Disasternomics

I hate to add to the blogosphere “literature” on the economics of Hurricane Sandy — and natural disasters, more generally — with what some might consider a mundane contribution, but the good news is that I might touch on some interesting points that aren’t necessarily directly related.

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Here’s my attempt at a simplified illustration of how I see “disasternomics” (it got more complicated as I developed it, but hopefully with a little explanation it will still get the point across),

The solid black line represents a hypothetical growth path of the capital stock (k) with no shock. Since the possible “stimulating” effects of a disaster are only relevant during what some may call a “demand shock” (but, I see both as a “demand shock” and a “supply [capital] shock”), there’s two additional lines. These both follow the same growth path as the solid line at ≤ t+1. The dotted line represents a single capital shock — an industrial fluctuation — and it returns to its previous growth path by t+3. The alternating dotted–solid line represents an economy subject to two capital shocks: a recession and a lesser natural disaster. It returns to its original growth path at some point that doesn’t concern us (let’s say t+4).

Kt+1 represents the trough of the shock(s); I made both shocks occur simultaneously, just to make it easier on me. Kt+2 represents an incomplete recovery (where completion is assumed to be reunion with the original growth path). Note, shock2 kt+2 > shock kt+1, which is meant to represent a net gain in the size of the capital stock. But, this gain is an accounting profit; there is an economic loss represented by the difference between shock kt+2 and shock2 kt+2. In other words, the economic loss is equal to the opportunity cost, and this is the real cost of capital shocks.

The slope of the recovery depends on many factors, and I’m abstracting from them. But, changes in these factors can hypothetically change the analysis.

An interesting case is made when considering the elasticity of expectations; I swore I read something similar recently, but I don’t remember where (maybe I was inspired by Daniel Kuehn’s brief distinction between stocks and flows). Let’s say that the growth path of the “single shock” capital stock isn’t decided just by limits to productivity (decided by k itself and “technology” [A]), but by expectations. If expectations (of income) are “depressed,” between t+1 and t+2 the capital stock might grow more slowly than it could. We can illustrate this by supposing that consumers/producers have two options during a recession/depression: spend or hold cash. The second capital shock causes a much steeper/greater decline in k, but since the loss in vital personal wealth requires spending to replace it there’s no longer an option to hold cash and spending spikes. Producers gain confidence and, assuming fairly elastic expectations, then k might rise at the maximum rate. The difference in expectations might be so great that the slope of shock2 between t+1 and t+2 is greater than the recovery from a single shock.

It’s certainly possible that changing elasticity of expectations plays a role in determining the rate of capital accumulation. As the recession is longer, the argument gets weaker. But, it also fails if you think costs of production are just as, or even more, important than expected demand, such that a fall in the prices of capital goods (which aren’t typically sticky) will increase profit margins. The expectations theory, which is a type of uncertainty theory, also falls flat if the problem isn’t low expectations, but a breakdown in the intermediation of savings. The problem in this case isn’t a lack of demand per sé, but an inability to capitalize on perceived opportunities to profit.

This “elasticity of expectations” case belongs to a set of theories that help explain the impact of disasters by distinguishing between stocks and flows. Two years ago, Daniel Kuehn posted on the topic, but more explicitly in the context of Bastiat’s parable on the “unseen” (opportunity cost) — the relevant point is listed as #2 in the post. Essentially, the argument is that a rise in GDP isn’t the same as a net increase in wealth. To fit it in with my example of the capital stock (k), let’s translate wealth, a stock variable, as k and GDP as the addition to k between time periods. Daniel’s point is that even if we assume k to suffer a net loss, we can say that a natural disaster might accelerate the rate of change (flow) as compared to what the rate of change would have been with only the business cycle occurring.

But, going only on this the distinction between stocks and flows doesn’t imply that natural disasters can increase the latter. In fact, the “opportunity cost” argument that talks about stocks of wealth must necessarily consider rate of change. If we assume that the only thing that influences the rate of change is the capital stock, k, then a smaller capital stock implies a reduced rate of change. There is an implicit loss in flow, where ∂f(x) > ∂g(x), where f(x) is the shock function and g(x) is the shock2 function between t+1 and t+2. The loss is represented by ∫t+2t+1f(x) – g(x)(dx). For flow to be greater as a result of a natural disaster there has to be other assumptions involved, such as the “elasticity of expectations” case described above. That is, there has to be other explicit factors which influence the rate of change.

Unless we make strong assumptions about what decides rate of change, not just in general but in specific cases, then even the “increase in GDP” argument is spurious. This being said, an econometric study of the effects of past natural disasters would be fascinating (and incredibly complicated).

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There is another thing I’d like to comment on, not necessarily related to natural disasters (but, it has been brought up in the blogosphere discussion of “disasternomics”): creative destruction versus capital shocks.

What brings me to address this is a recent post by Daniel Kuehn, linking to an article on a demolition to construct a brand new hotel building. (I don’t mean to be focusing only on Daniel; it’s not my fault his blog contains the most interesting points.) His argument seems to be that it’s hypocritical to lambast capital destruction as a result of capital shocks merely because k has been reduced, when we see benefits in capital destruction all the time. But, there is a crucial difference between the two! The latter doesn’t represent an economic loss.

Suppose our entrepreneur owns a given capital stock, φ, and the portion represented by the old building we’ll call λ. The intent is to destroy λ (let’s assume capital lost, or depreciated, in the process of destruction is insignificant) and replace it with a new building, which we’ll call ξ. It’s important to understand how all these fancy Greek letters (which, I admit, I use because it’s fun) relate to each other. When the old building is demolished, the new capital stock is represented by φ – λ = σ. The construction of the new building, in terms of physical capital left afterwards, doesn’t mean that the capital stock returns to φ. But, this physical reduction in capital stock from φ to σ doesn’t necessarily imply an economic loss. Assuming that our entrepreneur’s expectations are accurate, it means that σ is valued more than φ. Seemingly paradoxically, an accounting loss equates to an economic profit.

This obviously isn’t the case with natural disasters. Changes in the capital stock don’t reflect changes in valuation, but arbitrary capital consumption. As such, the physical reduction in k really does reflect an economic loss. In a nutshell, “capital shocks” refer to sudden reductions in value, rather than sudden reductions in quantity (although, the two can certainly move in the same direction).

This is a lesson which extracts from Austrian capital theory. Wealth isn’t physical, but subjective. We could have a physical capital stock of φ that is not valued at all, and its elimination wouldn’t be an economic loss. We can relate to business cycle theory, as well. Hayek’s notion of “capital consumption” doesn’t necessarily imply a physical loss of capital, but simply a reduction in the valuation of the existing physical stock of capital. We can conceive of two capital stocks, φ and σ, where in physical (objective) terms φ > σ, but in subjective terms σ > φ. A change from φ to σ would be an economic gain, even if k is now physically smaller.

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