How to Discover the Truth with Statistics

Regular readers may remember my post, "How to Lie with Statistics," where I criticized ASU economist Richard Rogerson for misleading the public with bad math. I showed the nonsense in his claim "that raising taxes will turn us into a bunch of lazy old Europeans."Since I'm going to be writing about taxes a lot this week, now is a good time to show how a responsible statistician approaches this issue. The following is a summary of two excellent posts by University of Arizona political scientist Lane Kenworthy.  First, you find comparable cases. Denmark, Sweden, and the United States started with roughly the same tax revenue (as a percent of GDP) in 1960 and have diverged since. That's as close to a quasi-natural experiment as you'll find in the macroeconomic world.

If tax rates have a significant effect on the economy, the U.S. should have performed significantly better than Denmark and Sweden. Did they? Nope. Not even a little.Are American businesses more competitive than Danish and Swedish businesses? Nope.Does the U.S. have more civil liberties than Denmark and Sweden, as Hayek would have predicted? Nope. They have fewer. Surely the U.S. has more economic freedom? No again.Does the U.S. have greater life expectancy? Nope. Lower. But surely Americans are happier than Danes and Swedes? Nope. Less happy.The U.S. does differ from Denmark and Sweden significantly in three areas: higher income inequality, lower middle-class income growth, and greater government debt. Those, apparently, are the only effects of ultra-low taxes.But maybe you're still not convinced. Maybe you remember hearing that workers in high-tax countries work fewer hours than workers in low-tax countries, exactly as Reagan and his supply-siders had warned......but a good statistician knows to check for "endogeneity" before communicating such a conclusion to the public. (This is another example of the value of experts.) "Endogeneity" is a big word for a subtle problem: What if tax revenues are a proxy for something else? What if high-tax countries share other factors in common, factors that low-tax countries don't have? Then it's entirely possible that the distribution of work hours is due to one of those other factors, not tax revenues.Sure enough, high-tax and low-tax isn't the only way to categorize them. We can also create groups based on their social and political structure. If we get rid of "tax revenues" and replace them with "institutional-political group," the same regression result remains. That's endogeneity: If you can replace your causal factor with another causal factor and get the same result, you can't conclude for certain which one is the actual cause!In fact, this relationship looks stronger! It's more likely that the difference in work hours is due to the difference in cultures and political systems -- e.g., the strength of labor unions, the preference for traditional family roles (maternity leave policies, payroll taxes, etc.), and the government's employment policies.I hope you followed all that, but if you didn't, there are a couple more ways to test whether taxes are causing the divergence in work hours: We can test whether the strength of the regression holds when we measure the change in tax revenue versus the change in work hours.If tax cut advocates are correct, greater increases in taxes should result in fewer hours worked. Do they? Hardly. Oh, the regression line slopes down, but just barely. Look at those datapoints. They're all over. Exceptions galore.One more test: The level of tax revenue versus the change in work hours. This one is even worse. No relationship whatsoever.Okay, enough statistics for one day. Sorry for all the graphs. But I can't emphasize this point enough: It's easy to lie with statistics. Choose your pundits carefully. And don't let anyone tell you that tax cuts are the sure way to prosperity.