Deep Analysis of the FRB/US Macroeconomic Model
This page reviews the Federal Reserve's FRB/US model and how it informs policy analysis. It summarizes the model's structure, key inputs, and the way staff use simulations to compare policy paths. Use the beginner/expert toggle at the top right to adjust the level of detail.
The Federal Open Market Committee meets eight times a year to set the federal funds rate. Those decisions shape borrowing costs, employment, and inflation. FRB/US is a core tool staff use to map policy choices to likely outcomes.
It is one input among many. The model provides scenario-based analysis alongside other models and judgment.
A model is a set of equations that link spending, hiring, prices, and financial conditions. Change a policy rate and the model traces how those links typically move over time. It is a disciplined way to compare options, not a forecast of surprises.
Policy affects the economy through many channels and with long lags. A model helps keep those interactions and timing consistent.
FRB/US divides the economy into sectors with distinct behavior:
Households decide how much to spend versus save. Higher rates tend to slow big-ticket purchases, though some households are liquidity-constrained and less sensitive to rates.
Firms invest and hire based on expected demand and financing costs. Higher rates raise the hurdle for new projects.
The Fed sets the overnight rate, which influences bond yields, mortgage rates, and equity valuations. The model captures these linkages.
Policy affects the dollar and trade. A stronger dollar typically restrains exports and lowers import prices.
In the model, a 1 percentage point tightening typically produces:
These are model-based tendencies, not point forecasts.
FRB/US is a large-scale estimated structural model that sits outside the DSGE tradition. It prioritizes empirical fit and institutional detail, with less emphasis on fully micro-founded optimization.
The model reflects the Fed's pragmatic approach to policy analysis. It replaced the MPS model in 1996 to modernize the macroeconometric framework and improve expectations handling.
Source: Federal Reserve FRB/US Project Page
The distinction matters for interpreting outputs and limitations:
DSGE models often calibrate key parameters and then evaluate fit. FRB/US estimates most parameters from aggregate data, improving empirical fit at some cost to structural interpretation.
FRB/US combines theory-consistent long-run relationships with empirical short-run dynamics. The consumption block blends lifecycle behavior with a rule-of-thumb component to approximate heterogeneity.
FRB/US embeds U.S. institutional details that are often abstracted in DSGE models:
The model can run under different expectation assumptions without re-estimation. Staff can compare VAR-based expectations with model-consistent expectations to test robustness.
Monetary policy operates through multiple channels with different lag structures:
| Channel | Mechanism | Peak Impact | Model Representation |
|---|---|---|---|
| Interest Rate Channel | Cost of capital → Investment, Housing | 4-6 quarters | User cost elasticities: $\epsilon_{I,r} \approx -1.0$ |
| Asset Price Channel | Equity valuations → Wealth → Consumption | 6-8 quarters | Wealth effect: $\partial C / \partial W \approx 0.03$ |
| Exchange Rate Channel | Rate differential → Dollar → Net exports | 3-5 quarters | Trade elasticity: $\epsilon_{NX,e} \approx -0.3$ |
| Expectations Channel | Forward guidance → Future rates → Current decisions | 1-3 quarters | Expectational terms in Euler equations |
| Credit Channel | Bank capital → Lending standards → Credit availability | 3-6 quarters | Financial accelerator via risk spread |
Solution Algorithm:
# Pseudo-code for FRB/US solution
1. Linearize system around steady state
2. For t = 1 to T:
a. Compute expectations: E_t[X_{t+1}] using VAR or RE
b. Solve non-linear block (pricing, investment) via Newton-Raphson
c. Solve linear block (identities, AR processes) analytically
d. Check convergence: ||X_t - X_t^{prev}|| < tolerance
3. If not converged, update and iterate
# Key parameters from estimation:
- Consumption smoothing: σ ≈ 2.0 (IES = 0.5)
- Calvo pricing: θ ≈ 0.75 (avg. 4-quarter price duration)
- Phillips curve slope: κ ≈ 0.01 (very flat)
- Taylor rule: ψ_π ≈ 1.5, ψ_y ≈ 0.5
Advantages relative to DSGE models:
Advantages relative to VAR/reduced-form models:
Key limitations (discussed in detail below):
FRB/US separates desired behavior from the frictions that slow adjustment. The gap between targets and actual outcomes drives the economy's dynamics.
Layer 1 - Long-run targets: Households and firms choose desired spending, hiring, and pricing based on incentives and expected income.
Layer 2 - Adjustment frictions: Financing, construction, and information delays slow the move toward those targets.
Households smooth consumption over time based on income, wealth, and interest rates.
Example: A prospective buyer evaluates:
The model aggregates these decisions into housing demand and consumption.
Firms hire and invest based on expected demand and financing costs.
Example: A manufacturer considering a new plant tracks:
Aggregated decisions drive employment, investment, and output.
Firms adjust prices infrequently because changes are costly. That is why inflation responds with a lag.
In practice: Firms update prices in batches, not continuously, which makes inflation gradual rather than immediate.
Expectations shape spending, pricing, and wage decisions today.
Fed Communication Matters: When the Fed signals a policy path, it shifts behavior immediately:
The model traces a feedback loop:
FRB/US decomposes behavior into optimization-based targets and empirical adjustment dynamics, combining tractability with strong empirical fit.
Financial markets are assumed to clear instantaneously via no-arbitrage conditions. The term structure of interest rates follows:
where $R_{t,n}$ is the n-period rate, $r_t$ is the one-period policy rate, and $\theta_{t,n}$ is a time-varying term premium. The term premium follows an AR(1) process estimated via Kalman filter:
Equity pricing follows a Gordon growth model with time-varying discount rates:
where $D_t$ are dividends, $g_t^D$ is expected dividend growth, $\phi_{eq}$ is the equity risk premium (estimated at 4.5% annually), and $\omega_t$ captures time-varying risk appetite.
Exchange rates obey modified uncovered interest parity:
where $\psi_t$ represents deviations from UIP (risk premium, safe-haven flows) estimated to have half-life of ~3 quarters.
Household Optimization:
Representative household maximizes discounted utility over infinite horizon:
subject to the intertemporal budget constraint:
The first-order condition yields the consumption Euler equation:
Assuming CRRA utility $U(C,L) = \frac{C^{1-\sigma}}{1-\sigma} + \psi \frac{(1-L)^{1-\nu}}{1-\nu}$, this becomes:
Log-linearizing around steady state:
where $\sigma \approx 2.0$ (estimated), implying intertemporal elasticity of substitution $1/\sigma = 0.5$.
Firm Optimization:
Firms maximize present value of profits using production function:
Capital accumulation follows:
FOC for capital yields the neoclassical investment equation:
where $MPK_t = \alpha A_t (K_t/L_t)^{\alpha-1}$ is the marginal product of capital and $P_t^I$ is the price of investment goods.
Price Setting: Firms face Calvo pricing with probability $\theta$ of being unable to adjust prices each period. The Phillips curve derivation yields:
where $\kappa = \frac{(1-\theta)(1-\beta\theta)}{\theta}$ and $mc_t$ are real marginal costs. With estimated $\theta \approx 0.75$, average price duration is $\frac{1}{1-\theta} = 4$ quarters.
The empirical Phillips curve in FRB/US incorporates additional persistence and indexation:
where $\gamma_f \approx 0.24$, $\gamma_b \approx 0.76$, $\kappa \approx 0.01$ (very flat), $\mu \approx 0.08$.
Wage Setting: Similar Calvo mechanism for wages yields:
with wage Phillips curve slope $\phi_u \approx 0.015$ and inflation pass-through $\phi_\pi \approx 0.60$.
FRB/US allows flexible expectations via three modes:
VAR-Based (Backward-Looking):
where $X_t$ contains endogenous variables and $Z_t$ contains exogenous variables. VAR parameters $\{\Phi_h, \Psi_h\}$ estimated via OLS on historical data.
Model-Consistent (Rational Expectations):
Expectations solved simultaneously with model via Newton-Raphson algorithm. For any variable $X$:
where $f_h$ is the h-step ahead model solution and $\theta$ contains structural parameters.
Hybrid: Convex combination of VAR and RE:
with $\lambda$ typically set to 0.75, reflecting survey evidence that most agents use adaptive rather than fully rational expectations.
The full model can be written in compact state-space form:
where $A_0, A_1, A_2 \in \mathbb{R}^{365 \times 365}$ are sparse matrices (90% zeros) containing structural parameters, $B \in \mathbb{R}^{365 \times 40}$ maps exogenous shocks, and $\epsilon_t$ are structural innovations.
Computational Implementation:
# Solution algorithm (simplified)
function solve_frbusmodel(params, exog_path, T):
X = initialize_state_vector()
for t in 1:T:
# 1. Form expectations
if expectations_mode == "VAR":
E_X = VAR_forecast(X[1:t], params.VAR)
elif expectations_mode == "RE":
E_X = RE_solve(X, params, t)
# 2. Solve for current period
# Non-linear block (4 key equations)
X_nl = newton_raphson(
F_nonlinear, X0=X[t-1],
args=(E_X, exog_path[t], params)
)
# Linear block (rest of model)
X_linear = sparse_solve(
A_linear,
b=B*exog_path[t] + C*X_nl
)
X[t] = [X_nl; X_linear]
return X
end
# Typical performance:
# - Single simulation: ~0.5 seconds (365 vars, 200 quarters)
# - Stochastic simulation (1000 draws): ~10 minutes
# - Full parameter estimation: ~2 hours on 32-core cluster
This section explains how the model treats household spending, saving, housing, and labor supply.
Households balance current spending against future needs. The model assumes decisions reflect lifetime income, not just today's paycheck.
Scenario: A new graduate starts a job paying $50,000 a year.
Near-term view: "I should keep payments low."
Lifetime view: "Expected earnings rise over time, so borrowing modestly can be affordable."
The model aggregates these decisions into overall consumption and saving.
In economics: This is called consumption smoothing: spending is steadier than income over the life cycle.
Housing is the largest purchase for most households. Mortgage rates therefore matter disproportionately.
| Mortgage Rate | Monthly Payment ($400K home) | Annual Difference |
|---|---|---|
| 6.0% | $2,398 | Baseline |
| 7.0% | $2,661 | +$3,156/year |
| 8.0% | $2,935 | +$6,444/year |
Higher rates raise monthly payments and reduce demand; the model maps that into lower housing activity.
People decide how much to work based on wages and preferences for leisure.
At $15/hour, someone might work 30 hours a week. At $25/hour, some will work more hours, while others choose more leisure. The model captures the average response.
| Average Household Income: | $78,500/year (up 3.8% from 2024) |
| Savings Rate: | 4.2% of disposable income |
| Household Debt: | $17.5 trillion total ($12.1T mortgages, $1.6T auto, $1.6T credit cards) |
| Wealth: | Average household net worth: $1.06 million |
What this means: Household balance sheets are solid but sensitive to interest rates. Higher borrowing costs weigh on housing and credit growth.
The household sector covers consumption, housing, portfolio allocation, and labor supply. The model uses a lifecycle framework with heterogeneity approximated by weighted aggregation.
Aggregate consumption is modeled as a weighted average of forward-looking (lifecycle) and backward-looking (rule-of-thumb) components:
Lifecycle Component ($C_t^{LC}$):
Derived from intertemporal optimization with log-linearized Euler equation:
where $w_t$ is household wealth (financial + human capital). Human capital is computed as the PDV of expected labor income:
Rule-of-Thumb Component ($C_t^{RT}$):
Constrained households consume a fixed fraction of current disposable income:
This specification implies the following MPCs and wealth effects:
Housing Demand:
Real housing demand (stock) determined by user cost of housing capital:
where the user cost is:
with estimated elasticities $\beta_1 \approx 1.0$ (unit income elasticity), $\beta_2 \approx -0.5$ (user cost elasticity).
Residential Investment:
Housing investment (flow) responds to gap between desired and actual stock:
where $\phi \approx 0.15$ (slow adjustment due to construction lags) and $\psi \approx 2.5$ (accelerator effect).
Aggregate labor supply (hours) is derived from utility maximization over consumption and leisure. The labor supply elasticity to real wages is:
This low elasticity reflects offsetting income and substitution effects. Participation elasticity is higher at $\approx 0.5$, particularly for secondary earners.
# Household Sector State (Q4 2025)
Consumption_total = 14.8 # $ trillion, real 2017 dollars
Disposable_income = 17.9 # $ trillion, real
Savings_rate = 0.042 # 4.2% of disposable income
# Wealth composition
Financial_wealth = 85.3 # $ trillion (stocks, bonds, deposits)
Housing_wealth = 47.8 # $ trillion (home equity)
Total_wealth = 133.1 # $ trillion
# Debt
Mortgage_debt = 12.1 # $ trillion
Consumer_credit = 5.1 # $ trillion (auto, cards, student)
Debt_service_ratio = 0.094 # 9.4% of disposable income
# Housing market
Home_prices = 329000 # $ median existing home
Mortgage_rate = 0.072 # 7.2% 30-year fixed
Housing_starts = 1.42 # million units, SAAR
# Labor market
Participation_rate = 0.625 # 62.5% of working-age population
Hours_worked = 34.3 # average weekly hours
Real_wage_growth = 0.018 # 1.8% y/y
# Key elasticities (estimated)
epsilon_C_r = -0.12 # consumption to real rate (semi-elasticity)
epsilon_H_r = -0.50 # housing to user cost
epsilon_L_w = 0.25 # labor to real wage
MPC_transitory = 0.40 # marginal propensity to consume
wealth_effect = 0.03 # consumption to wealth
| Quarter | Consumption (% chg) | Res. Investment (% chg) | Hours Worked (% chg) | Saving Rate (pp chg) |
|---|---|---|---|---|
| Q1 | -0.1 | -1.2 | -0.05 | +0.2 |
| Q4 | -0.4 | -4.5 | -0.18 | +0.4 |
| Q8 | -0.6 | -5.2 | -0.25 | +0.3 |
| Q12 | -0.5 | -3.8 | -0.20 | +0.1 |
Note: Housing responds faster than consumption because of leverage and the durability of housing capital. Consumption effects peak later as wealth effects accumulate.
This section covers how businesses make decisions about production, hiring, investment, and pricing.
Firms try to match production to demand, but output adjusts with lags because supply chains and staffing take time.
A toy manufacturer sees orders rise in October. Production increases only after:
The model captures these lags between demand and output.
Hiring is costly and uncertain, so firms adjust cautiously.
In practice: Firms often use overtime before adding permanent staff, and hire only once demand looks durable.
Cost to hire one employee:
Average salary is $60,000/year with $15,000 in benefits. Hiring is a long-term commitment.
Model implication: Employment typically lags output because firms wait for sustained demand.
Large investments take time and depend on expected demand and financing costs:
Scenario: A company considers a $10 million factory expansion.
| Interest Rate | Annual Loan Cost | ROI Needed | Decision |
|---|---|---|---|
| 3% | $300,000 | >5% | Proceed |
| 5% | $500,000 | >7% | Cautious |
| 7% | $700,000 | >9% | Postpone |
Higher rates raise the hurdle for investment and slow capital spending.
Firms do not change prices continuously because doing so is costly and risks customer backlash.
Costs of changing prices:
Model implication: Prices change infrequently, so inflation responds to policy with a lag.
| Business Investment: | $3.1 trillion/year (down 5% from 2023 peak) |
| Corporate Profits: | $2.8 trillion/year (profit margin: 11.2%) |
| Business Lending Rate: | 8.3% average (up from 4.5% in 2021) |
| Capacity Utilization: | 78.5% (below historical 80% average) |
What this means: Higher borrowing costs have cooled investment. Firms are using existing capacity rather than expanding, consistent with policy restraint.
The firm sector covers production, factor demand, price setting under nominal rigidities, and investment with adjustment costs. The model uses standard neoclassical production with Calvo pricing and Tobin's Q investment.
Aggregate production follows Cobb-Douglas with labor-augmenting technical progress:
where $K_t$ is capital stock, $L_t$ is employment, $H_t$ is hours per worker, and $A_t$ is labor productivity. Estimated output elasticity $\alpha \approx 0.33$ (consistent with capital share of income).
Productivity evolves as:
with trend growth $\mu_A \approx 0.005$ (2.0% annualized) and persistence $\rho_A \approx 0.3$.
Capital Stock Dynamics:
with depreciation rate $\delta \approx 0.025$ (10% annualized, weighted average of structures and equipment).
Investment Function:
Desired capital stock derived from profit maximization:
where user cost of capital is:
with $\tau_c$ corporate tax rate (currently 21%), $ITC$ investment tax credit, and $\pi_t^I$ capital gains on investment goods.
Actual investment follows Tobin's Q with adjustment costs:
where:
Estimated parameters:
Optimal Employment:
From production function, labor demand satisfies:
Log-linearizing yields labor demand:
Long-run elasticity of labor demand to real wages: $\epsilon_{L,W} = -\frac{1}{\alpha} \approx -3.0$.
Hours Adjustment:
Firms can adjust hours faster than headcount. The model specifies heterogeneous adjustment speeds:
with $\lambda_h \approx 0.33$ (one-third immediate adjustment via overtime, two-thirds gradual).
Employment adjustment is slower due to hiring and firing costs:
with $\lambda_\ell \approx 0.10$ (roughly 10 quarters to close the gap) and $\psi \approx 0.3$ (immediate response to output growth).
Calvo Pricing Framework:
Each period, fraction $\theta$ of firms cannot adjust prices. Optimizing firms set price $P_t^*$ to maximize:
First-order condition yields optimal markup:
Log-linearizing and aggregating yields the New Keynesian Phillips Curve:
where $\kappa = \frac{(1-\theta)(1-\beta\theta)}{\theta} \cdot \frac{1-\alpha}{1-\alpha+\alpha\epsilon}$.
Empirical Implementation:
The baseline FRB/US Phillips curve incorporates indexation and additional state variables:
Estimated parameters (2024 vintage):
The flat Phillips curve implies larger output gaps are needed for disinflation, which helps explain slow progress in recent years.
# Firm Sector State (Q4 2025)
GDP_real = 22.8 # $ trillion, 2017 dollars
Capital_stock = 48.2 # $ trillion, private nonresidential
Investment_rate = 0.128 # I/K ratio (12.8% of capital stock)
Depreciation_rate = 0.025 # quarterly (10% annualized)
# Production
Capacity_utilization = 0.785 # 78.5%
Labor_productivity = 2.1 # % growth rate
TFP_growth = 0.8 # % growth rate
# Employment
Employment_total = 159.2 # millions
Hours_weekly = 34.3 # average per worker
Unemployment_rate = 0.040 # 4.0%
# Pricing
Markup = 1.18 # Price/Marginal cost (18% markup)
Inflation_core_PCE = 0.026 # 2.6% y/y
Wage_inflation = 0.045 # 4.5% y/y
# Investment
Business_investment = 3.1 # $ trillion/year
User_cost_capital = 0.082 # 8.2%
Tobin_Q = 1.05 # slightly above replacement cost
# Corporate finance
Corporate_profits = 2.8 # $ trillion/year
Profit_margin = 0.112 # 11.2% of sales
Corporate_debt = 10.5 # $ trillion
Interest_coverage = 8.2 # EBIT/Interest expense
# Key elasticities (estimated)
epsilon_K_r = -1.00 # capital to user cost
epsilon_I_Q = 0.04 # investment to Tobin's Q
epsilon_L_W = -3.00 # labor to real wage
Phillips_slope = 0.009 # inflation to output gap
| Quarter | Investment (% chg) | Employment (% chg) | Capacity Util. (pp chg) | Core Inflation (pp chg) |
|---|---|---|---|---|
| Q1 | -0.8 | -0.02 | -0.3 | -0.01 |
| Q4 | -3.2 | -0.18 | -1.1 | -0.08 |
| Q8 | -4.5 | -0.42 | -1.5 | -0.22 |
| Q12 | -3.1 | -0.38 | -1.2 | -0.35 |
| Q16 | -1.8 | -0.25 | -0.7 | -0.42 |
Note: Investment responds earlier than employment, while inflation responds slowly given a flat Phillips curve.
Expectations are central: what people anticipate about inflation and growth influences wages, prices, and spending.
Expectations can be self-fulfilling when many actors respond to the same belief.
If workers expect higher inflation, they seek higher wages, and firms raise prices to cover costs. Those actions can validate the expectation.
Many households extrapolate from recent experience.
2019-2021: Inflation near 2% for several years
Typical expectation: "Inflation will stay around 2%"
2022: Inflation spikes toward 9%
Updated expectation: "Inflation may stay high"
2024-2025: Inflation cools to about 2.6%
Current expectation: "Inflation is easing but still above target"
This approach is simple but adjusts slowly.
Some households and most businesses pay attention to Fed guidance and projections.
Each quarter the Fed publishes its interest-rate projections ("dot plot"). When that path shifts, markets adjust quickly:
These moves occur before policy changes take effect.
More sophisticated actors use models and policy rules to form forward-looking expectations.
This approach is more complex and is the basis for the model's "rational expectations" option.
Early 2021: The Fed described inflation as transitory
→ Expectations remained contained
→ Wage and price adjustments were limited
Late 2021: Inflation persisted longer than expected
→ Expectations rose
→ Wages and prices adjusted more aggressively
Lesson: Weaker credibility raises the cost of disinflation. The model shows larger rate increases are needed to achieve the same result.
Household Inflation Expectations (Michigan Survey):
Market-Based Expectations (from bonds):
Professional Forecasters:
What this means: Long-term expectations remain near the Fed's 2% target, while short-term expectations are elevated. That mix supports a restrictive policy stance.
Expectations formation is a key driver of dynamics. The model supports multiple expectation modes to test how assumptions affect policy transmission.
Expectations formed via reduced-form vector autoregression estimated on historical data:
where $X_t$ contains endogenous variables (GDP, inflation, rates, etc.) and $Z_t$ contains exogenous variables. The VAR is estimated via OLS with lag length $p$ selected via BIC (typically $p=4$ quarters).
Properties:
Multi-step ahead forecasts:
Agents use the model itself to form expectations. For any variable $X_{t+h}$:
where $f_h$ is the h-step ahead model solution, $S_t$ is the current state vector, $\theta$ are structural parameters, and $\{Z_{t+j}\}$ is the path of exogenous variables.
Solution Algorithm:
# Model-consistent expectations solution (Newton-Raphson)
function solve_RE(model, T_horizon):
X = initialize_guess() # Initial trajectory
max_iter = 100
tolerance = 1e-6
for iter in 1:max_iter:
X_old = copy(X)
# Forward pass: compute expectations
for t in 1:T_horizon:
E_X[t] = model_solution(X[t+1:T_horizon])
# Backward pass: solve equilibrium conditions
for t in T_horizon:-1:1:
# Solve simultaneous system
X[t] = newton_solve(
F(X[t], X[t-1], E_X[t]) = 0,
jacobian = compute_jacobian()
)
# Check convergence
if norm(X - X_old) < tolerance:
break
return X, E_X
end
Properties:
Convex combination of VAR and RE expectations:
Default specification uses $\lambda = 0.75$ (75% adaptive, 25% rational), reflecting survey evidence that most agents use simple forecasting rules.
Rationale from micro data:
The degree of forward vs. backward-looking behavior critically affects inflation dynamics:
With estimated weights $\gamma_f = 0.24$, $\gamma_b = 0.76$, the Phillips curve is highly backward-looking, implying:
Alternative specification (2024 vintage):
Using 4-quarter ahead expectations rather than 1-quarter increases $\gamma_f$ to ~0.35, still dominated by backward-looking component.
Long-run inflation expectations modeled as:
where $\pi^* = 0.02$ is the Fed's target, $\phi \approx 0.95$ (highly persistent), and $\psi \approx 0.02$ (slow learning from actual inflation).
Interpretation: Long-run expectations are well-anchored but not perfectly so. Sustained inflation deviations gradually shift long-run expectations, capturing the risk of de-anchoring observed in 2021-2023.
FRB/US can be augmented with survey-based expectation measures:
where $\omega \in [0,1]$ controls the weight on surveys vs. model-generated expectations.
Survey sources:
# Expectations State Variables (Q4 2025)
# Consumer expectations (Michigan Survey)
inflation_1yr_ahead = 0.032 # 3.2%
inflation_5yr_ahead = 0.029 # 2.9%
# Professional forecasters (SPF)
GDP_growth_2026 = 0.022 # 2.2%
inflation_2026 = 0.023 # 2.3%
unemployment_2026 = 0.042 # 4.2%
fed_funds_2026Q4 = 0.045 # 4.5%
# Market-implied expectations (from TIPS)
breakeven_5yr = 0.024 # 2.4%
breakeven_10yr = 0.023 # 2.3%
breakeven_30yr = 0.024 # 2.4%
# Forward rates (expectations + term premium)
forward_1y1y = 0.038 # 1-year rate, 1 year ahead: 3.8%
forward_5y5y = 0.035 # 5-year rate, 5 years ahead: 3.5%
# Dealer survey (expected Fed path)
expected_cuts_2026 = 3 # Number of 25bp cuts
terminal_rate = 0.035 # Long-run neutral rate: 3.5%
# Model-internal expectations (VAR-based)
E_inflation_4q = 0.027 # 4-qtr ahead inflation: 2.7%
E_GDP_growth_4q = 0.021 # 4-qtr ahead growth: 2.1%
E_unemployment_4q = 0.041 # 4-qtr ahead unemployment: 4.1%
# Anchoring metrics
LR_inflation_exp = 0.024 # Long-run inflation expectations: 2.4%
anchoring_index = 0.85 # Index ∈ [0,1], 1 = perfectly anchored
dispersion_inflation = 0.012 # Cross-sectional std of forecasts: 1.2pp
# Expectation revision statistics
correlation_revision_actual = 0.65 # Forecast errors partly predictable
mean_absolute_error_1yr = 0.015 # 1-year ahead MAE: 1.5pp
rational_expectations_test_pvalue = 0.08 # Weak evidence of rationality
| Expectation Type | Inflation Persistence | Sacrifice Ratio | Forward Guidance Effect |
|---|---|---|---|
| Pure Adaptive (VAR) | High (0.95) | 3.5 | Weak (10% of RE) |
| Rational Expectations | Low (0.65) | 1.2 | Strong (full effect) |
| Hybrid (75/25) | Medium (0.88) | 2.8 | Moderate (35% of RE) |
| Empirical (FRB/US est.) | High (0.92) | 3.2 | Weak-Moderate (25%) |
Note: Sacrifice ratio = cumulative output loss (%-years) per percentage point permanent disinflation. Higher backward-looking weight → higher sacrifice ratio.
The model is only as good as its inputs. Accurate, timely data are essential for useful simulations.
Data are the model's ingredients. Weak or stale data lead to weak output.
| Agency | What They Measure | Update Frequency |
|---|---|---|
| Bureau of Labor Statistics (BLS) | Unemployment, jobs, wages, inflation (CPI) | Monthly |
| Bureau of Economic Analysis (BEA) | GDP, personal income, consumer spending | Quarterly |
| Census Bureau | Population, housing, business activity | Monthly/Annual |
| Federal Reserve | Interest rates, money supply, industrial production | Daily/Monthly |
| Treasury Department | Government debt, tax revenue | Daily/Monthly |
Not all inputs are public statistics:
| Real GDP: | $22.8 trillion (2017 dollars) | Growing at 2.4% annually |
| Unemployment Rate: | 4.0% | Low by historical standards |
| Labor Force Participation: | 62.5% | Still below pre-COVID 63.4% |
| Wage Growth: | 4.5% year-over-year | Moderating from 6% peak |
| Core PCE Inflation: | 2.6% year-over-year | Fed's preferred measure |
| CPI Inflation: | 3.2% year-over-year | What consumers see |
| Oil Price (WTI): | $82/barrel | Affects energy costs |
| Fed Funds Rate: | 5.25% | Fed's main policy tool |
| 10-Year Treasury: | 4.45% | Benchmark for mortgages |
| 30-Year Mortgage Rate: | 7.20% | Critical for housing |
| S&P 500: | 4,750 | Wealth effect on spending |
| Dollar Index: | 104.2 | Strong dollar = cheaper imports |
1. Revisions: GDP data are revised multiple times as more information arrives.
2. Time Lags: Some data is reported with delays:
3. Seasonal Adjustments: The economy naturally fluctuates with seasons (retail booms at Christmas). Statisticians adjust for this, but it's not perfect.
4. Measurement Errors: Surveys of confidence or expectations can be noisy.
Bottom Line: The model works with imperfect data, which is one reason forecasts are uncertain. Staff monitor revisions and adjust when data change.
FRB/US uses roughly 100 exogenous variables and 365 endogenous variables drawn from official statistics, market prices, and surveys, with attention to revisions, seasonal adjustment, and measurement error.
| Variable | Symbol | Frequency | Revision Schedule |
|---|---|---|---|
| Real GDP | $Y_t$ | Quarterly | 3 releases, then annual revisions |
| Personal Consumption Expenditures | $C_t$ | Quarterly | Synchronized with GDP |
| Gross Private Domestic Investment | $I_t$ | Quarterly | Major revisions possible |
| PCE Price Index (Core) | $\pi_t$ | Monthly | Minor revisions only |
| Corporate Profits | $\Pi_t$ | Quarterly | Subject to benchmark revisions |
| Variable | Symbol | Frequency | Sample Size / Coverage |
|---|---|---|---|
| Nonfarm Payroll Employment | $L_t$ | Monthly | ~130K establishments |
| Unemployment Rate | $u_t$ | Monthly | 60K household survey |
| Average Hourly Earnings | $W_t$ | Monthly | Production workers |
| Employment Cost Index | $ECI_t$ | Quarterly | Fixed job composition |
| CPI (All Urban Consumers) | $CPI_t$ | Monthly | ~80K price quotes |
| Labor Productivity | $A_t$ | Quarterly | Output per hour |
| Variable | Symbol | Frequency | Source System |
|---|---|---|---|
| Federal Funds Rate | $r_t^{FF}$ | Daily | H.15 Statistical Release |
| Treasury Yield Curve | $R_{t,n}$ | Daily | H.15 (constant maturity) |
| Corporate Bond Yields | $R_t^{corp}$ | Daily | Moody's / ICE BofA indices |
| Mortgage Rates | $R_t^{mort}$ | Weekly | Freddie Mac survey |
| Industrial Production | $IP_t$ | Monthly | G.17 Statistical Release |
| Capacity Utilization | $CU_t$ | Monthly | G.17 (manufacturing) |
Seasonal Adjustment:
Most series are seasonally adjusted using X-13ARIMA-SEATS:
where $S_t$ = seasonal factor, $TD_t$ = trading day adjustment, $H_t$ = holiday adjustment.
Chain-Weighting for Real Variables:
Real GDP and components use Fisher ideal chain-weighting to handle changing price structures:
Treatment of Revisions:
The model uses a "final revised" data vintage for estimation, but real-time forecasting must account for data uncertainty:
with revision variance $\sigma_{rev}^2$ estimated from historical revision patterns. For GDP, typical revision std dev ~0.5pp.
# Complete Input Data State (Q4 2025)
# Real Economy
GDP_real = 22.82 # $ trillions, 2017 dollars
GDP_nominal = 28.91 # $ trillions, current dollars
GDP_deflator = 126.8 # Index, 2017 = 100
GDP_growth_qoq_ar = 0.024 # 2.4% annualized q/q growth
# Labor Market
employment_nonfarm = 159.2 # millions
unemployment_rate = 0.040 # 4.0%
participation_rate = 0.625 # 62.5%
NAIRU_estimate = 0.042 # 4.2% (CBO estimate)
job_openings = 8.1 # millions (JOLTS)
quits_rate = 0.023 # 2.3% monthly
layoffs_rate = 0.011 # 1.1% monthly
# Wages and Productivity
avg_hourly_earnings = 35.20 # $/hour
wage_growth_yoy = 0.045 # 4.5%
ECI_growth = 0.042 # 4.2% (better measure)
productivity_growth = 0.021 # 2.1% y/y
unit_labor_cost_growth = 0.024 # 2.4% y/y
# Prices
PCE_inflation_headline = 0.028 # 2.8% y/y
PCE_inflation_core = 0.026 # 2.6% y/y (Fed's target)
CPI_inflation_headline = 0.032 # 3.2% y/y
CPI_inflation_core = 0.038 # 3.8% y/y
PPI_finished_goods = 0.022 # 2.2% y/y
import_prices_growth = -0.005 # -0.5% y/y (strong dollar)
# Consumption and Investment
personal_consumption = 15.78 # $ trillions
personal_income = 24.51 # $ trillions
saving_rate = 0.042 # 4.2%
retail_sales_growth = 0.032 # 3.2% y/y
gross_private_investment = 4.82 # $ trillions
residential_investment = 0.89 # $ trillions
nonresidential_investment = 3.93 # $ trillions
business_equipment = 1.65 # $ trillions
structures = 0.76 # $ trillions
# Housing
housing_starts = 1.42 # millions, SAAR
existing_home_sales = 4.1 # millions, SAAR
median_home_price = 412000 # $
months_supply = 3.8 # Months of inventory
mortgage_rate_30yr = 0.072 # 7.2%
# Financial Markets
fed_funds_rate = 0.0525 # 5.25%
treasury_2yr = 0.0475 # 4.75%
treasury_10yr = 0.0445 # 4.45%
corporate_AAA_yield = 0.0565 # 5.65%
corporate_BAA_yield = 0.0635 # 6.35%
credit_spread_BAA_AAA = 0.0070 # 70bp
SP500_level = 4750
SP500_PE_forward = 21.2
VIX_volatility = 16.5
equity_risk_premium = 0.045 # 4.5% estimated
# Exchange Rates (foreign currency per USD)
EUR_USD = 1.052
GBP_USD = 1.248
JPY_USD = 148.5
CNY_USD = 7.28
CAD_USD = 1.382
trade_weighted_broad = 104.2
# Fiscal
federal_deficit = 1.45 # $ trillions
debt_held_public = 28.2 # $ trillions
debt_GDP_ratio = 0.976 # 97.6%
government_purchases = 1.48 # $ trillions
transfer_payments = 3.92 # $ trillions
# Energy
oil_WTI = 82.0 # $/barrel
natural_gas = 3.2 # $/mmBTU
gasoline_retail = 3.45 # $/gallon
# Global
world_GDP_growth = 0.031 # 3.1%
EU_growth = 0.008 # 0.8%
China_growth = 0.048 # 4.8%
emerging_markets_growth = 0.042 # 4.2%
# Surveys and Expectations
michigan_inflation_1yr = 0.032 # 3.2%
michigan_inflation_5yr = 0.029 # 2.9%
SPF_GDP_2026 = 0.022 # 2.2%
SPF_inflation_2026 = 0.023 # 2.3%
consumer_confidence = 102.5 # Index
business_confidence_ISM = 48.8 # <50 = contraction
# Data quality metrics
GDP_revision_std = 0.005 # 0.5pp typical revision
employment_revision_std = 75000 # jobs
inflation_measurement_error = 0.003 # 0.3pp
Several variables are treated as exogenous (determined outside the model):
| Variable | Treatment | Baseline Path (2026) | Sensitivity |
|---|---|---|---|
| Oil Prices | Exogenous | $78/barrel (declining) | ±$10 → ±0.15pp inflation |
| Foreign Demand | Exogenous | 3.0% growth | ±1pp → ±0.3pp U.S. growth |
| Fiscal Policy | Exogenous | $1.6T deficit | $500B change → ±0.8pp GDP |
| Productivity Trend | Exogenous | 1.8% annually | ±0.5pp → ±0.5pp potential GDP |
| Labor Force Growth | Demographic model | 0.4% annually | Tied to population projections |
Measurement Error Variance:
These error variances are incorporated into stochastic simulations and forecast confidence intervals.
This section illustrates how the model turns current data into a baseline forecast and alternative scenarios.
The model produces conditional projections given assumptions about policy and shocks. It is a structured "what-if," not a promise.
The baseline assumes rates stay at 5.25% through mid-2026, then ease to 4.50% by end-2026 and to 3.50% by late 2027.
Q4 2025 → Q1 2026: Restrictive Policy Bites
Q2-Q4 2026: The Fed Starts Cutting
2027: Soft Landing
| Period | GDP Growth | Unemployment | Inflation | Fed Funds Rate |
|---|---|---|---|---|
| Now (Q4 2025) | 2.4% | 4.0% | 2.6% | 5.25% |
| End 2026 | 2.1% | 4.2% | 2.3% | 4.50% |
| End 2027 | 2.0% | 4.2% | 2.1% | 3.50% |
| Long Run (Sustainable) | 2.0% | 4.2% | 2.0% | 3.50% |
Interpretation: The baseline implies a soft landing: inflation falls without a recession, growth stays positive, and unemployment rises modestly.
What if: Inflation stays near 3% instead of falling to 2%?
Model prediction:
Lesson: Persistent inflation raises the risk of a more pronounced slowdown.
What if: A financial shock hits in 2026?
Model prediction:
Lesson: The recovery path depends heavily on the policy response.
What if: Productivity growth rises from 1.8% to 3.0%?
Model prediction:
Lesson: Faster productivity growth eases trade-offs between inflation and output.
Looking at past FRB/US forecasts compared to what actually happened:
Translation: Forecast accuracy declines with horizon. Shocks can dominate any baseline.
Fed's perspective: The model helps frame ranges and trade-offs, not precise outcomes.
This section provides a worked forecast using Q4 2025 data with explicit assumptions and methodology.
Policy Assumptions:
with terminal (neutral) rate $r^* = 0.035$ reached by 2027:Q4.
Fiscal Assumptions:
Exogenous Variable Paths:
# Full Quarterly Forecast: Q4 2025 through Q4 2028
Quarter GDP_gr Unemp Infl_PCE FF_Rate 10Y_Tsy Cons_gr Inv_gr Home_pr
2025:Q4 2.4 4.0 2.6 5.25 4.45 2.8 1.2 412000
2026:Q1 1.8 4.1 2.5 5.25 4.38 2.2 -0.8 408000
2026:Q2 1.9 4.1 2.4 5.25 4.32 2.3 0.2 405000
2026:Q3 2.0 4.2 2.3 5.00 4.18 2.4 1.5 403000
2026:Q4 2.1 4.2 2.3 4.50 3.95 2.5 2.8 405000
2027:Q1 2.2 4.2 2.2 4.25 3.85 2.6 3.2 408000
2027:Q2 2.1 4.2 2.1 4.00 3.75 2.5 3.0 412000
2027:Q3 2.0 4.2 2.1 3.75 3.68 2.4 2.5 415000
2027:Q4 2.0 4.2 2.1 3.50 3.60 2.3 2.2 418000
2028:Q1 2.0 4.2 2.0 3.50 3.58 2.3 2.0 420000
2028:Q2 2.0 4.2 2.0 3.50 3.55 2.3 2.0 422000
2028:Q3 2.0 4.2 2.0 3.50 3.55 2.3 2.0 424000
2028:Q4 2.0 4.2 2.0 3.50 3.55 2.3 2.0 426000
# All growth rates in % annualized, rates in %, prices in $
# GDP_gr = Real GDP growth
# Unemp = Unemployment rate
# Infl_PCE = Core PCE inflation
# FF_Rate = Federal Funds target
# 10Y_Tsy = 10-year Treasury yield
# Cons_gr = Real consumption growth
# Inv_gr = Real business investment growth
# Home_pr = Median existing home price
| Component | 2025 (pp) | 2026 (pp) | 2027 (pp) | 2028 (pp) |
|---|---|---|---|---|
| Personal Consumption | +1.9 | +1.6 | +1.6 | +1.6 |
| Business Investment | +0.2 | +0.3 | +0.5 | +0.4 |
| Residential Investment | -0.1 | +0.1 | +0.2 | +0.1 |
| Government | +0.4 | +0.3 | +0.2 | +0.2 |
| Net Exports | -0.2 | -0.3 | -0.4 | -0.3 |
| Inventory Change | +0.2 | 0.0 | -0.1 | 0.0 |
| Total GDP Growth | +2.4 | +2.0 | +2.0 | +2.0 |
Scenario A: "Persistent Inflation" (Adverse)
Assumptions: Core PCE stays at 3.0% through 2026, requiring more aggressive Fed response.
# Alternative Scenario A: Persistent Inflation
Quarter GDP_gr Unemp Infl_PCE FF_Rate Deviation_from_Base
2026:Q1 1.4 4.2 3.0 5.25 -0.4pp GDP
2026:Q2 1.2 4.3 2.9 5.50 -0.7pp GDP
2026:Q3 0.8 4.6 2.8 5.75 -1.2pp GDP
2026:Q4 0.5 4.9 2.6 5.75 -1.6pp GDP
2027:Q1 0.8 5.2 2.4 5.50 -1.4pp GDP
2027:Q2 1.2 5.3 2.2 5.00 -0.9pp GDP
2027:Q3 1.8 5.1 2.1 4.50 -0.2pp GDP
2027:Q4 2.0 4.8 2.0 4.00 0.0pp GDP
# Sacrifice ratio realized: ~3.2 (consistent with model calibration)
# Cumulative output loss: ~4.5pp-years
# Peak unemployment: 5.3% (vs 4.2% baseline)
Scenario B: "Financial Stress" (Tail Risk)
Assumptions: Credit spread shock of +300bp in 2026:Q2, lasting 3 quarters.
# Alternative Scenario B: Financial Crisis
Quarter GDP_gr Unemp Infl_PCE FF_Rate Credit_Spread
2026:Q1 0.8 4.3 2.4 5.25 180bp
2026:Q2 -2.1 4.8 2.0 4.50 480bp (shock)
2026:Q3 -1.5 5.5 1.5 3.00 420bp
2026:Q4 0.2 6.1 1.2 2.00 320bp
2027:Q1 2.8 6.0 1.4 2.00 220bp
2027:Q2 3.5 5.5 1.8 2.00 190bp
2027:Q3 3.2 5.0 2.0 2.25 180bp
2027:Q4 2.5 4.6 2.1 2.50 175bp
# Recovery profile: Sharp V-shape due to aggressive policy
# Peak-to-trough GDP: -3.6%
# Duration in recession: 2 quarters
# Time to return to baseline: ~10 quarters
Scenario C: "Productivity Surge" (Optimistic)
Assumptions: Trend productivity accelerates to 3.0% (AI-driven gains).
# Alternative Scenario C: Productivity Boom
Quarter GDP_gr Unemp Infl_PCE FF_Rate Real_Wage_gr
2026:Q1 2.8 3.9 2.3 5.25 5.2
2026:Q2 3.2 3.8 2.2 5.00 5.8
2026:Q3 3.5 3.7 2.1 4.75 6.1
2026:Q4 3.6 3.6 2.0 4.50 6.3
2027:Q1 3.5 3.6 2.0 4.25 6.2
2027:Q2 3.4 3.6 2.0 4.00 6.0
2027:Q3 3.3 3.6 2.0 3.75 5.8
2027:Q4 3.2 3.6 2.0 3.50 5.6
# Potential GDP grows at 3.2% (vs 2.0% baseline)
# No inflation pressure despite rapid growth
# Real wages accelerate substantially
# Policy can remain accommodative
Forecast uncertainty quantified via stochastic simulations (1000 draws):
| Variable | Horizon | 70% CI | 90% CI | Skewness |
|---|---|---|---|---|
| GDP Growth | 4 quarters | [1.0%, 3.2%] | [0.3%, 4.1%] | -0.15 |
| GDP Growth | 8 quarters | [0.8%, 3.5%] | [-0.5%, 4.8%] | -0.22 |
| Unemployment | 4 quarters | [3.8%, 4.6%] | [3.5%, 5.1%] | +0.35 |
| Unemployment | 8 quarters | [3.6%, 5.0%] | [3.2%, 5.8%] | +0.42 |
| Core PCE Inflation | 4 quarters | [1.8%, 2.8%] | [1.5%, 3.2%] | +0.18 |
| Core PCE Inflation | 8 quarters | [1.5%, 2.9%] | [1.2%, 3.5%] | +0.25 |
Note: Negative skewness for GDP (downside risks dominate), positive skewness for unemployment and inflation (upside risks dominate). Reflects asymmetric loss function and non-linearity of Phillips curve.
Root Mean Squared Errors (2000-2023):
| Variable | 1Q Ahead | 4Q Ahead | 8Q Ahead | vs. Naive Forecast |
|---|---|---|---|---|
| GDP Growth | 0.8pp | 1.5pp | 2.1pp | 28% improvement |
| Unemployment | 0.2pp | 0.5pp | 0.9pp | 35% improvement |
| Core PCE Inflation | 0.4pp | 0.8pp | 1.2pp | 22% improvement |
| Fed Funds Rate | 0.3pp | 0.8pp | 1.4pp | 15% improvement |
Directional Accuracy:
Bias Tests (Mincer-Zarnowitz Regression):
| Variable | $\hat{\alpha}$ | $\hat{\beta}$ | $H_0: (\alpha, \beta) = (0,1)$ p-value |
|---|---|---|---|
| GDP Growth (4Q) | 0.31 | 0.89 | 0.15 (no bias) |
| Inflation (4Q) | -0.18 | 1.08 | 0.22 (no bias) |
| Unemployment (4Q) | 0.42 | 0.91 | 0.08 (marginal bias) |
Interpretation: Forecasts are generally unbiased for GDP and inflation, slight upward bias for unemployment (tends to underpredict increases).
This section summarizes how the model is used in policy analysis, public communication, and stress testing.
The model does not make decisions. It helps staff compare outcomes under different assumptions and policy paths.
Monday-Tuesday:
Wednesday:
Thursday:
Meeting Day:
Each quarter the Fed publishes economic projections informed by model results and judgment.
What the Fed publishes:
Why it matters: Markets reprice quickly when the dot plot shifts:
Example (June 2022): The dot plot moved higher and mortgage rates rose quickly in response.
The Fed uses the model to design "severely adverse" scenarios for bank stress tests:
Typical stress scenario:
Banks must show: They have enough capital to absorb losses and keep lending.
Why it matters: Stress tests reduce the odds of another system-wide banking failure and help protect depositors.
The Crisis: The economy shut down abruptly in March 2020.
How the model helped:
Result: The policy response was large and the recovery was rapid by historical standards.
The Challenge: Inflation rose sharply, peaking near 9%.
Model's role:
Result (So Far): By late 2025, inflation had eased to about 2.6% without a recession, consistent with a soft landing.
The Crisis: A housing bust led to bank failures, a credit freeze, and a deep recession.
Model limitations exposed:
How this improved the model:
Lesson: Models evolve through experience and are updated after major shocks.
The model is a powerful tool, but it's not magic:
Bottom line: The model is one input among many, alongside market signals, surveys, and judgment.
The model evolves as the economy changes.
This section summarizes operational uses of FRB/US in policy deliberations, stress testing, and external research and market applications.
# Typical FOMC Cycle Policy Analysis (8 times per year)
## T-10 days: Data Compilation
- Collect latest releases: GDP, employment, inflation, financial data
- Perform seasonal adjustment and quality checks
- Update exogenous variable assumptions (oil, foreign demand, fiscal)
- Validate data consistency with NIPA identities
## T-7 days: Baseline Forecast Construction
# Generate baseline using VAR expectations
baseline = solve_frbusmodel(
mode = "VAR",
policy_rule = "inertial_Taylor",
horizon = 12_quarters,
initial_conditions = current_data,
exogenous_path = baseline_assumptions
)
# Alternative: RE expectations for selected scenarios
baseline_RE = solve_frbusmodel(
mode = "RE",
policy_rule = "optimal_commitment",
horizon = 12_quarters
)
## T-5 days: Alternative Policy Scenarios
scenarios = []
for policy_path in [
hold_current_rate_4qtrs,
cut_25bp_per_qtr,
hike_25bp_per_qtr,
outcome_based_rule
]:
scenario = solve_frbusmodel(
policy_path = policy_path,
mode = "VAR",
horizon = 12_quarters
)
scenarios.append(scenario)
## T-3 days: Stochastic Simulations
# Generate uncertainty quantification
stoch_results = run_stochastic_simulations(
n_draws = 1000,
shock_distribution = estimated_shock_cov,
forecast_horizon = 12_quarters
)
# Extract confidence bands
CI_70 = extract_quantiles(stoch_results, [0.15, 0.85])
CI_90 = extract_quantiles(stoch_results, [0.05, 0.95])
## T-2 days: Risk Assessment
# Asymmetric risks via scenario probability weights
downside_scenarios = [
"financial_stress": 0.15,
"persistent_inflation": 0.20,
"supply_shock": 0.10
]
upside_scenarios = [
"productivity_boom": 0.10,
"faster_disinflation": 0.15
]
risk_adjusted_forecast = compute_weighted_average(
[baseline] + scenarios,
weights = [0.50] + scenario_probs
)
## T-1 day: Prepare Briefing Materials
# Generate Tealbook charts and tables
- GDP growth fan chart with confidence intervals
- Inflation projection vs. target
- Unemployment gap visualization
- Taylor rule prescription vs. actual policy
- Alternative scenario comparisons
- Risk assessment summary
## Meeting Day: Presentation and Deliberation
- Staff presents baseline and alternatives
- FOMC members receive model outputs
- Discussion incorporates model + judgment + market signals
- Decision announced with SEP (Summary of Economic Projections)
FRB/US provides macroeconomic scenarios for Comprehensive Capital Analysis and Review (CCAR):
Severely Adverse Scenario Generation:
where shocks are calibrated to historical stress episodes (2008-2009, 1980-82, 1974-75).
# Severely Adverse Scenario Construction (Typical CCAR)
## Shock Specification
shocks = {
"financial_crisis": {
"equity_market": -50%, # S&P 500 falls 50%
"house_prices": -25%, # Home prices drop 25%
"credit_spread": +500bp, # Corporate spreads spike
"VIX": spike to 70, # Extreme volatility
"foreign_demand": -15% # Global recession
},
"real_shock": {
"productivity": -2%, # TFP decline
"labor_supply": -1%, # Participation drops
"confidence": -30% # Sentiment collapses
}
}
## Propagation Through FRB/US
severe_scenario = solve_frbusmodel(
initial_shocks = shocks,
duration = 13_quarters,
policy_response = "aggressive_easing", # Fed cuts to ZLB
fiscal_response = "automatic_stabilizers",
mode = "VAR" # Use adaptive expectations in crisis
)
## Typical Severely Adverse Output
# Peak impacts (trough quarter):
- Real GDP: -4.0% (cumulative)
- Unemployment rate: 10.0%
- Equity prices: -50%
- House prices: -25%
- Commercial real estate: -35%
- BBB corporate spread: +570bp
# Recovery path:
# Gradual return to baseline over 9-13 quarters
# Fed keeps rates at zero for extended period
# Fiscal deficit widens 4-5pp of GDP
Bank-Specific Application:
Banks use FRB/US scenarios to project losses under stress:
where probability of default (PD) and loss given default (LGD) are functions of the macroeconomic scenario.
CBO maintains a variant of FRB/US for 10-year budget window projections:
| Application | Modification from FRB/US | Key Usage |
|---|---|---|
| Baseline Budget Projection | Extended horizon (40 quarters) | 10-year deficit and debt forecasts |
| Tax Policy Scoring | Detailed tax code blocks | Revenue estimates for legislation |
| Entitlement Projections | Demographic transitions | Social Security/Medicare outlays |
| Fiscal Multiplier Analysis | Alternative expectation mechanisms | Stimulus package impact estimates |
Investment Bank Policy Desk Usage:
Example: Rates Desk Workflow:
# Investment Bank Rates Strategy Using FRB/US
## Step 1: Replicate Fed's Baseline
fed_baseline = solve_frbusmodel(
calibration = "Federal_Reserve_2024",
expectations = "VAR",
policy_rule = "estimated_historical"
)
## Step 2: Overlay Market Pricing
market_implied_path = extract_from_fed_funds_futures()
market_implied_terminal = extract_from_forwards()
## Step 3: Identify Mispricings
pricing_gap = market_implied_path - fed_baseline.policy_path
## Step 4: Risk Scenarios
# If model says Fed needs to hike more than priced:
scenario_1 = solve_frbusmodel(
policy_path = model_optimal, # Higher than market
compute_bond_yields = True
)
# If market is too hawkish:
scenario_2 = solve_frbusmodel(
policy_path = market_implied,
compute_growth_impact = True # How much growth damage?
)
## Step 5: Trading Recommendation
if pricing_gap > 50bp:
recommendation = "Short 2y Treasury (yields rise)"
rationale = "Market underpricing Fed hiking cycle"
conviction = high
Recent Research Using FRB/US:
| Research Question | Modification | Key Finding |
|---|---|---|
| Optimal inflation target | Vary $\pi^*$ from 1% to 4% | 2-2.5% minimizes loss function |
| Forward guidance effectiveness | Compare VAR vs. RE expectations | Effect is 30-40% of RE prediction |
| Fiscal multipliers at ZLB | Constrain $r_t \geq 0$ | Multipliers 2-3x larger at ZLB |
| Climate change impacts | Add productivity damage function | 0.1-0.3pp annual GDP drag by 2050 |
| Universal Basic Income | Add transfers, modify labor supply | Modest inflationary, depends on funding |
| Automation and inequality | Two-agent model (skilled/unskilled) | Capital share rises, wage polarization |
1. Tail Risk and Nonlinear Crises:
FRB/US is linearized around steady state, performing poorly in extreme events:
2. Expectation Formation:
VAR expectations inadequate during regime changes:
3. Financial Sector Simplicity:
Limited bank intermediation and credit frictions:
4. Heterogeneity:
Representative agent framework misses distributional effects:
5. Structural Change:
Parameters estimated on historical data may be unstable:
Fed staff use multiple models for robustness:
| Model | Type | Strengths vs. FRB/US | Usage |
|---|---|---|---|
| EDO (Estimated DSGE) | Bayesian DSGE | Theory-consistent, RE expectations | Cross-check policy scenarios |
| SIGMA (Multi-country) | Open economy DSGE | International linkages, exchange rates | Global spillover analysis |
| Factor models (forecasting) | Statistical VAR/factors | Short-term forecast accuracy | Nowcasting current quarter |
| Survey-based forecasts | Survey compilation | Market expectations, credibility | Assess expectations anchoring |
| Regional Fed models | Sectoral/regional | Industry detail, geographic variation | Regional heterogeneity |
Operational Practice: Fed staff prepare forecasts from 4-6 models, present range of outcomes to FOMC. Decision-makers weigh model-based analysis against real-time intelligence from business contacts, market signals, and qualitative factors.
This section summarizes FRB/US parameter estimation, identification strategies, and calibration choices.
FRB/US employs a hybrid estimation approach combining:
# Estimation Philosophy and Sequence
## Phase 1: Estimate reduced-form relationships
# Use OLS/MLE on individual equations
# Obtain consistent estimates ignoring simultaneity
# Example: Consumption function
C_t = β₀ + β₁·Y_t + β₂·W_t + β₃·r_t + ε_t
# Estimate via OLS with HAC standard errors
## Phase 2: Incorporate expectations
# Replace E_t[X_{t+h}] with VAR-generated forecasts
# Re-estimate equations with constructed expectations
# Example: Consumption Euler equation
C_t = γ₁·E_t[C_{t+1}] + γ₂·C_{t-1} + γ₃·(r_t - E_t[π_{t+1}]) + ε_t
# Estimate via GMM with E_t[·] replaced by VAR forecast
## Phase 3: Impose theoretical restrictions
# Apply long-run homogeneity, adding-up constraints
# Example: Production function
log(Y_t) = α·log(K_t) + (1-α)·log(L_t) + log(A_t)
# α calibrated to capital share in national accounts (≈0.33)
## Phase 4: Validate system properties
# Solve full model, check for:
- Stability (eigenvalues of linearized system)
- Cointegration relationships hold
- Impulse responses economically sensible
- Forecast performance on holdout sample
## Phase 5: Iterative refinement
# If system properties unsatisfactory:
- Adjust poorly-identified parameters
- Impose additional constraints
- Re-estimate with updated priors
Consumption Block:
| Parameter | Estimate | Std. Error | Interpretation |
|---|---|---|---|
| $\gamma_1$ | 0.38 | (0.08) | Forward-looking weight |
| $\gamma_2$ | 0.62 | (0.08) | Backward-looking weight (habit) |
| $\gamma_3$ | 0.03 | (0.005) | Wealth effect (3¢ per $) |
| $\gamma_4$ | -0.12 | (0.03) | Interest rate semi-elasticity |
Investment Block:
| Parameter | Estimate | Std. Error | Identification |
|---|---|---|---|
| $\phi_1$ | 0.042 | (0.012) | Q variations (stock market vol) |
| $\phi_2$ | 19.5 | (3.2) | Output growth correlation |
| $\phi_3$ | 0.18 | (0.06) | Cash flow sensitivity (liquidity) |
Phillips Curve:
| Parameter | Estimate (1985-2019) | Estimate (2000-2019) | Change / Instability |
|---|---|---|---|
| $\gamma_f$ | 0.32 | 0.24 | ↓ Forward-looking weight declining |
| $\gamma_b$ | 0.68 | 0.76 | ↑ More backward-looking |
| $\kappa$ | 0.019 | 0.009 | ↓ FLATTENING (critical finding) |
| $\mu$ | 0.08 | 0.075 | Stable import pass-through |
Key Finding: The Phillips curve has flattened post-2000, with the sacrifice ratio rising from about 2.0 to 3.5. This is the most important parameter instability in the model.
1. Simultaneous Equations Bias:
Many behavioral equations involve endogenous RHS variables. Example: consumption depends on income, but income depends on consumption.
Solution: Instrumental variables estimation:
where instruments $Z_t$ include lagged values, exogenous shocks (oil prices, foreign demand), policy variables.
2. Expectation Terms:
$E_t[X_{t+h}]$ is unobserved, requiring constructed regressors:
This introduces generated regressor bias, requiring bootstrapped standard errors.
3. Structural Breaks:
Parameters exhibit instability over time. Testing via:
Results: Significant breaks in Phillips curve (p < 0.01), modest breaks in consumption/investment (p ≈ 0.05-0.10).
Solution: Time-varying parameters via rolling windows or Bayesian methods.
| Parameter | Value | Source / Rationale |
|---|---|---|
| Production function $\alpha$ (capital share) | 0.33 | NIPA capital income share |
| Depreciation rate $\delta$ | 0.025 | BEA fixed asset tables (quarterly) |
| Discount factor $\beta$ | 0.995 | Implies 2% annual discount rate |
| Intertemporal elast. $\sigma$ | 2.0 | Micro studies (IES ≈ 0.5) |
| Frisch labor elasticity | 0.5 | Macro labor supply literature |
| Calvo price duration $1/(1-\theta)$ | 4 quarters | Bils-Klenow micro price data |
| Calvo wage duration | 4 quarters | Taylor contracts literature |
| Neutral real rate $r^*$ | 0.5% | Laubach-Williams estimates (2024) |
| NAIRU $u^*$ | 4.2% | CBO estimates, Kalman filter |
| Trend productivity growth $\mu_A$ | 1.8% | BLS projections |
Sample Period: 1966:Q1 - 2023:Q4 (232 quarters)
Rationale for start date:
Data Vintage: "Final revised" vintage (as of 2024:Q3)
Frequency: Quarterly (model native frequency)
Subsample Robustness:
1. In-Sample Fit:
| Variable | $R^2$ | RMSE | vs. AR(4) Model |
|---|---|---|---|
| GDP Growth | 0.68 | 0.9pp | 30% improvement |
| Unemployment | 0.92 | 0.3pp | 25% improvement |
| Core Inflation | 0.85 | 0.5pp | 20% improvement |
| Fed Funds Rate | 0.94 | 0.6pp | 15% improvement |
2. Out-of-Sample Forecast Accuracy:
Recursive forecasts from 2000-2023 (expanding window):
| Horizon | GDP RMSE | Inflation RMSE | Diebold-Mariano vs. VAR |
|---|---|---|---|
| 1 quarter | 0.8pp | 0.4pp | p = 0.03 (FRB/US better) |
| 4 quarters | 1.5pp | 0.8pp | p = 0.12 (marginal) |
| 8 quarters | 2.1pp | 1.2pp | p = 0.45 (no difference) |
3. Impulse Response Validation:
Compare FRB/US impulse responses to identified VARs (Romer-Romer monetary shocks):
Conclusion: Model dynamics broadly consistent with identified empirical evidence.
1. Time-Varying Parameters:
Key parameters exhibit drift over time, particularly:
Current research: Bayesian time-varying parameter models
2. Financial Frictions:
Limited financial sector detail leads to:
Current research: Integrate Bernanke-Gertler-Gilchrist financial accelerator
3. Heterogeneity:
Representative agent framework misses distributional margins:
Current research: Two-agent HANK (Heterogeneous Agent New Keynesian) variant
4. Expectations Formation:
VAR expectations perform poorly during:
Current research: Learning models, survey-consistent expectations
FRB/US model code is publicly available:
# Example: Running FRB/US in MATLAB
% Load model
load('FRBUSmodel_2024Q3.mat');
% Set baseline assumptions
baseline.initial_conditions = current_data;
baseline.exogenous_path = standard_assumptions();
baseline.expectations_mode = 'VAR';
baseline.policy_rule = 'inertial_Taylor';
% Solve model
[Y, info] = solve_frbus(model, baseline);
% Extract key variables
GDP_growth = Y.GDP_real_growth;
unemployment = Y.unemployment_rate;
inflation = Y.PCE_core_inflation;
fed_funds = Y.federal_funds_rate;
% Plot results
plot_forecast(GDP_growth, unemployment, inflation, fed_funds);
% Alternative scenario
alt_scenario = baseline;
alt_scenario.policy_rule = 'aggressive_hike';
[Y_alt, info_alt] = solve_frbus(model, alt_scenario);
% Compare
compare_scenarios(Y, Y_alt);
Every model has limitations. Understanding them improves how the results are used.
Model accuracy is higher at short horizons and lower for rare or extreme events. That trade-off also applies to economic models.
The Problem: The model assumes a baseline world and cannot foresee rare shocks:
Why it matters: These events often drive large deviations from any baseline.
What the Fed does: Staff run stress scenarios even though timing cannot be predicted.
The Problem: The model assumes forward-looking behavior. Actual decisions can be driven by psychology and uncertainty:
What this means: Models perform best in normal times and can miss turning points.
The Problem: The model uses representative households and firms. Distributional effects can differ:
When the Fed raises rates from 0% to 5%:
The model averages these effects and can miss distributional impacts.
The Problem: The relationship between unemployment and inflation (the Phillips curve) has weakened.
In the 1970s-80s:
Since 2010:
Then in 2021-2022:
Bottom line: Inflation forecasting has been less reliable because historical relationships have shifted.
The Problem: Banks, credit, and financial markets are simplified. This limited performance in 2008:
What the model missed in 2008:
The model predicted: A mild recession
What actually happened: A deep recession with sharp job losses
Lesson learned: Financial crises require richer financial-sector modeling than the baseline provides.
The Problem: Forecast accuracy degrades rapidly beyond 1-2 years:
| Forecast Horizon | Typical Error (GDP) | Reliability |
|---|---|---|
| 1 quarter ahead | ±0.8% | Higher |
| 1 year ahead | ±1.5% | Moderate |
| 2 years ahead | ±2.5% | Lower |
| 5+ years ahead | ±4%+ | Low |
What this means: Near-term forecasts carry more weight. Long-term projections are directional at best.
The Problem: The model is estimated on past data, while the economy evolves:
Major changes not fully captured:
What the Fed does: The model is updated over time, but revisions inevitably lag structural change.
The model is a useful advisor that:
How the Fed actually uses it:
Final verdict: FRB/US is a valuable tool, best used alongside other models, market signals, and judgment.
FRB/US is a tool, not a literal description of the economy. The Fed emphasizes cautious interpretation, reinforced by notable forecast errors in 2008 and 2021-2022.
This section summarizes known weaknesses from academic critiques, internal assessments, and comparative performance. The goal is to understand where the model tends to fail and how to interpret results.
Issue: Aggregation from heterogeneous micro behavior to representative agent loses critical transmission mechanisms.
Evidence from HANK literature:
Quantitative implications:
depending on wealth distribution. Current U.S. wealth Gini ≈ 0.85 implies $MPC_{true} \approx 0.30$, suggesting FRB/US overstates consumption response.
Monetary policy implications:
Interest rate changes affect households asymmetrically:
FRB/US averages these, potentially misestimating aggregate transmission by 30-40%.
Missing channels:
Consequence: 2008 forecast failure
FRB/US 2008:Q3 forecast (after Lehman bankruptcy):
Model lacked financial accelerator mechanism:
but missing:
Post-2010 improvements:
Added Bernanke-Gertler-Gilchrist financial accelerator:
where external finance premium rises with leverage. However, still lacks:
VAR expectations problematic during regime changes:
Case 1: Volcker Disinflation (1980-82)
Case 2: Forward Guidance at ZLB (2011-2015)
Hybrid approach limitations:
Static weights inadequate. Survey evidence suggests $\lambda_t$ varies with:
Structural break evidence:
| Period | Slope $\kappa$ | Sacrifice Ratio | Std. Error |
|---|---|---|---|
| 1960-1984 | 0.031 | 2.0 | (0.008) |
| 1985-1999 | 0.019 | 2.8 | (0.009) |
| 2000-2019 | 0.009 | 3.5 | (0.012) |
| 2020-2024 | 0.004 | 5.0+ | (0.018) |
Chow test for break between 1985-1999 and 2000-2019: F(3,150) = 8.42, p < 0.001
Competing hypotheses:
2021-2023 inflation episode failure:
FRB/US forecast (2021:Q1) for 2022 inflation: 2.3%
Actual 2022 inflation: 6.5% (off by 4.2pp!)
Post-mortem attribution:
RMSE comparison (2020-2024 vs. 2010-2019):
| Variable | 2010-2019 RMSE | 2020-2024 RMSE | Deterioration |
|---|---|---|---|
| GDP (4Q ahead) | 1.2pp | 2.8pp | +133% |
| Inflation (4Q ahead) | 0.6pp | 2.1pp | +250% |
| Unemployment (4Q ahead) | 0.4pp | 1.2pp | +200% |
Inflation forecast errors particularly severe, suggesting fundamental model misspecification for high-inflation regime.
Rational expectations solution:
Operational constraint: Cannot rapidly explore parameter uncertainty during FOMC cycle (1 week preparation window).
Workaround: Pre-compute sensitivity matrices, use linear approximations for real-time analysis.
Model estimated on "final revised" data, but policymakers see preliminary releases.
Typical GDP revision pattern:
Real-time forecast degradation:
Forecast RMSE rises ~20% when using real-time vintage vs. final revised data.
Orphanides critique (2001): Real-time output gap estimates highly unreliable, potentially leading to systematic policy errors. FRB/US suffers same issue—NAIRU and potential GDP estimates revised substantially ex-post.
| Model Class | Advantages vs. FRB/US | Disadvantages vs. FRB/US |
|---|---|---|
| DSGE (e.g., Smets-Wouters) | • Theoretical consistency • Policy-invariant • Credible commitment analysis |
• Worse empirical fit • Rigid structure • Computational complexity |
| HANK (Heterogeneous Agent) | • Captures distributional effects • Realistic MPCs • Fiscal targeting matters |
• Computationally intensive • Parameter proliferation • Forecast accuracy unclear |
| VAR/BVAR | • Superior short-term forecasts • Minimal structure • Fast computation |
• Atheoretical • Lucas critique • No policy experiments |
| Machine Learning | • Nonlinear relationships • High-dimensional data • Excellent in-sample fit |
• Black box • No economic interpretation • Overfitting risk |
1. Heterogeneous Agents:
Integrate limited heterogeneity (2-3 agent types) without full HANK complexity:
2. Time-Varying Parameters:
Estimate parameters via:
using Kalman filter for Phillips curve slope, neutral rate, NAIRU.
3. Financial Frictions:
Add Gertler-Karadi (2011) banking sector with:
4. Machine Learning Augmentation:
Hybrid approach: FRB/US structural core + ML for unmodeled dynamics:
where $g^{ML}$ is neural network capturing residual patterns in high-frequency data.
5. Climate Economics Integration:
Add climate damage function:
where $T_t$ is temperature anomaly, $\gamma \approx 0.002$ (0.2% TFP loss per °C²).
FRB/US remains the workhorse model for Federal Reserve policy analysis despite known limitations. Its advantages—empirical fit, computational tractability, institutional detail—outweigh disadvantages for operational use.
Key strengths:
Critical weaknesses:
Overall verdict: FRB/US should be ONE input into policy deliberations, complemented by alternative models, market intelligence, and judgment. Staff should explicitly communicate forecast uncertainty and model limitations to policymakers. Ongoing research and model updates are essential as the economy evolves.