Pursuit of Truthiness

my gut tells me I know economics

Archive for April 2011

A Naive Economist Analyzes Climate Data

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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.

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Written by James Bailey

April 23, 2011 at 12:00 am

Monetary Policy: The Most Important Policy

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Scott Sumner has said that monetary policy was the Achilles heel of conservative/libertarian/free market economics all through the world in the 20th century.  I am realizing how big a problem it still is.  I always thought that it we be great if some twist of fate brought us President Ron Paul, because I think most of his proposed policies would make Americans much better off; my only big disagreement is with his monetary policy.  However, I can’t say I disagreed when I read Adam Ozimek’s description of what hypothetical presidents would bring:

You know who else ran for President in 2008? Ron Paul. President Paul would have yanked out Bernanke and put in a gold bug, which would have outdone anything any other president could do, short of unnecessary nuclear war, in terms of a welfare loss. President Paul would have heralded in the Great Depression 2, not the Great Recession.

I don’t think it is unreasonable to expect a second Great Depression to do as much damage to free-markets and libertarian politics as the first.  You might think that a libertarian president could get lucky and get elected during good economic times, when tight money would not push us all the way to a Depression.  However, any President that does drastically shrink the government is going to cause a recession; almost every post-war demobilization is accompanied by a recession.  This doesn’t mean we shouldn’t end wars or shrink government of course, but such times do call for an accommodative monetary policy- and given the current state of libertarian beliefs and politics, we are likely to get just the opposite.  Unless we get a new Milton Friedman(who I guess is now a money-debasing statist), a libertarian president will be bent on bringing “sound money” and will be a disaster for the country and for free markets.

Written by James Bailey

April 6, 2011 at 2:53 pm

Lotto Tickets- A Potentially Good Investment

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Neither normal people nor economists can make much sense of those who buy lottery tickets hoping to make money.  To rescue the lottery from being an “idiot tax” they think of other reasons to play, such as the lottery being “entertainment” or a convenient way to donate to education.  However, in some reasonably common circumstances, the lottery makes perfect sense as an investment.

To see why, you have to calculate the implicit marginal tax rate people face.  The explicit marginal tax rate is what you see when you pay taxes, and for low-income people in the United States it is small.  The implicit tax rate is what you get by considering both taxes paid and subsidies received.  Many government subsidies in the US target the poor, which is nice, but it means that as people work more they receive fewer subsidies- reducing their incentive to work more.  Sometimes, earning more income from work will actually reduce what you are able to consume by making you ineligible for benefits- this means you face an implicit marginal tax of 100% or more.

Why does this matter for the lottery?  By one calculation (shown in the chart below, which I haven’t checked myself, but is close enough to being true for my argument), a significant number of people in the US see nearly no benefit from increasing their income from $15,000 to $40,000.  Say you have a job that pays $20,000.  Getting a second job or investing “responsibly” will not increase your income above $40000 and so will not make you better off.  A winning lottery ticket, however, could shoot you out of the “dead zone” and make you money you actually get to keep.  If you are stuck with a near-100% implicit tax rate until you can drastically increase your income, the lottery makes sense for you.  You just make sure the potential payoff is big enough to get you clear of the poverty trap, so go big or go home.

Written by James Bailey

April 5, 2011 at 10:53 pm