### Ricardo vs Heckscher-Ohlin

Here is an academic, but also policy-relevant, question. Which model is more useful in thinking through issues in trade policy: the Ricardian model or the Heckscher-Ohlin model?

In a post earlier today, I discussed the effects of trade policy using the Ricardian model, the model we teach in first week of ec 10. In a response to my post, Dani Rodrik questioned my conclusion about real wages based on the Stolper-Samuelson theorem, which in turn works within the Heckscher-Ohlin model. So I started wondering, which of these two models is the better workhorse for practical issues in trade policy? (Don't say we need to understand and appreciate all of the models. Of course we do, but that's a cop-out. We need to form judgments as well about the utility of alternative models.)

My first thought was, the Ricardian model is simpler, but it assumes only one factor of production--labor. The Heckscher-Olin model assumes two factors of production--capital and labor--which is surely more realistic.

But more notable in the Heckscher-Olin model may be the assumption that capital cannot move from country to country. That assumption is key to many results. Yet, in today's global economy, capital is highly mobile across national borders. In light of this fact, I wonder whether it may be better to work with a model that includes labor as the only immobile factor of production.

To explain a bit more technically, assume that an industry has production function:

Y = F(K,L).

And assume that the marginal product of capital is determined by the world rental price of capital R:

FK(K,L) = R.

Then with these two equations, we can eliminate K and solve for output as a function of L (and also R, which a nation takes as given). If F is homogeneous of degree one in K and L (that is, constant returns to scale), then the resulting reduced-form production function will be linear in labor, exactly as assumed in the Ricardian model.

As a tentative conclusion, therefore, I am inclined to think that in a world with significant capital mobility, the Ricardian theory of trade is more useful than Heckscher-Olin.

One might assume that physical capital moves internationally to equalize the marginal product around the world but that human capital cannot move. After all, as an American, I can easily invest in Toyota stock but not in a college degree of a Japanese worker. In this case, one might come to the conclusion that the right distinction for Heckscher-Olin is not capital and labor but instead skilled and unskilled workers.

But there's another way to think about the issue. Suppose every family decides how long to keep their children in school. Each faces a tradeoff between marginal investments in human capital and marginal investments in financial instruments, such as a savings account at a local bank. If financial returns are equalized around world through capital flows, and families make their human capital decisions based on opportunity cost, then rates of return on all forms of capital would move toward equality. Human capital could become, in effect, an internationally mobile factor of production.

Time horizon clearly matters here. Human capital is quasi-fixed. In the short run, we should take it as given. In the the long run, it adjusts in response to incentives. The same might true of physical capital because of adjustment costs, but for human capital, it takes longer to reach the long run.

In a post earlier today, I discussed the effects of trade policy using the Ricardian model, the model we teach in first week of ec 10. In a response to my post, Dani Rodrik questioned my conclusion about real wages based on the Stolper-Samuelson theorem, which in turn works within the Heckscher-Ohlin model. So I started wondering, which of these two models is the better workhorse for practical issues in trade policy? (Don't say we need to understand and appreciate all of the models. Of course we do, but that's a cop-out. We need to form judgments as well about the utility of alternative models.)

My first thought was, the Ricardian model is simpler, but it assumes only one factor of production--labor. The Heckscher-Olin model assumes two factors of production--capital and labor--which is surely more realistic.

But more notable in the Heckscher-Olin model may be the assumption that capital cannot move from country to country. That assumption is key to many results. Yet, in today's global economy, capital is highly mobile across national borders. In light of this fact, I wonder whether it may be better to work with a model that includes labor as the only immobile factor of production.

To explain a bit more technically, assume that an industry has production function:

Y = F(K,L).

And assume that the marginal product of capital is determined by the world rental price of capital R:

FK(K,L) = R.

Then with these two equations, we can eliminate K and solve for output as a function of L (and also R, which a nation takes as given). If F is homogeneous of degree one in K and L (that is, constant returns to scale), then the resulting reduced-form production function will be linear in labor, exactly as assumed in the Ricardian model.

As a tentative conclusion, therefore, I am inclined to think that in a world with significant capital mobility, the Ricardian theory of trade is more useful than Heckscher-Olin.

*Update*: Astute commenter mvpy points out the importance of human capital, which is left out of these conventional trade models. Human capital such as education is undoubtedly central to understanding cross-country differences, but it unclear to me what the best way to incorporate it for the issues at hand.One might assume that physical capital moves internationally to equalize the marginal product around the world but that human capital cannot move. After all, as an American, I can easily invest in Toyota stock but not in a college degree of a Japanese worker. In this case, one might come to the conclusion that the right distinction for Heckscher-Olin is not capital and labor but instead skilled and unskilled workers.

But there's another way to think about the issue. Suppose every family decides how long to keep their children in school. Each faces a tradeoff between marginal investments in human capital and marginal investments in financial instruments, such as a savings account at a local bank. If financial returns are equalized around world through capital flows, and families make their human capital decisions based on opportunity cost, then rates of return on all forms of capital would move toward equality. Human capital could become, in effect, an internationally mobile factor of production.

Time horizon clearly matters here. Human capital is quasi-fixed. In the short run, we should take it as given. In the the long run, it adjusts in response to incentives. The same might true of physical capital because of adjustment costs, but for human capital, it takes longer to reach the long run.

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