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Satellite models
Model

Smaller models that hang off the core macroeconometric system to handle housing, energy, financial conditions, or other special topics.

How do you add sectoral, financial, or distributional detail to a core macroeconomic model without rebuilding the entire system?

Background

Central banks and finance ministries operate core macro models -- semi-structural systems, DSGE, or macroeconometric frameworks -- that produce aggregate forecasts for GDP, inflation, and interest rates. But policymakers also need granular detail: How does a rate hike affect housing starts? What happens to bank credit losses under a stress scenario? How does an oil price shock propagate through the energy supply chain? Building all this detail into the core model would make it unwieldy and slow. The satellite model architecture solves this by linking specialized auxiliary models to the core, each handling one domain in depth while taking the core's aggregate projections as inputs.

The linkage is typically one-directional: the core model produces macro trajectories (GDP growth, unemployment path, interest rates, inflation), and each satellite model takes these as exogenous conditioning variables. The housing satellite uses GDP and interest rates to forecast housing starts, permits, prices, and mortgage originations. The banking satellite uses GDP, unemployment, and interest rates to project loan losses, provisions, and capital adequacy. The energy satellite uses GDP and commodity price paths to model electricity demand, emissions, and capacity investment. The satellite does not feed back into the core. This one-way coupling keeps the core model stable and the satellite models independently testable.

Some institutions allow limited feedback. Norges Bank's system feeds the housing satellite's house-price projection back into the core model's wealth effect on consumption. The Bank of England's suite allows bank credit conditions from the financial satellite to affect the core model's lending spreads. But full two-way coupling is rare because it reintroduces the simultaneity and convergence problems that the satellite architecture was designed to avoid.

The satellite approach became standard practice in the 2000s as central banks expanded their analytical toolkit beyond aggregate forecasting. The Basel II/III regulatory framework accelerated adoption by requiring banks to project credit losses under macroeconomic stress scenarios -- a task that requires sector-level satellite models (commercial real estate, consumer credit, corporate default) linked to a core macro scenario generator. The Federal Reserve's CCAR/DFAST stress-testing framework is essentially a mandated satellite-model architecture: banks must show how macro scenarios from the Fed's core model propagate through each line of business.

How the Parts Fit Together

The architecture has three layers. First, the core model: a semi-structural system, BVAR, or macroeconometric model that produces the macro conditioning path -- quarterly or monthly trajectories for GDP, unemployment, CPI, policy rates, exchange rates, and commodity prices. Second, the bridge layer: variable transformations that convert core-model outputs into satellite-model inputs. If the core produces quarterly GDP growth but the housing satellite needs monthly housing demand, the bridge interpolates, seasonally adjusts, or applies known leading relationships. Third, the satellite models themselves: each is a self-contained econometric model for its domain, estimated on domain-specific data, with the core's macro variables entering as exogenous regressors.

A typical central bank runs 5-15 satellites alongside the core. Common satellites include: housing (starts, prices, mortgage volumes), labor market (sectoral employment, wage distribution, participation by demographic group), fiscal (revenue by tax type, expenditure by program, debt dynamics), trade (bilateral flows by commodity group, services trade, tourism), financial (bank lending, credit losses by portfolio, insurance claims), energy (demand, prices, emissions), and regional (subnational GDP, employment, house prices). Each satellite has its own data, estimation sample, and model specification. Some are simple regression models; others are complex systems of equations in their own right.

Estimation is independent. Each satellite is estimated using its own data and the core model's historical output. In forecast mode, the core model runs first, producing the macro conditioning path. This path is fed to each satellite, which produces its domain-specific projections. The satellites can run in parallel because they do not interact with each other (unless inter-satellite linkages are explicitly modeled, which is uncommon). The total system forecast is the union of the core forecast and all satellite forecasts, providing a comprehensive picture of the economy at both aggregate and granular levels.

Applications

The Federal Reserve's stress-testing framework (CCAR/DFAST) is the largest mandated satellite-model system in the world. Banks must project loan losses, revenue, and capital under the Fed's macroeconomic scenarios. Each bank runs 20-50 satellite models covering commercial real estate (CRE), residential mortgages, credit cards, commercial and industrial (C&I) loans, auto loans, and trading revenue -- all conditioned on the Fed's core macro path. The Fed's own supervisory models follow the same satellite architecture.

Norges Bank operates a suite of 12 satellites around its semi-structural core (NEMO). These include a housing model (house prices, construction, mortgage credit), a petroleum sector model (oil investment, production, fiscal revenue), a labor market model (sectoral employment, wages by industry), and a government budget model. The quarterly Monetary Policy Report integrates the core forecast with all satellite projections to give the Executive Board a comprehensive economic outlook.

Climate scenario analysis uses the satellite architecture extensively. The Network for Greening the Financial System (NGFS) publishes core macro scenarios (GDP paths under different warming trajectories). Central banks then run their own energy, land-use, and financial satellites to assess physical and transition risks. The ECB's 2022 climate stress test conditioned bank-level satellite models on NGFS core scenarios to project credit losses from energy-intensive loan portfolios.

Do not use satellite models when the domain is tightly coupled to the macro cycle (strong bidirectional feedback), when the core model's forecast quality is poor (satellite errors compound core errors), when the domain lacks sufficient historical data for independent estimation, or when the bridge between core and satellite involves untested structural assumptions (e.g., a novel policy channel with no estimation base).

Literature and Extensions

Key Papers

  • Dieppe, Gonzalez Pandiella, and Willman (2012) -- ECB multi-country model with satellite modules for trade, labor, and fiscal projections
  • Covas, Rump, and Zakrajsek (2014) -- Fed stress-testing methodology: satellite models for bank credit losses conditioned on macro scenarios
  • Aron et al. (2012) -- Bank of England's COMPASS model with housing and financial satellites feeding into the semi-structural core
  • Hammersland and Traee (2014) -- Norges Bank's satellite model suite: housing, petroleum, labor, and fiscal modules linked to NEMO
  • NGFS (2022) -- Climate scenario design: macro core scenarios with sector-level satellite modules for physical and transition risk assessment

Named Variants

  • One-way satellite: core feeds satellites, no feedback. Simplest and most common architecture.
  • Limited-feedback satellite: selected satellite outputs (house prices, credit conditions) feed back to the core through one or two channels.
  • Full two-way coupling: core and satellites solved simultaneously. Rare due to convergence and maintenance complexity.
  • Hierarchical satellite: some satellites condition on other satellites' output (e.g., mortgage loss satellite conditions on house price satellite which conditions on core).
  • Stress-testing satellite: specifically designed for tail scenarios with nonlinear specifications (threshold effects, regime switching) that activate under extreme macro conditions.

Open Questions

  • How should satellite-model uncertainty be aggregated with core-model uncertainty? Running satellites with stochastic draws from the core's forecast distribution is computationally expensive and rarely done. Most institutions use deterministic core paths with satellite-level stochastic simulation, which understates total uncertainty.
  • Can machine learning satellites (gradient-boosted trees, neural networks) replace traditional econometric satellites? They often improve point forecasts but sacrifice interpretability, making it difficult to explain to regulators or policymakers why a projection changed.
  • What is the optimal level of feedback between satellites and the core? Too little feedback ignores important macro-financial linkages. Too much feedback reintroduces the simultaneity that the satellite architecture was designed to avoid.

Components

ztcore\mathbf{z}_t^{\text{core}}ztcore​Core macro conditioning path

Vector of aggregate variables from the core model: GDP growth, unemployment, inflation, interest rates, exchange rates. Treated as exogenous by all satellites.

yt(s)y_t^{(s)}yt(s)​Satellite target variable

The domain-specific variable each satellite forecasts: housing starts, credit losses, sectoral employment, trade volumes, etc.

xt(s)\mathbf{x}_t^{(s)}xt(s)​Satellite-specific regressors

Domain data not in the core model: building permits (housing satellite), loan-to-value ratios (banking satellite), plant capacity (energy satellite).

B(s)\mathbf{B}^{(s)}B(s)Bridge/transformation layer

Mapping from core-model outputs to satellite-model inputs. May include frequency conversion, variable transformations, and lag structures.

f(s)(⋅)f^{(s)}(\cdot)f(s)(⋅)Satellite model specification

The econometric model for satellite s. Could be OLS regression, error-correction model, VAR, panel regression, or a structural system of equations.

εt(s)\varepsilon_t^{(s)}εt(s)​Satellite residual

Stochastic disturbance for satellite s. Used in stochastic simulation to generate forecast uncertainty within the satellite's domain.

Assumptions

Exogeneity of core conditioning pathTestable

The satellite model treats the core macro variables z_t^core as exogenous. The satellite's domain variables do not feed back to affect the core's GDP, inflation, or interest rates.

If violated: If the satellite domain is macro-relevant (housing: wealth effects on consumption; banking: credit supply constraints on investment), ignoring feedback biases both the core and satellite forecasts. The housing satellite underestimates the drag from a housing bust because it does not account for the GDP decline that the bust causes.

Conditional independence across satellitesTestable

Each satellite is estimated and forecast independently of other satellites. Conditional on the core path, the housing satellite does not interact with the banking satellite.

If violated: In reality, housing prices affect mortgage losses (banking satellite), and bank credit conditions affect housing demand (housing satellite). Ignoring these cross-satellite linkages understates tail risk in stress scenarios where multiple sectors deteriorate simultaneously.

Stable core-satellite relationshipTestable

The estimated relationship between core macro variables and satellite targets is stable over the forecast horizon. The elasticity of housing starts to interest rates does not change.

If violated: Structural breaks in the satellite domain (e.g., mortgage market regulation changes, energy transition) alter the sensitivity of satellite variables to macro conditions. The satellite model must be re-estimated after such breaks.

Adequate bridge specificationTestable

The transformation from core-model variables to satellite inputs correctly captures the timing, frequency, and functional form of the linkage.

If violated: A misspecified bridge (wrong lag, wrong transformation) introduces systematic forecast errors in the satellite even when the core forecast is accurate. Example: if the housing satellite uses contemporaneous GDP but the true relationship has a 2-quarter lag, the satellite's timing will be wrong.

Satellite model correctly specifiedTestable

Each satellite includes all relevant regressors (macro and domain-specific) with appropriate functional form, and the error term satisfies classical assumptions.

If violated: Omitted domain variables or wrong functional form produce biased satellite forecasts. The satellite's errors may appear small in-sample (because the omitted variable is correlated with included regressors) but large out-of-sample.

Core model forecast qualityTestable

The core model produces unbiased and reasonably accurate macro conditioning paths. Satellite forecast quality is bounded above by core model forecast quality.

If violated: Garbage in, garbage out. If the core model's GDP forecast is off by 2pp, every satellite that conditions on GDP will inherit that error. Satellite models cannot correct for core model mistakes; they can only add domain-specific information conditional on the core being approximately right.