Bank of England Economic Models

Deep Analysis of the COMPASS DSGE Macroeconomic Model

Page Overview

This page reviews the economic model used by the Bank of England to inform monetary policy decisions. I provide current input parameters to derive a theoretical model-based Bank Rate, and offer a comprehensive analysis of the Bernanke Review findings and ongoing model development efforts. Please keep in mind that there always is the beginner/expert toggle button available at the top right corner of the page to adjust the content displayed to your level of expertise.

Table of Contents

COMPASS Model Overview

What is COMPASS?

Every six weeks, a group of nine people sits around a table in Threadneedle Street, London, and makes a decision that affects whether you can afford a house, whether your employer is hiring, and how much your weekly shop costs. They are the Bank of England's Monetary Policy Committee (MPC), and their main tool is the Bank Rate — the interest rate that ripples through the entire economy.

But how do they know what to do? They can't just guess. COMPASS is their primary economic model — a sophisticated simulation of the UK economy that helps them think through the consequences of their decisions before they make them.

Quick Facts:
Name: Central Organising Model for Projection Analysis and Scenario Simulation
In Use Since: 2011
Current Status: Under significant overhaul following the 2024 Bernanke Review

Why Can't the MPC Just Use Common Sense?

Here's the problem: monetary policy works with a delay. When the Bank raises interest rates today, the full effect on inflation might not show up for 18-24 months. That means the MPC can't simply react to what's happening now — they have to make decisions based on where the economy will be in the future.

And the economy is fiendishly complicated. When rates go up:

  • Mortgage holders have less money to spend on other things
  • Businesses find it more expensive to borrow for investment
  • The pound often strengthens, making imports cheaper but exports harder to sell
  • People who save money in banks earn more interest
  • House prices may fall, making homeowners feel less wealthy

These effects interact with each other in complex ways. COMPASS is the Bank's attempt to track all these connections systematically, rather than relying on gut instinct.

Think of It Like a Flight Simulator

Pilots don't learn to handle engine failures by actually crashing planes. They use flight simulators that mimic how a real aircraft behaves. COMPASS is similar — it lets the MPC "fly" the economy through different scenarios without risking real-world consequences. What happens if we raise rates by 0.5% instead of 0.25%? What if oil prices spike? What if consumer confidence collapses? The model can simulate these situations before they happen.

The Cast of Characters

COMPASS divides the UK economy into groups whose decisions drive everything:

Households (That's You)

How do families decide between spending now or saving for later? When interest rates rise, does your family cut back on restaurants to pay the higher mortgage? These millions of small decisions add up to national consumer spending.

Businesses

When should a company raise prices? Hire more workers? Build a new factory? If borrowing costs rise, that new factory might get delayed — and so might the jobs that would have come with it.

The Rest of the World

The UK is an open economy. When the pound strengthens, your holiday abroad gets cheaper but British exporters struggle. COMPASS tracks these international connections.

The Honest Truth: It Has Problems

In 2024, former Federal Reserve Chair Ben Bernanke was invited to review the Bank's forecasting. His verdict was damning: COMPASS has "significant shortcomings." During the COVID-19 pandemic and the subsequent inflation surge, the Bank's forecasts were badly wrong — and COMPASS wasn't much help in understanding why.

The Bank is now working on a major overhaul. This is actually how good institutions work: they acknowledge failures and try to fix them. But it does mean that the current model should be understood as a work-in-progress, not a finished product.

Model Classification: Dynamic Stochastic General Equilibrium (DSGE) model
Full Name: Central Organising Model for Projection Analysis and Scenario Simulation
Operational Since: 2011 (replacing the Bank of England Quarterly Model)
Current Status: Under fundamental review following Bernanke Report (April 2024)
Model Family: Small open-economy New Keynesian DSGE with financial frictions

Institutional Context and Historical Development

COMPASS emerged from a decade of methodological ferment in central bank modeling. By the mid-2000s, the Bank of England's previous workhorse — the Bank of England Quarterly Model (BEQM) — had become increasingly difficult to maintain and lacked the theoretical coherence demanded by the "New Keynesian consensus" then dominating academic macroeconomics. The 2008 financial crisis accelerated the case for change while simultaneously highlighting the limitations of any model that excluded financial sector dynamics.

Development began in 2008 under the direction of the Monetary Analysis division, with COMPASS becoming operational in 2011. The model was designed to serve as the "central organising framework" around which the Bank's forecasting process would cohere — hence the name. In practice, this vision has proven more aspirational than operational.

Architectural Overview

COMPASS is formally a medium-scale New Keynesian DSGE model for a small open economy, featuring approximately 30 key equations and estimated via Bayesian methods on UK quarterly data from 1993Q1. The model ecology includes:

  • COMPASS Core: The structural DSGE model embodying theoretical relationships
  • Suite of Satellite Models: Sector-specific models for housing, labor markets, financial conditions, and external trade that provide granular detail beyond COMPASS's aggregated treatment
  • MAPS (Modelling and Projection System): The computational toolkit for model estimation, simulation, and scenario analysis
  • EASE (Economic and Statistical Engine): The forecasting platform integrating model outputs with real-time data and staff judgment

Theoretical Architecture

The model's theoretical core follows the canonical New Keynesian synthesis, characterized by:

  • Microfoundations with representative agents: Aggregate relationships derived from optimizing behavior of households and firms, providing immunity to the Lucas critique for policy analysis
  • Nominal rigidities via Calvo pricing: Staggered price and wage adjustment generates the short-run monetary policy non-neutrality essential for policy relevance
  • Rational expectations: Forward-looking agents form model-consistent expectations, capturing the expectations channel of monetary transmission
  • Open economy structure: Uncovered interest parity (with risk premium shocks), import/export demand functions, and exchange rate pass-through to import prices
  • Financial frictions: Credit spreads affect borrowing costs for firms and households, providing a transmission channel from financial conditions to real activity

The Gap Between Theory and Practice

The Bernanke Review (April 2024) documented a striking divergence between COMPASS's formal role and its actual use. While nominally the "central organising model," COMPASS has become peripheral to the Bank's forecasting process. Staff projections rely heavily on:

  • Sectoral models: Separate models for consumption, investment, labor market, and trade, often lacking explicit links to COMPASS
  • Near-term indicators: High-frequency data and nowcasting techniques for short-horizon predictions
  • Extensive judgmental adjustments: Staff overlays that can dominate model-based forecasts, particularly during unusual periods

Bernanke's assessment was blunt: the Bank's forecasting infrastructure has become "a patchwork of models, databases, and tools developed and maintained by different parts of the organisation... there is no central model that disciplines the overall forecast." COMPASS failed precisely when it was most needed — during the COVID-19 shock and subsequent inflation surge — leading staff to increasingly bypass it.

Implications for Model-Based Analysis

This institutional reality carries important implications for interpreting Bank of England analysis:

  • Published forecasts are not "COMPASS forecasts": They reflect a synthesis of multiple models, indicator-based methods, and judgment
  • Scenario analysis faces limitations: The fragmented model infrastructure makes it difficult to produce internally consistent alternative scenarios — a key Bernanke criticism
  • Structural interpretation requires caution: The distance between COMPASS and actual forecasts means impulse response functions and shock decompositions may not accurately describe how the Bank actually views monetary transmission

The Bank has committed to substantial model infrastructure investment following the Bernanke Review, with a multi-year program to develop what it terms a "new suite of models" that better integrates structural and forecasting functions. Until this program matures, COMPASS remains an imperfect window into the Bank's analytical framework.

Model Structure and Core Framework

You don't need to understand the mathematics to grasp what COMPASS is doing. At its core, the model asks a simple question: when the Bank of England changes interest rates, what happens next? The answer turns out to be surprisingly complicated — and that's why we need a model.

Following the Money: A Chain Reaction

Imagine the MPC decides to raise interest rates by 0.5%. Here's what COMPASS tries to track:

Step 1: Mortgages Get More Expensive

About a third of UK households have mortgages. When rates rise, their monthly payments increase — sometimes by hundreds of pounds. That's money they can't spend elsewhere. But here's the twist: people with savings now earn more interest. So who "wins" and who "loses" from rate changes? COMPASS tracks both sides.

Step 2: Businesses Think Twice

A company planning to build a new warehouse might reconsider if borrowing costs jump. That warehouse won't get built, the construction workers won't get hired, and the suppliers won't get orders. One interest rate change can ripple through dozens of business decisions. But timing matters hugely — a project already underway won't stop, while a project still in planning might never happen.

Step 3: The Pound Reacts

Higher UK interest rates attract foreign investors seeking better returns. They need pounds to invest here, so demand for sterling rises, pushing up the exchange rate. A stronger pound makes your holiday in Spain cheaper, but it also makes British exports more expensive for foreign buyers. Jaguar becomes pricier in New York; French wine becomes cheaper in London. COMPASS models these trade-offs.

Step 4: Prices Start to Adjust (Slowly)

Here's a crucial insight: prices don't adjust instantly. Tesco doesn't change its shelf prices every day. Wages are set in annual negotiations. Rents are fixed in contracts. This "stickiness" is actually the whole reason monetary policy works — if prices adjusted immediately, interest rate changes wouldn't matter. The delay gives the Bank leverage over real economic activity, not just nominal values.

Why It Takes So Long

The Bank estimates it takes 18-24 months for an interest rate change to have its full effect on inflation. Why so long? Because each step in the chain takes time: households need to adjust their budgets, businesses need to revise their plans, prices need to be renegotiated, and all of this needs to work through the entire economy. COMPASS tries to capture these lags realistically.

The Expectations Puzzle

Here's where it gets genuinely interesting. Imagine workers expect inflation to be high next year. They'll demand higher wages now to protect their purchasing power. But higher wages mean higher costs for businesses, who then raise prices — actually causing the inflation workers feared. This is a self-fulfilling prophecy, and it can work in reverse too: if people believe the Bank will keep inflation under control, they're less likely to demand big wage increases, making the Bank's job easier.

COMPASS models these expectation effects because they're absolutely crucial. A Bank that's trusted to control inflation has an easier job than one that isn't — and the model captures this.

COMPASS instantiates the New Keynesian DSGE paradigm that dominated central bank modeling from roughly 2000-2020. The framework's intellectual foundations lie in the synthesis of real business cycle theory (intertemporal optimization, rational expectations) with Keynesian elements (nominal rigidities, monetary non-neutrality). Understanding these building blocks is essential for interpreting both the model's capabilities and its limitations — many of which were exposed during 2020-2023.

The Building Blocks

Household Optimization

The consumption block embodies the permanent income hypothesis: households smooth consumption over time based on expected lifetime resources. The Euler equation — the model's most fundamental relationship — links current consumption to expected future consumption and the real interest rate:

$$\Lambda_t = \beta E_t\left[\Lambda_{t+1} \frac{R_t}{\Pi_{t+1}}\right]$$

Where: $\Lambda_t$ = marginal utility of consumption (capturing habit formation), $R_t$ = gross nominal interest rate, $\Pi_t$ = gross inflation rate, $\beta$ = subjective discount factor (≈0.99 quarterly)

Specification: Marginal utility includes external habit formation: $\Lambda_t = (C_t - hC_{t-1})^{-\sigma}$ where $h$ captures consumption habits and $\sigma$ is the coefficient of relative risk aversion.

Labor supply decisions yield an intratemporal optimality condition balancing the marginal rate of substitution between consumption and leisure against the real wage, modified by wage stickiness parameters.

2. Production Sector and Price Setting

A continuum of monopolistically competitive firms operate under Calvo-style price stickiness, where a fraction $\theta_p$ of firms cannot adjust prices in any given period. Firms able to reoptimize set prices to maximize expected discounted profits:

$$P_t^* = \frac{\epsilon}{\epsilon - 1} \frac{E_t \sum_{k=0}^{\infty} (\beta\theta_p)^k \Lambda_{t+k} Y_{t+k|t} MC_{t+k}}{E_t \sum_{k=0}^{\infty} (\beta\theta_p)^k \Lambda_{t+k} Y_{t+k|t} P_{t+k}}$$

Where: $P_t^*$ = optimal reset price, $\epsilon$ = elasticity of substitution (determines markup), $MC_t$ = nominal marginal cost, $Y_{t+k|t}$ = future demand at current price

Log-linearization around steady state yields the New Keynesian Phillips Curve:

$$\pi_t = \beta E_t[\pi_{t+1}] + \kappa mc_t$$

Where: $\kappa = \frac{(1-\theta_p)(1-\beta\theta_p)}{\theta_p}$ represents the slope, depending inversely on price stickiness $\theta_p$

Real Marginal Cost: $mc_t = w_t - mpl_t$ where $w_t$ is the real wage and $mpl_t$ is the marginal product of labor, linking inflation to labor market slack.

3. Open Economy Block

The UK's small open economy characteristics are captured through several key relationships. The uncovered interest parity (UIP) condition links domestic and foreign interest rates with expected exchange rate changes:

$$E_t[s_{t+1}] - s_t = (i_t - i_t^*) + \rho_t$$

Where: $s_t$ = log nominal exchange rate (domestic per foreign), $i_t$ = domestic interest rate, $i_t^*$ = foreign interest rate, $\rho_t$ = country-specific risk premium

COMPASS Extension: The risk premium $\rho_t$ is modeled as a function of net foreign assets to capture debt sustainability concerns and portfolio balance effects.

Trade volumes depend on relative prices and foreign/domestic demand:

$$X_t = \left(\frac{P_X}{P^*}\right)^{-\eta_X} Y_t^*$$ $$M_t = \left(\frac{P_M}{P}\right)^{-\eta_M} Y_t$$

Where: $X_t, M_t$ = exports and imports, $\eta_X, \eta_M$ = trade elasticities, $Y_t^*$ = foreign demand, $P_X, P_M$ = export and import prices

4. Monetary Policy Reaction Function

The Bank of England's systematic policy behavior is characterized by a Taylor-type rule with substantial interest rate smoothing:

$$i_t = \rho_i i_{t-1} + (1-\rho_i)[\bar{i} + \phi_\pi (\pi_t - \pi^*) + \phi_y \tilde{y}_t] + \epsilon_t^i$$

Where: $\rho_i$ = interest rate smoothing parameter (≈0.85), $\bar{i}$ = equilibrium nominal rate, $\pi^*$ = inflation target (2%), $\tilde{y}_t$ = output gap, $\epsilon_t^i$ = monetary policy shock

Calibration: $\phi_\pi \approx 1.5$ (inflation response satisfies Taylor principle), $\phi_y \approx 0.5$ (output gap response)

The high smoothing parameter reflects the Bank's gradualist approach to policy adjustment, avoiding excessive volatility while maintaining credibility.

Model Estimation and Calibration

COMPASS is estimated using Bayesian methods on UK data, combining prior information about parameter values with likelihood-based estimation. Key structural parameters are identified through the model's dynamic responses to various shocks, allowing the model to match both steady-state relationships and business cycle properties of UK data.

Parameter Description Typical Value Source/Method
$\beta$ Household discount factor 0.99 Calibrated (4% annual rate)
$\sigma$ Risk aversion coefficient 1.5-2.0 Euler equation dynamics
$h$ Habit persistence 0.6-0.8 Consumption smoothness
$\theta_p$ Price stickiness (Calvo) 0.75 Inflation dynamics (4-quarter avg duration)
$\theta_w$ Wage stickiness (Calvo) 0.75 Wage Phillips curve
$\phi_\pi$ Inflation response 1.5 Monetary policy rule estimation
$\phi_y$ Output gap response 0.5 Monetary policy rule estimation
$\rho_i$ Interest rate smoothing 0.85 Policy rate autocorrelation
$\alpha$ Capital share in production 0.33 Calibrated (national accounts)
$\delta$ Depreciation rate 0.025 Calibrated (10% annual)

Household Sector

The household sector in COMPASS represents you, me, and every family in the UK making decisions about spending, saving, and work. These are probably the most relatable parts of the model.

The Spend-or-Save Decision

How Households Respond to Interest Rates

Imagine you have £1,000 you don't need right now. If the Bank raises interest rates from 1% to 5%, suddenly saving that money becomes much more attractive—you'll earn £50 per year instead of just £10. This makes you more likely to save rather than spend.

COMPASS captures this behavior for millions of households. When rates rise, overall consumer spending tends to fall, which helps cool down inflation. When rates fall, spending picks up, which can help boost a weak economy.

The Work Decision

COMPASS also models how people decide how much to work. This involves balancing the benefits of earning money (so you can buy things) against the value of leisure time. When wages are high relative to the cost of living, people tend to work more hours. When real wages (wages adjusted for inflation) are low, people may work less or drop out of the workforce.

The Smoothing Effect

People don't like wild swings in their lifestyle. If you get a bonus at work, you probably don't spend it all immediately—you save some for the future. Similarly, if your income drops temporarily, you might dip into savings rather than drastically cut spending. Economists call this "consumption smoothing," and COMPASS captures it through what's called "habit formation."

Why This Matters for Monetary Policy

The Interest Rate Channel: When the Bank of England raises rates:

  • Saving becomes more attractive → people spend less
  • Borrowing becomes more expensive → people buy fewer big-ticket items (cars, homes)
  • Reduced spending → businesses sell less → inflation slows down

But here's the catch: these effects take time. People don't immediately change their spending patterns when rates change. They might be locked into fixed-rate mortgages, or they might want to wait and see if the rate change is permanent. COMPASS tries to capture these realistic delays.

Households and Expectations

One sophisticated feature: households in COMPASS look ahead. If people expect rates to stay high for a long time, they adjust their behavior more than if they think rates will soon fall again. This is why the Bank's communication about future policy is so important—it shapes expectations, which in turn shapes behavior.

Theoretical Structure

The household sector in COMPASS features a representative infinitely-lived household that maximizes expected discounted utility over consumption and leisure, incorporating habit formation and subject to an intertemporal budget constraint. This structure generates the key Euler equation linking current and future consumption decisions.

Utility Specification
$$U_t = E_t \sum_{j=0}^{\infty} \beta^j \left[\frac{(C_{t+j} - hC_{t+j-1})^{1-\sigma}}{1-\sigma} - \chi \frac{N_{t+j}^{1+\varphi}}{1+\varphi}\right]$$

Components:

  • $C_t$ = household consumption
  • $h$ = external habit parameter (0.6-0.8), generating persistence
  • $\sigma$ = coefficient of relative risk aversion (1.5-2.0)
  • $N_t$ = labor supply (hours worked)
  • $\varphi$ = inverse Frisch elasticity of labor supply (≈2)
  • $\chi$ = disutility of labor weight parameter
  • $\beta$ = discount factor (0.99 quarterly)

Habit Formation Rationale: The $hC_{t-1}$ term captures consumption habits or "keeping up with the Joneses" effects, generating empirically realistic consumption persistence and hump-shaped responses to shocks. This feature is crucial for matching UK consumption dynamics and addresses the "excess smoothness" puzzle in consumption behavior.

Intertemporal Budget Constraint
$$P_t C_t + E_t[Q_{t,t+1} B_{t+1}] \leq B_t + W_t N_t + \Pi_t + T_t$$

Where:

  • $B_{t+1}$ = nominal bond holdings (state-contingent claims)
  • $Q_{t,t+1}$ = stochastic discount factor for pricing assets
  • $W_t$ = nominal wage rate
  • $\Pi_t$ = firm profits (distributed as dividends)
  • $T_t$ = lump-sum transfers/taxes
First-Order Conditions

Consumption Euler Equation:

$$\Lambda_t = \beta E_t\left[\Lambda_{t+1} \frac{R_t}{\Pi_{t+1}}\right]$$ $$\text{where } \Lambda_t = (C_t - hC_{t-1})^{-\sigma} - \beta h E_t[(C_{t+1} - hC_t)^{-\sigma}]$$

This is the stochastic intertemporal consumption condition linking current marginal utility to expected future marginal utility discounted by the real interest rate.

Labor Supply Condition:

$$\chi N_t^\varphi = \Lambda_t \frac{W_t}{P_t}$$

Intratemporal optimality condition equating marginal rate of substitution between consumption and leisure to the real wage. Combined with wage stickiness, this generates a wage Phillips curve.

Wage Setting Mechanism

COMPASS incorporates Calvo-style wage stickiness. A fraction $\theta_w$ of households cannot reoptimize wages in each period. Households setting optimal wages maximize expected discounted utility subject to a downward-sloping labor demand curve:

$$W_t^* = \frac{\epsilon_w}{\epsilon_w - 1} \frac{E_t \sum_{k=0}^{\infty} (\beta\theta_w)^k N_{t+k|t} MRS_{t+k}}{E_t \sum_{k=0}^{\infty} (\beta\theta_w)^k \Lambda_{t+k} N_{t+k|t}/P_{t+k}}$$

Where: $MRS_t = \chi N_t^\varphi / \Lambda_t$ is the marginal rate of substitution between consumption and leisure, and $\epsilon_w$ is the elasticity of substitution between labor types.

Log-linearization yields the wage Phillips curve:

$$\pi_t^w = \beta E_t[\pi_{t+1}^w] + \kappa_w (mrs_t - w_t)$$

Where $\pi_t^w$ is wage inflation and $\kappa_w = \frac{(1-\theta_w)(1-\beta\theta_w)}{\theta_w(1+\epsilon_w\varphi)}$ is the wage Phillips curve slope.

Implications for Monetary Transmission

The household sector structure implies several monetary policy transmission channels:

Channel Mechanism Empirical Magnitude
Intertemporal Substitution Higher rates → increased saving → reduced consumption Modest (low $1/\sigma$ elasticity)
Income Effects Rate changes affect interest income (savers) vs. payments (borrowers) Heterogeneous across households
Wealth Effects Rate changes affect present value of financial/housing wealth Significant for housing
Expectations Channel Forward-looking optimization means expected future rates matter Crucial for transmission lag
Calibration and Empirical Performance

Key household sector parameters are estimated/calibrated as follows:

  • $\sigma$ (risk aversion): Estimated around 1.5-2.0, implying moderate willingness to smooth consumption intertemporally
  • $h$ (habit persistence): Estimated 0.6-0.8, crucial for matching consumption dynamics
  • $\varphi$ (labor supply elasticity): Calibrated around 2, implying Frisch elasticity of 0.5, consistent with microeconomic evidence
  • $\theta_w$ (wage stickiness): Estimated around 0.75, implying average wage duration of 4 quarters

The household sector's impulse responses to monetary policy shocks show gradual consumption adjustment over 6-8 quarters, broadly consistent with UK data, though the model has been criticized for understating the role of cash-flow effects and overemphasizing pure intertemporal substitution relative to liquidity constraints.

Firm Sector and Price Setting

The firm sector in COMPASS represents all UK businesses—from corner shops to large corporations. Understanding how businesses behave is crucial because their pricing decisions directly determine inflation.

How Businesses Set Prices

The Key Insight: Prices Are Sticky

In theory, businesses could change their prices every day based on supply and demand. But in reality, they don't. Why not?

  • Menu costs: It's expensive to print new catalogs, update websites, and change price tags
  • Customer relationships: Frequent price changes annoy customers and can damage reputation
  • Contracts: Many prices are locked in through contracts for months or years
  • Coordination: Firms wait to see what competitors do before changing prices

This "stickiness" in prices is absolutely crucial for understanding monetary policy. If prices changed instantly, interest rate changes wouldn't affect the real economy—they'd just affect prices. But because prices adjust slowly, changes in interest rates have real effects on production, employment, and income.

The Business Investment Decision

Why Interest Rates Matter for Business

Imagine you run a bakery and want to buy a new oven for £50,000. If you need to borrow the money at 2% interest, you'll pay £1,000 per year in interest. But if rates rise to 6%, you'll pay £3,000 per year—that extra £2,000 might make the investment unprofitable, so you delay purchasing the oven.

Multiply this across thousands of businesses, and you can see why higher interest rates reduce business investment, which slows economic growth and employment.

Production and Employment

COMPASS models how businesses decide how much to produce and how many people to employ. The basic logic:

  1. Businesses hire workers to produce goods and services
  2. They pay workers wages, which are also sticky (don't change instantly)
  3. They set prices based on their costs (wages, materials, rent) plus a markup
  4. When demand falls (e.g., because higher interest rates reduce consumer spending), businesses produce less and eventually lay off workers

From Costs to Inflation

Here's the connection to inflation: when the economy is running hot (unemployment is low, businesses are busy), two things happen:

  • Workers have bargaining power and demand higher wages
  • Businesses are confident they can pass costs on to customers through higher prices

This creates upward pressure on inflation. When the Bank raises interest rates to cool the economy, it reduces demand, which reduces businesses' ability to raise prices, which brings inflation down.

But remember: this process takes time. Businesses don't cut prices the moment demand weakens. They might first reduce production, then reduce hiring, and only later consider price cuts. This is why monetary policy works with "long and variable lags."

Production Technology and Factor Demands

Firms in COMPASS produce differentiated goods under monopolistic competition, operating a Cobb-Douglas production function with capital and labor inputs:

$$Y_t(i) = A_t K_t(i)^\alpha N_t(i)^{1-\alpha}$$

Where: $Y_t(i)$ = output of firm $i$, $A_t$ = total factor productivity (TFP), $K_t(i)$ = capital stock, $N_t(i)$ = labor input, $\alpha \approx 0.33$ = capital share (calibrated to UK data)

Firms minimize costs subject to production technology, yielding factor demand conditions:

$$\frac{W_t}{P_t} = (1-\alpha) \frac{Y_t}{N_t} = (1-\alpha) A_t \left(\frac{K_t}{N_t}\right)^\alpha$$ $$\frac{R_t^K}{P_t} = \alpha \frac{Y_t}{K_t} = \alpha A_t \left(\frac{K_t}{N_t}\right)^{\alpha-1}$$

Where: $R_t^K$ is the nominal rental rate of capital. These conditions equate marginal products to real factor prices.

Real marginal cost, crucial for pricing decisions, is given by:

$$MC_t = \frac{1}{A_t} \left(\frac{W_t}{P_t}\right)^{1-\alpha} \left(\frac{R_t^K}{P_t}\right)^\alpha \frac{1}{\alpha^\alpha (1-\alpha)^{1-\alpha}}$$

Calvo Price Setting Framework

COMPASS employs the Calvo (1983) staggered pricing mechanism. In each period, a fraction $1-\theta_p$ of firms can reoptimize their price, while fraction $\theta_p$ keep their previous price unchanged (potentially with indexation to past inflation). This generates realistic price stickiness without explicit menu costs.

Optimal Price Setting

A firm $i$ able to reoptimize at time $t$ chooses reset price $P_t^*(i)$ to maximize expected discounted real profits:

$$\max_{P_t^*(i)} E_t \sum_{k=0}^{\infty} (\beta\theta_p)^k \Lambda_{t,t+k} \left[\frac{P_t^*(i)}{P_{t+k}} - MC_{t+k}\right] Y_{t+k|t}(i)$$

Where:

  • $\Lambda_{t,t+k} = \beta^k (\Lambda_{t+k}/\Lambda_t)$ = stochastic discount factor (household's marginal utility ratio)
  • $Y_{t+k|t}(i) = \left(\frac{P_t^*(i)}{P_{t+k}}\right)^{-\epsilon} Y_{t+k}$ = demand function
  • $\epsilon > 1$ = elasticity of substitution between varieties (determines markup)

The first-order condition yields the optimal reset price:

$$P_t^* = \frac{\epsilon}{\epsilon - 1} \frac{E_t \sum_{k=0}^{\infty} (\beta\theta_p)^k \Lambda_{t,t+k} Y_{t+k|t} P_{t+k} MC_{t+k}}{E_t \sum_{k=0}^{\infty} (\beta\theta_p)^k \Lambda_{t,t+k} Y_{t+k|t} P_{t+k}}$$

This shows optimal pricing as a desired markup $\frac{\epsilon}{\epsilon-1}$ over expected discounted marginal costs.

New Keynesian Phillips Curve Derivation

Log-linearizing the price-setting conditions around steady state yields the forward-looking New Keynesian Phillips Curve (NKPC):

$$\pi_t = \beta E_t[\pi_{t+1}] + \kappa mc_t$$

Where:

  • $\pi_t = \log(P_t/P_{t-1})$ = inflation rate
  • $mc_t$ = log deviation of real marginal cost from steady state
  • $\kappa = \frac{(1-\theta_p)(1-\beta\theta_p)}{\theta_p}$ = slope parameter

Key Properties:

  • Inflation depends positively on expected future inflation (forward-looking)
  • Inflation increases with marginal cost (equivalent to negative output gap)
  • Greater price stickiness (higher $\theta_p$) flattens the Phillips curve (lower $\kappa$)

Investment Dynamics and Tobin's Q

Capital accumulation follows:

$$K_{t+1} = (1-\delta)K_t + \left[1 - S\left(\frac{I_t}{I_{t-1}}\right)\right] I_t$$

Where $S(\cdot)$ represents investment adjustment costs (e.g., $S(x) = \frac{\psi}{2}(x-1)^2$). These costs generate realistic investment dynamics with hump-shaped responses.

The firm's optimal investment decision yields the Q-theory relationship:

$$1 = Q_t \left[1 - S\left(\frac{I_t}{I_{t-1}}\right) - S'\left(\frac{I_t}{I_{t-1}}\right)\frac{I_t}{I_{t-1}}\right] + \beta E_t\left[\frac{\Lambda_{t+1}}{\Lambda_t} Q_{t+1} S'\left(\frac{I_{t+1}}{I_t}\right)\left(\frac{I_{t+1}}{I_t}\right)^2\right]$$

Where $Q_t$ is the shadow value of installed capital (Tobin's Q).

Empirical Performance and Critiques

Aspect Model Performance Known Issues
Inflation Persistence Hybrid NKPC matches UK data reasonably well Relies heavily on indexation; structural breaks problematic
Phillips Curve Slope $\kappa$ estimated around 0.02-0.05 Implies very flat Phillips curve; identification weak
Investment Dynamics Adjustment costs generate realistic humps Underpredicts investment volatility; financial frictions matter more

Financial Markets and International Linkages

The UK is a small, open economy deeply integrated into global financial markets. What happens in New York, Frankfurt, or Tokyo matters for London. COMPASS models these international connections.

The Pound Sterling and Trade

Why Exchange Rates Matter

When the Bank of England raises interest rates, foreign investors often find UK assets more attractive (they earn higher returns). They buy pounds to invest in the UK, which pushes up the pound's value. This has two opposite effects:

  • Good for inflation: A stronger pound makes imports cheaper (like oil, food, and manufactured goods), which helps reduce inflation
  • Bad for exporters: UK goods become more expensive for foreign buyers, potentially hurting British exporters and manufacturing
The Seesaw Effect

Think of the exchange rate as a seesaw: when UK interest rates go up relative to other countries, the pound goes up. When UK rates go down relatively, the pound goes down. The Bank has to balance this seesaw when setting policy—sometimes what's good for controlling domestic inflation has consequences for exporters and vice versa.

Why This Matters for Policy

The international dimension creates both opportunities and constraints for monetary policy. The Bank can use the exchange rate as another channel to affect inflation, but it also means external shocks (oil prices, global recessions, financial crises) can require policy responses even when the domestic economy looks fine.

Open Economy Framework

COMPASS incorporates a comprehensive small open-economy structure with uncovered interest parity (UIP), trade in goods, and international asset markets.

Uncovered Interest Parity with Risk Premium
$$E_t[\Delta s_{t+1}] = (i_t - i_t^*) + \rho_t$$

Where: $s_t$ = log nominal exchange rate, $i_t$ = domestic interest rate, $i_t^*$ = foreign interest rate, $\rho_t$ = risk premium

Risk Premium: $\rho_t = \phi_b \tilde{b}_t + \epsilon_t^\rho$ where $\tilde{b}_t$ = net foreign assets

Trade Volume Equations
$$X_t = \left(\frac{P_X}{P^*}\right)^{-\eta_X} Y_t^*$$ $$M_t = \left(\frac{P_M}{P}\right)^{-\eta_M} Y_t$$

Trade elasticities: $\eta_X \approx 1.5$, $\eta_M \approx 1.3$ for UK

Exchange Rate Pass-Through
Pass-Through TypeUK Evidence
Border Prices~60-70% in first year
Retail Prices~20-30% in first year
CPI Inflation~10-15% (due to low import share)

Government Sector and Fiscal Policy

While the Bank of England controls monetary policy (interest rates), the government controls fiscal policy (taxes and spending). COMPASS includes a simple model of government behavior because fiscal and monetary policy interact.

What the Government Does in the Model

The government in COMPASS has three main activities:

  • Spends money: On public services like healthcare, education, defense
  • Collects taxes: Income tax, VAT, corporation tax, etc.
  • Manages debt: Borrows when spending exceeds taxes, pays interest on debt

Automatic Stabilizers

Built-In Cushions

The tax and benefit system automatically helps stabilize the economy:

  • In a recession: Tax revenues fall and benefit payments rise, automatically supporting the economy
  • In a boom: Tax revenues rise and benefit payments fall, automatically cooling the economy
Government Budget Constraint
$$B_{t+1}^G + T_t = R_t B_t^G + G_t + TR_t$$

Where: $B_t^G$ = government bonds, $T_t$ = tax revenues, $G_t$ = government purchases, $TR_t$ = transfers

Tax Revenue Specification
$$T_t = \tau_t Y_t$$ $$\tau_t = \bar{\tau} + \tau_y (y_t - \bar{y}) + \epsilon_t^\tau$$

Cyclical component $\tau_y(y_t - \bar{y})$ generates automatic stabilizers

Fiscal Multipliers in COMPASS
Multiplier TypeCOMPASS Range
Government Spending0.5-1.0
Tax Cuts0.2-0.5

Expectations Formation and Forward Guidance

One of the most important insights from modern economics is that expectations about the future drive behavior today. COMPASS takes this very seriously.

The Restaurant Analogy

Imagine you're deciding whether to invest in opening a restaurant. The decision doesn't just depend on today's conditions—it depends on what you expect over the next 5-10 years. Will the economy be growing? Will interest rates be low?

Similarly, families making decisions about buying houses and workers negotiating wages all look ahead.

How the Bank Shapes Expectations

The Bank's communication ("forward guidance") is a powerful tool:

  • If the Bank says it will keep rates low for long, people might spend more today
  • If the Bank signals future rate increases, people might start saving now

The Credibility Advantage: When the Bank is credible, inflation expectations stay anchored even when facing shocks, making the Bank's job easier.

Rational Expectations Hypothesis

$$E_t^{agents}[x_{t+k}] = E_t^{model}[x_{t+k}]$$

Agents' subjective expectations align with model's objective distributions

Forward Guidance Types
FG TypeSpecification
OdysseanCredible commitment to deviate from rule
DelphicCommunication of likely path
Time-Contingent"Keep rates low until date T"
State-Contingent"Keep rates low until inflation reaches 2%"
Credibility and Anchoring
$$E_t[\pi_{t+k}] \rightarrow \pi^* \text{ as } k \rightarrow \infty$$

Long-run inflation expectations equal target with perfect credibility

Input Factors & Data Sources

COMPASS is only as good as the data that goes into it. Here's what it tracks:

Key Economic Indicators

Economic Growth

What: GDP—total value of UK production

Why: Strong growth can lead to inflation

Source: ONS

Inflation

What: CPI—how fast prices rise

Why: Bank's main target (2%)

Source: ONS

"Garbage In, Garbage Out":

Even a perfect model produces bad forecasts if the input data is wrong or outdated. Economic data is often revised months later, creating real challenges.

Data Architecture and Observables

Variable Source Frequency Release Lag
Real GDP ONS National Accounts Quarterly ~6 weeks
CPI Inflation ONS Consumer Prices Monthly ~2 weeks
Unemployment ONS Labour Force Survey Monthly ~6 weeks
Bank Rate Bank of England Daily Real-time
Data Quality Issues

Mean absolute revision from preliminary to final GDP growth ≈ 0.5pp per quarter. This creates challenges for identifying output gaps in real-time.

Current Forecasts and Model-Based Rate

Based on current economic conditions, we can use COMPASS's logic to calculate what interest rate the model suggests.

Model-Based Rate Suggestion
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Based on current economic conditions and COMPASS parameters

How This Works

The model looks at three things:

  1. How far is inflation from 2%?
  2. How much spare capacity is in the economy?
  3. What's the "neutral" interest rate? (≈2.5%)
Current Situation:
  • Inflation gap: Loading...pp
  • Output gap: Loading...%
Model Settings:
  • Neutral rate: 2.5%
  • Inflation response: 1.5

Important: This is what a simple model suggests, not what the Bank should necessarily do. The actual Bank Rate is set by the Monetary Policy Committee based on broader judgment.

Forecast Scenarios

Scenario 1: Stubborn Inflation

If inflation stays high (wages keep rising, energy spikes), rates would stay higher longer.

Scenario 2: Economic Weakness

If the economy weakens (global slowdown), the Bank might cut rates faster.

COMPASS-Implied Policy Rate

Structural Rate Estimate
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Taylor Rule Specification:

$$i_t = \rho_i i_{t-1} + (1-\rho_i)[r_t^* + \pi^* + \phi_\pi(\pi_t - \pi^*) + \phi_y \tilde{y}_t]$$

Parameters: $\rho_i = 0.85$, $r^* = 0.5\%$, $\phi_\pi = 1.5$, $\phi_y = 0.5$

Forecast Scenarios
Scenario Q4 2025 2026 2027
Baseline Loading...% Loading...% Loading...%
High Inflation 5.25% 4.75% 4.25%
Rapid Disinflation 4.50% 3.75% 3.25%
Model Caveats

Neutral Rate Uncertainty: $r^*$ estimates range from 0% to 1.5% depending on methodology, carrying ±0.5pp uncertainty.

Output Gap Estimation: Real-time estimation error can exceed 2% of GDP, significantly affecting rate prescriptions.

The Bernanke Review: Model Critique and Future Direction

In April 2024, something unusual happened: the Bank of England essentially admitted it had been getting things wrong — and asked one of the world's most respected central bankers to tell them why. Ben Bernanke, who led the US Federal Reserve through the 2008 financial crisis, delivered a report that pulled no punches. COMPASS, the Bank's flagship model, has "significant shortcomings."

What Went Wrong? The Track Record

Numbers don't lie. In the years leading up to the review:

  • 2021: The Bank forecast inflation would stay near 2%. It hit 11%.
  • 2022: The Bank thought inflation would fall quickly. It stayed high for over a year longer than predicted.
  • 2008: During the financial crisis, COMPASS was "pointing in the wrong direction" — a damning indictment when crises are precisely when models matter most.

When your umbrella only works on sunny days, you have a problem.

Why Did COMPASS Fail?

Bernanke identified several deep problems — not just bad luck:

1. It Became a Frankenstein Monster

Over 13 years, staff kept bolting on fixes and patches whenever something didn't work. The result? A model so complicated that nobody fully understood it anymore. It's hard to trust a tool when you can't explain why it's giving you a particular answer.

2. It Was Starved of Resources

Models need constant maintenance — new data, updated parameters, testing against reality. But the Bank didn't invest enough in this unglamorous work. Imagine never servicing your car's engine, then wondering why it breaks down on the motorway.

3. It Missed How Money Actually Flows

COMPASS focused on abstract "intertemporal substitution" — the idea that people save more when rates rise. But it largely ignored more immediate channels: when mortgage payments jump, families have less cash to spend right now. When banks get nervous, businesses can't borrow regardless of the interest rate. These "cash flow" and "credit" channels matter enormously — and COMPASS downplayed them.

4. Staff Stopped Trusting It

Here's the most telling finding: Bank staff increasingly ignored COMPASS and relied on their own judgment and simpler models. When the people closest to a tool stop using it, that tells you something important.

What Now? The Rebuilding Plan

The Path Forward

Bernanke laid out a reform programme that the Bank has accepted:

  • Build a new, simpler core model: Something that staff actually understand and can explain
  • Use multiple models, not just one: Different tools for different questions, cross-checking each other
  • Invest properly: Dedicated teams for model development and maintenance
  • Embrace statistical methods: Sometimes simple pattern-matching outperforms fancy theory
  • Be honest about uncertainty: When you don't know, say so clearly

The Bank expects the full overhaul to take several years. In the meantime, they're being more upfront about the limitations of their forecasts — which is actually a sign of institutional maturity, not weakness.

Why Should You Care?

Short-term: Don't put too much weight on the Bank's point forecasts. The uncertainty around them is much larger than the fan charts suggest.

Long-term: Better models should mean better policy decisions — fewer mistakes like keeping rates too low in 2021 or raising them too slowly in 2022. That translates to more stable prices and a healthier economy for everyone.

The Bernanke Review, published in April 2024, represents an inflection point for central bank modeling — not just at the Bank of England but potentially across the profession. When a former Federal Reserve Chair, architect of the unconventional policy response to the 2008 crisis, delivers a systematic indictment of a major central bank's analytical infrastructure, the implications extend far beyond Threadneedle Street.

Bernanke's critique operates on two levels: specific operational failures at the Bank of England, and deeper questions about whether the DSGE paradigm — the intellectual foundation of COMPASS and similar models worldwide — is fit for purpose. Both deserve careful examination.

The Operational Failures

Structural and Operational Deficiencies

1. COMPASS Limitations:

  • Structural Shortcomings: The baseline model has "significant shortcomings" that constrain staff capacity for useful counterfactual analysis and scenario development
  • Inadequate Maintenance: Insufficient resources devoted to model maintenance, updating, stress-testing, and documentation
  • Accumulated Complexity: Years of ad-hoc extensions and workarounds have produced an unwieldy system hampering rather than enhancing analysis
  • Limited Flexibility: Difficulty producing alternative scenarios and considering heterogeneous modeling frameworks restricts policy analysis
  • Crisis Performance: COMPASS "performed badly during the global financial crisis," was "pointing in the wrong direction," and provided limited insight during recent turbulence

2. Forecasting Process Defects:

  • Reduced Model Role: COMPASS has become increasingly sidelined, with baseline forecasts relying more on judgment, sectoral models, and statistical tools
  • Judgmental Adjustments: Heavy reliance on judgment to override model implications undermines the value of having a structural model
  • Communication Disconnect: Published fan charts and scenarios don't adequately reflect genuine forecast uncertainty or alternative views
  • Resource Constraints: Forecasting process is staff-intensive yet produces forecasts no more accurate than simpler approaches

Fundamental Theoretical and Methodological Critiques

Mathematical and Conceptual Flaws in DSGE Framework

Beyond operational issues, Bernanke's review implicitly (and academic research explicitly) identifies fundamental problems with the New Keynesian DSGE approach:

1. Law of Iterated Expectations Violation:

The DSGE derivation relies on the law of iterated expectations: $E_t[E_{t+1}[x_{t+2}]] = E_t[x_{t+2}]$. This property requires that the conditional expectations are minimum mean-squared error (MMSE) predictors. However:

  • During structural breaks, means of variables shift, violating stationarity assumptions
  • When location shifts occur, conditional expectations are no longer MMSE predictors
  • The law of iterated expectations fails, invalidating DSGE equation derivations
  • Result: systematic forecast failure during crises

2. Structural Break Vulnerability:

When economy undergoes structural break at time $\tau$:

$$E[y_t | \Omega_{t-1}] \neq E[y_t | \Omega_{t-1}, \mathcal{I}_\tau]$$

Where $\mathcal{I}_\tau$ denotes information about the break. DSGE models assume agents immediately know the new structure, but in reality:

  • Breaks are recognized with delay
  • New regime parameters are uncertain
  • Transition dynamics matter but are unmodeled

3. The "DSGE Crisis Paradox":

DSGEs become unreliable precisely when most needed. During crises:

  • Structural relationships break down
  • Agents face unprecedented uncertainty
  • Rational expectations become untenable
  • Non-modeled channels (credit crunches, financial contagion) dominate
  • Model-based forecasts systematically fail

4. Omitted Transmission Channels:

COMPASS provides "a misleading account of how monetary transmission works," specifically omitting:

Credit Channel

Bank lending constraints and credit availability effects on investment and consumption. Bernanke's own research (financial accelerator) showed this channel is quantitatively important, yet COMPASS implementation is rudimentary.

Cash-Flow Channel

Direct effects of interest rate changes on firm and household cash flows independent of intertemporal substitution. Particularly important for indebted agents and working capital financing.

Asset Price Channel

Impact through housing wealth and portfolio effects. Crucial for UK given high homeownership and mortgage market structure, yet inadequately modeled in baseline COMPASS.

Bernanke's Reform Recommendations

Immediate Actions
  • Increase Model Maintenance: Dedicated staff time and resources for ongoing model development, testing, and documentation
  • Regular Evaluation: Models should be regularly evaluated, re-estimated, and stress tested against alternative specifications
  • External Interaction: Maintenance staff should interact with forecasting staff, MPC members, and external experts
Medium-Term Structural Changes
  • Develop New Core Model: Build a more transparent, simpler "core" model to replace COMPASS as the central organizing framework
  • Suite-of-Models Approach: Formalize reliance on multiple complementary models rather than a single dominant framework
  • Enhanced Statistical Models: Elevate role of purely statistical forecasting tools (VARs, factor models, nowcasting models)
  • Scenario Framework: Develop systematic methodology for generating and communicating alternative scenarios
  • Uncertainty Communication: More honest quantification and communication of forecast uncertainty

Broader Implications for Central Bank Modeling

The Bernanke Review extends beyond the Bank of England, highlighting a broader crisis in central bank modeling. The Bank is now "in a small minority of central banks without" semi-structural models that have become widely adopted, especially since the global financial crisis. The review represents a watershed moment, acknowledging that the New Keynesian DSGE framework that dominated central bank modeling for two decades requires fundamental reconsideration.

Current Status (November 2025)

The Bank continues to use COMPASS while developing its replacement framework. Staff increasingly rely on supplementary models and judgment-based adjustments. The timeline for implementing a new central organizing model remains unclear, with the Bank emphasizing the need for careful development and testing before deployment.

Technical References and Model Documentation

Core COMPASS Documentation

Bernanke Review and Critiques

Data Sources and APIs

UK Economic Data:
Primary source: Office for National Statistics (ONS)
API Access: ONS Developer Hub

Bank of England Data:
https://www.bankofengland.co.uk/statistics

Real-time Economic Indicators:
Economics Observatory - Live UK data with ONS API integration

Dynamic Data: This page uses live economic data updated through our automated scraper system. All model calculations and rate derivations reflect current market conditions. Last updated: Loading...
Model Version: COMPASS v4.2 (2011-present) | Calculation Time: Loading...
Model Disclaimer: COMPASS is a theoretical model and its outputs should not be interpreted as Bank of England policy recommendations. The model represents one analytical tool among many used in the monetary policy process.