Tuesday, June 16, 2009

 

Global Warming and Time Series Econometrics

Here's a long comment I posted at David Friedman's blog:

"There are better, more general models we can use. e.g. Cohn and Lins use ARFIMA, and report tests that take it into account. ...

As Cohn and Lins said, it may be preferable to acknowledge that the concept of statistical significance is meaningless when discussing poorly understood systems."

That article looks worth reading. It does address the deeper issues of how to test where it isn't clear which hypothesis is the null and where data is limited.

The first step to take isn't all that profound, though. I hope it isn't too boring if I lay out some basic possibilities. Compare these hypotheses for temperature, where we'll call the starting temperature 50 and u_{year} is a mean-zero random shock.

1. STRAW MAN. The temperature is

50 + 0*year + u_{year}

The expected value is always 50.

2. GLOBAL WARMING. The temperature is

50+ B*year+ u_{year}

The expected value is rising at rate B per year, regardless of what happened in the previous year.

3. RANDOM WALK. The temperature is

Temperature_{year-1} + u_{year}

The expected value is the same as last year, so warming and cooling shocks persist forever but there is no trend.

4. MEAN REVERSION. The temperature is

50 + C*(Temperature_{year-1} - 50) + u_{year} with C<1

The expected value is between 50 and the temperature last year, so warming and cooling shocks persist but dampen out to near zero effect in the long term.

5. GENERAL MODEL. The temperature is

50 + B*year + C*(Temperature_{year-1} - 50) + u_{year}

Model 1 has B=0, C=0.
Model 2 has B>0, C=0.
Model 3 has B=0, C=1.
Model 4 has B=0, C<1.

If the first random shock is a warm one, then models 2, 3, and 4 will all show a trend. JPL is wrong because if

Temperature_{year}< 50+ B*year+ u_{year}

that is evidence against GLOBAL WARMING and in favor of Models 1, 3, and 4. (I think this remains true even if temperatures are rising but below trend, i.e. Temperature_{year} < 50+B*year.)

Some commentors were saying that a declining temperature still supports GLOBAL WARMING over STRAW MAN. I think it's true that any temperature over 50 supports GLOBAL WARMING over STRAW MAN, though it will require the estimate of B to be reduced. But a temperature decline is even stronger evidence for MEAN REVERSION or RANDOM WALK.

This matters a lot, because if MEAN REVERSION is true, policies to limit global warming are completely unnecessary, and if RANDOM WALK is true, they are unnecessary at present because temperatures are as likely to fall as to rise any more.

All this is just time series talk, and it's good to have structural models to test. The global warming models of scientists *are* structural models, and they match GLOBAL WARMING best (though I think they have nonlinear trends). But since those models don't explain the vast majority of either temperature or climate changes (they explain zero about the changes before 1900, for example, and pretty near zero about year-to-year changes since then), it's reasonable to try to figure out the properties of the random shocks-- random shocks are really just the "everything else" part of a model.

 

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