Warren Buffet: Fighting Income Inequality with the EITC

Warren Buffet’s article in the Wall Street Journal reminds me of some posts I wrote a while back on fighting income inequality. His article contains a lot of wisdom. Some excerpts:

The poor are most definitely not poor because the rich are rich. Nor are the rich undeserving. Most of them have contributed brilliant innovations or managerial expertise to America’s well-being. We all live far better because of Henry Ford, Steve Jobs, Sam Walton and the like.

He writes that an expansion of the minimum wage to 15 dollars per hour

would almost certainly reduce employment in a major way, crushing many workers possessing only basic skills. Smaller increases, though obviously welcome, will still leave many hardworking Americans mired in poverty. […]  The better answer is a major and carefully crafted expansion of the Earned Income Tax Credit (EITC).

I agree entirely and so would Milton Friedman.

Unlike the minimum wage which draws money from an abstract group of individuals some of whom are not high income earners, the EITC draws funds from the broad U.S. tax base which in turn draws more heavily from upper income individuals. Unlike the minimum wage, the EITC can be directed at low income households rather than low wage individuals — many of whom are simply teenagers working summer jobs. Unlike the minimum wage which discouraged employment, the EITC encourages employment.

Buffet also proposes some common sense modifications to the EITC which I would welcome. In addition to reducing fraud, …

There should be widespread publicity that workers can receive free and convenient filing help. An annual payment is now the rule; monthly installments would make more sense, since they would discourage people from taking out loans while waiting for their refunds to come through.

The main problems with such an expansion of the EITC are political. Taking a serious swing at reducing income inequality would require a lot of money. Republican’s will likely oppose it because it is “socialist” or some nonsense. I’m sure that many Democrats would be very receptive to an aggressive expansion like Buffet alludes to but the cost in political capital might be too great for a politician to pay.

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(Paul) Romer’s Rant

Paul Romer has decided that it is time to air some grievances. In a widely discussed recent article in the AER Papers and Proceedings volume, he calls out some prominent macroeconomists for the alleged crime of “Mathiness.”  Several blog commenters have offered their interpretations of the main thrust of Romer’s thesis. I admit that after reading the article I am not entirely sure what Romer means by “mathiness”. Noah Smith interprets mathiness as the result of “using math in a sloppy way to support […] preferred theories.”  In his follow-up article in Bloomberg, Noah says much of the blame comes from abusing “mathematical theory by failing to draw a tight link between mathematical elements and the real world.”

Hopefully Romer is talking about something more than just mathematical errors in papers by prominent researchers. If this is his main gripe, let me break the bad news to you: Every paper has errors. Sometimes the errors are innocuous; sometimes they are fatal. Errors are not confined to mathematical papers either. There are plenty of mistakes in purely empirical papers. The famous mistake in the Reinhart–Rogoff debt paper; the results from Levitt’s abortion paper and so on…  Mistakes and mess-ups are part of research. Criticizing someone for making lots of mistakes is almost like criticizing them for doing lots of research. If you aren’t making mistakes you aren’t working on stuff that is sufficiently hard. This isn’t to say that I encourage careless or intellectually dishonest work. All I am saying is that mistakes are an inevitable byproduct of research – particularly research on cutting-edge stuff. Moreover, mistakes will often live on. Mistakes are most likely to be exposed and corrected if the paper leads to follow-up work. Unfortunately, most research doesn’t lead to such subsequent work and thus any mistakes in the original contributions simply linger. This isn’t a big problem of course since no one is building on the work.  Focusing on mistakes is also not what we should be spending our time on. We should not be discussing or critiquing papers that we don’t value very much. We should be focused on papers that we do value. This is how we judge academics in general. I don’t care about whether people occasionally (or frequently) write bad papers. I care whether they occasionally write good ones. We don’t care about the average paper – we care about the best papers (the orderstatistics).

If Romer is indeed talking about something other than mistakes then I suspect that his point is closer to what Noah describes in his recent columns: mathiness is a kind of mathematical theory that lacks a sufficiently tight link to reality. Certainly, having the “tight link” that Noah talks about is advantageous. Such a connection allows researchers to make direct make comparisons between theory and data in a way that is made much more difficult if the mapping between the model and the data is not explicit. On the other hand, valuable insights can certainly be obtained even if the theorist appeals to mathematical sloppiness / hand-waving / mathinesss, whatever you want to call it.  In fact I worry that the pressure on many researchers is often in the opposite direction. Instead of being given the freedom to leave some of their theories somewhat loose / reduced form / partial equilibrium, researchers are implored to solve things out in general equilibrium, to micro found everything, to be as precise and explicit as possible – often at the expense of realism. I would welcome a bit of tolerance for some hand-waviness in economics.  Outside of economics, the famous story of the proof of Fermat’s Last Theorem includes several important instances of at least what can be described as incompleteness if not outright hand-waving. The initial Taniyama–Shimura conjecture was a guess. The initial statement of Gerhard Frey’s epsilon conjecture was described by Ken Ribet (who ultimately proved the conjecture) as a “plausibility argument”. Even though they were incomplete, these conjectures were leading the researchers in important directions. Indeed, these guesses and sketches ultimately led to the modern proof of the theorem by Andrew Wiles. Wiles himself famously described his work experience like stumbling around in a dark room. If the room is very dark and very cluttered then you will certainly knock things over and stub your toes searching for a lightswitch. [Fn1]

In economics, some of my favorite papers have a bit of mathiness that serves the papers brilliantly. A good example occurs in Mankiw, Romer and Weil’s famous paper “A Contribution to the Empirics of Economic Growth” (QJE 1992).  As the title suggests, the paper is an analysis of the sources of differences in economic growth experiences. The paper includes a simple theory section and a simple data section. The theory essentially studies simple variations of the standard Solow growth model augmented to include human capital (skills, know-how). The model is essentially a one-good economy with exogenous savings rates. In some corners of the profession, using a model with an exogenous savings rate might be viewed as a stoning offense but it is perfectly fine in this context. The paper is about human capital, not about the determinants of the saving rate. But that’s not the end of the mathiness. Their analysis proceeds by constructing a linear approximation to the growth paths of the model and then using standard linear regression methods together with aggregate data. Naturally such regressions are typically not identified but Mankiw, Romer and Weil don’t let that interfere with the paper. They simply assume that the error terms in their regressions are uncorrelated with the savings rates and proceed with OLS. There is a ton of mathiness in this work. And the consequence? Mankiw, Romer and Weil’s 1992 paper is one of the most cited and influential papers in the field of economic growth. Think about how this paper would be changed if some idiot referee decided that it needed optimizing savings decisions (after all we can’t allow hand-waving about exogenous savings rates), multiple goods and a separate human capital production function (no hand-waving about an aggregate production function or one-good economies), micro data (no hand-waving about aggregate data), and instruments for savings rates, population growth rates and human capital savings rate (no hand-waving about identification).  The first three modifications suggested by the referee would simply be a form of hazing combined with obfuscation (the modifications make the authors jump through hoops for no good reason and the end product has an analysis that is less clear).  The last one – insistence on a valid instrument – would probably be the end of the paper since such instruments probably don’t exist. Thank God this paper didn’t run into a referee like this.

My own opinion is that mathematical sloppiness can be perfectly fine if it deals with a feature that is not a focus of the paper. Hand-waving of this sort likely comes at very little cost and may have benefits by eliminating a lengthy discussion of issues only tangentially related to the paper. On the other hand, if the hand-waving occurs when analyzing or discussing central features of the paper then I am much more inclined to ask the researcher to do the analysis right. This type of hand-waving happens sometimes but it is not clear that it happens more often in macroeconomics or in freshwater macro at that – ironically, the Freshwater guys that Romer criticizes are much more likely to demand a tight specification and precise analysis of the model (whether it is called for or not).

[Fn1] If you are interested in the modern proof of Fermat’s Last Theorem I highly recommend this documentary.

In Praise of Linear Models …

Noah Smith and Francis Coppola have recent columns discussing the prevalence of linear methods in economics and in particular in macroeconomics.

Coppola acknowledges that adding financial components to DSGE models is a step in the right direction but that it “does not begin to address the essential non-linearity of a monetary economy. … Until macroeconomists understand this, their models will remain inadequate.” (This is ok but to me it sounds like she’s going into Deepak Chopra mode a bit.)

Noah gives a good description of the properties and benefits of linear models.

“[Linear models are] easy to work with. Lines can only intersect at one point, so […] there’s only one thing that can happen.” In non-linear models “the curves can bend back around and [could] meet in some faraway location. Then you have a second equilibrium – another possible future for the economy. […] if you go with the full, correct [non-linear] versions of your models, you stop being able to make predictions about what’s going to happen to the economy. […] Also, linearized models […] are a heck of a lot easier to work with, mathematically. […] As formal macroeconomic models have become more realistic, they’ve become nastier and less usable. Maybe their days are simply numbered.”

There are elements of truth in both columns but on the whole I don’t share their assessments. In fact, I am firmly of the opinion that linear solution methods are simply superior to virtually any other solution method in macroeconomics (or any other field of economics for that matter). Moreover, I suspect that many younger economists and many entering graduate students are gravitating towards non-linear methods for no good reason and I also suspect they will end up paying a price if they adopt the fancier modelling techniques.

Why am I so convinced that linear methods are a good way to proceed? Let me count the ways:

1. Most empirical work is done in a (log) linear context. In particular regressions are linear. This is important because when macroeconomists (or any economist) tries to compare predictions with the data, the empirical statements are usually stated in terms that are already linear. This comparison between theory and data is easier if the models are making predictions that are couched in a linear framework. In addition, there aren’t many empirical results that speak clearly on non-linearities in the data. There is a statement that I’ve been told by empirical economists several times that a well-known economist said that “either the world is linear, or it’s log-linear, or God is a son-of-a-bitch.”

2. Linear doesn’t mean simple. When I read Francis’ column it seems that her main complaint lies with the economic substance of the theories rather than the solution method or the approximate linearity of the solutions. She talks about lack of rationality, heterogeneity, financial market imperfections, and so forth. None of these things requires a fundamentally non-linear approach. On the contrary, the more mechanisms and features you shove into a theory, the more you will benefit from a linear approach. Linear systems can accommodate many features without much additional cost.

3. Linear DSGE models can be solved quickly and accurately. Noah mentioned this but it bears repeating. One of the main reasons to use linear methods is that they are extremely efficient and extremely powerful. They can calculate accurate (linear) solutions in milliseconds. In comparison, non-linear solutions often require hours or days (or weeks) to converge to a solution. [Fn 1]

4. The instances where non-linear results differ importantly from linear results are few and far between. The premise behind adopting a non-linear approach is that knowing about the slopes (or elasticities) of the demand and supply curves is not sufficient. We have to know about the curvatures of the demand and supply curves too. On top of the fact that we don’t really know much about these curvature terms, the presumption itself is highly suspect. If we are picking teams, I’ll pick the first order terms and let you pick all of the higher order terms you want any day of the week (and I’ll win). In cases in which we can calculate linear vs. non-linear solutions, the differences are typically embarrassingly small and even when there are noticeable differences, they often go away as we improve the non-linear solution. A common exercise is to calculate the growth convergence path for the neoclassical (Ramsey) growth model using discrete dynamic programming techniques and then compare the solution to the one you get from a linearized solution in the neighborhood of the balanced growth path. The dynamic programming approach is non-linear – it allows for an arbitrary reaction on a discrete grid space. When you plot out the two responses, it is clear that the two solutions aren’t the same. However, as we add more and more grid points, the two solutions start to look closer and closer. (The time required for computation of the dynamic programming solution grows of course.)

5. Unlike non-linear models, approximate analytical results can be recovered from the linear systems. This is an underappreciated side benefit of adopting a linear approach. The linear equations can be solved by hand to yield productive insights. There are many famous examples of log-linear relationships that have led to well-known empirical studies based on their predictions. Hall’s log-linear Euler equation, the New Keynesian Phillips Curve, log-linear labor supply curves, etc. Mankiw, Romer and Weil (1992) used a linear approximation to crack open the important relationship between human capital and economic growth.

Given the huge benefits to linear approaches in the field. The main question I have is not why researchers don’t adopt non-linear, global solution approaches but rather why linear methods aren’t used even more widely than they already are. One example in particular concerns the field of Industrial Organization (IO). IO researchers are famous for adopting complex non-linear modelling techniques that are intimidating and impressive. They often seem to brag about how it takes even the most powerful computers weeks to solve their models. I’ve never understood this aspect of IO. IO is also known to feature the longest publication lags and revision lags of any field. It’s possible that some of this is due to the techniques that they are using; I’m not sure. I have asked friends in IO why they don’t use linear solutions more often and the impression I am left with is that it is a combination of an assumption that a linear solution simply won’t work for the kinds of problems they analyze together with a lack of familiarity with linear methods.

There are of course cases in which there is important non-linear behavior that needs to be featured in the results. For these cases it does indeed seem like a linear approach is not appropriate. Brad DeLong argued that accommodating the zero lower bound on interest rates (i.e., the “flat part of the LM curve” ) is such a case. I agree. There are cases like the liquidity trap that clearly entail important aggregate non-linearities and in those instances you are forced to adopt a non-linear approach. For most other cases however, I’ve already chosen my team …

 

[Fn 1] This reminds me of a joke from the consulting business. I once asked an economic consultant why he thought he could give valuable advice to people who have been working in an industry their whole lives. He told me that I was overlooking one important fact – the consultants charge a lot of money.

Back to Blogging …

I haven’t written a post in a long, long time.  Research, referee reports, teaching and administrative work have all been preventing me from contributing to the blog.  This summer I’m going to try to get back into writing somewhat regularly (famous last words).