An old result on automation and wages

The first issue of AER Insights is out and the very first article is one by Francesco Caselli  and Alan Manning on “Robot Arithmetic: New Technologies and Wages.” Here is the abstract:

Existing economic models show how new technology can cause large changes in relative wages and inequality. But there are also claims, based largely on verbal expositions, that new technology can harm workers on average or even all workers. This paper shows—under plausible assumptions—that new technology is unlikely to cause wages for all workers to fall and will cause average wages to rise if the prices of investment goods fall relative to consumer goods (a condition supported by the data). We outline how results may change with different assumptions.

The key result is that new technology will not cause wages for all workers to fall and, indeed, should increase average wages if the price of capital falls relative to consumer goods. This is a good, clean theoretical result that is far from appreciated by people who discuss things like automation in the popular press and even by those who study the impact of automation on labour markets.

Here is the interesting thing: the result is not new but the authors can be forgiven for not having known that as it was, it seems to me, rather buried in the literature and I only came upon it by luck.

While this paper has a more general presentation, the key result is in a book by Herbert Simon called The Shape of Automation for Men and Management published in 1965. This is a hard book to come by and I had ordered it several months ago from a used bookseller and it only arrived last week. (Caselli and Manning are now aware of it but it seems the paper was already too close to publication for an acknowledgment to be given). But I thought it would be useful to run through Simon’s treatment here as it is rather simpler than the paper published in AER Insights.

In the very first chapter, Simon starts wondering what happened to the horses and the jobs they held. He argues that the problem with horses was that their existence depended on market forces. In other words, when the demand for horses fell, soon after supply went down — that is something that doesn’t necessarily happen for labour.

To see all of this, Simon starts with a single commodity economy that can be consumed or saved (and converted to capital). The only other thing used for production is labour. There are different ways of combining labour and capital to produce the good — some more labour intensive than others. Technological change is a reduction in the number of labour hours and/or amount of capital required to produce a unit of the good. Labour is the only fixed factor of production.

If r is the rate of interest, the cost of using a unit of the good as capital is 1 + r which means that it is also the price of capital. If the price of capital is above this, then saving will rise and if it is below this, saving will fall.

If a production technique is employed in equilibrium, the value of output will equal the sum of labour and capital costs. If the price of the good is 1 then:

w * a + (1 + r) * b = 1

where w is the wage rate, a is the labour input coefficient and b is the capital input coefficient. Let L, C and P be the total quantities of labour, capital and output, then, on average, a = L/P and b = C/P so that total production is P = wL + (1 + r)C. This is the key equation that Caselli and Manning draw their insights from in their rediscovery of this result.

Now suppose there was a new production process with coefficients (a’, b’) such that

w * a’ + (1 + r) * b’ < 1

then producers would expand their production of the good. The pie will be increased but who will get what?

Simon considers two possibilities. First, suppose a’ < a but b’ = b. Then it must be that w’ > w. In other words, reduce the labour requirement in production and labour captures more and, indeed, all of the value arising from this technological change. Interestingly, because b/a has increased, this technological change is more capital intensive yet the benefits flow to labour.

Second, suppose that a’ = a but b’ < b. So capital is more productively efficient. So long as the rate of interest does not change (which it won’t if it is set by consumption level savings preferences), then once again w’ > w! So wages rise again. In other words, to quote Simon, “so long as the rate of interest remains constant, an advance in technology can only produce a rising level of real wages. The only route through which technological advance could lower real wages would be by increasing the capital coefficient (the added cost being compensated by a larger decline in the labor coefficient), thereby creating a scarcity of capital and pushing interest rates sharply upward.” In other words, the price of capital would have to rise by more than the price of consumption.

The article in AER Insight is more general than Simon’s treatment. It involves more goods and considers the role of worker types leading to a more nuanced set of conclusions. But I think it is safe to say that the central result which took up the entire abstract was, in fact, Simon’s and should be acknowledged as that.




6 Replies to “An old result on automation and wages”

  1. What am I getting wrong?
    w(L/P) +(1+r)(C/P) = 1
    0.9(1/2) + (1.1)(1/2) = 1
    If we go to 10% change in price (down)and productivity (up) of factor that changes
    Firstly raise labour productivity by 10%
    w'(1/2.2) + (1.1)(1/2) = 0.9
    Gives w’ = 0.99 (an increase of 10%)
    Secondly raise capital productivity by 10%
    w'(1/2) + (1.1)(1/2.2) = 0.9
    Gives w’ = 0.8

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