THE FRBUS Model JEANPHILIPPE LAFORTE FEDERAL RESERVE BOARD

THE FRB/US Model JEAN-PHILIPPE LAFORTE, FEDERAL RESERVE BOARD SEPTEMBER 25, 2019 (THE VIEWS EXPRESSED IN THIS MATERIAL ARE THOSE OF THE AUTHOR AND DO NOT NECESSARILY REFLECT THE POSITION OF THE FEDERAL RESERVE BOARD OR THE FEDERAL RESERVE SYSTEM. )

The FRB/US Universe I FRB/US model: a large-scale (~290 equations and ~370 variables) nonlinear macroeconomic model of the U. S. economy • Most of the stochastic equations are estimated independently, i. e. , “equation-by-equation” estimation. VAR system: a system of equations that characterize the expectations variables used in the estimation and simulation, i. e. , vector autoregression- (VAR-) based expectations • It is not the only type of expectations available. Supply-side state-space model: an auxiliary model used to generate historical estimates of the trending components of many supply-side variables Public version of the FRB/US model: publically available code, documentation, simulation programs, and database (including a forecast consistent with the Summary of Economic Projection) 2

The FRB/US Universe II Solving a large nonlinear macroeconomic model like FRB/US with shooting algorithms can be time consuming when performing certain tasks and types of simulations, especially if we impose model-consistent expectations (MCE). LINVER: a (mostly) automated linearized version of FRB/US • It can be efficiently solved in Dynare or any other RE solver (e. g. , GENSYS). s. FRB: a smaller (50 equations) linearized version of FRB/US designed specifically for use in complex monetary policy simulation experiments • Parameters are estimated so that the key Impulse Response Functions of s. FRB match as closely as possible to those of the full FRB/US model. 3

The 2018 Update Reflecting on the evolution of the model and its uses over time, as well as recognizing the nature of sociological and cultural aspects of macro modeling and economics in general, we developed and released in 2018 a new version of the model with some noticeable changes. • Reduce the complexity and size of the model (from 500 variables to about 370 variables). o Simplify the fiscal and business investment sectors. o Eliminate energy as a factor of production and simplify the energy sector. o Maintain only one concept of interest rates. o Eliminate details that are difficult to model or forecast and for which we do not have adequate expertise. • Facilitate the learning and use of the model as well as the communication processes surrounding it. • Improve the long-run properties of the model. o Replace chain aggregation formulas by linear approximations with fixed weights. 4

Core Features of the FRB/US Model Expectations Aggregate Demand: Consumption The Supply-Side Structure 5

Expectations in FRB/US • Expectations are explicit in many of its equations, i. e. , an explicit channel to model anticipated shocks. • Determining how expectations about future economic conditions can influence current prices and real activity is achieved primarily through an adjustment cost channel specified with the use of polynomial adjustment costs (PAC). • Decisions by households and firms rest on forecasts of equilibrium goals that would be selected in the absence of frictions but, because of costs in adjusting actions, are only gradually achieved. o There are tradeoffs between current and future costs of current actions. 6

Expectations in FRB/US In simulation, two general options for expectations formation (constrained VAR structure or MCE) are available in a framework that also permits the use of “mixed” expectations in which some sectors are VAR and some MCE. • Financial variables: ZRFF 10, ZRFF 5, ZRFF 30, DIVGR. . . • Price and wage: ZPICXFE and ZPIECI • Real activity/other: ZEBFI, ZECD, ZECO, ZECH, ZLHP, ZYHP, ZYHT. . . Shortcomings of the PAC approach • The estimation of the original specification does not impose restrictions that ensure that the net growth of the variables on both sides of the equation is the same in the long run. • Modeling the structures and dynamics of an “equilibrium” counterpart is not always easy. 7

Aggregate Demand Consumption expenditures on nondurable goods and non-housing services (ECO) • Rule-of-thumb consumers (~30 percent). • Optimizing households face adjustment costs in targeting a level of consumption implied by their anticipated and discounted streams of incomes (labor, transfers, and property income) as well as their stock of wealth. • The discount rate is assumed to be about 25 percent per year! A very early recognition and implementation of the idea that agents may discount the near future at a greater rate than the distant one and what is normally assumed in the New Keynesian dynamic stochastic general equilibrium literature (see "The Discounted Euler Equation: A Note, " Mc. Kay, Nakamura, and Steinsson). 8

The Supply-Side Structure The key production sector in FRB/US is the business sector and the production function is assumed to be Cobb-Douglas. A satellite state-space model is used to estimate the trending components of many supply-side variables: • natural rate of unemployment, potential output, multifactor productivity, trend labor force participation rate, and trend workweek • legacy of "From Many Series, One Cycle: Improved Estimates of the Business Cycle from a Multivariate Unobserved Components Model" (Fleischman and Roberts, 2011) Looking forward • The specifications of the processes in the auxiliary model are not necessarily identical to their counterparts in the full version of the FRB/US model. • Augment the set of estimated latent variables: natural rate of interest! 9

Working in the FRB/US Universe • Regular Policy Tasks • Research • Stochastic Simulations 10

Uses of the FRB/US Model: Regular Policy Tasks For each Federal Open Market Committee meeting • Its projection provides (very limited) input to the staff’s preparation of a judgmentally based forecast (FRB/US, VAR-based expectations). • Counterfactual scenarios reflect relevant sources of risk and uncertainty to current economic conditions and the staff projection (FRB/US, VAR-based expectations and MCE ). • Stochastic simulations create confidence bands around the staff projection and assign probabilities to some key future and hypothetical events (LINVER, VAR-based expectations). • Simulations are based on alternative characterizations of monetary policy, including optimal control (FRB/US, mix of MCE and VAR-based expectations). Other regular uses • There are simulations of scenarios for an annual bank stress test. 11

Uses of the FRB/US Model: Research on alternative policy strategies ◦ When effective lower bound (ELB) may occasionally bind: ◦ Usually some or all sectors have MCE. ◦ It is usually based on LINVER and simulated in Matlab. ◦ John Roberts will discuss such research in more detail later today. ◦ Some colleagues have used the s. FRB model for more complex experiments: ◦ Erceg, Christopher, James Hebden, Michael Kiley, David Lopez-Salido, and Robert Tetlow (2018). "Some Implications of Uncertainty and Misperception for Monetary Policy, " Finance and Economics Discussion Series 2018 -59. Washington: Board of Governors of the Federal Reserve System, https: //doi. org/10. 17016/FEDS. 2018. 059. ◦ Hebden, James, and Lopez-Salido (2018). "From Taylor's Rule to Bernanke's Temporary Price Level Targeting, " Finance and Economics Discussion Series 2018 -51. Washington: Board of Governors of the Federal Reserve System, https: //doi. org/10. 17016/FEDS. 2018. 051. ◦ Some research has looked at the effects of unconventional monetary policies: ◦ Chung et al. , "Monetary Policy Options at the Effective Lower Bound: Assessing the Federal Reserve's Current Policy Toolkit, " FEDS 2019 -3 (LINVER). ◦ Engen et al. , "The Macroeconomic Effects of the Federal Reserve's Unconventional Monetary Policies, " FEDS 2015 -5 (FRB/US). 12

Stochastic Simulations • The business cycles are not symmetric: Recessions are short lived and deep, while expansions are relatively mild and protracted. • González-Astudillo, Manuel, and Diego Vilán (2019). "A New Procedure for Generating the Stochastic Simulations in FRB/US, " FEDS Notes. • Simple (or even dependent) bootstrapping of the FRB/US model’s errors did not adequately capture the depth, duration, and frequency of recessions. • The standard bootstrap has serious difficulties in generating increases in the unemployment rate as large as those observed during the worst recession episodes in history. • It matters if one is interested in properly characterizing the stochastic nature of ELB episodes. • Define a recession as an event in which there are four or more consecutive quarters of an increase in the unemployment rate and at least two quarters, not necessarily consecutive, of declining real gross domestic product (Recession Proxy). 13

14

Stochastic Simulations (continued) Alternative procedure 1. 2. Cluster historical periods in three regimes: non-recessions, conventional recessions, and the Great Recession. Assume that the transition between regimes is Markovian. Probabilities are calibrated: Non-recession recession: conventional or Great Recession Non-recession . . . P(Non-recession) = 0. 958 P(conventional| recession) = 0. 036; P(Great| Recession) = 0. 006 Once the economy falls into a recession, a particular recessionary episode is picked randomly and its shocks are run through as they unfolded historically. Following the recession, the economy exits it with probability one. 15

16

FRB/US Model’s Properties • 100 bps Increase in the Policy Interest Rate • 100 bps Increase in the 10 -year Term Premium 17

18

19

IT Infrastructure and Software We are currently using EViews to work with the full version of the FRB/US model. We have developed an efficient nonlinear MCE solver written in EViews • Pros • User-friendly interface makes working with time-series data and models relatively easy. • Cons • EViews is not necessarily a widely known software, which may be a possible issue with newly hired economists and outsiders who would like to use the public version. • Computations with vectors and matrices are challenging when not impossible. The decision to use EViews was made slightly more than a decade ago. • The computing environment and software have evolved substantially since then. We are using Matlab to solve LINVER and s. FRB: • We have an efficient Matlab procedure for imposing the ELB in simulation of an otherwise linear RE model. 20

Beyond the Board’s Walls. . . The FRB/US model was made available to the public in 2014. ◦ We have seen a robust interest from outsiders (broker and financial institutions, central banks, etc. ). ◦ In part, this interest is based on the (mistaken) belief that the production of the staff projection relies primarily on the structure and dynamics of the FRB/US model. ◦ Interest from outsiders and use of the model outside of the Board suggest that this was a positive step. Reflections and speculations. . . ◦ Is it possible to improve the experience and the products? ◦ Facilitate the use of the model for outsiders and expand the range of materials available to the public. ◦ Try different software? ◦ Find ways to create and establish synergies? ◦ The Board can allocate only a limited amount of resources to this product. ◦ We have already seen projects that solve the FRB/US model using different computer languages (i. e. , python). 21

Conclusion The many uses of the FRB/US model require a large operation with multiple versions and (at least currently) multiple software platforms. 22