Technology and unemployment

A constellation of seemingly contradictory events over the past five years – high unemployment, stagnant wages, anecdotal evidence of astounding technological growth, alleged robotization of everything, all ensconced in a grim uncertainty about the future – has brought about something incredible: prominent economists can now reasonably question the value of new technology.

This ranges from Martin Wolf’s generic essay questioning techno-optimists to a star-studded paper arguing that “under the right conditions, more supply produces […] less demand as the smart machines undermine their customer base”. Economists as prominent as Larry Summers and Paul Krugman have voiced their fears about robot-driven unemployment, and a general stagnation in living standards, if we don’t radically reassess our relationship with inequality and capital-driven growth.

I’m not here to necessarily disagree with any of these sentiments as much as explore their implications when taken to a logical conclusion. As a first pass, let’s start with a simple economy, consisting of capital owners and rentiers providing capital, high-skilled technology workers producing innovation, and low-skilled laborers producing commodity goods and services. Your production function in this world would look something like Y = A*F(K, B*G(K_r, L)) where F is of Cobb-Douglas form and G is any more general CES function, K is capital, L is labor, and K_r is innovation.

From one perspective, this is the crux of the problem. Go back to Piketty whose argument can be summarized as “when the capital stock increases by n%, the marginal return on capital decreases by less than n% and therefore K/Y increases”. Summers (in his review of the book) noted that no studies suggested that capital-labor elasticity, net of depreciation, was greater than 1. But once you have the slightly modified production function, what matters is the substitutability between K_r and L which, as I’ve written before, is governed as mu = 1 – 1/sigma where sigma is the classical elasticity of substitution between capital and labor, and mu is the robot-labor substitutability. As mu tends towards 1 (which, with improving technology, is not unreasonable) sigma grows without bound.

So we can stipulate that in the world of our robot overlords it isn’t unreasonable to expect that an unprecedented proportion of national output would accumulate to capital owners. But what does this say about living standards and employment? For one there will be a shift in employment among the unskilled laborers from highly substitutable commodities to services that benefit from human interaction (artisans coffeeshops, massage parlors, art vendors, street artists, and botanical gardeners for example).

And while there will be displacement within the unskilled population, they will – as a whole – very likely be much better than they were before. This statement isn’t the result of a careful empirical study as much as a reflection of certain fundamental, economic gravities. Let’s say robots replace workers in all manufactured goods and consumer durables production. The high standard of living in the United States isn’t derived from that employment itself as much as the collective result of that unemployment – a middle class that has multiple cars, microwaves, abundant food, television sets, carpets, furniture, and other staples of the modern home.

So the stagnationists need to further argue that the purchasing power for these products will somehow evaporate from the laboring masses. This is where it gets much harder. Because if millions of workers who once had the employment (and, therefore, the skills) to build said products and the products themselves clearly – within this population – there exists a supply and demand which, in equilibrium, creates prosperity for the masses.

As the largest consumer base in the world, this market also provides abundant profits (if at low margins) for the capitalists – the old fashioned kind who buy the old-school machines and factories necessary for the production of the goods thereof. So in this hypothetical world it will by definition be economically profitable for a capitalist to finance the sort of old-school capitalism that brought so much wealth to the middle-class. And this is as true globally as it is domestically (Chinese, assembly-line workers are  the victims of the sort of automation we’ve just described).

So here is a challenge for anyone who believes technology will result in both unemployment and a broad-based decline in living standards for the unskilled. Describe the precise mechanism in this world that will prevent the old equilibrium – that is both preferable both for the marginal capitalist and the working class as a whole – from reemerging. Or, if that isn’t your preferred interpretation of the economy, explain why supply or demand have somehow changed among this working class to make the question moot in the first case.

If you want an economic intuition for why this will be highly improbable, notice that this technology effectively means the marginal cost of production will fall to the commodity cost (which, itself when automated will, in the perpetual run, be the cost of recycling that unit of ore, or whatever). You would have to believe wages falling below this level at a mass-scale (something like a physical paralysis overcoming all that exist) for this explanation to remain reasonable.

This isn’t a model, it’s imprecise and unrigorous but is still a better interpretation of the world than some of the more formal models I’ve seen written on the subject. Take the Benzell, Kotlikoff, LaGarda, and Sachs paper which uses an OLG model with low and high tech workers to map certain equilibria in which technology decreases consumer purchasing power. Even if this is the best paper on the subject I’ve seen, the model is baked with not just incorrect assumptions but mechanics that are fundamentally divorced from the way technology operates. For example, mapping “code” as some sort of capital-like stock makes little sense. They stipulate that A_t = d * A_{t-1} z * H_{t-1} where A is the stock of code, d is the depreciation rate of code, z is the productivity of high skilled laborers and H is the quantity of high skilled laborers.

Expect code doesn’t depreciate it the way they model it as. The crux of the problem, they say, is:

Things change over time. As more durable code comes on line, the marginal productivity of code falls, making new code writers increasingly redundant.

Eventually the demand for code-writing high-tech workers is limited to those needed to cover the depreciation of legacy code, i.e., to retain, maintain, and update legacy code. The remaining high-tech workers find themselves working in the service sector. The upshot is that high-tech workers can end up potentially earning far less than in the initial steady state.