Goodwin model

The Goodwin model is a foundational concept within Macroeconomic Theory that provides a dynamic framework for understanding cyclical fluctuations in an economy. Often placed within the broader field of Economic Dynamics, this model posits that the inherent conflict over income distribution between workers and capitalists can endogenously generate recurrent cycles in economic growth, employment rate, and wage share. Unlike many other macroeconomic models that attribute fluctuations to external shocks, the Goodwin model suggests these cycles are an intrinsic feature of capitalist systems, arising from the interplay of wages, profits, and investment.

History and Origin

The Goodwin model was first proposed by American economist Richard M. Goodwin in his seminal 1967 paper, "A Growth Cycle."⁴³ Goodwin's work synthesized aspects of the Harrod-Domar model of economic growth with the Phillips curve, which describes the relationship between inflation and unemployment.⁴² A significant intellectual influence on the Goodwin model was the Lotka-Volterra predator-prey model, originally used in biology to describe population dynamics.³⁹, ⁴⁰, ⁴¹ In Goodwin's adaptation, wages or the wage share act as the "predator," and the employment rate or the capitalist profit share acts as the "prey," leading to self-sustaining cyclical patterns.³⁷, ³⁸ The model emerged from a Marxian-Keynesian tradition, emphasizing the distributional conflict between labor and capital as a key driver of economic instability.³⁶

Key Takeaways

• The Goodwin model generates endogenous business cycles without relying on exogenous shocks, meaning fluctuations arise from internal economic interactions.
• It highlights the conflict between workers and capitalists over wage share and profits as a central mechanism driving economic cycles.
• The model predicts cyclical movements in the employment rate and the wage share of national income.
• Periods of high employment lead to rising wages, which can squeeze profits and reduce capital accumulation, eventually leading to a downturn.
• The model serves as a basis for understanding how income distribution can influence macroeconomic stability and growth.

Formula and Calculation

The Goodwin model is typically expressed as a system of two non-linear differential equations that describe the evolution of the employment rate and the wage share over time.³⁴, ³⁵ These equations capture the feedback loop between the labor market and income distribution.

Let (v) be the employment rate (proportion of the labor force employed) and (u) be the wage share (proportion of output going to wages). The core dynamic equations, in a common simplified form, are:

Where:

• (\dot{v}) represents the rate of change of the employment rate.
• (\dot{u}) represents the rate of change of the wage share.
• (\sigma) (sigma) is the constant capital-output ratio.
• (\alpha) (alpha) is the rate of growth of labor productivity.
• (\beta) (beta) is the rate of growth of the labor force.
• (\rho) (rho) and (\gamma) (gamma) are positive constants related to the Phillips curve, reflecting how real wages respond to the employment rate.

The first equation ((\dot{v})) suggests that the employment rate changes based on the profit share ((1-u)) and the combined growth rates of productivity and labor. The second equation ((\dot{u})) indicates that the wage share changes based on the employment rate and the constant growth rates of productivity and a wage adjustment parameter.³³

Interpreting the Goodwin model

Interpreting the Goodwin model involves understanding the cyclical dynamics it generates in a phase diagram, where the employment rate and wage share interact. As the economy expands and the employment rate rises, workers gain more bargaining power. This increased power leads to higher real wages and thus an increase in the wage share of national income.³¹, ³²

However, as the wage share increases, the share of profits for capitalists decreases. Reduced profitability discourages investment and capital accumulation, leading to a slowdown in economic growth and eventually a decline in the employment rate.²⁹, ³⁰ As employment falls, workers lose bargaining power, and wage growth slows or even declines, causing the wage share to fall. This decline in wage share then boosts profits, stimulating new investment and initiating another period of expansion, thus completing the cycle. The model's trajectories are typically closed orbits in the phase plane, illustrating perpetual, undamped oscillations.²⁷, ²⁸

Hypothetical Example

Consider a simplified economy operating according to the Goodwin model. Imagine the economy starts in a period of high investment and robust economic growth, leading to a low unemployment rate and rising employment rate.

1. High Employment, Rising Wages: With many people employed, workers have strong bargaining power. Wages start to rise, and the wage share of national income increases.
2. Profit Squeeze: As wages take a larger slice of the pie, the profits of businesses begin to shrink. This reduces the incentive for capitalists to invest in new productive capacity.
3. Slowdown and Contraction: Reduced investment leads to a deceleration of capital accumulation and, eventually, a slowdown in output growth and a decline in the employment rate.
4. Falling Wages, Rising Profits: As unemployment rises, workers' bargaining power diminishes. Wage growth stagnates or even declines, causing the wage share to fall. This, in turn, restores profitability for businesses.
5. Renewed Expansion: With higher profits, capitalists are incentivized to increase investment once more, leading to a recovery in economic growth and a rising employment rate, restarting the cycle.

This cyclical pattern continues indefinitely in the basic Goodwin model, driven by the internal "class struggle" dynamics.

Practical Applications

The Goodwin model serves as a significant theoretical framework for analyzing a range of real-world economic phenomena. It has been used to study economic crises by illustrating how inherent distributional conflicts can lead to downturns.²⁶ It also provides insights into the dynamics of income inequality and its relationship with economic fluctuations.²⁵

Furthermore, the model has been employed to explore the potential impact of government policies on labor markets and the overall economy.²⁴ Its non-linear, dynamic nature has inspired numerous subsequent models that incorporate additional factors, such as technological innovation, environmental constraints, global trade dynamics, and debt.²², ²³ Researchers have extended the Goodwin framework to analyze how different classes (e.g., workers, middle management, capitalists) interact and how their income shares affect economic outcomes.²¹ Empirical studies have attempted to test the Goodwin model's predictions against historical data for various countries, with mixed but often supportive results regarding the existence of distributive cycles.¹⁹, ²⁰ For example, analyses of the U.S. economy often explore the relationship between the labor share of income and employment figures, which directly correspond to the variables within the Goodwin model. FRED Labor Share of Nonfarm Business Sector Income

Limitations and Criticisms

Despite its elegance and influential insights, the Goodwin model faces several limitations and has drawn criticism. One primary critique is its simplifying assumptions, such as a closed economy with no technological change or external trade in its original form.¹⁸ While extensions address some of these, the basic model's highly stylized nature can limit its direct applicability to complex modern economies.

Empirical studies attempting to fit the Goodwin model to real-world data have yielded mixed results. While some studies find evidence that its predictions align with historical data during specific periods, the model's fit is often not perfect, particularly regarding the precise amplitude, time period, and direction of observed cycles.¹⁵, ¹⁶, ¹⁷ Critics also point out that the model's focus on class conflict may overlook the role of consumer behavior and other factors that influence aggregate demand. Additionally, the model assumes that all capacity is utilized and that investment always equals savings, which may not hold true in reality.¹⁴ Its deterministic nature, which generates perpetual cycles, does not fully account for the irregular and varied nature of actual business cycles and the myriad causes behind them.¹², ¹³ For some, the model is too stylized to fully explain long-run shifts in the growth cycle, suggesting it might be better suited for longer-term fluctuations rather than typical macroeconomics business cycles.¹¹

Goodwin model vs. Solow-Swan model

The Goodwin model and the Solow-Swan model are both influential economic models that describe economic dynamics, but they differ significantly in their focus, mechanisms, and implications.

While the Goodwin model provides a framework for understanding how distributional struggles can generate cyclical instability, the Solow-Swan model offers insights into the ultimate determinants of long-run growth rates and why economies might converge or diverge in their levels of output per capita.⁴ They represent different lenses through which economists analyze the complexities of economic dynamics.

FAQs

What is the main idea behind the Goodwin model?
The main idea is that regular business cycles are not caused by outside events but are an inherent part of the capitalist system. These cycles emerge from the ongoing struggle between workers and capitalists over how national income is divided, specifically concerning the wage share and profits.

How does the Goodwin model differ from other economic models?
Many traditional economic models focus on achieving an equilibrium state. In contrast, the Goodwin model is a dynamic model that explicitly generates continuous, non-dampening oscillations, suggesting that disequilibrium and cyclical behavior are normal. It emphasizes distributional conflict and the feedback loops between wages, employment, and investment.³

Is the Goodwin model still relevant today?
Despite its simplifications, the Goodwin model remains relevant. It helps economists understand the underlying forces that contribute to economic crises and persistent income inequality in capitalist economies. It also serves as a starting point for more complex models that incorporate additional real-world factors, continuing to contribute to Economic Dynamics research.¹, ²