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I am trying to understand the logic behind Lucas attempting to analyse the potential benefits of eliminating business cycles by attempting to calculate the percentage of income that individuals would be willing to pay to eliminate such cycles/fluctuations; My understanding is that Lucas proposed measuring the cost of business cycles as a percentage of consumption that would make a consumer indifferent between a world with and without business cycles - and that, this was found to be an unrealistically small proportion, from which it may be concluded that business cycle fluctuations are not very harmful for welfare(?), economic growth(?) etc.

However, how exactly is the impact of business cycles quantified in such a framework? In other words, if business cycles are so severe that many people lose their jobs, then if they were aware of this possibility, they'd pay a far greater insurance not to lose their jobs, i.e. to live in a world with no business cycles.

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  • $\begingroup$ Yes, his calculation does not take into account the fact that recessions affect the probability of a really bad outcome, like permanent unemployment for some people. However, what he is saying is not so much this as highlighting the utter importance of long-term growth above and beyond anything temporary. It's easy to argue that in terms of long term human welfare, a permanent increase of 1% in economic growth is far more important than making business cycles smaller. $\endgroup$ – Fix.B. May 10 '16 at 15:15
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The Lucas model does not address at all the points that you address of people losing jobs, as it utilizes just one agent that simply has a perfectly steady (perhaps growing at a constant rate) consumption path. A model with heterogeneous agents where they have the possibility of losing their jobs and having some periods with, supposedly, very low consumption, would give a much higher cost of business cycles.

Further, in a paper using robust preferences Sargent and some coauthors find that if the agent has fear that his model of where income fluctuations are drawn from is misspecified, the costs of business cycles are much higher.

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I intend this as only a comment - it is just too long for the comment section:

As it stands, I think you answer your own question. Lucas quantifies the impact of recessionary cycles by calculating how much an agent with a smooth consumption path would need to be compensated in terms of average consumption to instead endure a more volatile consumption path. He expressed the result as a percentage of average annual consumption. Remember, in economics more volatility usually implies more risk. And so what Lucas really did was create a function involving an agent's level of risk aversion that answered the question "how much do I need to compensate this risk averse person to endure 'this much' more risk?".

As for your ending bit - you're correct. The idea you're getting at is called stochastic discounting. Essentially - I will pay more to ensure myself against a negative outcome whenever I believe that negative outcome will occur with a high probability relative to when I believe it will occur with a low probability.

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From memory and the version of the Lucas critique presented to me:

The "impact" of the business cycle is quantified by imposing certain form and specific value assumptions about various parameters. For instance, form assumptions include the restriction that fluctuations are equal in absolute value whether positive or negative, the utility function is assumed to be of the constant relative risk aversion (CRRA) form, etc.

You can write the utility payoffs from two scenarios, one with fluctuations and one without, in terms of utility from consumption. The utility from the case without fluctuations can be re-written as a scalar multiple of the utility from the case with fluctuations. By imposing specific values on parameters, we can back out this multiple.

For instance, Lucas imposes that shocks are +/- 2% of GDP and that the constant which is a feature of the CRRA utility function is =2, and gets a result of 0.9996, meaning individuals will give up 0.4% of income to remove the cycles. Obviously if you change any one of these parameters (e.g. make cycles more extreme) then the results will be different.

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from which it may be concluded that business cycle fluctuations are not very harmful for welfare(?), economic growth(?) etc.

Only welfare. That fluctuations don't harm growth seems to be an assumption, not a result, of the analysis you are mentioning. This presupposes that the long-run path of the economy is driven by autonomous supply-side factors and is independent of the short-run fluctuations. So people will lose their jobs one day but get them back the other day, with equal probability. There is no serious crisis in that framework.

The permanent effect of the cycle in the long run is called hysteresis. I suspect that the more hysteresis you have, the weaker Lucas' result becomes.

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