# MPCs, multipliers, and our 1st year ECON model

I have been preparing my lecture content for macroeconomics later in the year, and have thought it would be a bit of fun to finish with the following: discuss why the initial marginal propensity to consumer and the final multiplier on any “initial expenditure impulse” need not be related to each other.

This is an issue that I’d cover after discussing Ricardian Equivalence, and think it matters given the increasing relevance of zero-lower bound economics for students in the current environment – and some of the discussion on NBER about multipliers, and HANK vs RANK (heterogeneous vs representative agent models) models of monetary policy.

Note: These non-standard models are cool, and much more “Keynesian” – but I think the more basic description below is important for keeping us humble about our ability to control things.

Now none of this will go into any detail on the more complex models (and ideas of expectations) – it will just ensure that we aren’t “losing money as an asset from our mental model” and should be read as such.

The circular flow (the description ECON141 is all about) describes the flow of funds around the economy, and the key thing is showing that if there is more dollars going around that flow in a period of time there is by definition more nominal activity – be it through higher prices or higher output. This insight can easily get lost in the discussion of individual channels during the course.

Happy with thoughts below – this is likely to be a non-assessed topic for eager students.

## The setup

The very idea that the initial MPC relates to the final increase in aggregate expenditure and thereby aggregate demand is incredibly natural – at least in how we’ve outlined it in class.  If higher income leads to households and firms buying more, then that is income for other households and firms, which leads to more expenditure etc etc!  The bigger the impulse the bigger the multiplier is a logical conclusion of the multiplier process.

As a result, a lot of discussion about stimulus is fixated on the ability to boost a specific component of GDP.  Often we hear PY = C + I + G + X – iM and get told that stimulus requires increasing those components to start a multiplier process.  And there is some truth to that.

However, like always it is not the full truth – and it is why Scott Sumner says monetary policy is not aimed at consumption.  And it is why the other identity PY = MV also matters.

Let me explain with a thought experiment.

## The thought experiment

Before doing our own thought experiment I wanted to start with the initial story that got me into economics, from a book my brother got me when I was 14.  Lets just use the picture:

Given that, what is our thought experiment:

Say that a helicopter flew out from underneath the central banks building, and deposited \$10,000 into every individual’s hands (a very accurate helicopter drop).  And that was only spent on imported goods.  It doesn’t go to the shoemaker, so he doesn’t get the income to spend on the fishmonger, who cannot spend at the butchers etc

This sounds like a failure, a complete leakage from the circular flow. In other words, since the increase in C is met by a lift in iM there is not increase in expenditure on domestic products, and so no increase in domestic incomes, and no multiplier process!

But we haven’t actually finished.  Say the government raised the funds from domestic bondholders who simply flipped these straight to the central bank for the current targeted yield (or even pretend the central bank purchased them directly from the government).

The increase in import demand based on the extra domestic dollars would increase demand for foreign currency and would drive down the exchange rate, which in turn would increase the incomes of exporters and increase the relative price of imports, which would then lead to increased demand for domestic goods and services.

So if more dollars are generated they either have to be spent on final production in the jurisdiction where those dollar are accepted as legal tender, or be held as an asset by someone (in this case the foreign seller or more likely their bank).

Note: This holds for any mechanism that will generate an increase in money, which as we discussed is a specific liquid type of asset. So the key question is how decisions by fiscal and monetary authorities can influence the amount of money and the role of the private sector (eg private credit creation through banks). A lot of the debates you’ll read come from different views about how this process works – we will leave it to the side here as an important question.

The lack of a central bank counter-reaction to the helicopter drop (total accommodation and so a corresponding increase in the money supply, so an unsterilised drop) implies that we can look at a one-off payment as a true “helicopter money drop”. Another way of saying it is that there are now more domestic dollars, and those dollars can only be held or used to buy domestic goods and services.  Whether they are initially used to buy them is irrelevant!

As a result remember, demand stabilisation isn’t all about picking specific channels and neatly guiding the economy – but ensuring there is sufficient growth in PY to prevent cyclical unemployment.

The Keynes Cross

In class we have defined everything with reference to the Income-Expenditure model, or Keynes Cross diagram. Here the expenditure on domestic products is given with reference to real output Y. Our MPC was considered to be the increase in spending that occurs from a lift in real income, keeping all prices fixed (exchange rates, interest rates, prices themselves).

In the above graph the MPC was less than one. The initial shock reduced expenditure, which then works through that multiplier process above. Now imagine we identify a household that has an MPC of 1 – if we drop the cash on their head will it lead to infinite economic activity … no because:

1. the transmission through other households involves an MPC of below 1
2. Other prices change (interest rates, exchange rates, goods prices, and factor prices)

So when we look at that nice neat graph we know it will be misleading us for two reasons.  i) it should be non-linear given the variabilities in MPCs as a shock transitions through the economy ii) it should be constantly shifting as the other “constant” prices are all changing.

Even though the interest rate is pegged at zero when we are at the zero lower bound there are other channels/prices, and focusing solely on the initial MPC alone misses this.

## But if we measure a higher MPC that is probably a higher velocity transaction right – so why split hairs!

I have some sympathy with this as well, and the recent focus on estimating the distribution of these figures suggests it is an issue of interest (here, here, here).  Furthermore, allowing for differences in the types of households in the economy appears to make these responses more salient.

But whenever I start to feel comfortable with that I remember that my PhD supervisor and practicing macroeconomists have told me that things aren’t so simple, and so it is important we are a bit more careful.

A topic we went through in ECON141 which may have seemed “random” is money supply and demand.

It is a topic that gets critiqued heavily due to the fact that – since monetary policy involves an interest rate peg rather than a quantity of money peg – any shift in credit demand (eg demand for funds for investment) is immediately accommodated.  So we abstract away and simply describe a Taylor Rule without the mechanics for the most part (the Monetary Policy Rule in our IS-MPR model).

However, the MD/MS model (and the LM curve it develops) is still consistent enough with that idea to get insights.  The one I want to use here is to think about money demand motives for a given stock of money.

When we measure an MPC it is for a period of time.  Say a quarter.  We have two identified consumers – one with an MPC of 1 in this quarter, and another with an MPC of 0.5.  They are spending on the same thing (so the transmission going forward is the same) and any marginal savings is expected to completely stall as financial institutions have a shortage of safe assets (so no marginal lending).

Here I can at least rely on the higher MPC right?  Well …….

What happens if that 1 MPC occurs because they spend the whole amount of money at once at the end of the quarter.  But the person with the 0.5 MPC spends it immediately.  If the transmission channel is sufficiently quick at turning over funds (eg spending the entire amount each week) then the lower measured MPC would correspond with a greater stimulus to AE.

If we instead thought in terms of money demand we would see this.  The household with an MPC of 1 has an elevated period of money demand, so the helicopter drop will be hoarded for a period of time.  In the end what matters is how quickly these funds are used – not just the proportion of the funds that will be spent in our defined period of time.  This is our velocity.

This example indicates two things:

1. A higher MPC does not imply a higher initial shock if there is a delay in consumption by the higher MPC household.
2. What matters isn’t the MPC in isolation, but the velocity of the entire funds – how quickly does the helicopter dropped dollar translate into another transaction (and onwards from that), be it spending by a butcher you purchased meat from or spending by a firm that borrows funds from a bank.

Now, no-one knows how these transmission channels work in perfect detail – all we know is that if we drop a dollar on someone it is implicitly hoarded in that instance, and its reintroduction to the circular flow depends on the factors that drive money demand for that individual.  The same thing happens once the funds find their way in another person’s hands – it is marginal VELOCITY of the dollar that determines what happens to expenditure.

Friedman was wrong to state this was a technological constant, but he was right to place emphasis on it.

### Sidenote:  This is about expenditure, not prices or output alone

All this discussion is about how a central bank could boost expenditure and how – rather than thinking in terms of C + I + G +X – iM, if we think in terms of M*V the central bank is only impotent if increase in the money stock are met with a corresponding drop in velocity.

Eg the bank performs open market operations (OMO) by buying bonds, knowing that the reduction in the yield will reduce interest rates and provide liquidity and wealth effects that increases consumption.  However, at the ZLB bond holders are indifferent between holding bonds and cash, so there is no interest rate or liquidity effects – and empirically the wealth effect is small.  So wooops, the OMO will increase the money stock by the money will be “hoarded” as an equivalent asset to bonds!

The increase in expenditure here is the goal – but we have no idea whether this will occur through prices or real output without more modelling.  However, if there is insufficient demand then by definition prices and real output are below target – so the question of how expenditure can rise is the key one.