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,    (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  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.