## Archive for the ‘**stuff I really don’t know that much about**’ Category

## A Naive Economist Analyzes Climate Data

Has global temperature risen significantly in the last century? I’m sure this post will settle the global warming debate once and for all.

Seriously though, I am surprised how economists feel the need to qualify their discussion of the subject by saying “I’m not an expert”. True, economists are not experts on climate, but many are leading experts on the analysis of time-series data. One of the biggest debates in economics for the last 3 decades is about the trend in a time series- not temperature, but gross domestic product.

I am not an expert even on this narrower subject, but in some sense this is an advantage- I don’t know enough to cheat. I can’t keep trying different approaches until the results come out the way I want, because I only know a couple of approaches. Compare this to graphs, where I know enough to get exactly the results I want. Here is a graph of global temperatures since 1881, data from NASA:

Hard to see an upward trend there. Case closed? Well, check out the temperature anomaly (difference from the average), graphed in a different way:

Now that’s an upward trend if I’ve ever seen one! These two graphs are two basically legitimate ways to look at essentially the same data, but they seem to point to opposite conclusions. This is one reason statistical tests are important- they can’t be fooled by changing axes or adding a constant to the whole series. Of course, the disadvantage is that they require a lot more knowledge to use and analyze than graphs do.

You can already see the result of one statistical test- the regression equation on the second graph that was used to draw the trend line. It estimates that temperature is increasing .006 degrees Celsius each year, and that this simple increasing-temperature model predicts 75% of the variation in the annual data. A regression on the first graph shows the same thing (rescaled), though I did not include it as it would undermine the how-to-lie-with-graphs point. Time is strongly significant in this regression (p-value 0.00)- so this basic analysis says the increase in temperate is statistically significant.

A more advanced way to test for a trend in data is an Augmented Dickey-Fuller test. This test also suggests there is an upward trend- technically, that we cannot reject the null assumption of a unit root (more technically, it looks like it is ARIMA(0,1,3), for those who care). So, according to my naive analysis, there certainly seems to be an upward trend in temperature.

What does this really tell us? Perhaps not much. First, I assumed that the dataset from NASA is correct. Second, I chose to analyze 130 years, but there is no reason to choose this number except that it is how much data I had; the results are certainly sensitive to the number of years included. Finally, I have done nothing to test the idea that increased carbon is causing this increase- perhaps I will in another post. So, with those three grains (big rocks?) of salt, it looks like we have global warming.

## String Theory

Watching the PBS documentary on Michael Greene’s The Elegant Universe. It’s fairly well done, though a bit slow and repetitive.

The most common criticism I’ve heard of string theory is that it is not really scientific at all, because it makes no testable predictions. This lack of observability and predictive power makes it completely useless, “not even wrong”. Greene insists that tests will emerge in the future. But the documentary makes the claim that string theorists predicted the existence of a gravity-particle in the 1980’s; and there are now experiments designed to detect these “gravitons” and “gravity-waves” (like LIGO ) I would think this is a great test, except that they completely fail to mention it in the documentary.