Computable general equilibrium models

What Are Computable General Equilibrium Models?

Computable general equilibrium (CGE) models are a class of economic models that use actual economic data to simulate how an entire economy might react to changes in policy, technology, or other external factors. Within the broader field of economic modeling, CGE models are distinguished by their comprehensive, economy-wide scope, aiming to capture the interdependencies among various sectors, agents, and markets. Unlike partial equilibrium models that focus on a single market, CGE models analyze the knock-on effects and adjustments across an entire economic system following a specific "shock," such as a new tax, trade agreement, or environmental regulation. They are often used to quantify the impact of a given policy by considering how supply and demand interact across all markets simultaneously, allowing for the observation of indirect or unintended consequences.

History and Origin

The conceptual roots of computable general equilibrium (CGE) models can be traced back to the work of Léon Walras in the late 19th century, who first formalized the idea of general equilibrium where all markets simultaneously clear. However, the "computable" aspect emerged much later with advances in computational power and data availability. A pivotal moment in the development of CGE modeling was the work of Norwegian economist Leif Johansen, whose 1960 model of the Norwegian economy is often considered the first practical CGE model. His work laid the foundation for using real-world data to numerically solve complex general equilibrium systems.,^21
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Early CGE models were also heavily influenced by the input-output models pioneered by Wassily Leontief, though CGE models assign a more significant role to price changes and how they influence the allocation of resources. Over time, the methodology evolved, incorporating more detailed representations of consumer behavior, production technologies, and institutional structures. The application of CGE models gained substantial traction in the 1970s and 1980s, particularly in analyzing trade policy and development issues in economies for which time series data were scarce., ¹⁹As noted by Kevin O'Rourke, these models fundamentally represent "theory with numbers," providing a quantitative framework to explore economic interactions.
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Key Takeaways

• Computable general equilibrium (CGE) models are economy-wide tools that simulate the interactions between all sectors, households, and governments.
• They are used to analyze the broader economic impact of policies, technology shifts, or external economic shocks.
• CGE models capture direct and indirect effects, showing how changes in one part of the economy can ripple through others.
• These models are widely employed by governments and international organizations for policy analysis, particularly in areas like trade, taxation, and climate change.
• A core input for constructing CGE models is a detailed social accounting matrix.

Formula and Calculation

Computable general equilibrium (CGE) models do not adhere to a single, universal formula in the way a simple financial ratio might. Instead, they are complex systems of simultaneous equations that represent the behavior of economic agents (households, firms, government, rest of the world) and the interactions across various markets. These equations are calibrated to a benchmark equilibrium analysis dataset, typically a social accounting matrix (SAM).

The general structure of a CGE model can be conceptualized as follows:

1. Production Functions: Describe how inputs (capital, labor, intermediate goods) are transformed into outputs. Often uses Constant Elasticity of Substitution (CES) or Cobb-Douglas forms.
   $Q_i = A_i \cdot [\alpha_i K_i^{-\rho_i} + (1-\alpha_i) L_i^{-\rho_i}]^{-1/\rho_i}$
   Where:

   • ( Q_i ) = Output of sector ( i )
   • ( K_i ) = Capital used in sector ( i )
   • ( L_i ) = Labor used in sector ( i )
   • ( A_i, \alpha_i, \rho_i ) = Parameters specific to sector ( i )

2. Demand Functions: Represent household consumption, government spending, investment, and intermediate demand by firms. Households maximize utility subject to their budget constraints.
   $C_h = f(P_c, Y_h)$
   Where:

   • ( C_h ) = Consumption of household ( h )
   • ( P_c ) = Vector of consumer prices
   • ( Y_h ) = Income of household ( h )

3. Market Clearing Conditions: Ensure that supply equals demand in all markets (goods, services, labor markets, capital markets).
   $\sum_{s} Supply_{s,i} = \sum_{d} Demand_{d,i} \quad \text{for each good/factor } i$
   Where:

   • ( Supply_{s,i} ) = Supply of good/factor ( i ) from source ( s )
   • ( Demand_{d,i} ) = Demand for good/factor ( i ) by demander ( d )

4. Income and Expenditure Identities: Link the income generated by economic activities to the expenditures of economic agents (e.g., wages from labor go to households, profits to capital owners).

These equations are solved simultaneously to find a new equilibrium set of prices and quantities after a policy shock is introduced. The "calculation" involves numerical methods to find this new solution, rather than a direct algebraic formula.

Interpreting Computable General Equilibrium Models

Interpreting the results from computable general equilibrium (CGE) models involves understanding the economy-wide adjustments and resource reallocations that occur following a simulated change. A CGE model output typically presents the percentage change in various macroeconomic indicators (e.g., gross domestic product, employment, trade balances) and disaggregated results for specific sectors (e.g., changes in output, prices, and factor demand for agriculture, manufacturing, or services).

For instance, if a CGE model is used to assess the impact of a new carbon tax, the interpretation would go beyond just the direct cost to polluters. The model would show how the tax affects production costs in energy-intensive industries, leading to price changes for consumers, shifts in demand, and potentially changes in capital allocation and employment across different sectors. It can highlight how industries might shrink or grow, how real wages might be affected, or how trade patterns might shift as the economy adjusts to the new policy. The model's strength lies in illustrating these complex, interconnected feedback loops, providing a holistic view of the policy's potential consequences.

Hypothetical Example

Imagine the government of "Diversiland" is considering implementing a new tariff on imported steel to protect its domestic steel industry. To understand the full economic impact, economists might employ a computable general equilibrium (CGE) model.

Scenario: A 15% tariff is imposed on all imported steel.

CGE Model Analysis:

1. Initial State (Base Year): The CGE model is calibrated to Diversiland's current economic data, including production levels, trade flows, consumer spending, and the existing structure of its industries (e.g., steel, auto manufacturing, construction).
2. Introducing the Shock: The 15% tariff on imported steel is entered into the model as an economic policy change.
3. Model Simulation: The CGE model then computes a new equilibrium where all markets adjust.
   • Direct Effect: Imported steel becomes more expensive. Domestic steel production might increase as it becomes relatively cheaper.
   • Indirect Effects:
     • Upstream/Downstream: Industries that use steel as an input, like auto manufacturers and construction companies, face higher costs. This could lead to higher prices for cars and buildings, potentially reducing consumer demand for these products.
     • Labor and Capital: As the domestic steel industry expands, it demands more labor and capital. Conversely, if auto manufacturing shrinks due to higher costs, it might reduce its demand for these factors, leading to reallocation across labor markets and affecting overall wages and returns to capital.
     • Consumer Spending: If overall prices rise, consumers' real incomes might decrease, affecting their spending patterns across the economy.
     • Trade: The tariff might lead to a decrease in overall steel imports and potentially affect Diversiland's trade balance. Other countries might retaliate with their own tariffs, which the model could also simulate.
4. Results: The CGE model would quantify these effects, perhaps showing a small increase in domestic steel output, a slight decrease in overall GDP due to reduced competitiveness in steel-using industries, and changes in household welfare.

This hypothetical example demonstrates how a CGE model provides a comprehensive, rather than isolated, assessment of a policy's potential impact.

Practical Applications

Computable general equilibrium (CGE) models are widely used by governments, international organizations, and research institutions to analyze the broad economic impacts of policy changes and external events. Their ability to capture inter-industry and inter-country connections makes them particularly valuable for complex analyses.
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Key areas of practical application include:

• Trade Policy Analysis: CGE models are extensively used to evaluate the economic consequences of trade agreements, tariffs, quotas, and other trade policy measures. For example, the Organisation for Economic Co-operation and Development (OECD) uses its METRO (ModElling TRade at the OECD) CGE model to explore the economic impact of changes in trade policy, technology, and other factors across 61 economies and 57 economic sectors.,^{16
  15}* Fiscal Policy and Taxation: Governments employ CGE models to assess the effects of changes in tax rates (e.g., income tax, value-added tax, corporate tax), subsidies, and government spending on economic growth, income distribution, and sectoral output. These models can shed light on the wider economic impact of policies and sometimes reveal their indirect or unintended effects.
  ¹⁴* Environmental and Climate Change Policy: CGE models are a popular tool for estimating the economic effects of measures to reduce greenhouse gas emissions, such as carbon taxes or emissions trading schemes., ¹³The International Monetary Fund (IMF), for instance, utilizes its IMF-ENV global dynamic CGE model to assess the medium- and long-term macroeconomic effects and structural shifts arising from climate mitigation, energy, fiscal, and trade policies.,^{12
  11}* Development Economics: For developing economies, where time series data may be scarce, CGE models are particularly useful for analyzing the impacts of structural adjustment programs, foreign aid, or agricultural policies.,
  ¹⁰* Sectoral and Regional Analysis: CGE models can be disaggregated to analyze impacts on specific industries or regions within an economy, providing insights into how different parts of the economy are affected.

Limitations and Criticisms

While powerful tools for economic analysis, computable general equilibrium (CGE) models are subject to several limitations and criticisms:

• Data Requirements and Calibration: CGE models require extensive and detailed economic data, primarily in the form of a social accounting matrix (SAM) for a base year.,^{9 8}While they do not require long time series like econometric models, the quality and timeliness of this benchmark data can significantly influence results. ⁷Moreover, many parameters, such as elasticities of substitution, are often "borrowed" from existing literature or calibrated, rather than econometrically estimated, which can introduce uncertainty.
  ⁶* Aggregation: Critics argue that CGE models can be too aggregate, failing to shed light on specific, relevant sectors or issues in sufficient detail. ⁵Although disaggregation is possible, an overly aggregated structure may mask important nuances of market behavior.
• Static vs. Dynamic: Many CGE models are comparative static, meaning they compare two equilibrium states (before and after a shock) without explicitly modeling the adjustment path or dynamic processes over time. While recursive-dynamic and fully dynamic CGE models exist, these add complexity and rely on assumptions about expectations and investment behavior.
  ⁴* Theoretical Assumptions: CGE models are generally neoclassical in spirit, often assuming optimizing behavior by producers and households, and competitive markets. While some models incorporate imperfect competition or rigidities, these assumptions can be a point of contention, particularly when applied to economies with significant market imperfections.
  ³* "Black Box" Concerns: For non-experts, the complexity of a CGE model can make it seem like a "black box," where the relationship between inputs, assumptions, and outputs is not always transparent. Understanding the model's structure, functional forms, and closure rules is crucial for proper interpretation. As Benjamin Mitra-Kahn argues in "Debunking the Myths of Computable General Equilibrium Models," understanding how causality is imposed and how exogenous variables define results is vital for users.
  ²* Policy Questions: Some criticisms suggest that CGE models may answer "wrong or ill-posed questions" due to the artificial context created by modeling demands. ¹The usefulness of the model is heavily dependent on the quality of the policy question being asked and the scenario being simulated.

Computable General Equilibrium Models vs. Dynamic Stochastic General Equilibrium (DSGE) Models

Both Computable General Equilibrium (CGE) models and Dynamic Stochastic General Equilibrium (DSGE) models are economy-wide frameworks used in economic analysis, but they differ significantly in their primary purpose, theoretical foundations, and typical applications.

While CGE models excel at detailing the economy-wide structural adjustments from a specific policy, DSGE models are designed to explain and forecast aggregate macroeconomic variables and business cycles, often incorporating forward-looking expectations and various types of economic shocks. The choice between CGE and DSGE depends on the specific research question or policy issue being addressed.

FAQs

What is the main purpose of a Computable General Equilibrium model?

The main purpose of a computable general equilibrium (CGE) model is to simulate and quantify the economy-wide effects of a policy change, technological advancement, or external shock. It helps analysts understand how an intervention in one part of the economy can ripple through other sectors, markets, and economic agents, affecting prices, production, and welfare.

How do CGE models differ from other economic models?

CGE models differ from other economic models, such as partial equilibrium models, by covering the entire economy and explicitly accounting for the interdependencies between all sectors and markets. Unlike simpler input-output models, CGE models incorporate both the supply and demand sides of the economy and allow for adjustments in both quantities and price changes.

What kind of data do CGE models use?

CGE models primarily use a comprehensive, snapshot-in-time dataset, most commonly a social accounting matrix (SAM). A SAM provides a detailed representation of the monetary flows within an economy for a specific base year. Additional data on elasticities (e.g., how demand or supply responds to price changes) are also used, which can be estimated or drawn from existing literature.

Can CGE models predict the future?

CGE models are simulation tools designed to understand mechanisms and assess the likely effects of hypothetical scenarios, rather than to provide precise forecasts of the future. They indicate how the economy might react given certain assumptions and policy changes, but their results are not guaranteed predictions and depend heavily on the model's structure and calibrated parameters.

Are Computable General Equilibrium models used in real-world policy making?

Yes, computable general equilibrium models are widely used in real-world economic policy making. International organizations like the World Bank, IMF, and OECD, as well as many national governments and research institutions, regularly employ CGE models to analyze the potential impacts of trade policies, tax reforms, climate change mitigation strategies, and other significant economic interventions.