Sunday, June 15, 2014

Climate Change as a Threat: How Big of a "Threat"? Write Down Your Economy's Equations

On Twitter, I see some chuckling that 51% of people polled in a Bloomberg Survey view climate change to be a "minor" or "no" threat.    While we don't know how people interpret the question;  what does the word "threat" mean and to whom and when,  what information would an empirical analyst need to answer the threat question?

To sketch a brief answer to this question; let's assume that every person is a risk neutral expected utility maximizer.

In each year, the following sequence plays out;

1.  The person either lives or dies.  Suppose the person dies with probability 1-h and this probability never changes and is independent over time.

2. If the person lives, there is a probability 1-g she is unemployed and receives pay of $0.   There is a probability of g that she is employed and earns a payment of $W.

3.    She only gains utility from eating Apples and the market price of an Apple is $m.  There are period by period budget constraints so she can't  borrow or lend.  Her annual discount factor is B

With this setup:  a consumer's lifetime discounted expected utility equals

sum from t = 0 to infinity     (h)^t*g^t*B^t*(W/m)

In this bad notation the math symbol "^" represents that I'm raising the variable to the exponent "t".  Note that this economy features no actual choice by the consumer.  Events such as survival or having a job just occur and this person only continues on consuming if they do occur.

To some provide intuition here, with a payment of W dollars which she only receives if she is alive and has a job, she can purchase W/m apples because each apple costs m dollars.  Future apple consumption is discounted because she is impatient and prefers consumption now.

In this silly simple urban economy, we can now talk about whether climate change is a threat to this representative agent.  This is an urban economy because the consumer doesn't grow her own food. Instead she buys it at a market.   For us to see that climate change is a threat to her lifetime expected utility, the climate scientist must either argue that:

1.  Climate change will lower the probability of survival (i.e h will decline).
2. Climate change will increase the unemployment rate (i.e g will decline)
3.  Climate change will lower her income if she has a job (W will decline)
4.   Climate change will raise the price of apples (i.e m will rise).

In my urban climate change adaptation work,  I reject #1.  (Read this paper).   Air conditioning and quality housing shield the urban population from death from heat waves, floods and other natural disaster spikes.  Hurricane Katrina's impact on New Orleans was quite a fluke.  NYC will suffer many fewer deaths when the next Sandy strikes.

In my Climatopolis work, I argue that in urbanized economies that #2 and #3 are not serious concerns.  Especially for those who can migrate within a system of cities and thus have a menu of alternatives.

#4 could certainly occur if nations have closed boundaries with respect to trade in agricultural goods.  Certain nations can certainly have bad harvests and this reduction in supply will drive up the price.  In a world of open trade in agriculture and spatially uncorrelated climate shocks and with inventories and substitution possibilities (note that this economy only produced apples), #4 will be a minor effect.

So, in this stylized economy we find a small impact of climate change.    For those who state that climate change is a major threat, what is your economic model of how we lose serious consumer surplus? Why don't households have substitution possibilities?

Note that in this economy, I didn't even introduce technological innovation.  For example , apples that can be produced in hotter climates and are more immune to bug infestations.

The broader lesson here is that the NY Times and other "doom and gloomers" need to be more explicit about who suffers because of climate change and why they suffer and how much they suffer.  Why would these "victims" allow themselves to be victims?  Why didn't they see the punch coming?   Does bad old capitalism offer any escape options for these suffering individuals?


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