The Black Death and the VoSL

30/03/2012 § 3 Comments

I have been reading about the Black Death, the pandemic that swept through Europe from 1347 to 1350. This has nothing to do with my day job, in case you’re wondering. Wikipedia has this to say (from the Bubonic plague entry):

It is commonly believed that society subsequently became more violent as the mass mortality rate cheapened life and thus increased warfare, crime, popular revolt, waves of flagellants, and persecution.

That seems a pretty¬†uncontroversial statement. As a matter of historical record, there was an increase in manifestations of violence. The violence was directed towards oneself (flagellation) or towards others, and was both petty (crime) and structural (peasant revolts). Historians have connected the dots: life became even nastier, more brutish, and shorter; its value was reduced; the costs of producing violence decreased; therefore, people produced more violence. It’s a simple question of the cost of a factor of production.

That’s a backward look. What if we look forward?

Let’s say that climate change leads to plague and famine. Wouldn’t we expect the same change in the value of a life? Couldn’t we change the sentence above to read, ‘It is commonly believed that society will become more violent as mass mortality cheapens life…?’ It seems, again, relatively uncontroversial to say this.

Now, let’s look at it from the perspective of today. Today, when we are contemplating what to do about climate change, we have in mind or in models some value of a statistical life (VoSL). That is, we put a value on the lives of our descendants. What value should we put on them? If we expect that climate change will lead to a cheapening of VoSL, should we use our current value, or the value we expect to arise in the future?

It’s even worse. Our current actions can affect climate change. We can make it more or less severe. The more severe we make it, the more those future lives may be cheapened, and the less we need to be concerned with the impacts. By taking action to reduce climate change, we are increasing the necessity of taking action. This is, mind you, in a purely in a statistical, intergenerational utility optimising framework.

So whose VoSL should we use, ours or theirs?


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§ 3 Responses to The Black Death and the VoSL

  • Shouldn’t the two approaches wind up giving similar numbers if you also account for that we’re reducing the experienced quality of life among those who die in that period, and that the VoSL reduction is just the capitalized value of that reduced flow?

  • Seamus Hogan says:

    Bill, Eric,

    I think what is going on is as follows: Quality of life in the future in BIll’s model is the number of people alive (n) times the dollar value of the quality of that life (q). (Let’s not even mention the repugnant conclusion, here.) Now let both of these be a function of the dollar cost incurred today to reduce global warming. Even if both n(x) and q(x) are concave function (that is, there is diminshing marginal benefit to spending money today on each of the seperate dimensions, the quality-of-live function, n(x)q(x) will not necessarily be concave. We could therefore have multiple local maxima where marginal benefit equals marginal cost, and even, possibly multiple global optima.

    This is where I think Bill was going. It may be that the conclusion is, if you are going to do anything, you need to do a lot.

  • WH says:

    Problem where there is an assumption that at time period 1000 (T-1000) there is a dramatic reduction in VoSL due to a mass disruptive event. There is a question of what is the total stock of well-being immediately prior to T-1000 and what the stock will be after T-1000.

    Bill poses that our current action’s can make the event more or less severe. Given the example of the Black plague which was a non-linear/ chaos/black swan event, we could suppose that until the arrival of T-1000 that it might be better to increase current activity to reach time period T-800 which may provide us with the technology or means to survive T-1000. This suggests some investment in technology or other savings to have a large enough stock or capability to survive the T-1000.

    If however T-1000 is a linear event then we should be seeing a reduction in the VoSL every year from now to T-1000 at the rate of x per time period (Tx). If we apply a zero discount rate (see Tyler Cowen on intergenerational discounting) then the current value of VoSL is the correct start point.

    The question then is what form of avoidance is undertaken insure, invest in technology or reduce consumption to provide savings?

    In consider policy choices it is worth considering if the T-800 is reliable see – alright thats my friday late afternoon amusement time used up.

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