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Marginal Propensity to Consume and the Velocity of Money

April 1, 2017 1 comment

My last post pointed out my frustration with the treatment of the marginal propensity to consume and the spending multiplier in a traditional principles text.  I just want to briefly point out how this whole business fits nicely into my alternate paradigm where the aggregate demand curve is thought of as PY=MV (as opposed to Y=C+I+G+NX).

Here is how Mateer and Coppock approach the MPC (emphasis added):

When a person’s income rises, he or she might save some of this new income but might be just as likely to spend part of it too.  The marginal propensity to consume (MPC) is the portion of additional income that is spent on consumption.

The problem here is the dichotomy between consumption and saving.  As I have mentioned before, it matters what we mean exactly by “saving.”  Normally (outside of the Keynesian AS/AD model) we assume that saving means investment and investment is also in the CIG equation (it’s the I).  So if “saving” means that you lend part of your income to a firm who buys investment goods, then doesn’t that part of your income become the income of the producer of those investment goods and isn’t that exactly the same as the portion you spent on consumption goods?  (Yes.)  So then is this all just nonsense or is there some grain of truth in here that we are just saying in an idiotic way?

Well, there is one and only one way of saving that is not exactly the same as consuming in the sense that when you do it, the money you devote to it becomes another person’s income.  That way is holding money.  So what happens if we change the way we explain this slightly so that instead of saying that people consume a fraction of their income c and “save” the rest, we say that people spend a fraction of their income c and hold the rest as money and this spending may be on either consumption or investment goods.

Now you can ask yourself “what is the effect on total spending of a given increase in government expenditure.  Let’s assume that the government borrows $100 from the central bank and spends it on something and let’s assume that the marginal propensity to spend (MPS) is 0.9.  Then the person who gets that initial $100 will spend 90 and the person who gets that will spend 81 and so on.  Take that series out to infinity and you will get the total increase in spending of 100/(1-MPS) or the familiar spending multiplier.

But now notice that another way to see this is to notice that people are holding 10% of their income as money and we have increased the money supply by $100.  This means that total incomes (which must equal total spending) must rise by–you guessed it–1/(1-.9) times the change in the money supply.  Or, to put it another way, incomes have to rise enough that people become willing to hold the new money.

But now you are coming strikingly close to another similar concept.  If people are willing to hold 10% of their income as money, that means each dollar in the economy will have to change hands 10 times on average for people to become willing to hold all the money.  Or in other words, the velocity of money will be one over the average propensity to hold money.  (There is, of course, the possibility that the average and marginal propensities may not be the same but that’s not of particular importance to my point.)  And that is just 1-MPS.  So in other words, if you characterize this thing correctly (it’s about spending and not consuming) then the Keynesian spending multiplier just becomes the velocity of money.

Of course, if you look at it this way, you are forced to notice that the real cause of the increase in aggregate demand in this case is an increase in the money supply not something magical about government spending.  If they just dumped the money into the economy from helicopters, the effect would mostly be the same.  And that’s exactly why this way is better, and probably also why it isn’t what we do.

However, there is one magical thing about government spending which is that the government can choose a higher MPS (usually 1) and so can get more spending bang  per dollar of increase in M in the first round.  So the “helicopter multiple” (if you will) would be slightly less ((1/(1-MPS))-1).  And because of this, it becomes theoretically possible that the government could boost aggregate demand without increasing the money supply by borrowing or taxing.

If they increase taxes by $100, they reduce private consumption and/or investment by $100 times the helicopter multiple but then when they spend it they increase private consumption and/or investment by the same amount but with the government spending added on top (assuming that the propensity to spend is unaltered).  This, of course, is a standard fiscal policy implication (see textbook claim 2 in the previous post).  But if you think about it in the context of the equation of exchange, you can actually see what’s going on here.  Essentially, the government is just increasing the velocity of money by taking it away from people and spending it at a higher rate than they would have.

And there you find the special power of government to boost aggregate demand.  Just like the special power of government to do anything else, it boils down to their ability to force people to do a thing more or less.  In this case it’s the ability to force them to spend more money.  The same thing would happen if you put a horde of killer robots on the streets programmed to shoot missiles at anyone they ran across holding any money.  Or, for that matter if–in some crazy, hypothetical, sci-fi universe–all money were somehow electronic and it was possible for the government to charge you interest for holding it and they simply increased the rate of interest so that you would want to hold less money for any given income level.  This would also increase the velocity of money and boost aggregate demand.  I wonder though, would they call it fiscal or monetary policy? (And would they call the increase in interest rates tightening or loosening?)

 

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Fiscal Policy I: The Spending Multiplier and the (False) Paradox of Thrift

December 30, 2016 Leave a comment

I’m going to write down some of my thoughts on fiscal policy here mostly for the sake of organizing my thinking.  There are a few issues to tackle here so I intend to take it in two or three bites.

As I have said in the past, I have some gripes with the way that AS/AD is taught.  I have more of a monetarist view of aggregate demand so I like to think of it as PY=MV instead of Y=C+I+G+NX.  This becomes especially important when considering fiscal policy.  The textbook treatment makes essentially two claims.

Textbook claim 1: Deficit spending boosts aggregate demand

When government spending increases it increases G and this shifts aggregate demand to the right.  When taxes increase it decreases C which shifts AD to the left.  So the government can increase aggregate demand by taxing less or spending more or some combination of both that results in a larger deficit.  Theoretically, this can be done in a counter-cyclical manner (deficits in recessions and surpluses during expansions) in order to smooth out the business cycle.  It’s pretty obvious that it doesn’t happen this way in practice but that’s a subject for another time.

Textbook claim 2: Even deficit-neutral spending can increase AD because of the spending multiplier.

Basically, because people don’t consume their entire income, if the government takes some of it and spends it, it will go back to them as income and they will spend just as much but we will get the government spending on top of the private consumption spending which means higher aggregate demand.  Or in other words, if we raise taxes and government spending by the same amount, the decrease in C will be smaller than the increase in G.

There were several things that bugged me about these claims when I was a student, and I’ve seen some of my more talented students grapple with the same issues.  The problem is that this Keynesian model contradicts much of the other stuff we tell them in a macro principles class.  The most obvious example of this is the “paradox of thrift.”

Savings=Destruction……or was it Investment?

We spend half the class telling students that saving equals investment.  This is very sensible.  In order for someone to invest, someone has to save.  This is one of those deep truths that economics is built on.  Problem is, as soon as we get to AS/AD we start saying silly things like “assume that people only consume x% of their income and they save the rest.” And from this we come to conclusions like “if the marginal propensity to consume increases, C increases and that increases AD.”  Or textbook claim #2 above.  But these conclusions only follow from the assumption that “saving” in this context is destruction.

A smart-Alec, teacher’s-pet type who has been paying attention and thinking carefully up to this point might ask the question: “Wait, if people want to consume more of their income and save less, isn’t that exactly the type of thing we just got done saying shifts the supply of loanable funds/goods to the left and causes a decrease in investment?  Does it really make sense to just ignore the effect on investment?  And if we don’t just ignore it, won’t it completely annihilate these claims we are making?  And doesn’t the answer to that last question imply an answer to the second-to-last question?  And which parts of this are going to be on the final?”

These are almost all fantastic questions.  So how do you answer them? Maybe smarter people who have been teaching this longer have good answers within the CIG framework.  However, I’m skeptical.  As far as I can see, that framework is not capable of dealing with stuff like this and that is a real problem!  These little contradictions lurking under the surface make it so that the more carefully you think about what you are being taught, the less sense it all makes and that’s super annoying.

So what can be done?  Well, you can re-frame aggregate demand in a monetary way.  Let aggregate demand be PY=MV.  This doesn’t necessarily change any implications of the model but it forces you to talk about the things that affect aggregate demand in a monetary way.  And this is appropriate because aggregate demand is a fundamentally monetary phenomenon.  And this is what the Keynesian perspective is overlooking.

So now what can we say about fiscal policy in this MV framework?  Well any affect on aggregate demand must be either from a change in M or a change in V.  We could get these.  But in order to figure out what is really going on we have to ask a couple questions.

Question 1: Is the spending funded by increased taxes?

If yes: OK, then consumption and/or investment probably went down.  So it depends how much they went down.  This depends on the marginal propensity to spend.  Notice, that I am not talking about saving now.  Most of what people save is investment.  So it’s not their propensity to consume or save that matters.  We can lump all households and firms together and talk about what is actually at issue here, namely the willingness to hold money.

Note that if I “save” half of my income by buying a corporate bond or a stock, that money goes to a firm and they spend most of it on investment.  But there is one–and only one–type of “saving” that is destruction in the sense commonly proposed.  This is holding money. (Of course this is still hyperbole…) It’s the willingness to hold money, both by firms and households that determines velocity and therefore aggregate demand.  So if everyone holds 10% of their income in the form of money and we take some of it, spend it, then it goes back to them and they hold 10% of it still, we can increase aggregate demand by increasing both taxes and spending together in nearly the exact way described by the spending multiplier because this will increase velocity. This can even be shown mathematically rather easily.  You just have to change “saving” to “holding money” and “marginal propensity to consume” into “marginal propensity to spend” and the spending multiplier basically becomes velocity.  I love it when a plan comes together!

Now, the smart-Alec, Keynesian is probably thinking: “so if it works out the same, what difference does it make?”  The difference is that now I have explained it without saying something idiotic that contradicts a bunch of stuff I was saying a week ago.

No, the government spending is funded by deficits: Proceed to question 2.

Question 2: Who are they borrowing from?

If the private sector: Then this must affect the market for loanable funds in the way described above.  Specifically, the demand must increase  which will cause an increase in real interest rates and crowd out some private consumption as well as some private investment.  Does this change aggregate demand?  Maybe.  A first approximation would be to say that the sum of the private consumption and investment crowded out would be exactly equal to the amount of government spending.  This is what you would see if you just look at a partial equilibrium in the loanable funds market and assume the private supply and demand are unchanged.  However, disturbing this market may very well affect the willingness to hold money which will affect velocity and may have some effect on velocity and therefore aggregate demand.  However, this is much more suble than just saying “G increases and C stays the same.”

If the central bank: Ok, let’s say you have the government borrow money but instead of dipping into the private market and pulling loanable funds away from consumers and investors, their spending is actually financed by the creation of additional money by the central bank.  Now we will almost certainly see an increase in aggregate demand as we will see a pure increase in the desire to purchase goods and services without any direct offsetting decrease in some other sector (much like what is commonly assumed).  But in our MV model, this is easy to see.  It’s just an increase in M.  Unless it causes a corresponding decrease in V for some reason it will be an increase in aggregate demand.  But then is it actually fiscal policy or is it monetary policy?

In my opinion this last case is the most important one and is the source of a considerable amount of bickering about the efficacy of “fiscal policy” especially in the presence of a “liquidity trap” or the zero lower bound.  I will leave these issues for later but I think the paradigm in the principles texts makes it very difficult to sort these things out.  Mine is better.

[By the way, note that if the central bank is targeting an interest  rate, then an increase in demand for loanable funds caused by an increase in government spending may very well cause an increase in the money supply in a way that would appear automatic in the sense that no explicit action would be observed on the part of the central bank.  In other words, the same interest rate target might become more expansionary monetary policy in the presence of deficit spending.  In this case was fiscal policy effective?  Was it necessary?  It depends.  Are you a Keynesian or a monetarist?]

 

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A Fiat Money Origin Story

April 3, 2016 13 comments

Nick Rowe has a recent post about Chartalism which got me thinking about the fundamental explanation for the value of money again.  He calls this an “origin story” and seems to be of the opinion that the origin doesn’t really matter, once it gets going you can remove the original source of fundamental value and it just stays up.  Kinda like Wile E. Coyote running off a cliff.  As long as nobody looks down, we’re fine.  I personally think this is nuts.  But I figure, why not try going through the explanation like an “origin story” from primitive commodity money to modern fiat money.  Maybe that will help?  I have mostly tried to avoid all of that because it seems unnecessarily confusing and I usually want to distill the story down to its most fundamental point as much as possible.  However, I think maybe this leaves people too much room to fall back on little misconceptions that are deeply lodged their thinking about this.  So why not start from the beginning and try to hammer out all the points (or most of them) in one try?  For the record, this is not a historical work.  It’s a made-up history that I think is fairly consistent with reality as it unfolded in the western world.  Whether or not the Chinese had some type of script that was linked to taxes thousands of years ago or there were some hunter-gatherers somewhere with a credit-based economy before commodity money became prevalent is not relevant to my point. Read more…

LOL

So I’ve been away for a while and I was looking through a few comments I missed in the last few months and someone linked my post about Austrian economics and libertarianism right in the middle of posts by HuffPo, Slate, and Daily Kos.  I can only assume that the author didn’t actually read my post because I wasn’t conflating the two things at all.  My whole point was that Austrian economics is making libertarians look bad.  Clearly, that wouldn’t make sense if I thought they were the same thing….Right?  At any rate, I consider it an honor to have turned up in a hastily executed google search of “Austrian economics” and “libertarians” along with those fine paragons of this perpetual food fight we call the internet.  So I’m providing a reciprocal link.  I suspect it will get him about as many hits as his link got me.

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You Heard Me!

September 16, 2015 Leave a comment

I’ve been out of blogging for a while with other stuff to do but with commodities tanking and the Fed seemingly poised to raise short-term rates in the near future, and some commentators remarking that “QE risks becoming a semi-permanent feature,” I feel like the world is largely conforming to my view.  However, this is an easy feeling to have erroneously and I kind of wish I had made more official predictions in the past, even though that’s sort of a dangerous business to get into.  No doubt, if I had them, I would wish I hadn’t made them but at least then I would be humble.

So just to get myself on the record, partly for fun, and partly so that if they happen, I can point to them and say “neener, neener, I told you so” to the world, I want to take a page from my blogging hero and do an economic version of “You Heard Me.”  The premise behind this game is to make bold predictions which would make someone who hears them remark something along the lines of “wait, what did you just say?” to which you reply “you heard me!”  The point is not necessarily to nail the prediction exactly but to boldly state a general feeling about something, be it a football player or an economy.  Basically this is one prediction but I will try to add a little bit of flesh to the bones.

  1. If you watch CNBC or any show like that, in almost every discussion about the FED, someone will say “look, we know rates are going up eventually” and everyone agrees with them.  That’s wrong.  Rates are never going up again.  You heard me!

Of course, it’s possible that rates could go up a little.  Short-term rates may indeed be raised this week.  I don’t claim to know what the Fed will do in two days.  But there is a meme of “normalization” going around which is wrong.  Somehow people have gotten the idea that it is “normal” for short term rates to be something like 2-4% and this “low rate environment” must be only temporary.  It’s not.  Maybe they get rates to 1% for a while, maybe not, I don’t know (my guess is not).  But they will be doing QE again before short-term rates ever hit 2%.  By “they” I mean the FED but basically this applies to the whole world.

10 year treasury

There is the 10-year treasury rate since about 1980.  See if you can spot the “normal” level.

2. Inflation will continue to run below the FED’s target and will intermittently cause prices of commodities, stocks, real estate, etc. to nosedive requiring the FED to take action to stave off a full-on deflation.

3. QE will become the new standard policy tool.  You heard me!

The “low rate environment” is not because of temporary exogenous shocks, it is the deterministic result of our monetary system (not policy, system. You heard me!)  This system requires either: people to become continually more leveraged, governments/central banks to buy continually more stuff, or lots of people to go bankrupt.  For the last 35 years or so, we have been exhausting our ability to induce people to become continually more leveraged by continually lowering interest rates.  When we can’t do that, we need either the government (“fiscal policy) or the central bank (“quantitative easing”) to just start buying stuff.  Because we are not going to significantly lift off of the lower bound, and because remaining at the lower bound will not be sufficient to stave off a wave of defaults forever, we will eventually need to reinstate QE.  The next time, they will drop the pretext of a temporary support measure and just start adjusting it up or down every month and that will become the policy tool of choice to smooth out the path of the economy.

4. QE will tend to get bigger over time relative to the rest of the economy.  This is for the same reason described above.

5. QE will spill over into other assets, like stocks.  You heard me!

This is already going on in Japan and China.  Note that 3, 4, and 5 will tend to require bouts of 3 in order to get done because they will be viewed as “extraordinary.”  This means that they will not dare to do these things until it gets bad enough that people are jumping up and down shouting “do something!”

6.  Keynesians will constantly complain that we need more fiscal stimulus to get off the lower bound.  They will be half right.

Okay, that’s not very bold but how many years do we have to hear that line before we start to wonder if it’s not just a matter of smoothing out short-run fluctuations in the real economy?  My prediction: a lot.  You heard me!

7. Market monetarists will insist that our problems are all because central banks are too tight.  They will be about 3/4 right.

It will be true that if central banks were looser, NGDP would grow faster and inflation expectations and nominal rates would pick up.  It’s just a question of what they would have to do to “ease” further.  The MM line seems to be just talking about being looser (and I guess, to be fair, holding interest rates lower for longer) will get us back to normalcy.  The problem with this is that it still relies on the myth of “normalization.”  In order to ease more, in the long run, the FED would eventually have to do more of the things I mention above, not just change their language.  It’s true that if they just did them without waiting for recessions and financial crises to force their hand, those things might be avoided but the MMers haven’t quite come around to accepting the ultimate consequences of this.  (Bonus prediction: we won’t adopt NGDP futures targeting, even though it is a way better idea than what we are doing.)

8.  Scott Sumner will continue to make the occasional snide remark about the Central Bank buying up the whole world in order to argue that monetary policy can always get looser.  He will be 100% right.  At some point it will stop being funny….You heard me.

 

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The Backwards Brain Bicycle

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Land Theory of Value

March 15, 2015 2 comments

Nick Rowe has (tongue-in-cheek) post about the land theory of value.  I know he isn’t pushing that theory but as an exercise, let me try to address his ultimate question:

Plus, the Land Theory of Value is worth considering in its own right, or simply as an exercise in studying value theory. Why is it wrong? What are we looking for in a theory of value? What counts as success?

Bound up in this question is the question “what is value anyway?”  I think what most classical, and modern mainstream economists are looking for in a theory of value is a way to explain (relative) prices.  In other words, when they say “theory of value” they mean “theory of relative prices.”  They take for granted that prices are a measurement of “value” and try to construct a theory that explains how this is true.  This seems to be what Nick is after.

On the other hand, in my opinion–and internet Marxists will probably argue with this– the Marxist version of the labor theory of value is an attempt to define “value” independently of prices and then construct a theory which says that market prices are not representative of “value.”  If this is the case, then you have a way of claiming that mutually voluntary (or, in other words, free) trade can be exploitative (someone wins and someone loses) and this is a foundational assumption underlying most Marxist rhetoric.

So if you take the latter approach and assume that all value comes from labor, then nobody can prove you wrong.  If they say “okay, but what about this diamond, it is highly valuable but it takes very little labor to produce it,” you just respond “no, it isn’t highly valuable, because it didn’t take very much labor to produce it.”  And if that makes you uneasy, then maybe you make up alternate definitions of value like “use value” and “exchange value” so that you can avoid reconciling your definition of value with the actual prices of things.

So I think most economists find the latter approach unappealing.  The standard (subjective) theory of value also defines value independently of prices.  Value means the quantity of other goods (somehow measured) which someone is willing to give up for something.  This value is subjective and there is no attempt to explain where it comes from.  We merely assume that people have some willingness to trade goods for other goods.  A nice feature of this definition of value though is that, once you use it to explain prices, you find that prices are, in fact, a measure of value (specifically marginal value).  So if, when you say “a theory of value,” you really mean “a theory of prices,” then this theory works for you, because it does explain prices.

Now what Nick seems to be describing is a theory of prices.  He (or technically, his Dutch ancestor) is basically arguing that you can explain the prices of things in reference to land.  It is not an independent theory of “value” (meaning independent of prices).  It takes for granted that price is a measure of “value” and seeks to explain these measurements.  But the theory described here does not explain these at all, it only shows that prices can be measured by a standard unit of land.  This should not be surprising if you believe in the standard (subjective value) theory.  In that model, you can measure the value of any good in terms of any other good.

Take this part.

You have to consider the marginal land, that is exactly on the margin between producing wheat and producing barley. If that marginal land could produce two tons of wheat or four tons of barley per acre, then the value of one ton of barley must be half the value of one ton of wheat. That way we can compare the value of land that only grows wheat to land that only grows barley. And the market prices will themselves tell us the relative values of all different sorts of land, so we can convert them all to standard land.

So you can observe the marginal rate of transformation between wheat and barley and that will be equal to the price.  That’s fine.  But that does nothing to determine why the margin is where it is.  If there is a concave PPF, then the marginal rate of transformation between wheat and barley depends on how much of each the society chooses to produce.  How do they determine how much wheat and how much barley to produce?  Well if you believe in subjective value, then they buy whatever they value more until, on the margin, they are indifferent between $1 worth of wheat and $1 worth of barley (or if you prefer, you can measure the market price in any other good).  This subjective value, along with the various production possibilities, determines a price.

If you wanted to, you could take some wheat land and use it to raise cockroaches.  Assuming that no land is being used for this and the market price of cockroaches is negative (you pay to get rid of them).  Do we conclude that the true “value” of cockroaches is determined by the amount of cockroaches you could raise on a “standard” unit of land?  If so, is the price wrong?  The lack of an existing margin also presents other problems but it’s not necessary to go into them.  The point is that chickens are more valuable than cockroaches not because they take more land to produce but because we subjectively are willing to give up other goods for one and not the other.

Now, of course, if things work the way the standard theory says, then the relative price of wheat and barley will be equal to the marginal rate of transformation between the two.  So if you can observe the marginal rate of transformation, you can observe the price.  But this is different from explaining the price.  In order to do that, you have to explain why the margin is where it is.  And in order to do that, you need subjective value.  Of course, Nick pointed this out to his ancestor and his ancestor made a meaningless reply.

Preferences! We cannot observe preferences. Land is real and objective. And the margin of cultivation between wheat and barley is real and objective, and we can observe it. We don’t need no stinking preferences to determine value!

But, again, the only difference between preferences and the margin of cultivation is that the latter is observable and the former isn’t.  So if all you want in your theory is a way of observing value, then this works fine.  But if you want to explain value, then you need subjective preferences.  And besides, if you just want to observe value, you can just look at prices.  So what is the point of a supposedly deeper “theory” based on land which only amounts to a more difficult way of observing the same thing?

The same argument applies to Van Rowe’s argument about crop rotation.

If there are three different crops, and three different ways of rotating them that are not linearly dependent, and all three rotations produce the same rate of profit, as they must, it is trivial matrix algebra to solve for the values of each crop.

There is no sense, independent of market prices, in which all 3 rotations must have the same profit.  They must have the same profit only if prices are such that the farmer is indifferent between them.  In a large market like those that people like me imagine, this will always be the case somewhere for someone and therefore, in theory, if you could find all of the marginal farmers and observe their production matrixes, you could back out the market prices.  But, again, you would not have explained why those margins are where they are.  In order to do that, you need a market to determine prices and that requires a demand curve, and that requires preferences.

All of this is ultimately equivalent to saying: “Supply determines the price, you don’t need demand.  See, we can always just look at the marginal cost of production and figure out the price.”  That’s nonsense, and so is this theory.

 

 

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