How ToTEM III shapes monetary policy in a commodity-dependent economy
Understanding Canada's unique modeling challenges and approach
Technical analysis of ToTEM III DSGE model and research framework
Comprehensive documentation of modeling methodology and calibration
The Bank of Canada relies on ToTEM III—Terms-of-Trade Economic Model, version III—as its primary framework for analyzing monetary policy and forecasting economic outcomes. This page examines how the model addresses Canada's distinctive economic structure: heavy commodity dependence, significant household debt, close trade integration with the United States, and regional economic disparities that challenge single-model forecasting.
This page provides comprehensive technical analysis of the Bank of Canada's ToTEM III DSGE model, including structural specifications, calibration methodology, and comparative analysis with other central bank models. Focus on small open economy features and commodity sector integration.
ToTEM III—Terms-of-Trade Economic Model, third generation—serves as the Bank of Canada's main quantitative tool for policy analysis and forecasting. Developed over fifteen years and substantially revised in 2021, it represents the Bank's accumulated understanding of how Canada's economy operates differently from other advanced economies.
The model builds on economic theory but incorporates features specific to Canadian reality. Where standard models assume a closed economy dominated by domestic factors, ToTEM III recognizes that Canada's GDP fluctuates substantially with commodity prices, that household balance sheets are stretched thin by housing debt, and that U.S. economic conditions often matter more for Canadian growth than domestic policy decisions.
Understanding ToTEM III matters because it directly shapes policy. When you read in the Bank's Monetary Policy Report that inflation will likely fall to 2.5% by mid-2025, that projection reflects ToTEM III's assessment of how various economic forces—wage growth, consumer demand, energy prices, exchange rate movements—will interact. The model doesn't make decisions, but it structures how policymakers think about trade-offs and risks.
The Bank of Canada can't simply borrow the Federal Reserve's models and adapt them for Canadian data. Canada's economy functions fundamentally differently, requiring modeling choices that reflect three core realities:
Commodity dependence: Energy and mining account for roughly 11% of Canadian GDP but generate far larger swings in national income when prices move. The 2014-2016 oil price collapse pushed Alberta into recession while leaving Ontario relatively unscathed—standard models that treat the economy as homogeneous couldn't capture this divergence. ToTEM III explicitly models commodity production with prices set in global markets, allowing the Bank to forecast how terms-of-trade shocks propagate differently across regions and sectors.
Household indebtedness: Canadian household debt-to-income ratios have consistently exceeded those in the United States since the mid-2000s, driven by housing market dynamics in Vancouver and Toronto. When the Bank raises interest rates, mortgage payment increases hit Canadian households harder than comparable tightening affects Americans—many of whom locked in thirty-year fixed mortgages at low rates. ToTEM III distinguishes between "patient" households with substantial savings and "impatient" borrowers constrained by debt, capturing these asymmetric responses to rate changes.
Trade integration: Roughly 75% of Canadian exports go to the United States, making Canada's business cycle heavily correlated with American growth. But the relationship isn't symmetric—Canadian policy rate changes have minimal impact on U.S. conditions, while Fed decisions spill over immediately via exchange rates and cross-border capital flows. ToTEM III models Canada as a "small open economy" where foreign conditions are exogenous, reflecting this asymmetric dependence.
The 2021 release of ToTEM III addressed specific shortcomings identified during the 2010s. Version II struggled to match observed housing price dynamics and underestimated the impact of debt service costs on consumption. The financial crisis revealed that models treating all households as identical missed critical transmission channels—interest rate increases hurt leveraged borrowers immediately while barely affecting savers. Version III's borrower-saver framework, estimated with Canadian mortgage market data, substantially improved the model's ability to forecast consumption responses to rate changes.
Full Name: Terms-of-Trade Economic Model, Third Generation
Type: Open-economy Dynamic Stochastic General Equilibrium (DSGE) model
Operational Since: 2021 (replacing ToTEM II)
Estimation Method: Bayesian estimation with informative priors
Key Technical Specifications:
1. Household Heterogeneity: Explicit borrower-saver distinction with different intertemporal elasticities
2. Housing Market Integration: Endogenous house price determination with housing investment dynamics
3. Financial Frictions: Household borrowing constraints linked to housing collateral
4. Improved Estimation: Bayesian methodology with expanded observable variable set
5. Export Disaggregation: Commodity vs. non-commodity export distinction
Current Version: ToTEM III (2021-present)
Database Frequency: Quarterly (1981Q1-present)
Forecasting Horizon: 3-4 years ahead
Computational Platform: MATLAB/Dynare implementation
The Bank of Canada's modeling infrastructure didn't emerge suddenly—it evolved through distinct phases, each responding to practical forecasting failures and methodological advances in macroeconomics. Understanding this evolution reveals how economic crises and policy mistakes drive modeling innovation, and why no single framework ever proves sufficient.
Context: The RDX models (Research Department eXperimental) represented the Bank's first systematic forecasting frameworks. RDX1 (1972) contained over 2,000 equations estimated from historical Canadian data, attempting to capture every observable relationship between economic variables.
Failure mode: The models collapsed during the 1970s stagflation period. Estimated relationships that held during stable times—like the Phillips curve linking unemployment to inflation—broke down when oil shocks hit. Critics invoked the Lucas Critique: parameters estimated from historical data couldn't be trusted for policy analysis if they changed when policy regimes changed.
Legacy: Despite their shortcomings, RDX models established the Bank's commitment to quantitative forecasting and revealed the inadequacy of purely statistical approaches during structural breaks.
Innovation: QPM marked a philosophical shift toward forward-looking, optimizing behavior. Rather than estimating correlations, QPM derived equations from assumptions about rational agents maximizing utility or profits. This "New Keynesian" framework became the Bank's workhorse just as Canada adopted formal inflation targeting in 1991.
Key insight: QPM recognized that credible policy commitments affect current behavior through expectations. If businesses believe the Bank will maintain 2% inflation, they price accordingly today—making the target self-fulfilling. This expectations channel became central to modern monetary policy.
Limitation: QPM treated Canada as a relatively closed economy and aggregated production into a single sector, missing the commodity boom-bust dynamics that would dominate Canadian growth in the 2000s.
Motivation: The 2000-2008 commodity supercycle exposed QPM's blind spot. As oil rose from $30 to $140 per barrel, Alberta boomed while Ontario manufacturing struggled with an appreciating Canadian dollar. A single-sector model couldn't explain why the same interest rate tightening affected regions so differently.
Structure: ToTEM I (2005) and its 2011 successor ToTEM II introduced explicit commodity and manufacturing sectors with different price-setting mechanisms. Commodity prices were treated as exogenous (determined in global markets), while manufacturing faced import competition calibrated to match Canadian trade patterns.
Gap identified: The 2008 financial crisis revealed another weakness—both ToTEM versions assumed a "representative household" with identical saving rates and balance sheets. In reality, some Canadian households carried massive mortgage debt while others held substantial assets, creating asymmetric responses to interest rate changes that the model missed.
Major revision: ToTEM III (2021) addressed household heterogeneity head-on by splitting the population into "patient savers" and "impatient borrowers" constrained by housing collateral. This modification, inspired by academic work on heterogeneous-agent models, substantially improved forecasts of consumption responses to rate changes.
Complementary framework: Recognizing that no single DSGE model excels at both structural policy analysis and near-term forecasting, the Bank developed LENS (2017)—a hybrid approach combining theory with statistical flexibility for nowcasting. Policy staff now cross-check ToTEM III projections against LENS and other tools, accepting that model uncertainty requires ensemble approaches rather than reliance on a single framework.
Each modeling generation responded to a forecasting failure that couldn't be fixed through parameter re-estimation. RDX models failed when structural relationships broke during the 1970s. QPM missed commodity cycles. ToTEM II underestimated debt effects. This pattern suggests inherent limits to model-based forecasting—economic structure evolves faster than models can adapt, guaranteeing that today's state-of-the-art framework will eventually prove inadequate for tomorrow's shocks.
The Bank's modeling framework has evolved from large-scale econometric models to theoretically-grounded DSGE models, reflecting broader trends in macroeconomic modeling and lessons from policy experience:
| Period | Model | Methodology | Key Innovation | Limitations |
|---|---|---|---|---|
| 1970-1993 | RDX Series | Large-scale econometric | Detailed sectoral disaggregation | Lucas critique vulnerability |
| 1993-2005 | QPM | Optimizing framework | Forward-looking expectations | Limited sectoral detail |
| 2005-2015 | ToTEM I/II | DSGE with commodities | Terms-of-trade shocks | Representative agent |
| 2015-Present | ToTEM III + LENS | Multi-model approach | Household heterogeneity | Computational complexity |
Transition from monetary targeting to inflation targeting required models with explicit price-setting mechanisms and credible nominal anchors. QPM development aligned with this policy framework shift.
Academic advances in DSGE methodology, particularly Smets-Wouters (2003) framework, influenced ToTEM development. Emphasis on microfoundations and policy invariance.
Crisis highlighted importance of financial frictions and heterogeneous agents. ToTEM III development explicitly incorporated these lessons with borrower-saver framework.
Recognition that no single model captures all relevant dynamics led to complementary model development (LENS) and ensemble forecasting approaches.
ToTEM III divides the Canadian economy into distinct sectors, each with different behavioral characteristics and policy sensitivities. This disaggregation matters because interest rate changes affect various economic actors differently—understanding these heterogeneous responses helps the Bank forecast aggregate outcomes more accurately than models that assume everyone behaves identically.
The model's most significant innovation relative to earlier Canadian models is its explicit treatment of household financial heterogeneity. Rather than assuming a single "representative household," ToTEM III distinguishes between two groups with fundamentally different saving behaviors and constraints.
Patient households maintain positive net financial wealth—they hold more assets than debts. These households, representing roughly 40% of the population, respond to interest rate increases by increasing savings modestly, as higher deposit returns improve their income. Their consumption adjusts gradually to policy changes, dampening immediate effects but creating persistence.
Impatient households carry substantial mortgage debt and face binding borrowing constraints tied to housing collateral values. Representing about 60% of Canadians, these households respond sharply to rate changes. When the Bank raised rates from 0.25% to 5% during 2022-2023, impatient borrowers saw monthly mortgage payments jump by thousands of dollars, forcing immediate consumption cuts. ToTEM III captures this asymmetric transmission by modeling borrowing constraints explicitly—impatient households can't smooth consumption over time when debt service costs spike, creating the strong near-term effects observed empirically.
This heterogeneity generates aggregate dynamics that differ substantially from representative agent models. A 100 basis point rate increase affects patient households minimally but hits impatient borrowers hard, with the net effect depending on the population distribution. As household debt rose from 100% to 185% of disposable income between 1990 and 2023, the impatient-borrower share grew, amplifying monetary policy transmission through this channel.
Canadian firms face distinct challenges depending on their exposure to commodity prices and foreign competition. ToTEM III models this by separating production into commodity-producing sectors (oil, gas, mining, forestry) where prices are set in global markets, and domestically-oriented sectors (construction, services, non-commodity manufacturing) where Canadian demand conditions dominate.
Commodity sector investment responds primarily to global price expectations rather than Bank of Canada policy rates. When oil prices collapsed from $105 to $26 per barrel during 2014-2016, Alberta energy firms slashed capital spending by 45% regardless of low Canadian interest rates—because project economics depended on global crude markets, not domestic financing costs. ToTEM III treats commodity prices as exogenous, acknowledging that domestic monetary policy can't offset terms-of-trade shocks originating abroad.
Non-commodity business investment responds more conventionally to interest rates through cost-of-capital channels. Higher rates increase financing costs for expansion projects, reducing net present values and delaying investment. But even here, Canadian firms face constraints absent in closed-economy models: persistent exchange rate appreciation during commodity booms erodes manufacturing competitiveness, depressing investment even when domestic demand remains strong.
Canada's small open economy status creates dependencies that constrain policy effectiveness. With 75% of exports destined for the United States, Canadian business cycles correlate heavily with American growth—recessions in the U.S. inevitably spill over via reduced export demand. ToTEM III treats U.S. variables as exogenous, reflecting this asymmetric relationship where Fed policy affects Canada substantially but Bank of Canada actions barely register in U.S. data.
The exchange rate serves as the primary adjustment mechanism linking Canadian and foreign conditions. When the Bank cuts rates below Fed levels, the Canadian dollar typically depreciates, improving export competitiveness but raising import costs and inflation. ToTEM III's uncovered interest parity condition allows for time-varying risk premia—investors sometimes demand higher returns for holding Canadian assets during periods of elevated uncertainty, temporarily breaking the mechanical interest rate differential relationship.
This external dependence limits policy autonomy. The Bank cannot maintain interest rates far below U.S. levels indefinitely without triggering capital outflows and currency weakness that fuel inflation. Conversely, maintaining rates substantially above U.S. levels attracts capital inflows that appreciate the dollar and hurt exporters. ToTEM III captures these constraints, helping policymakers assess the feasible range for independent monetary policy given external conditions.
ToTEM III employs a small open economy DSGE framework with the following core structural elements:
Household Sector Heterogeneity:
Savers: λs,t = βs Et[λs,t+1 Rt+1 / πt+1]
Borrowers: λb,t = βb Et[λb,t+1 Rt+1 / πt+1] + μt Rt+1 / πt+1
Where μt is the Lagrange multiplier on the borrowing constraint
Yc,t = Ac,t [αc Kc,t-1ρc + (1-αc) (zt Lc,t)ρc]1/ρc
Separate production technology with sector-specific productivity shocks and capital-labor ratios
Resource extraction technology with depletion effects and commodity price pass-through
Residential investment with construction-specific inputs and land constraints
| Friction Type | Mechanism | Calibration | Economic Role |
|---|---|---|---|
| Price Stickiness | Calvo pricing | θp = 0.75 | Inflation persistence |
| Wage Stickiness | Calvo wage setting | θw = 0.65 | Labor market dynamics |
| Investment Adjustment | Quadratic costs | κ = 4.0 | Smooth capital accumulation |
| Borrowing Constraints | Housing collateral | m = 0.85 | Financial accelerator |
ToTEM III divides Canada's economy into different "sectors" - think of them like different neighborhoods in a city, each with their own personality and rules:
ToTEM III's sectoral disaggregation addresses a fundamental challenge in Canadian monetary policy: shocks affect different regions and industries asymmetrically, creating trade-offs that single-sector models cannot capture. The 2014-2016 oil price collapse illustrated this starkly—Alberta's unemployment rate jumped from 4.5% to 8.6% while Ontario's remained stable, yet the Bank of Canada sets a single nationwide interest rate. Understanding these divergent dynamics helps policymakers assess whether aggregate indicators mask underlying tensions.
Oil, gas, and mining account for roughly 11% of Canadian GDP but generate outsized volatility in national income and the exchange rate. Commodity prices are determined in global markets—Canadian production represents small shares of world supply—making domestic policy ineffective at offsetting terms-of-trade shocks. When oil fell from $105 to $26 per barrel during 2014-2016, Alberta energy firms slashed employment and capital spending immediately, regardless of the Bank of Canada's accommodative interest rate response.
ToTEM III treats commodity prices as exogenous, with sector output responding to profitability at prevailing world prices. This specification acknowledges reality: monetary policy cannot stabilize commodity-dependent regions experiencing global price shocks. The model instead focuses on capturing spillovers—how commodity sector income changes affect aggregate demand through employment, business investment, and exchange rate adjustments.
Residential construction and housing services together account for 15-18% of Canadian GDP, with residential investment highly sensitive to interest rates through mortgage financing costs and housing affordability. ToTEM III models housing investment as responding to expected housing price appreciation and mortgage rate changes, with typical lags of 2-4 quarters from rate adjustments to construction activity.
The housing sector's dual role—as investment good and consumption good—creates complex transmission channels. Higher rates depress housing investment directly through increased financing costs, but also affect existing homeowners' wealth and consumption through house price adjustments. With Canadian household debt-to-income ratios exceeding 180%, these wealth effects amplify the aggregate consumption response to monetary policy beyond direct income effects.
Canadian manufacturing—concentrated in Ontario and Quebec—faces persistent headwinds from exchange rate appreciation during commodity booms. The 2002-2012 period exemplified this Dutch disease dynamic: rising oil and metals prices appreciated the Canadian dollar from 63 cents to par with the U.S. dollar, eroding manufacturing competitiveness. Ontario lost roughly 300,000 manufacturing jobs during this period, even as Alberta resource sector employment surged.
ToTEM III captures this cross-sector tension through endogenous exchange rate determination. Commodity price increases appreciate the dollar, hurting manufacturing exporters but reducing import costs for consumers. The Bank must balance supporting struggling manufacturing regions against preventing overheating in commodity-producing areas—a trade-off that standard models assuming sector homogeneity cannot represent.
ToTEM III employs a disaggregated production structure to capture sectoral heterogeneity in production technologies, price-setting behavior, and external linkages:
Technology: CES production function with capital-labor substitution
Price Setting: Calvo staggered pricing with inflation indexation
Trade: Armington aggregation of domestic and imported varieties
Pc,t1-η = αc Pc,h,t1-η + (1-αc) Pc,f,t1-η
Technology: Sector-specific productivity shocks and adjustment costs
Demand Sources: Business investment, residential investment, government investment
International Integration: High import content, machinery and equipment focus
Resource Extraction: Cobb-Douglas technology with natural resource inputs
Price Determination: Small open economy price-taking behavior
Export Orientation: Primarily destined for international markets
| Sector | GDP Share (%) | Export Intensity | Import Competition | Rate Sensitivity |
|---|---|---|---|---|
| Consumption Goods | 35-40 | Low | High | Medium |
| Investment Goods | 15-20 | Medium | Very High | Very High |
| Commodities | 10-12 | Very High | Low | Low |
| Housing Services | 12-15 | None | None | Very High |
ToTEM III incorporates input-output linkages through:
ToTEM III's design choices reflect three structural features that distinguish Canada from other G7 economies. These aren't peripheral details—they're core characteristics that drive macroeconomic volatility and constrain policy effectiveness in ways that wouldn't apply to the United States, the eurozone, or Japan.
1. Commodity Dependence and Terms-of-Trade Volatility
Canada ranks as the world's fourth-largest oil producer and holds substantial reserves of potash, uranium, and various metals. While energy and mining account for roughly 11% of GDP, their influence on national income far exceeds this share because commodity prices fluctuate violently while prices for manufactured goods and services remain relatively stable.
Consider the 2014-2016 oil price collapse, when West Texas Intermediate crude fell from $105 to $26 per barrel. Alberta's economy contracted sharply—unemployment rose from 4.5% to 8.6%—while consumers in Ontario and Quebec benefited from cheaper gasoline. The Bank of Canada faced an impossible trade-off: cutting rates to support Alberta risked overheating the rest of the country, while holding rates steady deepened Alberta's recession.
ToTEM III models this explicitly by treating commodity prices as exogenous (determined in global markets) while allowing the exchange rate to adjust endogenously. When oil prices rise, the Canadian dollar typically appreciates through a "Dutch disease" mechanism—commodity export revenue drives up currency demand, making manufacturing less competitive. The model quantifies this trade-off, helping policymakers assess whether commodity booms justify tolerating manufacturing weakness.
2. Household Debt and Housing Wealth Effects
Canadian household debt-to-disposable income ratios reached 186% by 2023, consistently exceeding U.S. levels since 2005. This wasn't driven by credit card borrowing or auto loans—it reflects housing market dynamics in Vancouver and Toronto, where prices rose over 400% between 2000 and 2022 before correcting. Mortgage debt accounts for roughly 70% of household liabilities, creating acute sensitivity to interest rate changes.
The transmission mechanism matters critically. Most Canadian mortgages carry terms of five years or less, meaning borrowers refinance frequently. When the Bank hiked rates from 0.25% to 5% during 2022-2023, mortgage reset sticker shock hit immediately—families who financed $500,000 mortgages at 2% suddenly faced 5.5% rates upon renewal, adding $1,500+ monthly to debt service costs. American households with thirty-year fixed mortgages felt no such shock.
ToTEM III's borrower-saver framework captures this asymmetry. "Impatient" households, constrained by debt and facing binding loan-to-value limits, cut consumption sharply when rates rise. "Patient" savers, holding assets rather than liabilities, increase spending modestly as deposit returns improve. The net effect depends on the distribution between these groups—a parameter the Bank estimates from Survey of Financial Security data and mortgage market statistics.
3. U.S. Economic Dependence and Policy Spillovers
Roughly 75% of Canadian exports—$450 billion annually—flow to the United States, while only 18% of U.S. exports head to Canada. This asymmetry makes Canada's business cycle heavily correlated with American growth (correlation coefficients typically exceed 0.8) while U.S. conditions barely register Canadian influence.
The policy implication is stark: the Bank of Canada cannot deviate far from Federal Reserve policy without provoking destabilizing capital flows. If Canadian rates fall significantly below U.S. rates, investors shift funds south, depressing the Canadian dollar and potentially fueling imported inflation. Conversely, maintaining rates well above U.S. levels attracts capital inflows that appreciate the currency and hurt exporters.
ToTEM III models Canada as a "small open economy" where U.S. variables—output, inflation, interest rates—are exogenous. This reflects reality: the Fed sets policy for U.S. conditions, and Canada must respond, not vice versa. The model's uncovered interest parity condition allows Canadian rates to diverge from U.S. rates only if investors demand a risk premium, which varies with economic conditions and fiscal sustainability perceptions.
Standard DSGE models developed for large, relatively closed economies like the United States miss these features entirely. They assume terms-of-trade shocks are small and infrequent, that household heterogeneity doesn't matter much for aggregate dynamics, and that foreign conditions respond to domestic policy. For Canada, all three assumptions fail badly—forcing the Bank to develop specialized frameworks or accept forecasts that systematically miss turning points.
ToTEM III incorporates several features specifically designed to capture Canadian economic structure and external dependencies:
Key Canadian Characteristics Modeled:
ToTt = (Px,t / Pm,t) * (St / Pt)
Where Px = export prices, Pm = import prices, S = nominal exchange rate
Transmission Channels:
| Housing Feature | Model Implementation | Calibration Target | Policy Relevance |
|---|---|---|---|
| House Price Determination | Endogenous equilibrium | Price-to-income ratios | Wealth effects on consumption |
| Borrowing Constraints | Loan-to-value ratios | Mortgage market data | Financial stability implications |
| Housing Investment | Residential construction | Housing starts | Business cycle amplification |
| Mortgage Renewal | 5-year rate reset mechanism | Mortgage market structure | Monetary transmission |
Trade Linkages: Bilateral trade equations with income and relative price elasticities
Financial Linkages: Uncovered interest parity with time-varying risk premium
Labor Market Spillovers: Cross-border migration effects on wage dynamics
Synchronization: Business cycle correlation through demand linkages
it = itUS + Et[Δst+1] + ρt
Where ρt = time-varying country risk premium
Regional Heterogeneity: National model abstracts from provincial differences
Institutional Details: Simplified financial system representation
Structural Breaks: Difficulty capturing permanent structural changes
High-Frequency Dynamics: Quarterly frequency limits monetary policy analysis
Imagine ToTEM III as a giant sound mixing board with hundreds of dials and sliders. Each dial controls how sensitive different parts of the economy are to changes. The Bank's economists have to set all these dials correctly so the model behaves like the real Canadian economy.
They study decades of Canadian economic data to see how people and businesses actually behaved in the past. If the model doesn't match history, they adjust the dials.
Academic studies tell them things like "when interest rates go up 1%, housing investment falls by 3%." They use this research to set the sensitivity dials.
They run the model through historical events (like the 2008 financial crisis) to see if it predicts what actually happened. If not, they keep tweaking the dials.
Setting these parameters is part science, part art. The economy changes over time, so what worked in the 1990s might not work today. That's why they constantly update and improve the model.
ToTEM III employs Bayesian estimation techniques with informative priors derived from microeconomic evidence and previous model generations. The estimation sample covers 1981Q1-2019Q4, with recursive estimation for out-of-sample validation.
Observable Variables (14 series):
| Parameter | Symbol | Prior Mean | Posterior Mean | 90% Interval | Economic Interpretation |
|---|---|---|---|---|---|
| Price Stickiness | θp | 0.75 | 0.78 | [0.72, 0.84] | Average price duration: 4.5 quarters |
| Wage Stickiness | θw | 0.65 | 0.71 | [0.64, 0.79] | Average wage duration: 3.4 quarters |
| Investment Adj. Cost | κ | 4.0 | 3.8 | [2.9, 4.8] | Investment smoothing parameter |
| Borrowing Constraint | m | 0.85 | 0.82 | [0.78, 0.87] | Maximum loan-to-value ratio |
| Trade Elasticity | η | 1.5 | 1.7 | [1.3, 2.1] | Import-domestic substitution |
Technology Shocks: Identified through long-run restrictions on productivity growth
Monetary Policy Shocks: Contemporaneous restrictions on policy rule
Commodity Price Shocks: External block identification from global markets
Housing Demand Shocks: Exclusion restrictions on non-housing sectors
Ytobs = Ytmodel + vt
Where vt ~ N(0, Σv) accounts for model misspecification
Log Marginal Likelihood: -2,847.3 (improvement over ToTEM II)
RMSE (1-step ahead): GDP growth: 0.89%, CPI inflation: 0.34%
Forecast Performance: Comparable to VAR benchmarks at 1-2 year horizons
Moment Matching: Successfully replicates key Canadian business cycle facts
Both Canada and the US use sophisticated computer models to understand their economies, but they're built differently because the countries are different. Let's compare them:
Main Focus: Small, open, commodity-dependent economy
Special Features:
Best For: Understanding how global shocks hit Canada
Main Focus: Large, diverse, relatively closed economy
Special Features:
Best For: Understanding domestic US economic dynamics
Canada: Small economy, very affected by what happens globally
US: Huge economy, more insulated from global shocks
Canada: Heavily dependent on natural resources
US: More diversified across services, manufacturing, tech
Canada: Housing wealth is huge part of household finances
US: More diverse sources of household wealth
These modeling differences reflect genuine structural distinctions rather than arbitrary design choices. ToTEM III's emphasis on commodity sectors, housing wealth, and external linkages responds to Canadian economic realities where these channels dominate transmission. FRB/US's greater sectoral detail and emphasis on financial market microstructure reflects the U.S. economy's size, depth, and complexity. Neither approach is inherently superior—each optimizes for its target economy's characteristics.
Comparative analysis of central bank DSGE models reveals systematic differences reflecting underlying economic structures and policy priorities:
| Feature | ToTEM III (Canada) | FRB/US (United States) | Rationale |
|---|---|---|---|
| Economy Type | Small open economy | Large closed economy | Trade/GDP: 65% vs 27% |
| Sectoral Detail | Commodity sector explicit | Aggregate production | Resource share: 11% vs 2% |
| Household Heterogeneity | Borrower-saver framework | Representative agent | Mortgage market structure |
| Housing Sector | Integrated in utility | Separate housing block | Housing wealth/income ratio |
| Exchange Rate | Endogenous determination | Exogenous/limited role | Trade-weighted importance |
| Financial Sector | Stylized banking | Detailed credit markets | Financial system complexity |
ToTEM III Approach:
FRB/US Approach:
ToTEM III Strengths:
FRB/US Strengths:
Financial Crisis Prediction: Neither model anticipated 2008 crisis severity
Structural Change: Difficulty incorporating permanent shifts (digitalization, climate)
High-Frequency Dynamics: Quarterly models miss intra-quarter monetary policy effects
Expectation Formation: Rational expectations assumption increasingly questioned
ToTEM III isn't just an academic exercise - the Bank of Canada uses it for real decisions that affect millions of Canadians. Here's how:
What they do: Run the model to predict GDP, inflation, and unemployment 2-3 years ahead
Why it matters: These forecasts appear in the Bank's quarterly reports and guide rate decisions
Example: "The model suggests inflation will return to 2% by late 2025"
What they do: Test "what if" scenarios like oil price crashes or US recessions
Why it matters: Helps them prepare for different possibilities
Example: "If oil drops to $40/barrel, here's how it would affect each province"
What they do: Test how different interest rate paths would affect the economy
Why it matters: Helps them choose the best policy for Canada
Example: "Cutting rates now vs. waiting 3 months - which is better?"
What they do: Study how rate changes affect housing prices and household debt
Why it matters: Prevents housing bubbles and protects financial stability
Example: "Higher rates will cool Toronto housing but hurt Alberta recovery"
When the pandemic hit in 2020, ToTEM III helped the Bank understand:
The model's insights helped guide Canada's response, including keeping rates low until 2022.
ToTEM III serves multiple functions within the Bank of Canada's policy framework, from routine forecasting to crisis response and unconventional policy analysis:
Integration in Decision Process:
Scenario Analysis: ToTEM III decomposed COVID shock into supply, demand, and uncertainty components
Policy Evaluation: Quantified effectiveness of various policy tools (rate cuts, QE, forward guidance)
Sectoral Impact: Modeled differential effects across commodity, services, and housing sectors
Target Evaluation: Simulated performance under alternative inflation targets (1.5%, 2.5%)
Dual Mandate Analysis: Assessed trade-offs between inflation and employment objectives
Digital Currency: Preliminary analysis of central bank digital currency implications
Macroprudential Analysis: Interaction between monetary policy and borrowing constraints
Regional Spillovers: Vancouver/Toronto price effects on national consumption
Financial Stability: Household vulnerability stress testing
| Variable | Horizon | RMSE (ToTEM III) | RMSE (Benchmark) | Relative Performance |
|---|---|---|---|---|
| Real GDP Growth | 4 quarters | 1.12% | 1.28% | 12.5% improvement |
| CPI Inflation | 4 quarters | 0.67% | 0.71% | 5.6% improvement |
| Employment Growth | 4 quarters | 0.89% | 0.94% | 5.3% improvement |
| CAD Exchange Rate | 4 quarters | 6.2% | 5.8% | -6.9% deterioration |
Climate Change Integration: Incorporating physical and transition risks into model framework
Digital Economy: Modeling productivity effects of technology adoption
Labor Market Dynamics: Enhanced modeling of participation and matching frictions
Global Value Chains: Supply chain disruption analysis and resilience measures
Real-Time Data: Model requires fully revised data, limiting nowcasting capability
Structural Breaks: Difficulty capturing permanent economic changes during estimation
Judgmental Adjustments: Staff overlay frequently needed for specific shocks
Communication: Complexity makes public communication of model insights challenging
Want to dig deeper into how the Bank of Canada uses economic models? Here are some great resources:
Note: Unlike the Federal Reserve's FRB/US model, ToTEM III source code is not publicly available. However, the Bank provides: