A Racetrack Model of the Macro-economy: Or what transportation can teach economists.


If I understand correctly, many macroeconomists believe that the current economic troubles are due to a decline in aggregate demand for goods. (Or an excess of demand for jobs on the part of labor, or a contraction in the supply of jobs for labor, leading to unemployment, and therefore not enough spending).

In queueing theory, we have a cumulative input-output diagram. When the inputs at a given time exceed the amount that can be served (or output), a queue results, and there is a loss in terms of delay. This wasted time can never be recovered.

Future wasted time can be prevented if we align supply and demand, so the number of people arriving at the back of the queue exactly equals the number of people that can be served at the front of the queue (and we have no standing queue at the beginning of this process). We exactly use the available productive capacity, with no over-production or under-production. Over-production, or attempted over-production results in queueing. Under-production is people sitting on the sidelines when the capital is capable of producing more. In either case there is wasted labor (either queuing or people on the sidelines).

We can map the economy as a racetrack (see movie below). Upon passing the some point, let’s say the South-East “corner” of the racetrack, and call that point “Go”, money is exchanged. People are paid for their work. Flow (vehicles per hour) past a point is the analog to GDP, and is the measure of the productivity of the system.

The economy is maximally productive when vehicles circulate on the road as fast as possible. We can increase output by increasing labor productivity (the speed at which drivers drive, and their reaction time when someone ahead slows down), thereby reducing headways. Racecar drivers are more productive that normal drivers, because they have greater skill, but they might be troublesome if they increase the risk of crash. We can increase output by adding labor (more drivers) if we have increased productivity, or if we have remaining under-utilized productive capacity. We can increase output through technological advances, like driver-assistive vehicles that allow cars to follow more closely.

We can also increase productivity by adding capacity to the road if there are more vehicles that want to use the road than currently can. Reinvesting in the road, rather than paying workers more now, makes sense for an economy that expects to grow either due to a larger population (more cars) or higher productivity (drivers who can driver faster and closer at the same safety level). We will lose long term productivity if we allow capital (the road) to wear out without renewal, preservation, replacement, repair, or rehabilitation.

The risk of over-heating is a crash (literally), two cars collide, slowing down the road for everyone else, since productivity drops, fewer people get paid, etc. Driving is a trade-off between value of time (I want to driver faster to save time) and value of life (I want to drive slower to decrease the likelihood of death from crash). Labor is a trade-off between production and consumption. If everyone produces and no-one consumes, no-one can pay the producer. It is our patriotic duty to consume, even if that contravenes the Protestant work-ethic.

A central planner could come in and tell the racetrack to hire more workers (drivers), induce the firm to hire more workers (by lowering some cost of hiring such as taxes or regulation or required benefits), seize the firm and hire more workers itself, or open up a bypass to the firm and hire these workers itself. This would increase revenue in the pockets of consumers, and consumer spending, assuming people thought this change was permanent.

In this story, the deadweight loss of unemployment would be eliminated in the short run.

The problem is the long run dynamics. In the long run, people tire of the good that is being produced, or its market saturates, and consume less of it. Then unless the firm retools to match demand, it has to lower employment. A new firm, with a new bypass, could come in, create a new good people are interested in, hire workers, and so on. These “Gales of Creative Destruction” sweep the old firm/economy/racetrack away.

The real world is comprised of millions of bypasses (firms) which transform labor and capital into goods, and labor itself is not homogeneous, each worker has her own path from consumption to production.

The question is then empirical, whether a short-term “stimulus” by hiring more workers and eliminating that dead-weight loss, but also eliminating incentives to invent and create by reducing the risk of unemployment, outweighs the incentive effects.

Ideally the system is self-correcting. A capitalist seeing unemployed labor which can be hired inexpensively to produce some good

We then get to the empirical question of whether there is excess productive labor sitting on the sidelines in the real US economy (e.g. as indicated by a relatively high unemployment rate), or whether those excess workers are just unproductive or negatively productive, i.e. drivers who would just gum up the works for other drivers (because, to extend the analogy their driving skills are sufficiently poor to increase the likelihood of crashes, etc.). I expect the first is true, that is, there is excess productive labor, and the imperfections of the economy, stickiness of labor, regulation, mis-information, animal spirits, etc. are leading to less productivity than the US, and certainly the world, might achieve given existing technologies and labor pools.

That said, whether just dumping money into the system will lead to the economy actually moving faster I think is still an open question. That money comes from somewhere, either devaluing the currency, or future earnings. But if productivity creates wealth, and increasing the size of the active workforce increases output, output that would otherwise be lost forever (just as when a plane takes off, it can no longer fill a vacant seat), it would seem to make sense to borrow from the hopefully wealthier future to increase output now to fulfill our hopes that the future will be wealthier.

“Who should do the borrowing?”, the central planner or millions of individual planners, is also an empirical question. There are always tradeoffs between economies of scale and span of control. There is also the information problem (Hayek’s Fatal Conceit) about directing the money, as well as the belief problem (Keynes’ Animal Spirits) which suggest that if everyone believes things are going well, they will invest, and if they believe things are going poorly, they will disinvest, fulfilling their own prophecy. If capital is indeed sitting on the sidelines because people’s beliefs about other people’s beliefs are negative, the confidence game that is the economy will come to a screeching halt. This self-fulfilling prophecy phenomenon may require a possibly counter-intuitive, contra-cyclical contrarian to set right, the scale of which may need to be central (and large) to be effective. This empirical question is unresolvable (and following Popper, all hypotheses are unprovable anyway), because we have only one economy, and are thus running only one experiment, there is no control. Econometrics could come in and use a panel data set of many historical events over many places and tell us some things, but I believe any conclusions from these kinds of statistical models will be contentious rather than consensus.

Caveat. I know this is a grossly over-simplified model, but hopefully it elucidates some things.

See also: The Transportationist: Quantity theory of money and fundamental equation of traffic

One thought on “A Racetrack Model of the Macro-economy: Or what transportation can teach economists.

  1. Very thoughtful post.
    I believe agent based modeling will change the way macro economics is studied during my lifetime. Emperical formulas developed to model aggregate behaviors will be replaced by simulations using hetrogeneous agents with utility functions that vary accros time to model system behavior.
    We have seen traffic modelling change in the past 10 – 15 years as simulations have replaced earlier models. Weather models, and many other models used in physics, model the interaction of discrete elements.
    It will come as no surprise that the result of individual simulations will be highly sensitive to initial conditions, and fiscal stimulus will not always be a good response as so many assume today.


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