# Modern macro was invented by a Soviet economist

Here’s the story.

In 1927, a Russian economist by the name of Eugen Slutsky wrote a paper entitled “The Summation of Random Causes as the Source of Cyclic Processes“. At the time Slutsky was working for the Institute of Conjuncture in Moskow. That institute was headed by a man called Nikolai Kondratiev.

This was in the early days of the Soviet Union, before Stalin managed to turn it into a totalitarian hellhole, a time when the Communist leadership was relatively tolerant towards scientists and even occasionally listened to their advice. The institute’s job was basically to collect and analyze statistics on the Russian economy in order to help the Party with their central planning. But Kondratiev seemed to take the view that it would be best to allow the market to work, at least in the agricultural sector, and use the proceeds from agricultural exports to pay for industrialization. Lenin apparently took the advice and in 1922 launched the so-called New Economic Policy which allowed private property and markets for land and agricultural goods and re-privatized some industries which had been nationalized after the October Revolution. This policy turned out to be rather successful – at least it ended the mass starvation which War Communism had caused during the years of the Russian civil war.

But then Lenin died and Stalin took over and decided that time had come to get serious about socialism again and finally abolish private property and markets for good. Dissenting voices like Kondratiev’s clearly couldn’t be tolerated in this great enterprise, so in 1928 Kondratiev was sacked and the institute was closed down. Some time later, Kondratiev was arrested, found guilty of being a „kulak professor“ and sent off to a labor camp. Even there he continued to do research until Stalin had him killed by firing squad during the Great Purge of 1938.

But I’m digressing, so back to Slutsky. His 1927 paper was written in the wake of Kondratiev’s 1925 book “The Major Economic Cycles“. That book claimed that capitalist economies exhibit regular boom-bust waves of about 50 years duration, known today as Kondratiev Waves. Other „conjuncture” researchers had claimed the existence of shorter waves.

Slutsky’s first observation was that when you really look at time series of aggregate economic output, you don’t see regular waves, but a lot of irregular fluctuations. So trying to find deterministic, sinusoidal waves in economic time series is probably not a very fruitful exercise.

Slutsky’s second observation was that when you draw a long series of independently and identically distributed random variables (modern terminology, not his) and then take some moving average of them… you get a time series that looks an awful lot like real-world business cycles!

He showed that in two ways. First, he performed simulations. Remember this is 1927 – so how did he simulate his random numbers? Well, the People’s Commissariat of Finance ran a lottery. So Slutsky took the last digits of the numbers drawn in the lottery (this is the basic series shown in figure 1). He then computed a bunch of different moving average schemes one of which is shown in figure 2. See the boom-bust cycles in that picture? Pretty cool, huh?

But Slutsky didn’t just show cool graphs. He also had a beautiful argument for why these moving averages looked like recurrent waves:

We shall first observe a series of independent values of a random variable. If, for sake of simplicity, we assume that the distribution of probabilities does not change, then, for the entire series, there will exist a certain horizontal level such that the probabilities of obtaining a value either above or below it would be equal. The probability that a value which has just passed from the positive deviation region to the negative, will remain below at the subsequent trial is 1/2; the probability that it will remain below two times in succession is 1/4; three times 1/8; ans so on. Thus the probability that the values will remain for a long time above the level or below the level is quite negligible. It is, therefore, practically certain that, for a somewhat long series, the values will pass many times from the positive deviations to the negative and vice versa.

(For the mathematically minded, there’s also a formal proof just in case you’re wondering.)

Since it was written in Russian, the paper went unnoticed by economists in the West until it came to the attention of Henry Schultz, professor at the University of Chicago and one of the founders of the Econometric Society. He had the paper translated and published in Econometrica in 1937.

And so Slutsky’s „random causes“ provided the first stepping stone for the modern business cycle theories which explain how random shocks produce, via the intertemporal choices of households, firms and government agencies, the cyclical patterns we see in aggregate time series.

P.S.: All this time you have probably asked yourself: Slutsky, Slutsky,… that name rings a bell. Oh right, the Slutsky Equation! Yep. Same guy.

# Monopoly power and corporate taxes

There has been a fair amount of debate about corporate taxes in the econ blogosphere. The debate was framed early on by a cute little exercise on Greg Mankiw’s blog which was supposed to  show that, in a small-open economy with perfect competition, a 1 dollar cut in capital taxes raises wage income by more than 1 dollar.

Paul Krugman and others have rightly pointed out that Mankiw’s toy example, its cuteness notwithstanding, provides little to no insight into the real policy debate now going on in the US, because (i) the US is not a small open economy and (ii) there is evidence that much of corporate profits are monopoly rents rather than returns to capital, which casts doubt on the relevance of perfect competition models.

Indeed, there’s a new paper documenting that mark-ups (difference between price and marginal costs) have increased in practically every industry in recent decades. The paper has not yet gone through peer review, so it’s probably wise not to jump to conclusions from it. Nevertheless, it’s useful to think about potential implications.

One of the basic results in public finance is that taxes on rents produce no deadweight loss. So if corporate profits are just monopoly rents, we can tax them away at zero social cost. Right?

Wrong.

# “Self-financing” tax reforms: a simple formula

There is much talk these days about tax reforms, both in Austria and around world. Most political parties seem to agree that taxes on labor are too high and that cuts should be made. There is disagreement as to whether these tax cuts should be accompanied by cuts in government spending or increases in other taxes.

One recurrent issue in this debate is the extent to which tax cuts are “self-financing”. This usually comes from a vague notion that reducing tax rates has a “stimulating” effect on “growth” and “job creation”. Such “stimulus” makes the tax revenue increase thus offsetting some of the revenue loss due to the reduction in tax rates.

Although I usually take great pleasure in brutally debunking popular myths with my profound knowledge of Economic Science (insert resounding laughter here), let me say that I think that in this matter the vague notion of the layman is broadly correct.

Economics being a hard quantitative science, the careful economist always strives to replace broadly correct but vague notions with mathematically exact but only vaguely correct formulas. In this spirit, I offer a formula for calculating to which degree a cut in the marginal labor tax rate is “self-refinancing”.

We start from a definition: total tax revenue (T) is the tax rate (t) times income (Y):

$\displaystyle T = t\times Y.$

We treat t as both the average and marginal tax rate. In fancy language: income taxes are assumed to be linear. Not true, but (one hopes) true enough.

We want to know how T changes if t is reduced by a small amount dt. There are two effects, one direct, one indirect. The direct effect is to reduce T by an amount $\displaystyle Y dt$. The indirect effect comes from realizing that Y depends on labor input L which, in turn, depends on the tax rate. So therefore, if we reduce the tax rate by dt, labor supply rises by $\displaystyle n dt$, where n is the elasticity of labor supply. The increase in labor input raises output and thus income. Suppose the elasticity of output with respect to labor input is a. Then the total change in income is: $\displaystyle dY = (\alpha\times n)dt.$

The indirect effect is where “self-financing” comes from. Let us measure the self-refinancing effect of the tax cut by $\displaystyle X = t\times dY/Y,$ which is the indirect change in revenue measured in percent of income.

$\displaystyle X = (t\times\alpha\times n)dt.$ *

The self-financing share X is larger, the higher the initial tax rate, and the higher the two elasticities $\displaystyle \alpha$ and n.

How big is $\displaystyle \alpha$? Well, consider a Cobb-Douglas production function $\displaystyle Y=K^{1-\alpha}\times L^{\alpha}$, where K stands for other factors of production which we hold fixed for purposes of this exercise. The labor elasticity of output is $\displaystyle \alpha.$ It is well-known that under competitive conditions a is equal to the labor share of income. In Austria, as well as in most developed countries, this share is about 2/3. So let’s take that as our answer.

How big is n? That’s a tough one to measure. Theoretically, it depends on the labor-leisure preferences of households as well as on other „deep” parameters of the economy. The empirical evidence I have seen suggests that a 1 percent decrease in t increases L by less than 1, but more than 1/3 of a percent. Let’s take 1/2 as a guess.

Finally, what is t? In Austria the marginal income tax rate is close to 50%, the average rate is in the area of 30%.

Feeding these numbers to our formula we arrive at the following conclusion. The self-financing share of a tax cut is in the range between 10 and 17 percent. This means that a tax cut of 1 billion euros indirectly creates additional revenues between 100 and 170 million euros. That still leaves a hole in the public budget of at least 830 million euros, though.

*) The General Formula is:

$\displaystyle dT = Ydt + t\times\frac{dY}{dL}\frac{L}{Y}\times\frac{dL}{L}\frac{1}{dt}\times Y dt$

# Disequilibrium economics is a logical impossibility

This is going to be super abstract, potentially infuriating and probably wrong.

I sometimes hear people talk about „disequilibrium economics“ and I think I know what they have in mind. Equilibrium is often associated with a system at rest. That’s the physicist’s notion of equilibrium: a ball sitting at the bottom of a bowl, a planet moving around the sun in a stable orbit, etc. Disequilibrium is something not at rest: you hit the ball and it jiggles around inside the bowl, a planet collides with another and flies off its orbit.

Economists have a different notion of equilibrium. Indeed, they have several different notions depending on the context. But basically, an economic equilibrium is a consistency condition imposed on a model by the economist. It follows that „disequilibrium economics“ is a logical impossibility.

Let me explain. Economists build models to explain certain real-world phenomena, say bank runs. Inside these models there are agents, e.g. savers, banks, firms, each described by their preferences, beliefs and constraints. For instance, a saver wants to keep her money in the bank as long as she believes she will get it back eventually. Whether she can get it back depends on the number of savers who demand their money back. As long as most of them don’t want to withdraw their money, everything is fine. However, if there is a critical mass of savers who want their money back, the bank needs to liquidate its assets prematurely at „fire-sale“ prices, which means it cannot repay all the savers’ deposits in full. You have two equilibria: one in which nobody runs on the banks, the banks carry their investments to maturity, everyone gets repaid; another one in which everyone runs, the banks liquidate their investments prematurely, people don’t get repaid in full.

Only the first of these equilibria can sensibly be characterized as „a system at rest“. In the second equilibrium, nothing is at rest: there is chaos in the streets, banks go bust and people get hurt.

What characterizes both equilibria are two conditions:

1. Everyone is doing the right thing given their preferences, beliefs, and constraints. The saver who runs on the bank is doing the right thing: Given that everyone else runs, she should run, too, or else she will get nothing. This is called rational behavior, but it should really be called consistent behavior. It’s behavior that is consistent with an agent’s preferences, beliefs and constraints.
2. Things need to add up. Or to put in fancier language: individual decisions need to be consistent with each other. The total value of deposits repaid cannot exceed the total value of assets held by the banks. If there are 10 cookies and I want to eat 8 and you want to eat 5, that’s not an equilibrium. It’s a „disequilibrium“. It’s a logical impossibility.

If you’re a behavioral economist, you may take issue with condition (1). You may argue that people often don’t do the right thing, they are confused about their beliefs and they don’t understand their constraints very well. That’s fine with me. Let agents do their behavioral thing and make mistakes. (Although you must be explicit about which mistake out of the approximately infinite number of mistakes they could make they actually do make.) But still, things need to add up. I may be mistaken to want 8 cookies and you may be confused to want 5, but there are still only 10 cookies. Behavioral economics still needs condition (2).

If you’re a first-year undergrad, you may think equilibrium means that markets clear. Then you learn about asymmetric information and realize that things like credit rationing can occur in equilibrium. And you learn about the search models. Adding up constraints may be inequality constraints.

Finally, you cannot „test for equilibrium“ with data. Equilibrium is that which your model predicts. If your prediction is contradicted by the data, it’s because your model is wrong, not because there is „disequilibrium“. I have heard econometricians talk about error correction models where they call the error correction term a measure of „disequilibrium“. What they mean by that is that their economic model can only explain the long-run relationship between variables (the cointegration part), from which there are unexplained short-run deviations. But that just means the model is wrong for these short-run movements.

Equilibrium means consistency at the individual and at the aggregate level. It doesn’t mean stable, it doesn’t mean perfect. In fact, it is completely devoid of empirical content in and of itself. It only becomes meaningful in the context of a concrete model. And without it, economic models wouldn’t make any sense.

# Schnupperuni 2017

Ein Beispiel einer Vorlesungsstunde für potentielle angehende Studierende. Es geht um rationales Herdenverhalten. Wenn ein Produkt von vielen Menschen gekauft wird, heißt das dann, dass es ein gutes Produkt ist? Warum gehen wir lieber in das volle Lokal? Und was bedeutet das für andere?

# Die Gegenfinanzierung von Steuerreformen: Eine Pi-mal-Daumen-Rechnung

Vor der anstehenden Nationalratswahl haben die wahlwerbenden Parteien ihre Steuerpläne vorgestellt. Sowohl SPÖ als auch ÖVP und FPÖ versprechen Steuersenkungen, hauptsächlich bei der Lohn- und Einkommenssteuer. Wie immer bei solchen Versprechen stellt sich die Frage der Gegenfinanzierung, d.h. an welcher Stelle im Staatsbudget Ausgaben eingespart werden soll. Und dabei sorgt ein Punkt immer wieder für Verwunderung: das Volumen der vorgeschlagenen Einsparungen ist immer geringer als das Volumen der Steuersenkungen. Zum Beispiel: Im Reformvorschlag der Volkspartei steht eine Senkung der Steuern und Abgaben von 12 Milliarden einer Ausgabensenkung von 8 Milliarden gegenüber. Woher sollen die restlichen 4 Milliarden kommen? Die Antwort lautet: aus Mehreinnahmen durch höheres Wirtschaftswachstum.

Wie soll das gehen und sind Mehreinnahmen in dieser Höhe realistisch?

# Economics on the beach IV: welfare optimal pricing – a model

This post builds on the previous two, economics on the beach II and economics on the beach III. I have started this, so I need to finish this now. In this post I will finally try to build a small model in which it is true that “charging a perhaps even substantial price for beach access would be welfare improving for all potential beach goers”.