Notes on Economics
The Social Effects of Lead
- "The Lead-Crime Hypothesis: A Meta-Analysis," Anthony Higney , Nick Hanley and Mirko Moro
"Does lead pollution increase crime? We perform the first meta-analysis of the effect of lead on crime by pooling 529 estimates from 24 studies. We find evidence of publication bias across a range of tests. This publication bias means that the effect of lead is overstated in the literature. We perform over 1 million meta-regression specifications, controlling for this bias, and conditioning on observable between-study heterogeneity. When we restrict our analysis to only high-quality studies that address endogeneity the estimated mean effect size is close to zero. When we use the full sample, the mean effect size is a partial correlation coefficient of 0.11, over ten times larger than the high-quality sample. We calculate a plausible elasticity range of 0.22-0.02 for the full sample and 0.03-0.00 for the high-quality sample. Back-ofenvelope calculations suggest that the fall in lead over recent decades is responsible for between 36%-0% of the fall in homicide in the US. Our results suggest lead does not explain the majority of the large fall in crime observed in some countries, and additional explanations are needed. "
- [https://stevenpinker.com/files/pinker/files/pinker_comments_on_lead_removal_and_declining_crime_0.pdf "A few off-the-cuff comments by Steven Pinker to a journalist on the hypothesis that the
removal of lead from gasoline in the 1970s caused the Great American Crime Decline in the 1990s:"]
"The lead hypothesis correlates the first and last link in this chain, but it would be more convincing if there were evidence about the intervening links. Such correlations should be far stronger than the one they report: presumably most kids with lead are more impulsive, whereas only a minority of impulsive young adults commit crimes. If they are right we should see *very* strong changes in IQ, school achievement, impulsiveness, childhood aggressiveness, lack of conscientiousness (one of the “Big Five” personality traits) that mirror the trends in lead exposure, with a suitable time delay. Those trends should be much stronger than the time-lagged correlation of lead with crime itself, which is only indirectly related to impulsiveness, an effect that is necessarily diluted by other causes such as policing and incarceration...
Note that this is the flaw that torpedoed the Freakonomics abortion hypothesis, which also correlated widely separated variables. When you zoom in on the causal chain, the intervening links (e.g., whether girls in crime-prone areas have more abortions), it fell apart. Note, in contrast, that putative causes such as policing or incarceration are very close to the putative effect: you don’t need a whole lot of unproven assumptions to believe that every man behind bars is one fewer man out on the streets committing a crime. Also, the parallelism in curves for lead and time-shifted crime seem too good to be true, since the lead hypothesis assumes that the effects of lead exposure are greatest in childhood. But 23 years after the first lower-lead cohort, only a small fraction of the crime-prone cohort should be lead-free; there are still all those lead-laden young adults who have many years of crime ahead of them. Only gradually should the crime-prone demographic sector be increasingly populated by lead-free kids. The time-shifted curve for crime should be an attenuated, smeared version of the curve for lead, not a perfect copy of it. Also, the effects of age on crime are not sharply peaked, with a spike around the 23rd birthday, and a sharp falloff—it’s a very gentle bulge spread out over the 15-30 age range. So you would not expect such a perfect time-shifted overlap as you might, for example, for first-grade reading performance, where the measurement is so restricted in time."
Proving the Central Limit Theorem
Clever Central Limit Theorem proof: If you have a sequence Xn of random variables, start with a Normal sequence Zn with Xn's means and variances. The Theorem for Zn is trivial. The Lindeberg trick is to swap Xn for Zn one term at a time.
Econ Video Clips
Econ Media Library @EconMedia on Twitter. https://twitter.com/EconMedia Mix of television, movies, comedy specials, or news clips that can be used to #TeachEcon. If you've got recommendations, @ me! Created by @Wootenomics
"The Economics of Seinfeld" site, video clips indexed by concept (large site): https://yadayadayadaecon.com/index/
"Contrary to popular belief, however, market failure theory is also a reproach to every existing government. How so? Because market failure theory recommends specific government policies–and actually-existing governments rarely adopt anything like them."
Florian Ederer @florianederer Literature controversies in econ ranked
1) Minimum wage 2) Inflation-government debt 3) Markups 4) Immigration wage effects 5) Inequality measurement 6) Wealth & corporate taxation 7) Common ownership 8) Monopsony 9) Spending-educational outcomes 10) Innovation-competition
Professor Michael Huemer's I Love Corporations at Fake Nous:
I have had personal experience with individuals, corporations, and government. All three are, of course, sometimes unsatisfactory. But my experience with large corporations is way better than my experience with either individuals or government — better from the standpoint of my ending up feeling satisfied, or being made better off by interacting with them.
Reflections on Lakatos’s “Proofs and Refutations”
My advanced math classes in college followed a standard pattern: in the beginning of the semester were the definitions, then came the lemmas, then the theorems, culminating at the end of the semester with the big proofs and then, if there was time, maybe some applications along with the much-despised “heuristics.” And not a counterexample to be found. These were theorems, after all. A theorem is true and so has no counterexamples, right?
It was only in my senior year that I learned the proper order of mathematical reasoning: first the problem, then the theorem, then the proof, with the definition at the very end. The definitions come at the end because they represent the minimal conditions under which the theorem is true. The statement of the theorem itself changes as the proof and definitions develop. And, just as a country is defined by its borders, a theorem is bounded by its counterexamples, which are duals to its definitions. --https://statmodeling.stat.columbia.edu/2021/02/11/reflections-on-lakatoss-proofs-and-refutations/#comment-1711825
Theoretical economics research is just like Lakatos says too. You can prove anything, if you get to choose all the assumptions and definitions. What you actually do is start with an idea, such as "The set of equilibrium prices is unique". You set it up precisely, as a theorem defining "equilibrium", "unique", "set". Then you try to prove it. You *always* find that your theorem is false. In this case, what came up was that you need to make an assumption called "gross substitutes", I think, (or "just two goods" might do the trick). You're sad. While the idea isn't dead, it's much weaker than you thought, and it's uglier because of the caveat. Sometimes, your idea does die--- it has a fatal flaw at its heart, and you don't think it's worth fixing. If it doesn't die, you keep finding problems. Eventually, though, with enough extra assumptions or caveats on what "equilibrium" or "set" means, you've got a true theorem. The problem is that very often when you send it to the journal, or tell it to a friend, the response is "That's just a weird special case with all those assumptions and that funny definition that you should just toss it."
So the enterprise in economic theory is to find not an idea that can proved, but an idea that can be proved cleanly enough. My impression is that the same is true in math and stats.
It really is not unfair to compare the early Nazis to the current Democratic Party, and fascists generally to the Clinton Wing. The early Nazis were a mix of nationalist members who hated big business and wanted to kill it, and nationalist members who wanted the government to control big business, but didn't care who got the profits. They all hated Jews, of course, but half of that hate was that Jews were, they thought, too strong in business (the other half was that other Jews wanted to destroy traditional society). In 1934 Hitler purged the business-killers. This bodes ill for the Berniebros.
More generally, the fascist idea was that it was fine for business to make big profits, so long as the businesses obeyed every command of the government. That's the regulatory state, except that it used executive orders instead of legislative statutes, a slow process of bureaucratic regulation-issuing, and legal opinions the courts create to bypass legislation.
That's just like the Clinton Wing. They love millionaires, and millionaires love them. They do require the millionaires to do their bidding, however, in matters they are about like abortion insurance coverage, affirmative action, small toilet tanks, etc.