The price of nails since 1695 and its lessons

There is a new paper in Journal of Economic Perspectives. Its author, Dan Sichel, studies the price of nails since 1695 (image below). Most of you have already tuned off your attention by now. Please don’t do that: the price of nails is full of lessons about economic growth.

Indeed, Sichel is clear in the title in the subtitle about why we should care — nail prices offer “a window into economic change”. Why? Because we can use them to track the evolution of productivity over centuries.

Take a profit-maximizing firm and set up a constrained optimization problem like the one below. For simplicity, assume that there is only one input, labor. Assume also that a firm is in a relatively competitive market so as to remove the firm’s ability to affect prices so that, when you try to do your solutions, all the quantity-related variables will be subsumed into a n term that represent’s the firm share of the market which inches close to zero.

If you take your first order conditions and solve for A (the technological scalar). You will find this this identity

What does this mean? Ignore the n and consider only w and p. If wages go up, marginal costs also increase. From a profit-maximizing firm’s standpoint trying to produce a given quantity, if prices (i.e. marginal revenue) remained the same, there must have been an increase in total factor productivity *(A).* Express in log-form, this means that changes in total factor productivity are equal to αW – αP. This means that, if you have estimates of output and input prices, you can estimate total factor productivity with minimal data. This is what Sichel essentially does (and Douglas North did the same in 1968 when estimating shipping productivity). All that Sichel needs to do is rearrange the identity above to explain price changes. This is how he gets the table below.

The table above showcases the strength of Sichel’s application of a relatively simple tool. Consider for example the period from 1791 to 1820. Real nail prices declined about 0.4 percent a year even though the cost of all inputs increased noticeably. This means that total factor productivity played a powerful role in pushing prices down (he estimates that advances in multifactor productivity pulled down nail prices by an average of 1.5 percentage points per year). This is massive and suggestive of great efficiency gains in America’s nail industry! In fact, this efficiency increases continued and accelerated to 1860 (reinforcing the thesis of economic historians like Lindert and Williamson in Unequal Gains that American had caught up to Britain by the Civil War).

I know you probably think that the price of nails is boring, but this is a great paper to teach how profit-maximizing (and constrained optimization) logic can be used to deal with problems of data paucity to speak to important economic changes in the past.