Dynamic Scoring Using the FRB/US Macroeconomic Model

Introduction

Conventional budget estimates incorporate behavioral feedback that does not reflect broader economic effects. In particular, these estimates typically hold macroeconomic aggregates such as output, employment, wages, and prices fixed. However, policy reforms can affect the overall economy through their impacts on work incentives, investment and savings decisions, and the federal deficit. When individuals or firms change their economic decisions, a chain reaction of responses may follow until the economy reaches a different equilibrium with new values for wages, prices, interest rates, output, and more. Dynamic scores account for these broad macroeconomic changes and their feedback effects on the federal budget.

In this report, we describe how the Budget Lab estimates these dynamic effects by linking our tax microsimulation model to the FRB/US macroeconomic model, an open-source general-equilibrium model of the U.S. economy used by staff at the Federal Reserve since 1996. Our model code, with additional explanation and detail, can be found on our GitHub page.

We emphasize that the Budget Lab’s macroeconomic modeling efforts are a work in progress. Estimates of the macroeconomic effects of policy changes are, in general, highly sensitive to both the choice of economic model that analysts use, and the assumptions that they make about key variables within those models. As such, the Budget Lab’s dynamic estimates for any given policy proposal will necessarily differ from others' analyses. A preliminary comparison of our method with those used by the Congressional Budget Office (CBO) and the Joint Committee on Taxation (JCT) in their analysis of the 2017 Tax Cuts and Jobs Act suggests that our method yields dynamic effects that are smaller than those estimated by Congressional scorekeepers’ models. Understanding the source of these differences remains a topic of ongoing investigation at the Budget Lab, and we plan on refining our approach further in the future.

What is FRB/US?

FRB/US, which Federal Reserve staff use for forecasting and policy analysis, is a large-scale general equilibrium model of the U.S. macroeconomy. It consists of approximately 375 equations and includes all major components of the National Income and Product Accounts and major labor-market variables. The key relationship in the model is a New Keynesian Philips Curve equation that simultaneously links core price inflation and compensation growth. 

Unlike many macroeconomic models, FRB/US does not require all agents to have perfect foresight or to have rational expectations; instead, the model provides multiple options for how different agents form expectations (including both perfect foresight and adaptive expectations). The model also includes a number of options for the potential response of monetary policy to shocks in the economy.

The dataset used in the public version of FRB/US, which Federal Reserve staff update each quarter, uses quarterly historical values for dates up to the present. For future values, key variables initially follow the median path in the FOMC Summary of Economic Projections (SEP), and then eventually converge to the median long-run SEP forecasts. Variables not explicitly forecasted in the SEP, such as the ten-year Treasury yield, are projected in a model-consistent way with the SEP forecast. The resulting baseline FRB/US forecast is illustrative and is not an official Federal Reserve forecast.

Additional information on the FRB/US model, as well as implementations of the model in Python (PyFRB/US, the version used by the Budget Lab) and in EViews, can be found on the Federal Reserve Board’s FRB/US site.

Fiscal Policy in FRB/US

A given policy reform can include changes to a large number of parameters of the U.S. tax-and-transfer system. FRB/US, however, has a relatively aggregated set of fiscal variables; for federal taxes, the model contains as variables only:

• the average personal income tax rate;
• the tax subsidy for mortgage interest;
• the average corporate tax rate; and
• the marginal corporate tax rate. 

Each of the four tax rates in FRB/US affects the macroeconomy differently. The primary effects of changes to each rate in the model, holding changes to other rates fixed, are as follows:

• Increases (decreases) in the average personal income tax rate directly reduce (increase) households’ disposable income, reducing (increasing) aggregate household demand for goods and services.
• Increases (decreases) in the average marginal income tax rate for those claiming the mortgage interest deduction increase (reduce) the value of the mortgage interest deduction, increasing (decreasing) demand for housing.
• Increases (decreases) in the average corporate income tax rate reduce (increase) after-tax corporate profits, which, after flowing to households, affect household demand. They also decrease (increase) the returns (in terms of future profits) of investment in new ventures, dampening (spurring) business fixed investment.
• Finally, increases (decreases) in the marginal corporate tax rate increase (decrease) the value of the investment interest deduction, spurring (dampening) business investment. 

It is important to emphasize that the magnitudes of these effects, as well as their timing, are highly dependent on assumptions about the response of monetary policy to fiscal shocks (both temporary and permanent). For example, the extent to which fiscal stimulus via increased spending (or tax cuts) translates into higher real output, faster price growth, or a combination of the two will depend on how the Federal Reserve changes interest rates following the change in fiscal policy. 

How the Budget Lab Uses FRB/US

To use FRB/US for dynamic revenue estimation, we translate the output of the Budget Lab’s tax simulator into exogenous changes in each of these four tax rates, and then allow all other variables in the model to adjust endogenously, typically over a thirty-year timespan. The remainder of this document explains this process in detail.

Key Assumptions

As noted above, the response of the Federal Reserve is a key input to the path of economic variables as they respond to changes in fiscal policy. This is especially true in the case of interest rates, since the interest rate’s response to changes in the federal deficit is driven almost entirely by  the Federal Reserve’s reaction to changes in fiscal variables (revenue and outlays) driving the change in the deficit. (In other words, there is no independent “crowd-out” in the FRB/US model due directly to changes in federal borrowing or the stock of public debt.) In all of our simulations, we assume that the Federal Reserve follows an inertial Taylor rule in setting interest rates,¹ and that the equilibrium real federal funds rate (r^*) adjusts dynamically.

In order for FRB/US to solve, users must specify an assumption about how the federal government will achieve fiscal stability, as measured by either the debt-to-GDP ratio or the deficit-to-GDP ratio, in the long run. For our simulations, we assume that fiscal closure occurs via stabilization of the deficit-to-GDP ratio, but that this happens sufficiently far in the future so that this assumption does not affect agents’ behavior during our thirty-year simulation period. (As such, the specific choice of fiscal closure in the model does not matter for our results in practice.)

Finally, for our initial set of results, we use FRB/US’s default VAR-based expectations, in which agents are backward-looking when forming expectations of the future paths of economic variables, rather than making model-consistent predictions with perfect foresight. In future work, we plan to investigate further how modifying this assumption affects the response of macroeconomic aggregates to changes in various aspects of fiscal policy.

In addition to the assumptions described above – which all represent user choices made within the FRB/US model – we make one adjustment to the FRB/US model itself when using it for dynamic revenue estimation. In the Federal Reserve’s existing configuration of FRB/US, all government net interest payments flow to U.S. households, appearing as taxable household income within the accounting equations used for the income side of national accounts. One interpretation of this assumption is that, within FRB/US, all federal debt held by the public is held passively by U.S. households. This assumption can be problematic for two reasons:

• First, in reality, approximately one-quarter of federal net interest payments flow to non-U.S. entities. As such, FRB/US assumption will tend to overstate the contribution of interest from U.S. government securities to taxable household income.
• Second, and more importantly, changes in net interest payments translate mechanically to changes in taxable household income because of the assumption that households do not change their holdings of government securities in response to changes in the economy. For example, if the stock of debt held by the public increases due to a policy reform, the additional interest payments on that debt will mechanically increase taxable household income and will in turn mechanically increase personal income tax payments.

To address these issues, we modify FRB/US so that the share of government interest payments flowing to U.S. households matches that in the NIPAs, and so that U.S. households’ taxable income is not affected mechanically by changes in the stock of federal debt. To achieve the latter, we assume that any changes in government net interest payments relative to baseline flow to non-U.S. entities.

Step 1: Producing the Dynamic Baseline

The quarterly dataset used by FRB/US is based on the Federal Reserve’s Summary of Economic Projections (SEP). This forecast will necessarily differ from the economic and budgetary forecasts of the Congressional Budget Office (CBO), which the Budget Lab uses as the basis for its annual tax microsimulation for future years. As such, our first task is to create a set of quarterly fiscal variables in FRB/US that sum to their annual totals from the tax simulator when expressed as a share of baseline GDP.

For both the tax subsidy for mortgage interest (the trfpm variable in the FRB/US dataset) and the marginal corporate tax rate (trcim), we replace quarterly values in the FRB/US dataset with the corresponding value for the year in question from the tax simulator. For the average personal income tax rate (trp) and the average corporate tax rate (trci), we proceed as follows:

• We start with the annual time series of federal personal income tax payments and corporate tax payments from the tax simulator baseline.
• Next, to account for the fact that the government sector in FRB/US also includes state and local government, we multiply the personal income tax payments series by the historical ratio of government personal income tax payments to federal personal income tax payments in the NIPAs.
• We next use the second-differences method of Boot, Feibes, and Lisman (1967), a special case of Denton's benchmarking method, to interpolate quarterly values for each series. As part of this method, we require that these values, when expressed as a sum of FRB/US’s baseline GDP, sum annually to the share of CBO’s baseline GDP represented by the corresponding series in the tax simulator.

These steps produce two quarterly time series of tax revenues, one for personal income taxes and one for corporate taxes. To create a macroeconomic baseline consistent with these series, we next run FRB/US with the following constraints using the model’s built-in mcontrol feature:

• All SEP macroeconomic variables are constrained to follow their original paths in the FRB/US dataset;
• Tax revenues are constrained to follow the timeseries derived above, with average tax rates (trp and trci) adjusting to meet this target;
• Marginal tax rates (trfpm and trcim) are constrained to follow their annual paths from the tax simulator; and
• The federal deficit is constrained to follow CBO’s forecasted path (as a share of GDP).

The output of this run of FRB/US is the dynamic baseline that we use for all subsequent scenario analysis.

Step 2: Estimating Dynamic Changes in Tax Bases

The dynamic baseline produced in Step 1 includes time series for each of the tax bases (personal income and corporate) included in FRB/US. Our next step is to estimate how the size of each of these bases changes in response to the policy reforms under consideration. To do so, we adjust the tax rates associated with each base from the dynamic baseline as follows:

• Marginal tax rates (trfpm and trcim) are assumed to follow their annual paths from the tax simulator’s analysis of the scenario.
• For average tax rates, we derive quarterly revenue series from the tax simulator output, using the same method found in Step 1. However, because these revenue series assume no changes to economic behavior (i.e. they are conventional scores), we cannot use them directly as we did above. Instead, we calculate the average tax rate in FRB/US consistent with each series, assuming tax bases follow the paths of the dynamic baseline. In other words, we solve for the average tax rate that, when applied to the dynamic baseline calculated above, yields the conventional change in revenue that the tax simulator produced.

We then run FRB/US for the scenario, constraining tax rates to follow the paths described above using the mcontrol feature. The resulting output is the dynamic scenario and contains our estimates of the behavior of macroeconomic variables in the counterfactual world where the policy in question is implemented.

Step 3: Computing Dynamic Revenue Feedback

Finally, we translate the dynamic changes in the size of tax bases that we estimate in Step 2 into macroeconomic feedback for the scenario in question. To do so, we first compute the change in real national income (adjusted for inflation using the GDP deflator) for each year of the analysis. We then multiply this figure by the conventional level projection of government revenue. From this value we subtract the conventional baseline revenue projection, which yields a budget score accounting for changes in the macroeconomy as estimated by FRB/US.