Why Can’t We All Just Get Along? The Great Multiplier Debate

I’ve been thinking about why the numbers that are typically bandied about in policy circles (at least that I’m familiar with) have so little impact on the overall general and blogosphere debate (see some examples here and here). I think it’s part ideological, and part methodological. I can’t do much about the first (e.g., tax cuts good, spending on goods and services bad — unless on defense; or alternatively “let the market adjust no matter how long it takes”). But at least I can lay out why reasons why there is disagreement on the size of the multipliers.

I leave aside the “timely” issue, since others have discussed it [0], and I think it less relevant given the likely extended duration of this recession, and the time-pattern of stimulus, as depicted in Figure 1 reproduced from this post.


Figure 1: Estimated spending and tax revenue reductions, per fiscal year, embodied in HR 1. Shaded areas pertain to spending occurring outside of the 20 month time frame. Source: CBO, Cost Estimate of HR 1 (January 27, 2009).The starting point in the analysis is to realize that there are three key ways in which to obtain “multipliersâ€.

  • Estimation of structural macroeconometric models, with identification a la the Cowles Commission approach.
  • Calibration of microfounded models (including real business cycle models, and New Keynesian dynamic stochastic general equilibrium models).
  • Estimation of vector autoregressions (VARs) and associated impulse-response functions, with identification achieved by a variety of means.

Traditional macroeconometric models. Most of the estimates I have cited [1] [2] are based upon the first approach. One estimates a model with many equations, including the components of aggregate demand (C, I, G, X, M), supply side (price setting, wage setting), and potential GDP. The framework most popular in policy circles is one that might be characterized as “the neoclassical synthesis”, wherein wherein prices are sticky in the short run, and perfectly flexible in the long run. The OECD Interlink model is of this nature, as is Macroeconomic Advisers’ model. The latter was the standard off the shelf model referred to at CEA when I was on staff in 2000-01. The Fed’s FRB US model also falls in this camp. Now even within this category, there is a wide diversity of specifications in terms of the number of equations, level of disaggregation, lag length, what variables are included in each equation, etc. For instance, in the consumption function, how many lags of disposable income, is wealth included, is wealth disaggregated into housing and non-housing wealth? Does one explain aggregate consumption, or durables, nondurables and services consumption? People who blithely argue for or against a given specification with certitude are likely to have never had to face these choices. They’re hard!

Perhaps the key dividing line is between models that incorporate adaptive expectations (operationally, include lags, perhaps imposing a functional form on the lag structure) and using model consistent expectations (i.e., the equations incorporate expectations of future variables, and those expectated values are calculated in a manner consistent with the model). John Taylor was a leader in incorporating model consistent expectations in macro models (as laid out in his 1993 book.

A key reason for the academic disenchantment with these types of models included the view that the identification schemes used were untenable (e.g., why is income in the consumption function but not in the investment?). Another source is the combined impact of the inflationary 1960’s and 1970’s, and the Lucas Critique. On the latter point, I’d point out that unless policy changes are really massive, the Lucas Critique (a.k.a. Econometric Policy Evaluation Critique) isn’t really relevant(see [1]).

Models with micro-foundations in general equilibrium Micro-founded models are often associated with real business cycle models. However, the association is not one-for-one. It’s true the early real business cycle models worked off of utility functions and production functions. But the modern generation of dynamic stochastic general equilibrium (DSGE) models in the new Keynesian mode incorporate microfoundations as well (utility functions, production functions, investment functions, etc.) but also incorporate rigidities such as price stickiness. Purists will say everything has to be microfounded. Well, that’s a matter of taste, but the fact of the matter is that it’s very hard to calibrate simple real business cycle models without rigidities to match the moments of actual real world data, even after the data’s been HP-filtered (I’m sure this blanket statement will get me in trouble, but I think that that’s a fair assessment). So DSGEs do better at mimicking real data, especially after numerous rigidities are incorporated. In the earliest incarnation of the Fed’s Sigma model, for instance, there are rule of thumb consumers (shades of Campbell-Mankiw!). For a survey of how DSGEs have been incorporated into policy analysis, see the survey by UW PhD Camilo Tovar.

It’s useful at this point to ask how are these models calibrated? For the deep parameters (intertemporal rate of substitution, for instance), one can rely upon some estimates — then pick the one that you like (and is in the range of estimates). Oftentime, the combination of parameter values is selected to mimic the time series properties of actual (filtered) data. So say one believes one should not appeal to ad hoc Keynesian models. It’s not clear that RBCs or DSGEs get you away from the problem that one has to appeal to the data to get multipliers since the models are calibrated to mimic real world data. In other words, while the theoretical bases of the models may differ, and important insights can be gleaned from these models (e.g., distinctions between temporary and permanent changes), the differences in terms of multipliers might not be as big as one might think.

VARs Vector autoregressions are regressions of multiple variables on lags of themselves. The underlying shocks can be identified by putting them in a recursive ordering (called a Cholesky decomposition), or using restrictions based on theory (say, money has no contemporaneous impact on prices; or money has no impact on output in the long run). VARs were initially proposed as a way of getting around “incredible identifying assumptions”, in the Cowles Commission approach to econometrics embodied in the old style macroeconometric models. But of course, people can disagree about which restrictions make the most economic sense. (For instance money is neutral in the long run seems natural, but not all theoretical models have that implication.)

The much cited Romer and Romer model of fiscal policy impacts is a particular sort of VAR, in which only one equation is focused on, and extra-model information is used to identify exogenous tax changes (remember, they don’t analyze government spending changes). (It’s an autoregression in log GDP, to the extent that the dependent variable is log first differenced GDP).

A good summary of where these types of fiscal multipliers come from was in Box 2.1 in Chaper 2 of the April 2008 World Economic Outlook.

My bottom line There are indeed a wide variety of estimates regarding the size of multipliers. Different models — and assumptions within those model categories — lead to different estimates. It’s important to understand the underpinnings of those estimates (and this is where many of the people who cited the Romer and Romer study went wrong). Hence, one has to have an understanding of the very complicated models before taking strong stands in favor of one estime over another.

In my experience, as far as policy organizations such as central banks, government agencies and multilateral agencies go, reference is made to a number of models. Their assessments of multiplier magnitudes will then reflect some weighting of the various model predictions. That is why I will put more wieght upon assessments by organizations (that have to make decisions upon these judgments) than a single academic study, regardless of how well I respect the academics involved (and sometimes, these academics are working outside their area of research expertise…)

As an aside, here are the impacts of various fiscal experiments in response to a negative shock in a DSGE developed by the IMF:


Figure 1: Figure from Box 2.1 in Chaper 2 of the April 2008 World Economic Outlook.

“Expansion through transfers is defined as a one percentage point increase in debt-financed transfers in year one and 0.5 percentage point in year two. Expansion through labor tax cuts is defined as a reduction in the labor income tax rate by 1.5 and 0.75 percentage points in year one and year two. Expansion through government investment is defined as a combination of higher transfers and an increase in productive government investment by 0.25 and 0.125 percent of GDP in year one and year two.”

Notice that the public investment shows the biggest impact, while under the base assumptions the impact of transfers and tax cuts are about the same.

Originally published at Econbrowser and reproduced here with the author’s permission.