but then worry about the effects of immigrant culture. For instance, in a syndicated column titled Gingrich and Immigration, Thomas Sowell (a supporter of free trade) writes:
  

  The more doctrinaire libertarians see the benefits of free international trade in goods, and extend the same reasoning to free international movement of people. But goods do not bring a culture with them. Nor do they give birth to other goods to perpetuate that culture.

  Why do people want to come to America in the first place? Because America offers them something that their native countries do not. This country has a culture which has produced a higher standard of living and a freer life than in many other countries.

  When you import people, you import cultures, including cultures that have been far less successful in providing decent lives and decent livelihoods. The American people have a right to decide for themselves whether they want unlimited imports of cultures from other countries.

• In the article The Case for Free Trade and Restricted Immigration (PDF, 13 pages), Hans-Hermann Hoppe makes a more principled case in favor of free trade and against open borders based on his interpretation of libertarian philosophy. For more on Hoppe’s line of reasoning, see the anarcho-capitalist counterfactual page.

Related blog posts and articles

• Dani Rodrik argues for more migration, a blog post by Nathan Smith on the Open Borders blog about Dani Rodrik’s view that trade is too liberalized and immigration is not sufficiently liberalized.
• The Case for Unilateral Free Trade and Open Immigration by Jacob Hornberger.
• Immigration, trade, and reciprocity, a blog post by Vipul Naik on the Open Borders blog drawing a parallel between the case against “reciprocity” for immigration and the case for unilateral free trade.