Winner of the New Statesman SPERI Prize in Political Economy 2016

Tuesday 2 June 2015

Faith in multipliers

Economists could skip to the penultimate paragraph

The multiplier is the size of any decrease in output that results from a fiscal contraction (lower government spending or higher taxes), both measured in the same units. Why am I confident that multipliers that result from temporary decreases in government spending in current conditions will be somewhere around one rather than somewhere around zero? It is not because of empirical studies that try to directly estimate multiplier sizes.

Do not get me wrong. Such studies are very important, as are meta studies that try and pull together and synthesise the large number of individual studies. However I tend to use them to either confirm or question my priors. My priors come from thinking about models, or perhaps more accurately mechanisms, that have a solid empirical foundation. Let me explain.

Some of the terminology makes more sense if we talk about an increase in government spending (for example, a new school being built), so from now on I’ll consider that. A multiplier around one means that for every school built GDP increases by the cost of that school (a multiplier of exactly one) plus or minus some private sector expenditure (hence around one). If private sector expenditure falls we talk about it being crowded out, but if private sector spending increases we can talk about that expenditure being encouraged or crowded in by the additional public spending. The first point to note is that by thinking in this way I’m focusing on aggregate demand rather than aggregate supply, which I think is appropriate in the situation we have recently been in. If, in contrast, everyone was already working as much as they could, it might be more natural to start from a multiplier of zero, because the school will have been built with labour that otherwise will have built something else. A multiplier of zero is called complete crowding out.

Will we get crowding in or crowding out? Here my starting point is to note that because the increase in government spending is temporary, any impact on pre-tax income or taxes will be relatively small relative to a consumer’s lifetime income. As a result, aggregate consumption is likely to change either way by an amount that is a lot less than the cost of the school. For similar reasons firms think long term when planning investment, so they are not going to invest that much because of a temporary increase in government spending and GDP. There is a lot more we could say here, but I want to keep it simple.

We next need to think about whether this reasoning could be upset by some change in a price that results from the extra school being built. The two key prices here are the real exchange rate and the real interest rate. My basic model of exchange rates is that they are grounded in some medium term view concerning competitiveness, plus beliefs about what might happen to short term interest rates. If the spending is temporary medium term competitiveness is largely unaffected, so what happens to real interest rates is critical. If they rise as a result of the additional employment required to build the new school, then this might lead to a real exchange rate appreciation. This will reduce the demand for domestically produced goods, and higher real interest rates will also discourage private spending directly. So what happens to interest rates is critical.

This is the second point at which actual circumstances are important. Nominal interest rates have been stuck at their Zero Lower Bound, which suggests that they would be quite likely to remain there despite any increase in employment generated by our additional school. If the additional GDP adds a bit to inflation, real interest rates might actually fall, leading to crowding in. (The point is reinforced if we reverse the sign and think about fiscal austerity - central banks will be unable to cut rates to offset austerity’s impact.)

That is where my priors come from: thinking about the structure of the economy, and situation we are in and the nature of the experiment involved. The problem for empirical studies that directly relate changes to output to changes in government spending is that they face huge difficulties in relating the data to particular circumstances and the kind of experiment involved. For example, is any increase in government spending observed in the data expected to be temporary (with relatively minor consequences for tax) or permanent (with implications for tax that could lead to complete crowding out as a result of lower consumption)? Some studies try and take account of this by focusing on shocks to spending, but that is not quite the same thing. (A new school will tend to raise GDP whether it is expected or not.) Even if the change in government spending is expected to be temporary, if any additional borrowing is paid for by cutting future spending rather than increasing taxes this will in theory make some difference.

Up until recently studies have not really controlled for monetary policy, which as we saw was crucial. This recent study from the IMF is an exception, although if you read it you will see just how difficult trying to control for monetary policy actually is. They find that monetary policy does have a large influence, which fortunately agrees with the analysis above. What some earlier studies have shown (I’ve often referenced a study by Jorda and Taylor, but here is another, and a meta analysis is here) is that multipliers tend to be larger when economies are depressed. What has not been clear is whether this is picking up a monetary policy effect (if economies are depressed, monetary policy is unlikely to try and offset the impact of any fiscal expansion), or whether it is picking up something else (for example, multipliers could be larger in a recession because more consumers are credit constrained). This IMF study, which is just based on US data and which does allow for monetary policy, finds no additional depressed economy effect. It will be interesting to see if that result proves robust to alternative treatments of monetary policy and data for other countries.         


  1. In the third last paragraph you say the slight inflation will cause interest rates to go down, but will central banks not want to push them higher in the face of this new inflationary pressure?

    1. Not if interest rates are at the ZLB and inflation is below target

  2. So you are saying that you believe government spending is good in the present Situation even if you have no proof.

    Surely, that ought to lead you to understand those who want proof before raising public debt.

    In other words, you are preaching a belief, an act of faith. But why should one believe you?

    1. "... before raising public debt."

      Not a zero sum game. If GDP goes up, and tax receipts go up, then the debt/GDP ratio is likely to fall.

    2. Clearly it is better to assume that under all possible circumstances any increase in government spending will always fully crowd out the intrinsically more efficient private sector.

    3. @Magnus - I presume that comment was ironic.

    4. gastro george2 June 2015 at 01:42

      How do you know that will happen?

      Your economics seems to be as faith-based as Simon Wren-Lewis's.

    5. @Anon - AFAICS the first assertion was "... before raising public debt." How do *you* know what will happen?

    6. gastro george2 June 2015 at 04:53

      Haven't you read S.W-L? His belief is "not because of empirical studies that try to directly estimate multiplier sizes."

      So that is an a-priori belief. If you share that faith and therefore want to expand government expenditure, it will have to go deeper into debt. Now, a large part of the population is against an expansion of public debt, as the election has shown.

      Those are the people who require proof before agreeing to raising public debt, which is very high as it stands

    7. You are misinterpreting what I said. Read the whole paragraph and the next.

    8. @gastro george, Yes, I'd hoped that was obvious, but indeed there are many who believe this.

      @anon, by using the word 'proof' I guess you get to inure yourself against evidence that conflicts with your ideological worldview. However, if you were at all interested in evidence, you might consult the IMF paper linked by SWL.

    9. @Magnus - apologies.

      @anon - you need to employ rather more logic and deduction in your analysis. You are assuming a few a priori beliefs of your own. Your phrase "... before raising public debt", as Magnus points out, implies that any government expenditure just replaces private sector activity, so the only change is an increase in debt - hence my comment about zero-sum games.

      But Simon is discussing the multiplier. Your implication is that the multiplier is zero (complete crowding out) or close to that. My argument would be that the multiplier is much higher than that. Any multiplier that is above zero takes us out of the zero-sum game. There *will* (by definition) be an increase in GDP, and an increase in taxation receipts. The important figure now is not the *total* debt, but the debt to GDP ratio. The question to ask now is whether the multiplier would be high enough for debt/GDP to drop. Which was all my initial comment was stating.

      Note that there is no faith here - this is just basic economics. Now if you want to make an argument that the multiplier is zero or close to zero, then go ahead.

    10. I think that you need empirical studies to determine the multiplier and where it is located. All "science" needs to be tested against reality.


    11. rob sol2 June 2015 at 13:45

      How right you are! Unfortunately, there are contradictory empirical studies. That is probably why SWL prefers to argue from a priori assumptions.

    12. Krugman thinks that net/net the studies show a multiplier (I guess for the US) of about 1.5. I am not in a position to evaluate the evidence.

    13. Mainly Macro2 June 2015 at 07:38

      rob sol2 June 2015 at 13:45

      Allow me to quote Paul Krugman

      "Wren-Lewis argues for a multiplier of around one, based not on empirical evidence but on a priori reasoning. "

      That is what I call an act of faith.

    14. So you would rather quote Paul miss-characterizing me than what I originally wrote - that tells me a lot! Here is what I actually said:

      "My priors come from thinking about models, or perhaps more accurately mechanisms, that have a solid empirical foundation."

    15. Mainly Macro4 June 2015 at 04:39

      Where is your "solid empirical foundation"? There are a number of empirical studies with contradictory results. If you then choose the ones that suit you, that is an act of faith (isn't that called "confirmation bias"?).

  3. How is this 'increased government spending' to be achieved?
    By issuing more currency - thereby reducing the value of the currency (generating inflation), whereupon the government's creditors require higher interest payments.
    Or by taxing value from the more productive part of the economy to put it into a less productive part?

    1. Oh dear. The point is that there is spare capacity. Also, which parts of the economy are productive and which are unproductive?

    2. There is always 'spare capacity'. Times of unemployment, for example, can and do coincide with times of inflation. One does not preclude the other.
      Parts of the economy that are efficient at providing goods and services can be considered productive, parts that don't are not. We can see that the market economy allocates resources somewhat inefficiently. The State, however, is worse.

    3. But at times when there's lots of slack, expansionary policy isn't going to result in runaway inflation, is it?

      Parts of the economy that are efficient at providing goods and services can be considered productive, parts that don't are not.

      Something is productive if it produces goods or services with value.

      We can see that the market economy allocates resources somewhat inefficiently. The State, however, is worse.

      So now we've switched to from talking about production to talking about allocation. What you say here may be true in many cases, but there are some obvious counterexamples. Healthcare for example.

    4. Command economies have not been a great success.
      Also, 'runaway inflation' does occur at times when 'there is lots of slack'.
      The extreme examples being the incidences of hyperinflation.
      So, no: I do not have much faith in either increasing the public sector (at the expense of the private) or the issue of more currency as 'magic bullets' that will increase the value of goods and services available in the economy.

    5. What do we think the GDP multiplier is for the issuance of non government financial liabilities? Put differently, how many units of private debt/bank credit must be issued to get x% growth. If we know that we can see which form of money issuance gives the biggest bang for buck at this time. Clue, with hours hold debt north of 170% GDP, you might not like the answer.

    6. That's household not hours hold, sorry

    7. Stuart P,

      If there is significant spare capacity, i.e. unemployment, then “issuing more currency” will NOT BE inflationary: inflation arises when the ability of an economy to SUPPLY is exceeded by DEMAND.

      A very elementary point.

    8. Your 'spare capacity' argument may be 'very elementary' but does not tally with what occurs in real life. Also, as I said, there is always spare capacity yet inflation exists. Have we forgotten 'stagflation' already?
      Let's issue a more currency:
      Everyone can add a zero (using a pen) to any UK banknote that comes into their possession.
      £5 becomes £50.
      £10 becomes £100.
      Do we expect price inflation as a result, or is that prevented by 'spare capacity'?

  4. Page 14 of the IMF paper:

    "This conjecture is confirmed ex-post: we find that the Fed funds rate falls following
    a positive federal spending shock under accommodative monetary policy, though inflation
    rises. As a consequence, the real interest rate falls even sharper (see Section III.C)."

    !!! That's not just "accommodative" monetary policy. That's *looser* monetary policy, under any reasonable definition.

    Increases in incantations cause GDP to rise, if those incantations coincide with looser monetary policy.

    BTW, I think my comment on your previous post is stuck in spam.

    1. Eyeballing Figures 5 and 6 of the IMF study, for "accommodative" monetary policy it looks like a 1% positive shock to G "causes" (in the IRF sense) a 50bp decline in the nominal FFR, that lasts 4.5 years, and a 50 bp decline in the real FFR that lasts for at least 5 years. That seems to me to be the right order of magnitude to explain away their Government spending multipliers in figure 3.

      (Interestingly, the IRF for G shows that shocks to G are *permanent* (at least, they last at least 5 years) when monetary policy is "accommodative". Which doesn't fit NK theory.)

      Good post, BTW, but I don't think that IMF study really shows what you want it to show.

    2. I agree the study raises a lot of issues about how you capture the monetary policy response (hence my last para) but I hope you would agree that this is a step in the right direction.

    3. I think it tries (rather hard) to take a step (or two) in the right direction, but I think it fails.

      (I would feel less guilty about dumping on it if I thought I could do better.)

      Another thought: suppose we define "non-accommodative" as "following a Taylor-type rule with a coefficient on the lagged interest rate". Theory tells us that increases in G will cause a (temporary) increase in Y and inflation with a "non-accommodative" monetary policy like that. Because the increase in G causes an immediate jump in the natural rate of interest, but the central bank will only slowly raise the actual rate in response to the rise in Y and inflation. But their IRF shows basically a zero multiplier in that case.

    4. It does seem that the data will always be insufficient to make a firm conclusion on this issue.

      The part I don't understand is that this analysis assumes the starting level of Government spending (as a share of 'potential' GDP) to be 'correct', and then asks what impact do cyclical fluctuations in fiscal policy have on non government investment and consumption.

      But it seems to me we could be starting from three different places.
      1) Government is too small, and the economy is below potential because government spending is too low and household consumption and investment are fine
      2) Government is the right size and the economy is indeed below potential due to one or both of household consumption or investment being to low.
      3) both G and C&I are too low

      Lets say you study three historical slumps and they happen to represent one each of these three scenarios, why wouldn't you expect a different multiplier in each slump? never mind a different multiplier at different points during the slump.

      In any case, If Government spending can be too low or too high given some potential gdp, wouldn't that very fact answer the question? Government spending isn't a function of monetary policy - low rates don't call forth more activity even when Larry Summers thinks low rates do justify more government spending on infrastructure.
      So if the slump in the economy is due to C&I use monetary policy.
      If its due to G being too low, use fiscal policy.
      in which case, who cares what the multiplier is; or more likely you'd care about the multiplier of investment spending in one case, and of government spending in the other.

      I still would like some answer to the question what is the correct share of G as a percent of potential gdp.

  5. The problem with multipliers is are they multiplying the right things?

  6. The problem with multipliers is are they multiplying the right things?

  7. It strike me that in the IMF paper, they are trying to calculate something very complex without many data points. I may be wrong.

  8. This is my usual comment. I think it might be well worth ignoring.

    I get the impression that you consider the range of debate (the Overton window) to be from RBC to New Keynesian (with a bit of open-ness to aggregate modelling). The reason is that you consider only two possible beliefs about multipliers "will be somewhere around one rather than somewhere around zero"

    You don't consider the possibility that the government spending multiplier (for an economy at the ZLB) might be well above 1, as it would be in a paleo Keynesian IS-LM model.

    "any impact on pre-tax income or taxes will be relatively small relative to a consumer’s lifetime income. "

    "My priors come from thinking about models, or perhaps more accurately mechanisms, that have a solid empirical foundation. "

    Also perhaps less accurately. You have a strong prior that consumption mainly depends on lifetime not current income. Importantly, you are discussing macro and multipliers so you have a strong prior that aggregate consumption mainly depends on permanent not current income.

    Yet you discuss strong empirical support. I ask whether there is any empirical support for your view. There is an over long timesome literature on testing the PIH, but there is not a similarly large literature on testing the hypothesis that only current and lagged income matters.

    At the very least, there should be evidence of Ricardian effects -- that if one considers consumption and disposable personal income, then high budget deficits should correspond to surprisingly low consumption. I know of no evidence of this (of course I am considering market economies without legal rationing so not WWII).

    Surprisingly high consumption should be followed by unusually rapid income growth. It is not for the USA.

    What is the empirical basis for your beliefs that there is something to the PIH, and that the economy can be understood by assuming that consumption of the non-liquidity constrained roughly fits the PIH ?

    I think consumption can be fit almost exactly using disposable personal income and the ratio of non-human wealth to disposable personal income. That non-human wealth includes a lot of common stock -- whose price is not correlated with future dividend growth (as noted by Robert Shiller).

    Investment is highly correlated with GDP growth. It may be that firms should think of the medium term when choosing investment. I note that a large part of the cyclical variation of NIPA investment is variation of net inventory investment. I do not see why firms should think of the medium long term when choosing inventory levels. Another very important component of investment is residential investment -- that is the type which responds noticeably to real interest rates.

    I think your priors come from thinking about models.

    1. In my post I wrote that we could say more here, and it was issues like this that I had in mind. Anyone care to counter with emipirical evidence for smoothing?

  9. Shouldn't we pay some attention to whether the increase (say) in government spending displaces future government spending?

    Case 1: Spending 100,000,000 pounds on a yacht to celebrate some royal jubilee. If you decide not to, the jubilee will come and go, and there is no expectation that you will buy the yacht later.

    Case 2: Spending 100,000,000 pounds on fixing bridges that will need to be fixed at some point, because otherwise they'll fall down.

    Obviously this question has a theoretical and an empirical component, so I will direct is also to Robert. Possibly the empirical answer is pretty simple: when deciding what to spend now, no one considers future taxes to pay for the Queen's yacht, or future taxes they won't have to pay because the bridges are already fixed. But actually, is there empirical research along these lines? The theoretical question is more vexing because in principle expected future taxes will diminish current consumption (at least so say the fresh water folks) in one case but not the other, but this never seems to enter the discussion, not just here, but in almost all the discussion of fiscal policy at the ZLB that I have seen.

  10. I am puzzled by the search for A fiscal multiplier. Surely, the fiscal multiplier will depend on how the fiscal impulse is financed (unless this is controlled for in some other way). I can see how, in the absence of full Ricardian equivalence, a fiscal impulse financed by external asset (typically debt) sales would stimulate GDP. But fiscal stimulus financed by internal bond sales or taxes seems to me to be simply putting back in with one hand what is taken out by the other. And money financed fiscal stimulus is different again, more like monetary policy.

  11. All discussions of multipliers should define (a) the baseline scenario in absence of stimulus and (b) the time over which the multiplier is calculated.

    I wrote a piece on fiscal multipliers and the assumptions behind them. It also includes a method to visualize circular flow of income. My multiplier explanation works for an arbitrary number of periods.

    As hyperlinks are not permitted in the comments, click on my name to find my blog post.


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