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Savings = Investment

January 2, 2012 Leave a comment

I was poking around on Nick Rowe’s blog, and came across this piece on Keynesian economics.  If you recall in this post I recently pointed out a peculiar aspect of Keynesian economics:

[H]ow is it that if savings equals investment and savings equals income minus consumption, that when you lower interest rates investment increases but consumption stays the same?

When I was reading Nick’s post, I couldn’t help but think about this and think how ridiculous Keynesian economics would seem to people if they explained what they were really doing in the same way I think about it in my mind.  So naturally I figured I should take a stab at this.

As Nick explains, the model begins with two identities (assuming a closed economy and no government for simplicity): Y=C+I and S=Y-C.  This gives you S=I as an identity.  In other words, given the way we have defined the variables, this must be true.  This is different from an equilibrium condition such as quantity supplied = quantity demanded which is true only in an equilibrium.   So at this point no economics has been done.

In order to do some economics, you must assume some values of variables and some causal relationships which determine the values of the other variables.  The way Keynesians go about this is to assume the following equations from Nick’s post (to simplify even further I will assume that autonomous spending, which is “a” in his model, is equal to 0)

8. Cd = b*Y   (where a>0 and 0<b<1)

9. Id = Ibar

Where Cd and Id are desired consumption and investment respectively.  Then if you assume that in equilibrium C=Cd and I=Id, you have a model (6 equations and 6 unknowns).  But here is what we have done in plain english:

1.  We have assumed that investment is equal to a certain value no matter what.  This value is not explained in any way in this model and nothing in the model can change it.

2.  We have assumed that consumers spend a certain proportion (b) of their income on consumption.  This proportion is not explained in any way by the model and nothing in the model can change it.

3.  Based on our definition of savings, savings must be the amount of income not consumed, which by assumption is (1-b)Y.

4.  Since, by definition, savings is always equal to investment, we know that the amount of savings must be equal to the value we assumed for investment.  (Ibar=(1-b)Y)

5.  The only thing we haven’t assumed yet is Y (output) so that must be whatever value makes the proportion we assumed would be saved equal to the value we assumed for investment.

To make this even simpler consider a numerical example.  Assume the following:

1. People consume half of their income and save the rest.

2. Investment is $100.

3.  Savings equals investment.

Now it follows logically that Income is $200.  Why is that?  Well it’s simple, since savings equals investment and investment is $100, then savings must be $100.  And since people save half of their income and savings is $100, then their income must be 2×100=$200.  This does nothing to explain where income actually comes from!  Now if, for some reason, people decide to save only 1/4 of their income, then, by assumption, investment doesn’t change so the amount of savings must still be $100.  But since people are saving more, their income must be higher in order to generate this arbitrary amount of savings.  Therefore, income must increase to $400 to bring the model into equilibrium.  This is essentially how Keynesians arrive at the “paradox of thrift,” by assuming that savings will have to be a fixed amount so if people insist on saving a smaller proportion of their income, then income will have to get larger to make that smaller proportion equal to the presumed constant level of savings.

This model works mathematically but it is a terrible way to do economics.  Proper economics assumes some scarcity fixed by nature and some purposeful economic agents which choose between different ways of dealing with that scarcity.  In other words, the degree of scarcity is constant and the model determines what people do in the face of it.  On the other hand, this Keynesian approach takes human behavior for granted and assumes that the degree of scarcity in the system adjusts to make an equilibrium given this behavior.  It’s an economic paradigm custom-made for people who think that human nature is the source of all the world’s problems and if only we could get better at social engineering, everything would be great.  But this is a mistaken view of reality, and it leads to a mistaken view of economics.  Perhaps more troubling, is that the converse is also true.  Tread carefully, “practical men who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist.”

 

Note: If I were a Keynesian I would probably be fuming at this post and I would point out that the Keynesian cross is only *part* of the Keynesian model, and that it is misleading to present this part as a complete model.  For instance, in the larger model, investment is not fixed, it is determined by interest rates.  However, it still enters the Keynesian cross part of the model independently of the other variables in that part.  It is my belief that the same general criticism is valid with regard to the larger IS/LM model but my goal here was to make the case as simply as possible and it would be much more complicated to analyze that entire model in the same way.  So, I will leave it to the interested reader to look into it further, but this should get you started seeing it for what it is.

Mainstream (Keynesian) Economics

December 22, 2011 1 comment

Since I recently took on Austrian economics, I would be remiss if I didn’t turn my ire on mainstream economics before moving on to my ultimate purpose.  First of all, mainstream micro is great (at least most of it), even though it sometimes falls back on cardinal utility.  My problem is with the macro.  Mainstream macro is essentially Keynesian.  I’m already on record as thinking the neoclassical synthesis is the worst thing that ever happened to economics.  I want to focus on a particular aspect of modern macroeconomics though which I think is the root of most of its issues.

In an economic model there are two types of variables.  There are certain variables representing the state of nature which are determined exogenously.  These exogenous variables represent the scarcity which is inherent in nature.  Remember this line about mainstream economics:

It begins with the premise that resources are scarce and that it is necessary to choose between competing alternatives.

This is key, we will come back to it.  Other variables are determined in the model (endogenously).  These are the result of the actions people take to deal with the scarcity inherent in nature and are the things the model tries to explain.  So in the model of the market for some good, incomes, tastes, prices of other goods, and costs of production are exogenous.  They represent the nature of the scarcity faced by these economic actors (buyers and sellers).  The model takes these exogenous variables and uses them to determine the endogenous variables price and quantity.  When the exogenous variables change the endogenous variables change in predictable ways.  This is economics.  Note that when modelling the market for a good, when the quantity of that good increases it comes at the expense of other goods which are not produced.

The Federal Reserve has had a subtle but pervasive corrupting influence on macroeconomics.  Pretty much every modern macro model treats interest rates as an exogenously given policy tool.  This is because that’s what they are….now.  The Fed sets interest rates (sort of).  Economists want to predict what will happen in the real world.  To us the “real world” is one in which interest rates are set arbitrarily by a handful of people in private with unknown motives.  In other words it’s exogenous to the economy under study.  Mainstream economists basically take this for granted.  After all it’s been that way their entire lives.  But this is not the natural role of interest rates.  Interest rates are a price: the price of money today in terms of future money.   In a free market, prices are determined in the market.  They adjust due to changing market forces (exogenous variables) in order to bring the system into equilibrium.  Once you make them exogenous you remove the whole mechanism by which markets allocate scarce resources between alternate uses.

This leads the thoughtful student in intermediate macro to some confounding paradoxes.  For instance: how is it that if savings equals investment and savings equals income minus consumption, that when you lower interest rates investment increases but consumption stays the same?  The astonishing answer, according to the model is that you just get more stuff.  Where did that stuff come from?  What competing use were these resources taken from?  There is no such competing use.  Income just increased.  Why?  Because it must have increased if investment increased and consumption stayed the same, and investment must have increased if interest rates decreased.  In other words, by making price (interest rates) exogenous, they have to let another variable adjust to bring the model into equilibrium.  Keynesians assume that this is output.  So in this model, you exogenously lower the price and this reduces scarcity.  The whole model is turned upside down!

To better see what I mean consider a simpler example.  You observe a dam on a river with a reservoire behind it.  Water flows out of the mountains and into the river from sources unknown.  You observe that the pressure with which the water flows through the dam depends on how high the water is in the reservoire.  You construct claculate an equation which gives the water pressure as a function of the height of the water behind the dam.  Let’s call this P=f(L) where P is pressure, L is the water level and f() is some function.  You declare that for any amount of water behind the dam the water pressure flowing through must be the value determined by this equation.  This is good science.

This is bad science.  You take the equation above: P=f(L) and declare that this must hold, therefore if you increase the pressure with which the water flows through the dam the water level behind the dam must increase.  You build a pump that forces the water through at a higher pressure and assume based on the above equation that this will cuase more water to flow down from the mountains from parts unknown and raise the level of the reservoire.  It’s the same equation but these relationships which make perfect sense when causality goes one way make absolutely none when it is reversed.

This same flaw leads to other head scratchers like: if the government increases taxes and spending by the same amount output increases.  Where do these additional resources come from?  The model doesn’t say anything about where output comes from (parts unknown….?) or what tradeoffs are involved.  It is just a set of monetary equations which must hold in equilibrium.  As it turns out the only real source of scarcity in the model is the tendency of people to save some of their income.  If people just didn’t save at all then money would keep circulating infinitely making everyone infinitely wealthy.  That is the actual implication of the model: infinite output if nobody saved.  So naturally, if the government takes some of your money and spends it all they are spending what you would have plus what you would have saved so this somehow magically causes more goods to come into existence.

This is why our whole economic understanding is upside down.  We treat spending as the genesis of economic activity not production.  I just heard my hero, Charles Barkley, say that they were helping the economy because they had to hire a translator for Shaq.  While hilarious, this is “turrable” economics.  We treat waste as production.  This is all because of an upside down model.

If you really want something to think about try this one: If the real rate equals the nominal rate minus the inflation rate, and the real rate is determined by real factors like time preferences and marginal productivity, then how is it that lowering the nominal rate increases inflation?

All of these paradoxes are not paradoxes when the proper things are endogenous and exogenous.  But remember, the Fed was created in 1913.  Keynes was doing most of his damage in the 30s.  The change in economic thought is the result of a real change in the economic system.  It is this change in the system which really needs to be undone but in order for that to happen we will have to start analyzing the effects of this change, which means creating a model with real scarcity and causal relationships with the dependency going in the right direction.

 

 

 

Still More Broken Window Economics

September 6, 2011 16 comments

Here is a simple explanation of the Keynesian view of “broken window” stimulus.  It makes perfect sense and I agree completely with it (although there is an important distinction between the “economic activity” of a society and the wealth of a society).  But this argument (as all similar arguments I have heard) leave a gigantic question on the table that nobody seems to be talking about.  Why are there so many unemployed subsistence farmers?   In fact, this difficulty is so pervasive that it is inherent in the setup of this example.  After all, a subsistence farmer does not need the wealthy loaner to have work, they work for their own subsistence.  But let’s ignore the reality that a man always has himself (or each other) as the employer of last resort and assume that they do need the rich guy in order to have anything to do.  Maybe he owns all the land and resources that could be used to produce the conveniences and necessities of life.

In this scenario, the peasants represent a resource.  They could be producing things of value to themselves and the rich guy.  Knowing this, why would the rich guy allow them to be idle and starving to death?  By assumption this guy owns land or resources that they could work in order to produce something.  Presumably they would be willing to work on his land to produce something if they got to keep some of it.  Presumably they would be willing to work for less than the full amount that they could produce using his land and/or other resources.  And presumably he would be willing to let them work his land in return for some portion of their produce rather than let the resources (land and labor) go to waste right?  Or is that the rub?  See, this premise seems to assume that the rich guy is completely satiated, that he has no desire for any more stuff.  And not only does he have no desire for any other stuff but he would rather not have any other stuff and he prefers to watch all the peasants starve rather than make any use of his wealth because if he were satiated, he could still let them work and keep all of their produce.  This would make him no worse off, unless of course he just likes to see them suffer.  In this case a hurricane is only a device that undoes the satiation of the rich guy and allows the economy to work again.

So once again we have a model that begins by implicitly assuming there is no scarcity, at least for the rich guy.  Or could there be another reason that there are so many people/resources lying around going unused despite their obvious productive capabilities?  What might account for that?  What if there were a minimum wage that were higher than what they could produce?  Or a union that had the ability to keep them from working for such a low wage?  Or what if the rich guy had to pay taxes and social security and unemployment and medicare and pension and workers comp and liability insurance and hire a lawyer to help him comply with all relevent regulations every time he wanted to hire a peasant?   That would probably have some effect right?  But all that isn’t even the main reason.  The main reason is much more unspeakable than that.

Broken Windows and the Theory of the Second Best

September 1, 2011 9 comments

While I was on vacation the Keynesians and Austrians have been continuing their immortal struggle over Krugman’s alien attack and Bastiat’s broken window fallacy.  Let me remind the reader that when it comes to Keynesians vs. Austrians I come down in the Austrian camp so I am writing this for their benefit.  Austrians, you are losing this argument because you think you are still just fighting the same intellectual battles of 200 years ago, but they have changed the battleground.  Yglesias’s response is actually spot on.

Austrians seem to be in the habit of going to great lengths trying to explain why a fiat money system and a central bank are bad for the economy and a gold standard would be preferable and then as soon as the subject turns to something like fiscal policy, ignoring the difference and acting as though fiat money and central banks didn’t exist or had no important effect on how the economy works.  In doing this they are not only fighting a losing battle but they are missing the more important point.

So please Austrians (or whomever it may concern) let’s take a step back and reevaluate things.  But let’s begin by recalling a different well-established bit of economic lore–the theory of the second best.

Canadian economist Richard Lipsey and Australian economist Kelvin Lancaster showed in a 1956 paper that if one optimality condition in an economic model cannot be satisfied, it is possible that the next-best solution involves changing other variables away from the ones that are usually assumed to be optimal.[1]

This means that in an economy with some uncorrectable market failure in one sector, actions to correct market failures in another related sector with the intent of increasing overall economic efficiency may actually decrease it. In theory, at least, it may be better to let two market imperfections cancel each other out rather than making an effort to fix either one. Thus, it may be optimal for the government to intervene in a way that is contrary to usual policy. This suggests that economists need to study the details of the situation before jumping to the theory-based conclusion that an improvement in market perfection in one area implies a global improvement in efficiency.

To put it simply: once you screw one thing up, it’s not so obvious what the effects of screwing other things up will be.  Now notice that the whole Keynesian argument turns on two points.  They acknowledge that the broken window fallacy holds when there is commodity money and full employment but that when there are idle resources and fiat money, anything that expands the money supply (even breaking a window or fighting a war) can help.  This could very well be true (in fact I think it is true) but the real question we should be asking is “why is there so much persistent unemployment in the first place?”  It is this original distortion, caused by the monetary system, that is the real problem.  After this distortion is acting on the economy it is no miracle that something else which would be an undesireable distortion if starting from a perfect world, might actually cause an improvement.  It’s just a way of partially undoing the damage caused by an inherently deflationary monetary system.

There are a lot of unfortunate distortions in our economy.  If we got rid of all of them we would be much better off.  If Austrian economists ran the country we would be a lot better off.  We would have real money and no superfluous government intervention or spending.  This would be the first best.  But when you argue that in the face of a serious monetary distortion (among others), an additional monetary distortion can’t possibly benefit the economy, you are inadvertently denying the existence of the first distortion.  We (the proponents of limited government and economic freedom) would do much better to focus on the question “how have we arrived in a situation where we need a war to keep the economy running?”

My God! Lord, my God! Please Make the Devil Keep his Word!

August 18, 2011 3 comments

So I’m a libertarian–a real libertarian, not a leftlibertarian (it’s like a really bad horror movie, you know it’s sick and wrong but for some reason you can’t help watching it again and again).  I think the government should be a lot smaller and generally leave us alone.  Also, I’m an economist (more or less) and I especially think it should stay out of markets and economics.  Lots of people agree with me.  Lots of people don’t.  The ones who do seem to be growing in number which is good.  But there is something problematic going on intellectually in the movement and it could very well be our undoing if we don’t sort it out quickly.

Over the past century there has developed a major divide in macroeconomic thought.  The two sides can be represented by the Keynesians and the Austrians with several other schools falling somewhere in between (monetarists, RBC, etc).  To put things simply, the Keynesians are the big-government types and the Austrians represent our side.  For the most part the Keynesians have been winning the battle.  Naturally, the two sides don’t care much for each other and if you go on the Austrian blogs you will find a general dismissal of Keynesian ideas as confused and intellectually bankrupt.  I have no interest in defending Keynesianism, I have been an ardent critic of it.  But these people aren’t as confused as Austrians seem to think.  In fact the root problem with Keynesianism is that it is morally bankrupt.  It’s true that there are important theoretical flaws in their models but these are not so simple as the broken window fallacy. The flaws are there to cover up the moral foundation which would terrify most people if it were revealed.  But the general conclusions are largely correct.  This should concern us much more than if they were just completely misguided but if we are going to do anything meaningful about it we have to acknowledge how and why their theories “work.”

I will try in coming weeks/months/years to make the case that orthodox Keynesian economics is largely correct and that this is why we should be concerned.  But this is too large a task to undertake in this post.  So my appeal to you the reader is not to believe me but just to admit that it’s possible.   So let me try to explain why there is so much distance between the two sides.

Austrians are like scientists and Keynesians are like engineers.  Just as a scientist tries to describe the laws of nature, Austrian (and most of classical) economics is concerned with describing how a natural, free market economy functions.  Just as an engineer tries to construct devices to overcome the laws of nature, Keynesians concern themselves with designing a system to overcome the laws of economics.  Of course neither of them can change the natural law, but they can often overcome what seem to be the obvious implications of those laws.  The law of gravity says there is a force pulling things down (more or less).  The obvious implication of this is “what goes up must come down.”  Nonetheless, an engineer can design a craft that flies.

Hundreds of years ago, people claimed that government spending creates jobs and grows the economy.  Austrians and classical economists correctly identified that government spending misallocates resources and doesn’t help the economy.  But the other side didn’t just say “oh I guess you’re right, we give up.”  And what’s more, they didn’t just keep making the same flawed argument (though this seems to be the view of most people on my side).  They actually constructed an economy in which the broken window fallacy is seemingly not a fallacy.  Of course, there is a fundamental law of nature underlying the concept and they can’t change that.  Yes, it’s true that destruction (in this sense) is inefficient and governments misallocate resources.  Yes we would be better off if the government didn’t do this stuff and we had a free market.  But we don’t have a free market, we have a contraption constructed by progressives to make these fallacies hold.

So is it so hard to believe that Krugman might be right, that more government spending–even wasteful spending–might actually improve the economy?  This doesn’t invalidate any tenants of Austrian or classical economics any more than observing an airplane flying negates the law of gravity.  But just like an airplane, an artificial device constructed to combat the laws of nature can do so only temporarily.  The economy is an airplane and we are citing the law of gravity to deny that we are flying.  But this doesn’t do anything to save us.  The plane is going somewhere.  That is what they don’t tell us.  They tell us “just don’t worry it’s flying, as long as it keeps flying we’ll be fine, we know what we’re doing.”  The insight that we need to glean from our knowledge of the laws of nature is not that planes don’t fly but that eventually they come down somehow.  If we notice this we can start asking when, where, and how it will come down (the answer is not good).  But in order to answer these questions we have to understand how planes fly in the first place.

So please, just ask yourself if you are willing to go down this road.  If you are, please stay tuned to my blog.  Like I said, I don’t expect you to be convinced by this that Krugman is right.  I’m not arguing that we should do what he is prescribing and I’m certainly not trying to convince you to become a Keynesian.  But if we don’t understand why he wants to do it we can’t work toward a real viable alternative.  Intellectuals on our side of the debate are well aware that what we have is not really free market capitalism.  They are well aware that the Federal Reserve manipulates the economy and creates bubbles.  In other words they are aware that they have constructed a system capable of making the economy function in ways which are different from a natural free market economy.  But then when a Keynesian comes along and says “look, the machine works like this,” all I hear from my side is “the machine doesn’t exist!”  But never forget my dear brothers, “when you hear the progress of enlightenment vaunted, that the devil’s best trick is to persuade you that he doesn’t exist!”

The Compartmentalization of Economics

August 18, 2010 Leave a comment

Alright, before I begin I want to acknowledge that the field has been working on these issues for a while and has made significant progress.  So to some extent I’m arguing with a historical phenomenon here.  But I think this is still important for a couple of reasons.  First, we still teach econ majors the version of economics that suffers from this deficiency, and our policy makers seem to rely largely on the same models.  Second, from a historical perspective I think it is important to ponder how things like this happen.

As you may know by now, I have been trying to develop the idea on this blog that our monetary system is of such a nature that lowering the interest rate causes inflation in the “medium run” and then deflation in the long run.  The argument for this is amazingly straight forward.  All you have to do is look at the Fisher equation and believe that in the long run, the real interest rate is determined by real factors (which I suspect most economists would concede).  And yet I have never heard another economist make this observation (of course that doesn’t mean it has never happened, but if it was common it seems like I would have noticed).  How can this be?

My opinion that Keynesianism marked a radical departure from sound economic reasoning is well documented but how was this able to happen and persist for all these years?  There are several reasons I think.  Part of it is that it has enjoyed some degree of empirical success (though with much help from progressives manipulating the economy into something that doesn’t make much sense).  This brings up the old rationalism vs. empiricism debate which I don’t intend to have here.  Another (big) reason is that the theory is convenient to politicians and other “powers that be” who enjoy having an intellectual justification for a lot of interventionist policies and Keynesian economics suits that purpose nicely (see the above parenthetical comment).  But I think another important component in this formula is the compartmentalization of the discipline.

What I mean by that is dividing the subject into multiple “schools” which peacefully coexist and yet are logically incompatible.  I am talking of course, about the neoclassical synthesis in which  economics was divided into microeconomics and macroeconomics.  This allowed the sound reasoning which had come to dominate all of economics up to the time of Keynesianism to be cordoned off and kept away from the Keynesian paradigm which was to become the accepted mainstream approach to macro.  Before this, economists were not macroeconomists or microeconomists they were just economists.  Their theories had various implications and often these extended to both of what we now call micro and macro. 

The problem with this is that if you really understand classical micro concepts, you can’t really understand Keynesian economics.  This is because Keynesian economics is hopelessly flawed.  It in fact takes a drastic step back in the area of economic understanding in the sense that it revives the old confusion between a supply relationship and a demand relationship as I pointed out in this post.  If you let capable microeconomists think about this long enough, certainly they would notice.  But certainly they couldn’t hope to overturn a century and a half of progress in the field.  They would have to find a way to let them keep that knowledge but also accept the new incompatible model.  The answer is natural.  Just create a new field. 

This has two important implications.  The first, and most obvious, is that most people don’t carefully study both micro and macro now.  You can ask an accomplished microeconomist about Keynesian economics and they will just shrug and say “I don’t know. I don’t think about that stuff.” and macroeconomists will say the same thing if you ask them about industrial organization.  But the second, and I think even more significant issue, is that the two fields, by their different natures, select certain kinds of people into them.  Specifically, people who have a strong intuition regarding things like market equilibrium and Pareto efficiency find micro fascinating.  Alternatively, people who like the idea of empirical knowledge and a giant machine called the economy that we can control by pulling the right levers at the right time gravitate toward macro.  These people (macroeconomists) tend to be the last people who want to discover that the economy can’t be controlled in a way that is good for society.  So can we be surprised when they don’t notice that a model which says all the things that get them excited is contradicted by the basic principles of another field which doesn’t really turn them on that much?

But it doesn’t stop there.  Macroeconomists know about the Fisher equation.  But they have actually further compartmentalized macroeconomics.  They did this by dividing it up into the short, medium, and long-run.  Again, newer models don’t do this but this is what we still teach in intermediate macro.  To see the importance of this, you must notice that what Keynesian economics says about the effect of increasing the money supply (lowering the interest rate) on the price level.  It says that in the short run, prices are fixed (again see previous parenthetical comment) so prices don’t change (or don’t change much) and then in the medium run expectations adjust and prices go up, and then in the long run blank out.  “Wait, what happens in the long run” you ask?  Well when we analyze the long run we use the Solow growth model.  It deals with saving and capital accumulation.  You: “but what happens in the long run when the money supply increases?” Smart professor: well, in the long run model there is no money supply, it’s all real variables…  You: hmph [rolling eyes] ok, so what’s going to be on the test….

Is it possible that the things we’re doing to save ourselves in the short run actually have long run implications?  Maybe a better question is: is it possible to answer the first question with this approach to economics?  And furthermore, is it surprising that we haven’t managed to stumble onto the answer to a question which doesn’t even exist in the framework on which we have built our knowledge? 

Ok, so in physics they had a theory of gravity that didn’t really work the same near earth as in space for a while but they fixed it.  Ok, so now they have a different theory for quantum physics than for astrophysics but at least they have the decency to be uneasy about that and realize that one or both must be wrong.  And when they find something that is logically consistent, they will stop teaching the one (or both) that’s wrong!