RDP 2014-02: Fiscal Policy and the Inflation Target 4. The FRB/US Model

Estimates of the effect of fiscal stimulus require a macroeconomic model. I use the FRB/US model of the US economy, one of the main macroeconometric models used at the Federal Reserve Board of Governors. This model has been used in some key contributions on the setting of the inflation target (Reifschneider and Williams 2000; FOMC 2005; Williams 2009), though without countercyclical fiscal policy. It has also played a prominent role in assessing the consequences of fiscal stimulus (Romer and Bernstein 2009; CBO 2010; Coenen et al 2012), though not in a stochastic setting.

FRB/US differs from many models published in textbooks and academic journals in that it is not designed for expositional purposes. Rather, it is intended to provide a credible basis for policy advice.[6] That, in turn, requires closely fitting the data and paying detailed attention to the various transmission mechanisms that policymakers regard as important. As a result, the model is large and detailed. It contains approximately 500 variables and 170 estimated equations. Unfortunately, that makes the model something of a black box to outsiders.

It is not possible to document the model here. Rather, interested readers are referred to descriptions published elsewhere. Brayton and Tinsley (1996) is the most detailed overview. Reifschneider and Williams (2000) provide a summary that focuses on the zero bound. Elmendorf and Reifschneider (2002) discuss fiscal multipliers. Coenen et al (2012) compare fiscal multipliers of FRB/US to those of other structural models used by policymaking institutions. The references in these papers provide further information.

In brief, the model is designed and revised with the intent of closely fitting the data. The main behavioural relationships are derived from explicit optimisation problems, under the assumption of costly adjustment. Most equations are estimated individually, with explicit expectational terms. When it is difficult to explain the data with optimising behaviour, further ad hoc terms are added. For example, the consumption equations include rule-of-thumb behaviour. For estimation, most operational work, and this paper, expectations are determined by small-scale vector autoregressions (VARs). However, in deterministic settings the model can also be solved under model-consistent expectations.

The channels through which monetary and fiscal policy work in FRB/US are summarised by intermediate macroeconomics textbooks (for example, Mankiw (2010, Chapter 10)). For more detail, consider as an illustration the consumption response to a reduction in taxes or an increase in transfers. Rule-of-thumb households (accounting for about one-quarter of total private consumption) are assumed to increase their consumption immediately. Other households raise their consumption, somewhat more gradually, to match the increase in perceived permanent income. Households are not assumed to have perfect foresight regarding the duration of the increased income. Rather, they regard their permanent income as the annuitised present value (calculated with a high discount rate) of the sum of expected wages, taxes, transfers and so on, with expectations being the predictions of small-scale VARs. So the contribution of transfers to perceived permanent income, for example, reflects the estimated persistence of transfers in the historical data. Normally, the monetary policy rule would increase interest rates in response to the increase in consumption, in turn raising longer-term rates and the exchange rate and lowering equity prices. However, at the zero bound, these offsetting effects are greatly muted. FRB/US does not include an effect of government debt on bond risk premia, explicit ‘Ricardian equivalence’ effects, or hysteresis in the labour market.

In deterministic settings, the model can be solved assuming that households know how long a zero bound episode, and hence the fiscal stimulus, will last. In stochastic settings, alternative assumptions are needed. In my simulations, households are assumed to expect historical correlations to persist, even though policy has changed. In principle, this assumption is susceptible to the Lucas critique and I discuss it in Section 7.

Any macroeconomic model rests on a large number of debatable assumptions. One way of assessing these assumptions is by examining the model's multipliers. A wide range of FRB/US multipliers have been publicly documented; see, for example, Brayton and Tinsley (1996) or footnote 6. For this paper the fiscal multipliers are particularly relevant. Table 1 shows the estimated response of real GDP to sustained variations in key fiscal variables with nominal interest rates held fixed. As a guide to interpretation, estimates in the top row imply that were government purchases to deviate from baseline by 1 per cent of GDP for the duration of the experiment, then the level of GDP would be 0.99 per cent above baseline after four quarters and 1.22 per cent above baseline after twelve quarters.

Table 1: FRB/US Fiscal Multipliers at Fixed Nominal Funds Rate
Effect on level of GDP (per cent deviation from baseline) of a sustained change in fiscal variables by 1 per cent of GDP
After four quarters After twelve quarters
Government purchases 0.99 1.22
Reduction in personal tax receipts 0.31 0.56
Transfers 0.42 0.50

Source: author's calculations

Estimation of fiscal multipliers is controversial and subject to uncertainty. I do not wish to enter this debate here, beyond some brief comments as to why the estimates in Table 1 provide an interesting and relevant benchmark. The FRB/US multipliers are similar to many other estimates that assume constant nominal interest rates. For example, a survey by the OECD (2009) concluded ‘[a] review of the evidence … typically suggests a first-year government spending multiplier of slightly greater than unity, with a tax cut multipliers of around half that’. Overviews of the literature by Christina Romer (2011), David Romer (2011) and DeLong and Summers (2012) conclude that fiscal multipliers are substantial. Coenen et al (2012) present a more detailed comparison of structural (mainly DSGE) models used by central banks, international organisations, and academics; they found FRB/US fiscal multipliers at fixed nominal interest rates to be similar to those of other models. As noted above, FRB/US multipliers have been one of the main sets of estimates relied upon by policymakers. The CBO (2010, Appendix) compares fiscal multipliers from models like FRB/US with other estimates in the literature and concludes that the FRB/US multipliers are a useful basis for policy in current conditions.[7]

Cogan et al (2010) have argued that FRB/US multipliers are too high. Part of their argument is that the FRB/US model is ‘Old Keynesian’ and out of step with modern modelling techniques. However, the extent to which FRB/US is ‘old-fashioned’ and whether or not this would be a problem is debatable. More important, Coenen et al (2012, Figure 7) find that FRB/US multipliers are similar to those of recent DSGE models, including the model used by Cogan et al. As Woodford (2011) and Coenen et al discuss, the apparent disagreement occurs because Cogan et al compare multipliers like those in Table 1 with multipliers that assume government spending is expected to substantially outlast the zero bound. The possibility that stimulus measures may outlive their rationale is an important concern, but it is not the policy I am considering here.


For regular applications of FRB/US, see the alternative scenarios and confidence intervals typically published around page I-17 in each Greenbook presented to the FOMC, available at <http://www.federalreserve.gov/monetarypolicy/fomchistorical2005.htm>. [6]

The estimates in Table 1 differ from FRB/US multipliers published elsewhere, given that my purposes and context are slightly different. My multipliers are higher than FRB/US multipliers that assume monetary policy follows a Taylor-type rule, for example, if the zero bound is explicitly expected to stop binding soon. My multipliers are lower than estimates that assume the zero bound is expected to last many years. [7]