Global warming has quickly become the talk of the town, so to speak. And, unfortunately, it is tied to various political agenda. But is there actual scientific evidence for global warming?
Let me rephrase the question. Global warming theorists affirm the following two postulates:
1. That the temperature of the earth is increasing abnormally.
2. That this increase in temperature is caused by human activity.
First, I’m going to examine postulate one. And I promise, this will be pure econometrics. No tricks, and no political agenda.
The data come from the Vostok Ice Station and can be downloaded here. They include data on global temperatures over the past 400 thousand years. First, let’s generate a time series plot of global temperatures.
The x axis has years (with 0 being the start of the Vostok data some 400,000 years ago). The y axis has temperatures measured in deviation from 0, where 0 is the temperature for the last observation (at depth 1m). Observe that global temperatures have varied significantly over the past 400,000 years. Let’s zoom in at the last few thousand years.
In this figure, we’re looking at global temperatures in the last 20,000 years. Notice that temperatures have increased significantly after the last ice age and then oscillated around a mean of somewhere a little below zero.
OK. Now for the econometrics. We’re going to try to forecast future temperatures. One simple way to do that is to use an autoregression. An autoregression regresses current temperatures on past temperatures. The natural question is how many lags of past temperatures to use. A common way to select a model is to minimize a statistical gadget called the Schwartz-Bayes Information Criterion. SBIC minimization tells us to use a model with five lags (each lag is a meter of ice-core data, about 17 years). So we’re going to try to predict temperature with 17×5= 85 years of temperature data. Here’s the estimation:
Vector autoregression Sample: 5 - 3310 No. of obs = 3306 R-squared: 0.9847 Chi2 = 213231.2 deltats | L1. | 1.215386 .0172881 70.30 0.000 L2. | -.6118803 .027076 -22.60 0.000 L3. | .4853331 .0278409 17.43 0.000 L4. | -.2038723 .0270751 -7.53 0.000 L5. | .1084196 .0172866 6.27 0.000 Constant | -.0301335 .0116195 -2.59 0.010 ------------------------------------------------
In this model, L1-L5 are the five lags of temperature. The regression coefficients are in the first column; they have no causal interpretation, so we’ll ignore them. The second column has the standard errors. The third column has the t-values and the fourth – the associated p-values. The fact that all five are statistically significant at any level tells us that they have predictive value in our model. Also note that the R-squared is 0.98. So 85 years worth of temperature data explains 98% of the variation in current temperatures. Not bad for an autoregressive model.
Armed with our new model, let’s predict temperatures for the next 170 years.
The blue line is our prediction. We expect temperatures over the next 170 years to decline slightly. The grey area is the 95% confidence interval.
Hm. Something to think about. Next time, I’ll look at global CO2 levels.
Even if scientists disagree I list on my site ways to save money and help the environment. Frankly, it is hard to know what to believe.