It All Depends on the MPC

UPDATE (01/25/12):  This post is erroneous and none of its conclusions should be relied upon.

OK, so it has come down to this.  I just asserted that the way to translate Lucas and Cochrane into the Keynesian model is to set the mpc equal to zero.  In that case, any increase in government spending that is offset by taxes causes no net increase in income, because as, Lucas puts it, the increase in government spending is exactly offset by a decrease in consumption of an equal amount thanks to the reduction in after-tax income.  This exercise is predicated on the assumption that the equal increase in government spending and taxes is permanent.  But in the exercise proposed by Wren-Lewis, the increase in government spending is temporary and the increase in taxes is also temporary.  How does the transitory nature of the increase in government spending and taxes alter the analysis under a Lucasian version of the Keynesian model?

Wren-Lewis claimed that you get a stimulative effect.  The increase in government spending is concentrated in the present, but the reduction in spending is spread out over the future, leaving a net positive effect in the current period.

Thanks to Scott Sumner’s comment on my previous post (which I too confidently pronounced definitive), I now see where Wren-Lewis and the rest of us went wrong.  The stimulative effect of the government spending is depends on the existence of a simple multiplier greater than 1 (i.e., an mpc greater than 0) [This is in error, a stimulative effect is present for any value of the MPC less than 1 for which a unique equilibrium exists in the simple Keynesian model.].  So to say that government spending must be stimulative, even if offset by taxation, begs the question whether government spending generates any increase in income beyond the amount of initial spending.  If you assume fully rational maximizing on the part of households (Ricardian equivalence), their mpc is equal to 0 (though that may perhaps be subject to some quibble, in which case there would still be room for argument on the effect of tax-financed government spending).  [The balanced budget multiplier is 1 in the simple Keynesian model even if the MPC equals 0.]

But if you are willing to grant for the sake of argument that the mpc is equal to 0, then it does seem that even a temporary increase in government spending would imply no net increase in income because of the absence of multiplier effects.  The increase in government spending would be offset by an equal decrease in consumption spending caused either by 1) increased taxes today or 2) by increased saving today in the expectation of future tax payments.  (I am now a bit troubled that this doesn’t seem to accord with Nick Rowe’s analysis, but I will  have to live with that until he weighs in again on the subject.)  [I should have realized that I was confused at this point and started over.]

Note that I didn’t need to say anything about accounting identities to get to this result.  (Gotta find that silver lining somewhere.)  But Scott can still feel good about having convinced me that his basic intuition was right.  The should teach us all to remember the old maxim, “Don’t Mess with Scott.”

PS At this stage, I am fully prepared to be proven wrong yet again, so I will be reading your comments very carefully to find the next surprise lying in store for me.


32 Responses to “It All Depends on the MPC”

  1. 1 Kevin Donoghue January 24, 2012 at 1:17 pm

    No, if you want to see what Wren-Lewis is driving at your best approach is to make no assumption about MPC or multipliers. Instead, work out what the change in G-T does to C and Y. It turns out that dY/d[G-T] is 1.0 provided the current period is a small fraction of the household’s life.

    But rather than speak for him, better to just link:


  2. 2 D R January 24, 2012 at 1:31 pm

    “In that case, any increase in government spending that is offset by taxes causes no net increase in income, because as, Lucas puts it, the increase in government spending is exactly offset by a decrease in consumption of an equal amount thanks to the reduction in after-tax income.”

    I don’t understand. Isn’t the government spending income as well? If G and T each rise by 100, then disposable income does not change, and hence there is no obvious reason for consumption to fall.


  3. 3 David Glasner January 24, 2012 at 1:35 pm

    I went there and will read his argument on the way home. My initial take is that you need to assume that the bridge has a net marginal social product and will increase Y in the next period. If so, households will increase consumption in the present period and income will rise. Nick Rowe actually made that point, so there are ways to avoid the result, but I do think that assuming MPC = 0 makes it hard, though not impossible. Nor am quite sure exactly what micro assumptions are required to derive a zero MPC.


  4. 4 Kevin Donoghue January 24, 2012 at 4:11 pm

    David, I just noticed that you have Simon Wren-Lewis’s name wrong.


  5. 5 David Glasner January 24, 2012 at 4:27 pm

    Kevin, Thanks for catching that one for me. I just changed it.


  6. 6 Scott Sumner January 24, 2012 at 7:41 pm

    David, I wouldn’t blame you if you just shot me, but I think Kevin has a point. If you make the period of increase in G very short, it’s more and more likely that the multiplier will approach one. That’s because in a very short period the other two variables (C&I) are not likely to change too much (assuming the economy has slack.)

    The downside of this argument is that if you make the period of extra G very short, then there’s not much spillover benefit and you go right back into recession when it’s over. So you probably need several years of extra G, which then might reduce C+I significantly.

    It might seem odd for me to be supporting Kevin and DR at this late date, but my point was never that C would fall as much as G increased, I agreed with W-L that it probably won’t because of smoothing, but rather that there’d also be some decline in S&I. Again, the only way S&I don’t fall is if (G-T) and C don’t fall, but in that case there’s no consumption smoothing.


  7. 7 Scott Sumner January 24, 2012 at 7:43 pm

    There’s a mistake in my previous comment, the last sentence should read “if (Y-T) and C don’t fall.”


  8. 8 D R January 24, 2012 at 7:58 pm


    I don’t want to pile on, but I still don’t understand how you come to that last sentence. Private agents may smooth consumption by lending to one another, creating no change in Y-T or S or I. All that is required is for the disposable income of some agents to rise by the amount the disposable income of the other agents falls.

    If I take 100 from A and give to B, then doesn’t consumption smoothing imply B wants to increase consumption by 20 while A wants to decrease consumption by 20? No investment is required to make this happen.


  9. 9 Mitch January 24, 2012 at 9:21 pm

    I have to say that I find all of this stuff comic. I am a physicist. Watching a bunch of economists arguing whether government spending has a stimulative effect on the economy during a recession strikes me as just absurd. Isn’t this the most trivial of possible questions? If it isn’t straightforward to answer this question using your frameworks, what can the economics profession possibly answer that anyone would be expected to believe?

    It’s as though a bunch of physicists were unable to compute the period of a pendulum.

    I still fail to understand why the obvious argument isn’t right. I’ve said it before, but here it is again:

    1) During a recession, none of the labor, lending, nor bridge markets is clearing. There is unemployment, money unlent, and industrial capacity that is not utilized. WE ARE NOT ALLOWED to reason as though there were economic equilibrium.

    2) Because there is money in bank vaults (and other places) unlent, the government can go borrow money without crowding out other borrowing or driving up interest rates.

    3) Because there is unemployment, the government (or its contractors) can hire people without driving up wages.

    4) Because there is idle capacity in the industrial sector, bridges can be bought without driving up the prices of anything.

    5) Since the bridge is built (and has utility) and companies and workers have income they otherwise wouldn’t have had, Y goes up. Ta-da.

    6) Anyone who thinks that people will substantially cut back spending in the short run because they know that in the future some tax increase might be needed is living in another country – probably another planet. I defy anyone to come up with any real study of actual people that shows that sort of behavior.

    6b) For one thing, there’s no reason for any individual person to know in advance how much of the tax will fall on him. For another, it’s not even obvious that the tax rate will actually increase. After all, the borrowing is being done at low interest rates – if they’re lower than the growth in real GDP, the debt doesn’t even have to get paid back, it disappears over time into insignificance.

    Now, what I am saying doesn’t depend on accounting identities or multipliers or anything. There is nothing in it that’s conceptually confusing. It actually isn’t really even a macroeconomic argument – it is essentially microeconomic. So please, if there’s some way to see that somehow this obvious analysis is wrong, please give me the number of the step that I have mistaken.

    David, believe you have agreed with this analysis before, so I await hearing how it could be that the conclusion can now be shown to be wrong.


  10. 10 Benjamin Cole January 24, 2012 at 9:31 pm

    Oh, yes, this is how we convince the body politic to come over to Market Monetarism.

    I am just glad you guys are not heading up our war effort—or, I am wrong? Are Market Monetarists in charge of our Afghanistan expedition?

    Now everything becomes clear…as mud.


  11. 11 Daniel Kuehn January 25, 2012 at 5:15 am

    You don’t even need Ricardian equivalence and mpc=0 to get that. mpc=0 gets you a multiplier of 1 if there’s no crowding out of investment at all. If there is crowding out of investment, an mpc of zero is going to get you a negative multiplier.

    Similarly, an mpc > 0 could give you a multiplier of 1 if there is sufficient crowding out.

    This is all academic, of course. Right now there doesn’t seem to be much reason to worry about crowding out. I doubt there’s much reason to expect a low mpc either.


  12. 12 Ron Ronson January 25, 2012 at 6:35 am

    I was very late to this discussion and just want to make sure I have got it.

    The issue is what effect the reduction in savings caused by consumption smoothing will have on investment and on AD, right ?

    If that is the right question then the surely the answer depends upon how Investment will respond to the lower pool of (new and old) savings. In a healthy economy then the reductions in savings will cause a reduction in I but not to the full amount of the fall in S because the higher ensuing interest rates would cause more savings to be forthcoming (I think Scott make this point early on)

    However in an unhealthy economy where the loans market is not clearing even at low interest rates then a reduction in S would lead to a small (or no) reduction in I and overall AD to rise. I assume this is is the scenario that Wren-Lewis envisioned.


  13. 13 Kevin Donoghue January 25, 2012 at 6:40 am

    From the one comment Simon Wren-Lewis left on Scott Sumner’s blog: “consumption smoothing is about consumption plans, not outturns.”

    Exactly. He has a new post up, a summary of the many points which have come up in the discussion:


  14. 14 Rob January 25, 2012 at 7:03 am

    “my point was never that C would fall as much as G increased, I agreed with W-L that it probably won’t because of smoothing, but rather that there’d also be some decline in S&I”

    Where did Wren-Lewis ever claim that I remaining fixed was a key part of his consumption smoothing argument (as opposed to merely being a common Keynesian assumption) ?


  15. 15 D R January 25, 2012 at 8:34 am


    Wren-Lewis did not discuss investment at all. It is simply not a part of his model as he tried to clarify in subsequent writing. Just as he did not discuss international trade, and so it was understood that the economy was closed.


  16. 16 Kevin Donoghue January 25, 2012 at 9:07 am

    The usual way to think about investment is, it’s just the addition to the stock of capital: K(t+1) = K(t) + I(t). So, if you want to argue that a temporary increase in G (paid for by a temporary increase in T) is going to affect I, you need some story about why firms will respond by wanting a smaller stock of capital in the future as a result of the bridge-building.

    It’s not hard to think up such a story. Maybe nobody believes the bridge-building will be temporary, because every other community on the river will want its own bridge. Alternatively, the bridge may put the local ferries out of business, so they won’t be replaced. Crowding-out can take many forms.

    But Lucas and Cochrane didn’t choose that line of attack. Their story, such as it was, related to consumption. Krugman, DeLong and Wren-Lucas simply pointed out that the story was incoherent. It’s a bit much to say they should have discussed the factors affecting investment when Lucas and Cochrane never made it part of their case.


  17. 17 Kevin Donoghue January 25, 2012 at 9:11 am

    Ye gods, dyslexia must be infectious. s/b Wren-Lewis, obviously.


  18. 18 Rob January 25, 2012 at 9:16 am

    D R,

    In this link he explicitly addresses savings and investment

    I don’t think there is anything in that post that suggests that Investment would not also decline to some degree if savings decline – which Scott appears to say was his main point of disagreement.


  19. 19 D R January 25, 2012 at 9:43 am


    That was a general discussion of savings and investment.

    Try here:


  20. 20 D R January 25, 2012 at 9:48 am

    Whoops. Responding the the wrong point.

    Yes, I think it is totally clear that Wren-Lewis understands that point– if there is a decline in ex-post-savings then there must also be a decline in ex-post investment.

    As far as I can tell, the actual disagreement is at what point(s) in the story savings (and therefore investment) have or have not declined.


  21. 21 Rob January 25, 2012 at 11:39 am


    Scott says above “my point was never that C would fall as much as G increased, I agreed with W-L that it probably won’t because of smoothing, but rather that there’d also be some decline in S&I”

    Hard to interpret this any other way than that Scott thinks W-L had the view that I would not decline.and Scott disagreed with that view.


  22. 22 D R January 25, 2012 at 12:07 pm


    What difference does it make what Sumner reads into it? Wren-Lewis said nothing about savings or investment, just as he said nothing about imports or exports.

    Yes, I agree that Wren-Lewis argues that investment does not fall, because it seems not to be a part of the model at all. Yes, I agree this implies that savings does not fall. So what? That doesn’t invalidate Wren-Lewis’ argument.


  23. 23 Rob January 25, 2012 at 12:31 pm

    It probably doesn’t make any difference at this stage. I’m just trying to clarify what the original dis-agreement was and how (if at all) it got resolved.


  24. 24 D R January 25, 2012 at 12:44 pm

    Well, here’s one way to resolve it:

    Suppose that private agents are not identical. They get taxed equally, but the money goes to 1 percent of the population which was not busy working– for which those idle workers must now produce something of value. Then G and T rise by 100, but what about C? Well the 99 percent all try to smooth the effect of the tax– that is, they collectively want to reduce their consumption by a mere 19.80 (rather than the 99 they were taxed collectively.) Likewise, the 1 percent all try to smooth the effect of the tax and the additional income– that is, they collectively want to increase their consumption by… 19.80 (rather than the 99 their collective disposable income rose.) Therefore, the 1 percent lend 79.20 to the 99 percent, preventing the consumption of the 99 percent from falling by more than 19.80.

    Even if we erroneously ignore the increase in consumption on the part of the 1 percent (a collective 19.80) then “consumption” falls by 19.80 and the resulting BBM is 0.802. If we correctly count their increased consumption, then there is no change in consumption overall, and the BBM is 1.0.

    Does that clear things up?


  25. 25 Rob January 25, 2012 at 2:06 pm

    Yes, that’s a smart scenario that proves Wren-Lewis’s point. My problem has never been seeing this, but rather seeing why Scott objected to it.


  26. 26 D R January 25, 2012 at 3:38 pm


    Thanks. I don’t think you are alone. I think– but am by no means certain– that Sumner doesn’t necessarily think that Wren-Lewis is *wrong* but rather that Wren-Lewis wrote something incorrect when he told his story. That is, Sumner simply is giving Wren-Lewis a poor mark on his exam.


  27. 27 Rob January 25, 2012 at 6:39 pm

    D R,

    Yes, possibly that explains it. It just seemed such an obvious argument to me that when there are excess cash balances in the system that reduced savings as a result of consumption smoothing will not affect investment borrowing. This seemed consistent within a market monetarists model and so I was surprised by Scott’s stance


  28. 28 David Glasner January 30, 2012 at 9:53 am

    I’ve been very late in responding to comments on this post, which turned out to be very seriously mistaken. So I will just make some quick responses now in light of all that has transpired in the interim.

    Scott, You obviously were trying gently to point out to me that I had gotten myself all confused. I generally agree that as the current period becomes short relative to the future, the income-smoothing argument implies an increasing multiplier in the current period, with limits of 0 and 1 for the multiplier. You are positing that an increase in G reduces C + I, but you have to be clear about what mechanism is causing C+I to fall. My argument with you about all this started because you just asserted that the fall in C+I was somehow required by an accounting identity. It’s not you have to spell out an economic model to explain why an increase in G will cause C+I to fall. Your statement about S and I having to fall also seems to me to be based on reasoning from an accounting identity rather than making an economic argument.

    Mitch, Why is this more straightforward than the question whether light is a particle or a wave? What most people believe about economics is what they want to believe. Very few people in my experience allow themselves to be forced by the power of reasoning to accept as valid a proposition that they find distasteful on other grounds. Comparisons between physics and economics, comparisons often foolishly encouraged by economists, are obviously off-base. Does the motion of particles (large or small) depend on the particles expectation of where it is going to wind up? Would a mechanical theory be possible if the expectations of the moving bodies had to incorporated into the model?

    You assume that market clearing is a simple unambiguous concept. It is not. You cannot interpret market clearing unless you have specified the price expectations of the transactors. The meaning of unemployment also becomes ambiguous when you define a labor supply function that includes the wage expectations of workers as an argument of the function. I don’t say that your substantive arguments are wrong, I am just pointing out to you that the relevant theory is a lot more complicated than you are assuming. That doesn’t mean you should take what economists seriously it just means that your expectations of what is theoretically possible in economics are unrealistic because you are assuming that economics is really like physics. It’s not.

    Benjamin, There is no point pretending something is clear before we really understand it.

    Daniel, I agree that there are many ways to get a multiplier of 1. What I was trying to do was to take what I understood to be the Lucas/Cochrane objection to the standard Keynesian multiplier analysis and incorporate that into the model. It’s not that hard to do, but I got confused. What you need is just that consumers decide how much to consume in the current period based on their expectation of their permanent income, in which case mpc=0 if the current period is not too long relative to their future time horizon. In this framework, an increase in government spending causes a recalculation of the consumption function to reflect expected present or future tax liabilities but the mpc remains at zero. That should be a model that Lucas and Cochrane would be willing to discuss and not just dismiss out of hand as Keynesian hydraulics.

    Ron, Your take seems basically right to me.

    Rob, D R, Kevin, I think Kevin summed it up correctly.


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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

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