Sunday, April 15, 2012

Scientific "controversy" and a misunderstanding of science

Tennessee has just passed a law that allows science teachers to teach both sides of scientific theories that are subject to "dispute" or "debate."  While it's obvious to me that this is aimed squarely at evolution and global warming, and thus that it's really motivated by politics rather than improving science education (after all, teachers have never gotten into trouble for teaching students legitimate scientific inquiry and skepticism), I think someone needs to step in and remind people (a) how science works, and (b) what actually constitutes scientific "dispute" or "debate."  I'll be that someone.

Let's start with how science works: anyone who suggests that science can prove anything is full of beans.  Scientific methods and science cannot prove anything.  Now that might sound like a controversial and ridiculous statement, but let me clarify it: science can only disprove things.  This is why they are called scientific theories and not scientific facts.  A theory is good as long as it is not disproved.

This sounds counter intuitive, but it actually makes sense.  We view data about the world around us and form a hypothesis for what is going on.  A hypothesis must be testable (you can design an experiment to see if it works); otherwise, it is faith.  Nothing wrong with faith, but faith is not useful for describing the "how" of the world around you.  A hypothesis must also be able to make predictions, or else it is not terribly useful.  When we design an experiment to test a hypothesis, we are actually looking not to see if we can prove the hypothesis, but rather if we can disprove it.  If the experiment is inconsistent with the hypothesis, then it cannot be true - it is disproved and thus should be discarded, since it obviously and demonstrably doesn't work.  If it is consistent with the hypothesis, though, that doesn't mean the hypothesis is right, it just means that it could be right.

The simple example here is the hypothesis "all swans are white." (Apologies to Taleb)  You can design an experiment to test this: gather all the swans you can find, look at their color, and see if they are all white.  If you gather a million swans and they are all white, then your hypothesis is certainly looking pretty good, but - and this is key - it is not proven.  All it takes is one black swan and you have to throw it out.

This distinction between "proven" and "not proven wrong" is a subtle one, and when an idea is repeatedly tested and not disproved, we become casual about the distinction.  Newton's laws of motion (for example, distance = speed x time) have worked so well for centuries that we can on an everyday basis treat them as fact, although a pesky upstart scientist named Einstein showed that around the edges (namely approaching the speed of light) Newton's models are demonstrably wrong.

But that's how science works: when a model is shown not to work (or shown not to work in a particular domain), it must be thrown out and replaced with another model that does work.  It is only "proven" until it is disproved.

So, in a sense, all science is subject to "dispute" and "debate".  But some dispute/debate is more legitimate than others.  Particularly in the politically sensitive areas of climate change and evolution, people tend to make four critical errors:
  • Confusing "not yet disproved" with "insufficiently proven."  In American criminal trials, we have the idea of proof "beyond a reasonable doubt," and we sometimes apply this threshold to scientific theories, especially ones (like climate change) where it is difficult or impossible to do controlled experiments.  But this is the wrong threshold - as described above, Newton's laws, on which our ability to fly airplanes and drive cars relies - could not meet this threshold.  It is not reasonable to expect any theory to meet this bar; the correct bar is "not contradicted by observable data."
  • Treating flaws or open questions in a theory as proof for an alternate theory.  In the case of "intelligent design" as an alternative theory to evolution (which it isn't because it is neither disprovable nor predictive), perceived holes in evolution are used as proof that a higher being must have been involved.  This is a basic flaw in logic.  If there is a hole in evolution, that doesn't make an alternative theory any better.  Only if the alternative theory fits the facts better - and is predictive and testable (disprovable) - should the alternative gain any traction.
  • Confusing debate over the details of how a theory works with the overall idea of the theory.  Both evolution and climate change have lots of unanswered questions about the mechanics of how they work.  Climate change cannot be tested with controlled experiments, so it relies on models and fitting to observed data, and the overall system is so complex and chaotic that there are always huge margins of error in any model.  Debate over these issues is healthy; models should be refined and reworked as more data comes in, and we need to always remember that a model is just that - a model.  But whether someone is correctly accounting for heat-island effect or cloud reflectivity (or whatever) has no bearing on whether the basic idea of pumping CO2 into the atmosphere traps heat.  Almost all of the debate in the scientific community about climate change is about the accuracy of the models, not over the basic principle of greenhouse gases trapping heat.
  • Confusing "some people disagree with this" with "there is debate about the validity of the theory."  There are still people who believe the world is flat.  That does not mean that there is any debate about the shape of the earth.  Just because someone who calls himself a scientist openly questions something does not mean that the questions are worthy of discussion.  It is worth noting that most significant scientific advances were radical ideas from people who could be considered "crackpots" in their day : Galileo, Newton, Darwin, Einstein.  (I've written on this very topic.) But it is also worth noting that for every "crackpot" who turns out to be a genius, there are 99 crackpots who are simply...crackpots.  I'm not asserting that people who question climate change are crackpots (although some certainly are); rather, I'm pointing out that to date they have pretty much all either focused on the details (as above), or their "smoking gun" evidence disproving the bulk of climate change theory has either not matched facts, or has not actually been a "smoking gun" at all.
Questioning scientific theories - including evolution and climate change - is healthy and necessary.  It is how our understanding of the world, umm, evolves.  I suspect (though I cannot prove!) that both of these theories will undoubtedly be ultimately disproved, but I also suspect that - like Newton's laws - the subsequent theories will not be wholesale replacements but rather incremental refinements (as Einstein's models were refinements on Newton's).  These theories, after all, have held up for so long precisely because they fit the observable data so well.

Unfortunately, Tennessee's new law is not aimed at this sort of productive questioning.  It is aimed at legitimizing pseudo-science under the guise of scientific discussion.  There is no meaningful scientific debate about whether evolution is real (although there are lots of questions to answer about how it works).  And there is no meaningful debate about whether the basic theory of climate change is valid - not because there is some liberal conspiracy to which most experts in the field somehow subscribe, but because the basics of the theory have failed so consistently and for so long to be disproved.  There is indeed plenty of debate about the accuracy of various models, whether it is man-made or natural, or whether we can (or should) do anything about it; some of that is scientific, some of that is policy, and all of it is healthy.  But when the number of Americans who doubt the basic ideas of evolution and climate change is large and growing, treating these debates as a debate over the larger idea is misleading and does not teach our students critical thinking on scientific issues.

Wednesday, April 11, 2012

Can tax cuts pay for themselves?

I think it's interesting the notion that people have that tax cuts either pay for themselves (via increased economic growth), or that they simply drive the country deeper into deficit.

It seems to me that neither is always the case; it all depends on the tax being cut, from what level, and to what level.  I'm not an economist, so forgive my naivete on this, but a simple thought experiment and math suggests that some tax cuts sometimes can more than pay for themselves, while others would not.  In particular, is there any reason that tax cuts wouldn't work like any other price-elasticity supply-demand curve?

As a thought experiment, let's think about how pricing would affect sales of, say, a Ford F150 truck.  Let's suppose that Ford prices the truck at $1M.  It's pretty safe to assume that this is such a high price that it will choke off all demand for the vehicle.  Now, suppose Ford lowers the price by 10% to $900K.  You're still so far out on the curve that this will not nudge demand - there will still be no sales.  Suppose, instead, that they lower the price to, say, $40,000.  I don't know if that's a good price or a bad price for an F150, but you can imagine that the demand will be a large multiple more than the demand was at near a million.  If that multiple is more than 25x, then Ford will make more revenue selling F150s at $40,000 than they made at $1,000,000. 

Now lets lower the price (we're ignoring cost and profit here!) from $40,000 to $30,000, then $20,000, then $10,000, and finally to just $1,000.  The first few price reductions will likely increase sales further as the truck becomes more affordable to more and more people.  But at some point, everyone who wants an F150 can afford one and the later price reductions have negligible (if any effect) on demand.  A price cut from $1,000 to $500 is unlikely to result in double the demand because $1,000 for a new truck was hardly any barrier at all.

What does this have to do with taxes?  Everything, really.  From 1944-1963, the highest marginal personal income tax rate was in the 91% range.  That is a hugely burdensome tax rate, and puts a huge damper on the resources people have to invest in economic activity.  That rate fell to about 70% in the 1960s.  Taxes on this income bracket dropped by about 23% (91% to 70%), so if economic activity caused taxable income in this bracket to increase by 30% (= 1 / 0.77), the tax cut would have paid for itself.  The economy did noticeably pick up in this time period, though proving a causal relationship to the tax cuts is obviously difficult to do.  But it certainly passes the sniff test that a 23% cut from 90% could yield 30% more growth.

Fast forward to now with a 35% top marginal tax rate.  Imagine the same amount of rate reduction - 21percentage points.  (This represents the same portion of income that the government in the 1960's stopped laying claim to.)  The top rate would go from 35% to a mere 14%.  The same 21 points that represented 23% of the 90+% tax rate now represents a 60% reduction, and that means that taxable income in that bracket would need to grow 250% (= 1 / 0.40) to pay for itself.  35% may be a "high" tax rate, but it isn't so high one can reasonably imagine that it is restraining a more than doubling of economic activity.  Even if one proposed a proportional tax cut - 23% off of 35% (to 27%), that 8-percentage-point reduction is unlikely to yield the required 30% growth to be self-funding.

Now, nobody is proposing cuts like this on our current tax rates.  My point here is that, in the same way that each dollar of price reduction on the truck affected demand for the truck differently depending on what the overall price of the truck was, each percentage point of tax reduction also has a different impact on both the tax burden and the threshold to be "self-funding" depending on what the overall tax burden is.  A 21-point reduction from 91% behaves very differently than a similar reduction from 35%.

My analysis above is greatly simplified, and I'm not responding to any particular proposal.  My only point is to say that "self funding tax cuts" bear the burden of proof: one must not assume that a proposed tax change is or is not self-funding.