What If People Lived Forever . . .

In a New Keynesian DSGE (or a RBC)

Infinite-Lived vs. Finite-Lived Agents


Jim Hamilton’s discussion of the Mankiw Dorian Gray pill reminded me that we already have the pill, distributed for free to all the residents of a typical DSGE implementation of New Keynesian models. Hence, in these models with agents living forever, economies exhibit tendencies toward Ricardian equivalence. That’s why in most of these models, the fiscal multiplier is relatively small. Even with the inclusion of hand-to-mouth consumers, in the long run fiscal policy would have little effect.


Simon Wren-Lewis discusses how, in the short-run, fiscal policy at the zero lower bound works in a New Keynesian model:

The New Keynesian Phillips curve basically says inflation today depends on expected inflation tomorrow and the output gap today. Additional output tomorrow will raise inflation tomorrow. However it also raises inflation today because it raises expected inflation. Higher output today only raises inflation today. So for given nominal interest rates, higher output tomorrow gives me two periods of lower real interest rates, while higher output today just gives me one. A one-off addition to government spending tomorrow, because it raises output tomorrow, gives me a greater impact on real interest rates and therefore consumption than the same one-off increase in government spending today.

Obviously, at the zero lower bound, increases in inflation reduce real interest rates thus increasing consumption. But this effect clearly disappears in the long run, or if fiscal policy is sufficiently large to push one above the ZLB (see Erceg et al., 2010)


Here’s the question of the day: What happens if one allows for finite lived agents, a la overlapping generations (OLG)? Then the results are altered. Fiscal policy, including transfers and taxes, can affect output, either by shifting income to groups with different discount rates, or directly affecting spending.


From Charles Freedman, Michael Kumhof, Douglas Laxton, Dirk Muir, and Susanna Mursula, “Fiscal Stimulus to the Rescue? Short-Run Benefits and Potential Long-Run Costs of Fiscal Deficits,” IMF Working Paper 09/255:

Fiscal stimulus has effects on both the demand and the supply side of the economy. The demand effects come from the fiscal action feeding directly into aggregate demand (in the case of government investment expenditures), or from increasing real disposable incomes that partly result in higher spending (in the case of increases in general or targeted transfers and decreases in tax rates on labor income). The magnitude of the effect on aggregate demand of higher real disposable incomes in the case of an increase in general transfers will depend on the proportion of households that are liquidity-constrained, since such households will spend a much higher share of the increase in their disposable income than will OLG households. All of these demand effects will have the usual secondary multiplier effects, as the recipients of higher spending (in the form of increased labor incomes and dividends) in turn increase their spending.

This observation is important, as some observers lump all New Keynesian models together. For instance, Econbrowser reader Jeff (2/14, 3:28PM) has argued:

… pick your favorite NK/DSGE model. In that model you will most likely see that AD is determined by real interest rates, inflation, and some exogenous discount factor(s). Assuming the third is fixed and out of the control of the Fed, we’re left with interest rates and inflation. You want to argue that because interest rates are at the ZLB, the Fed is stuck and can not control AD, i.e. the ZLB has some bite. But that is only true if the Fed can’t control inflation. And when I see the Fed carefully maintaining inflation around 2% for the last 4 years I find that claim very dubious. This is rather simple analysis from just a basic understanding of the models. …

(As an aside, one could coin a phrase for such people who deny the existence and/or any relevance of the liquidity trap – I’ll call them “trap-ers”. As demonstrated in the comments to this post, some even disbelieve that interest rates were near zero during the Great Depression – I kid you not!)


Well, I don’t know if the IMF’s GIMF is my favorite NK/DSGE, but I have cited it on numerous occasions, [1] [2] [3] (in which reader Jeff misreads the graphs and fails to see investment crowding in) and so I don’t believe this reader’s characterization is correct. There are other variables that can freely move. From my own perspective, the complete empirical failure of full Ricardian equivalence to hold [4] suggests to me we give credence to these types of models.


Multipliers in a New Keynesian Model with Finite Lived Agents at ZLB


Here are the multipliers derived from this model. Even when not at the ZLB, the multipliers are larger than the typical NK DSGE.


Excerpt from Figure 5 from Freedman et al. (2009).

Crowding In of Investment, Again


Notice that even with perfectly accommodative monetary policy for two years, there is little crowding in of investment. This changes substantially if one introduces a financial accelerator. Then the multipliers are larger, and there is much more investment crowding in.


Excerpt from Figure 5 from Freedman et al. (2009).


It is true that inflation rates rise so that the real interest rate declines. But there are also direct increments to GDP from government investment. When government transfers are the instrument, the multipliers are smaller than those for government investment. Nonetheless, they work in part through redistribution from agents with lower to higher rates of discount, a channel not in the standard NK DSGE.


My conclusion: Don’t take a specific model too seriously, when making inferences about reality.

17 thoughts on “What If People Lived Forever . . .

  1. jonathan

    Ideas like Ricardian Equivalence are misused very frequently. You actually see people, including economists, talk as if this were a real world law. Barro gave an interview to the Minny Fed’s magazine in which he referred to RE as a first order proposition. It is … in a model not in real life.

  2. Ricardo

    From the Simon Wren-Lewis article:
    Higher output today only raises inflation today. So for given nominal interest rates, higher output tomorrow gives me two periods of lower real interest rates, while higher output today just gives me one.
    Implicit in this article is the unfounded Keynesian assumption that increased government spending and monetary expansion will increase output, yet this is never proven to be true, even though it is a basic assumption of the analysis. A thought experiment – take out this assumption and reread the piece. It totally falls apart – is actually nonsense to read.
    What we know is that since at least 2007 the FED has been attempting to create inflation to no avail. Bernanke is not holding inflation down intentionally. Bernanke is frustrated that he cannot generate inflation no matter how much money he pumps into the system.
    Additionally, a massive increase in government spending, from the Bush/Paulson TARP to the Obama/Romer stimulus plan, has done nothing (perhaps worse) to create increased output.
    There is ample evidence that the basic assumption, on which this analysis is founded, is not true. We must ignore what our current credit crisis has taught us, that QE and government stimulus do not increase output, otherwise, this entire analysis is meaningless.

  3. Bruce Carman

    Returns to labor’s share of GDP is at a record low in the post-WW II period and likely back to the levels of the 1930s and 1890s in equivalent after-tax purchasing power terms to GDP for the bottom 90% of workers.
    Non-financial US corporate debt as a share of GDP is at a record high going back to 1929 and Japan in 1990-85.
    Total state, local, and federal gov’t debt to GDP is at a record high.
    Bank assets and imputed compounding interest claims to after-tax wages and profits and gov’t receipts are at a record high going back to 1929.
    Total gov’t spending, including Social Security and Medicare transfers, is at 100% equivalent of private wages.
    Growth of public and private debt and gov’t taxing, borrowing, and spending is not flowing in the form of increasing employment, wages, salaries, and benefits to the bottom 90% of households and thus increasing returns to labor’s share of GDP for the vast majority of Americans.
    Imperialist rentier-financier “capitalism” has “worked” ASTONISHINGLY well for the top 0.1-1% to 10% of households, including benefiting BIG gov’t, but it has “worked” at the increasing cost to the bottom 90% of American households.
    The bottom 90% of American households don’t need more gov’t spending, credit (debt-money), or debt/income, they need HIGHER AFTER-TAX PURCHASING POWER AND/OR A LOWER COST OF LIVING from INCREASING GAINS FLOWING TO LABOR (or per capita) from technological advances and higher productivity.
    Increasing gov’t spending, public and private debt, and productivity from offshoring labor only to see wealth and income increase to the top 1-10% and labor product and purchasing power fall for the bottom 90% is failed policy and a failed (un)economic system.
    There won’t be comprehensive, viable solutions until we collectively admit as a society, including the top 0.1-1%, that the system is FUBAR.

  4. tj

    So for given nominal interest rates, higher output tomorrow gives me two periods of lower real interest rates, while higher output today just gives me one
    I think the problem is in assuming continuity with respect to consumer behavior. Consumers don’t continuously adjust their consumption/saving decision based on small changes in real rates of interest.
    It’s lumpy. Consumers maintain their same consumpton/saving pattern until the change in the real rate is noticiable. i.e. I notice my savings no longer provide the same cushion it did in the past. If you spend all your income, then the change in the real rate matters even less.
    Have you ever been listening to the radio in your car while driving away from the station? The signal gets weaker and weaker but you do not keep your hand on the volume knob and continually make adjustments. You might make a small change or 2 until the reception is so bad you have to change the station.
    Same thing with real interest rates. The change in real rates has to be large to have an impact. The real rate can move up and down within a band around the trend and have little to no impact on consumption/saving.

  5. 2slugbaits

    Ricardo What we know is that since at least 2007 the FED has been attempting to create inflation to no avail.
    So did you cancel your subscription to Shadowstats? For years you kept telling us that the govt was hiding the true inflation, referring to the Fed Head as “Zimbabwe Ben” and fretting over hyperinflation any day now. What made you change your tune?
    tj It’s lumpy. Consumers maintain their same consumpton/saving pattern until the change in the real rate is noticiable.
    Interesting comment. A kind of Calvo consumption function. So you’re saying there are some psychic transaction costs associated with changing consumption patterns. Could be.

  6. Rick Stryker

    I’m posting this comment from 35,000 feet and maybe it’s because the oxygen level is low, but I think you are making a very good point. The limitations on fiscal stimulus from the NK models are very much driven by the assumption of dynamic optimization over an infinite life. Myopic agents are not the right way to go in my view but it is also hard to buy the assumption of infinitely-lived agents, based on casual empiricism at least. It’s ultimately an empirical question of where in the spectrum the truth is, of course, and how much it matters.

  7. Joseph

    So does this mean that Keynes was not speaking metaphorically when he said “in the long run we are all dead”?

  8. ppcm

    An other theory and robber practice at work that is, move slowly one object out of sight and when the eyes are used to the disappearance of the said object, take it away from the owner.
    Inflation there is not, should one not be willing to find a shelter, that is a dwelling or cavern hole. A favourite play of the elected public functions, that is politicians and non elected members of central banks. Inflation there is not, if the eternal ape is not consuming food and energy.
    IMF data (assumption, wages expectations are in SDR)
    Indices of Primary Commodity Prices, 2003-2013 (in terms of SDRs) (293KB pdf)
    Should the ape, be willing to throw a stone at the inflation expectation theory and practices, the same gender will notice that when meeting the worse « great recession » ever recorded in the economic history, the commodity sector is faring well, when it did not in previous downturn cycles.
    But those raw observations will not raise the ape at the pinnacle of the social observation and economic thoughts. Needs are to show that the public sector consumes and invest better than the private sector Fig 5 of the post are a testimony, and the private sector is crowding in.
    Needs may require to revisit the Cobb-Douglas functions production and consumption so widely left in the memoranda, two factors labour and capital and two functions production and consumption.
    The ape may be eternal, its planet hopefully the same,but the real issue is the cloning of the gender.

  9. jonathan

    The UK is an interesting study. Not easy to understand, but my take is they’ve pursued exactly the wrong policies. UK spending hasn’t changed much – it tends to go up – but that hides a big (for them) shift from government investment spending to social safety net spending. In other words, spending more to keep afloat, like bailing out a boat filling with water, and while at the same time doing nothing to get the boat to shore. The drop in the various categories of investment spending has been severe.
    It’s a little tough to see how exports work into things, but part may be an effect of the pound being pushed up – down at first, then up, then down – versus the euro. That isn’t the UK’s “fault”; better to have the pound. But it has not given UK exporters any leg up versus European competitors. But this doesn’t explain how poorly the UK is performing versus euro competitors: they’re all pretty much doing better exporting. That may tie back to point 1 above. Or it may be something else.

  10. jonathan

    I forgot to mention that bank lending has been feeble and that directly connects to the government policies mentioned. In other words, there seems to have been a spillover from the decrease in public investment spending into less investment spending in the private sector.

  11. Bruce Carman

    Steven and Menzie, regarding the UK’s recession, it’s a characteristic of the debt-deflationary Schumpeterian depression of a Long Wave (LW) Trough and secular bear market, including decelerating real GDP per capita from a secular peak lasting 16-25 years.
    Historically, there are 4-5 cyclical recessions and bear markets during a debt-deflationary LW Trough and secular bear market. We have had only two recessions and bear markets to date. We are due at least two more recessions and bear markets, and perhaps three more.
    The problem, of course, is that we have yet to even begin the debt-deflationary phase of the secular era, with non-financial corporate debt at secular “bull market” highs as a share of GDP and total local, state, and federal gov’t debt at an all-time high (not counting tens of trillions in unfunded obligations).
    Even Japan in the early ’00s cleared the decks to a certain degree with a 30-40% decline in bad bank loans, which is what the historical precedent implies US, UK, Canada, Australia, and EU banksters and their equity holders and creditors face.
    The Schumpeterian debt-deflationary regime has barely begun to clear the decks of excessive private debt and imputed compounding interest claims in perpetuity on wages, profits, GDP, and gov’t receipts.
    We have banksters arguing for imposition of “austerity” on the bottom 90% while printing profits and bonuses for themselves.
    We have Keynesians proposing more central bank printing (liquidation of bank balance sheets, actually) and gov’t deficit spending as if deficits and public debt and interest claims do not matter.
    We have the bottom 90% seeing their after-tax purchasing power continuing to decline and net wealth evaporate (not that they really had any).
    We have retirees getting a negative real return on fixed-income assets, requiring that they draw down on assets for subsistence.
    We have a secular Boomer demographic drag effect taking hold in earnest (as in Japan in the early ’00s) for which there are no textbook policies to overcome the effects.
    We have unregulated, unsupervised offshore bankster PTFs via pass-through entities in Caribbean banking centers and exchange-sponsored HFT bots using massive leverage backstopped by central banks to “manage” equity futures to keep stock market indices within 3-7% of the 50 and 200 DMAs.
    What’s wrong with this picture . . .?

  12. Steven Kopits

    In fact, if I look at the IMF data, I see the US budget deficit contracting faster than in either the UK or Japan since 2009. And yet, both Japan and the UK have suffered recessions since then, and the US has not. And the UK is threatening to totter into recession again, even though its deficit is closing more slowly than the US and is at just about the same level in terms of GDP. Japan’s deficit has actually increased, and yet growth of only 1% is expected there, versus 2.4% or so in the US.
    As regards monetary policy, UK inflation is at 2.7%. US 2012 CPI was 1.7%. So is monetary policy tighter in the UK?
    In the end, you offered two explanations: one that said no one knows what’s going on, and Krugman, who argued the fiscal case. But it’s not clear that Krugman holds up when you look at the actual data.
    The US fiscal deficit has been closing the quickest, and yet US growth has been the highest.
    Any more explanations?

  13. Menzie Chinn

    Steven Kopits: I’m not sure I understand your assertion. Using the IMF’s WEO data (September 2012), the change in the UK’s structural budget balance to potential GDP ratio is 3.1 ppts going from 2010 to 2012 (i.e., consolidation). The US figure is 1.9 ppts. So…I think the US has pursued a less contractionary policy (and if one starts from 2008, a more expansionary).

  14. Ricardo

    Slug wrote:
    For years you kept telling us that the govt was hiding the true inflation, referring to the Fed Head as “Zimbabwe Ben” and fretting over hyperinflation any day now. What made you change your tune?
    Yes, I have altered my view of inflation over the past few years, but you are conflating my views with some others who have posted here. I am not the one who quotes Shadowstats, though their stats are probably more accurate than the government propaganda. I also still believe that Ben is following the same path as Zimbabwe and will lead us to the same results over time, but our economy is much larger and can hold together much longer than Zimbabwe.
    The reason I altered my view is two events. First, I believed as most economists including “Zimbabwe Ben” that the FED could create inflation by monetary expansion, but the evidence has been overwhelming that the FED has failed miserably in its attempts to generate inflation. Even Professor Hamilton was calling for higher inflation and Krugman seemed to want to commandeer all the printing presses in the world to print dollars. So I was faced with the question of why there were no price increases in the face of massive and frequent QE schemes.
    Second, what was causing the huge excess reserves. It is obvious that if banks could lend at even 1% they would not hold money aside to gain .25%. Something was preventing the money from getting into the economy.
    Two good friends who are brilliant economists helped me refocus on the real purpose of money as a medium of exchang and nothing else. They helped me understand that the fiscal policies, especially taxes and regulations, of the federal government had created a massive economic contraction. This destroyed the credit system that is vital to transmitting money into the transactional economy. The economic contraction has prevented traders from raising their prices, people can’t afford higher prices, and no amount of monetary stimulus will change that. Because the broken credit system prevented money from being transmitted into the transactional economy all the QE by “Zimbabwe Ben” was forced to flow into excess reserves.
    Just for the record this also happened in the Great Depression. I ran across this about 10 years ago when investigating claims that the 1937 Recession within the Depression was caused by the FED increasing reserve requirements. The excess reserves during the 1930s simply did not support the theory, but I could not explain why. Now I understand.
    You would do yourself a favor if you were to honestly look at the huge failure of the theories you espouse and try to understand why your predictions fail to forecast and explain events.
    two good friends who are brilliant economists showed me the evidence

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