The Epiphenomenon of Low Risk

Tyler Cowen and Mark Thoma take us to Karl Smith on social risk:

Yet, lets imagine a simple model where we have two sources of risk. There is background you cannot avoid. And, there is personal risk that you create by through your own choices.

Policy makers have since Thomas Hobbes been attempting to drive down background risk. They have [sic] larger been successful. As a result our lives are getting more and more stable.

As that happens, however, folks are going to tend to take on more personal risk. There is a tradeoff between risk and reward. As you face less background risk, for which you not rewarded it makes sense to go for more personal risk for which you are rewarded.

When I take on more personal risk, however, it bleeds over slightly into everyone else’s background risk. People depend on me. If I take risks and lose so big that I debilitate myself then my family and my friends will surely suffer. But, so will my employer, my creditor and the businesses who count on me as a regular. When I go down, they go down.

So, putting it all back together and we come up with something of a risk floor, if you will.

Smith is arguing, effectively, that any attempts to manage background risk – incessant war, say – will (after a point) be offset by an increase in personal risk which, on the aggregate, drives background risk back to the initial condition. In other words, we’re always slouching towards an inescapable equilibrium.

But the delineation between social and personal risk is not so clear. Take the example of America being a big hedge fund – lower rates have driven America to sell bonds and invest in equity, earning a pretty penny from investments abroad. By any standard model, this is risky behavior, but is it social or personal? And, if the former, unlike the social risk in Smith’s model, rents from foreign assets do have benefits. Let’s ignore modern public choice theory and assume that governmental choice to do this is the simple aggregation of risky personal preferences. Fine.

We can’t make the distinction so clearly in other examples. Let’s say a culture is particularly risk-averse. They will tolerate – given decreased background risk – increased social risk, but only up to a point. In other words, there is an absolute risk ceiling. Depending on where this ceiling falls, decreases in background risk will always result in lower long-term interest rates.

This brings up an important point that Smith ignores, that risk and associated uncertainty by itself is a cost. Classical behavioralism tells us that most people would rather be given $1,000 unconditionally than $2,500 on a coin toss. This means there is a cost associated with risk and hence even at the margin decreases in background risk do not ipso facto imply higher personal risk.

It is also important to note that, to the extent that risk creates wealth, increases in individual risk do not imply so on the aggregate. Let’s assume that education means a richer and more productive society. Perhaps decreases in background risk make a family more willing to undertake a student loan (or just save less and pay directly) to fund a college degree.

In the near-term, this would be reflected in higher rates as the supply of loanable funds shrinks on the margin. Smith would be vindicated. But not really. Eventually, the college degree would more than pay for itself, not just in immediate earning power, but also the greater likelihood descendent will attend college – a geometric scaling.

If you don’t believe in the value of college education, think about the stock market. When Americans invest, money is allocated to the worthiest initiatives allowing Apple and Google to thrive, and forcing crappy companies like Hostess to fail. Buying equity is definitely a “riskier” personal choice than is buying bonds, but in the aggregate it generates wealth and makes us all richer. And deep equity markets make it less risky to start a company. If everyone was all about debt, I’d be scared as hell to found a startup. Equity reduces the risk vis-a-vis the producer.

Of course, as we get richer (either from the stock market or education) on the margin we save more and have stabler jobs which decreases risk, both at the personal level as well as the aggregate on the loanable funds market.

Let’s say income is exogenous to a family. Standard economic theory (rightly) suggests that the marginal propensity to save scales directly with income. But background risk decreases with higher incomes. As I move into the $30-50k range I probably don’t need to worry that my kids will have food on the table. As I move into the $60-70k range (if I’m smart) I probably don’t need to worry about my retirement. As I move into the $70-90k range I probably don’t need to worry about college fees. But at $20k I’ll be really worried about the big risks.

Basically, every marginal dollar I receive is “freer”. If Smith was right, I’d just spend more. But I don’t. Of course, income isn’t a exogenous like a storm, but it really captures the idea of “background” risk. (Wars won’t matter much with enough money). If I was rich in ancient times, I didn’t need to worry about much. Today, many more people would be considered “rich”. Hence overall risk in the aggregate is lower, reflected in cheap money.

This reminds me, in some sense, of the paradox of thrift. A simplistic argument for thrift in hard times forgets that my consumption is your income and that systemic reduction of personal consumption will decrease saving in the aggregate. This, of course, is at the bedrock of the argument against austerity – fiscal or monetary – in hard times. But one form of risk doesn’t fluidly shift between the too. In fact, the argument makes a pretty strong assumption that movement in risk is precisely linear: that a unit increase in personal risk has proportional decrease in social risk. However, it is entirely possible that the risks I pursue with my increased freedom don’t have any bearing on real, social risk, or that even if it does it may never move linearly with background factors.

Now let’s take the idea of reduced background risk to its logical conclusion. If we lived in the uber-welfare state, that provided for education, retirement, unemployment, what have you. They would, basically, invest it all in stocks, right? Lets take a look at Europe which should have higher direct stock ownership rates than America. But it doesn’t, lets see ownership trends across the world:

  • 50% of Americans 
  • 20% of Swiss
  • 22% of  British
  • 16% of Germans

So clearly, decreased background risk is not the answer. Indeed, in the early 2000s, aggregate risk across Europe fell as the cost of capital of Eurozone nations converged to a historic low.

I understand there are caveats to all my points. Of course Europeans are poorer and have less disposable income than Americans which, by my own suggestion, implies a higher “risk”. But this is covered by the government, and the delta doesn’t warrant the huge differences in ownership we see.

Whatever be the case, I do think that Smith’s theory is handcuffed by reality. While the idea of a “risk equilibrium” is attractive, it just doesn’t make sense. Indeed, if the marginal decrease in background risk, at one point, equals the marginal increase in personal risk – and the relationship is continuous (economists hate broken functions, after all) the logical conclusion of a world without background risk would be rampant personal risk taking. That just doesn’t happen.

Finally, we can’t “over solve” the problem as Karl claims. I highly doubt that personal risk is linear on background risk, but even if it is, it comes with a benefit as he suggested. Background risk like wars and government default (both of which are basically solved with democratic electorates who own sufficiently distributed government debt) are never good. There is no upside.

My theory isn’t nearly as clean, and I definitely haven’t mathematized it. It’s anecdotal. And it’s not scientific. But I seriously doubt it’s as simple as he claims!

Addendum: It’s important to note that after a point, real interest rates can only be so low, somewhat like the zero lower bound. We can tolerate negative nominal rates for only ridiculously short periods of time because of obvious arbitrage. Similarly (functionally, if not structurally), lower real rates require a certain level of inflation, which society may tolerate for only so long. Indeed, as inflation is a tax on capital, there is a limit to where long-term rates can fall.

  1. GPWM. I read Tyler Cowen’s post on this and I was utterly unconvinced too. It reminded me of the micro-economics ‘imposing safety belt and airbags doesn’t affect car accidents and mortality overall because people decide to speed up more when they feel safer’.

    It might satisfy their micro rational agent model but that’s it…

    And, in any case, being French, I’ve seen how a decrease in overall background risk can make people even more risk averse! Which, btw, is why I don’t think the argument ‘general health care in the US will enable more risk taking’. I wish it were true – and, in the US, at this present time, it might work out that way – but it’s not as simple as that at all…

    • arra95 said:

      Great analogy, wish I had thought of it!

      Healthcare, and insurance in general, are a great example. I didn’t get around to talking about this, but one of the suggested reasons for extremely, uselessly, high savings rates in countries like China are highly underdeveloped insurance markets.

      Modern and robust insurance schemes would decrease the need to save, but the expected decrease in savings is not equal to the gains from lower background risk. Further, today saving in China can’t even be considered a good, “unrisky”, policy. As Karl Smith has himself argued, savings in China are past the maximum point in a basic Ramsey model (w/o discounting).

      Whatever the case, this is a complex phenomenon that can’t so simply be abstracted.

      • Don’t get me wrong. I think there are lots of benefits to be had from a solid safety net, from healthcare to retirement and, yes, I’ve heard of the over-saving by Chinese too.

        But that’s the interesting point, innit? The US has a pretty patchy social safety net and people don’t save much. China has a pretty patchy social safety net and people save too much.

        I do think that interest rates (and rates of return to capital) have come down due to a drop in background risk. Compare and contrast ‘The Merchant of Venice’ where loosing 4 out of 4 ships was an unlikely but possible outcome with modern international freight transport where losing one ship must be a relatively rare occurrence…

        But that’s about all you can say about this without overly straining things, imho…

  2. BSEconomist said:

    It so happens that my thesis (when it is finished) has some relevance to this debate. I don’t want to discuss that now, exactly, except to say that I think it is totally reasonable to say that current models of choice under risk are not very good and that the individual risk vs. social/aggregate/background risk is a poor framing.

    I think that all we can really say about the individual vs social risk–for certain and using standard tools–are direct implications of the nature of risk. Distributing risk can often mean diversification, which means that what we often call “moral hazard” can often work for the benefit of society, rather than necessarily against it. I think this is one way of summarizing your point. Regardless my point is that there are both costs and benefits (in terms of aggregate/social/background risks) to individual risk taking, and therefore we shouldn’t talk about risk-sharing a la Karl Smith and think instead about optima a la… well let me come back in a few months to finish that thought…

    • arra95 said:

      Consider me interested in your thesis, would love to hear more when it is ready.

      “Distributing risk can often mean diversification, which means that what we often call “moral hazard” can often work for the benefit of society, rather than necessarily against it.”

      Right, I think this is a good way of capturing my point. Emphasis definitely on the “necessarily”. I find this too complex a phenomenon, with very intricate behavioral as well as economic/institutional factors to neatly convey it as Smith did.

  3. ThomasH said:

    I was utterly un-persuaded that lower background risk would lead persons to increase personal risk.

    Flash! Scientists now discount possibilities of an asteroid striking Earth within the next million years. What a relief! Hand me that revolver for a nice game of Russian roulette.

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