Solow Growth Model - Videos

Teaching

A video tutorial and walk-through of the Solow growth model, beginning with the basic setup and assumptions, the capital accumulation equation, the steady state, the Solow diagram, transition dynamics, and convergence. The model is then extended to incorporate population growth and labor-augmenting technological progress.

Author

Curtis Kephart

Published

Dec 20, 2012

Solow growth diagram showing output, investment, and break-even investment curves meeting at the steady state.

The Solow diagram with technology and population growth — output per effective worker \(y=f(k)=Ak^{\alpha}\) (red), investment per effective worker \(i_t=sy=sAk^{\alpha}\) (green), and break-even investment \((g_L+g_A+\delta)k\) (yellow) — meeting at the steady state \(k^{*}\), \(y^{*}\).

The following videos are designed as a teaching aid for my intermediate level macroeconomics discussion tutorial. All errors are my own.

Solow Growth Model - Video Tutorial

The Solow Growth Model (aka the Solow-Swan model, the exogenous growth model, or the neoclassical growth model) is a model of long-run economic growth. It relates growth in a model economy to productivity (via a production function & a process for technology growth), capital accumulation (via a law of motion of capital, with investment defined by an exogenous savings rate, and exogenously defined depreciation), population growth, and a process for technology to accumulate.

At its simplest, the model demonstrates how these features can combine into a neoclassical framework (i.e. the set of model features we usually start off the course with: production function, rational economic agents, markets in equilibrium, etc.) and result in steady state level of capital (or steady state per-effective worker level with labor-augmented technology growth), which results in balanced growth of output-per-person. Usefully, the model can also show how various shocks and policy tweaks may result in different economic outcomes.

However, the Solow model is only part, and just the start of the story explaining economic growth.

Outline of Solow Model Series:

  • Introduce simple solow model.
    • Model’s set-up and assumptions.
    • Capital accumulation equation
    • Steady state
    • Solow diagram
    • Transition dynamics and convergence
    • Time Series chart of solow model
    • Applications of the simple version of the model.
  • Extend model to include population growth.
  • Extend model to include technology growth (exogenous and constant labor augmented technology).
    • Growth Rates of key variables - level effects vs. growth rates.
    • Empiricals: How well does the solow model fit the data? How well does the model explain economic growth?
    • Applications & examples of “full” solow-swan model.
  • Odds and ends.
    • Golden rule level of capital (and savings rate)
    • Solow residual

Key Concepts

  • Solow growth model
  • Savings Rate
  • Depreciation
  • Stock vs flow
  • The capital accumulation equation (the law of motion of capital)
  • Diminishing returns
  • Net investment
  • Steady state
  • Solow Diagram
  • Absolute vs. conditional convergence

Simple Solow Model

We walk through the simple Solow model (no population growth, no technology growth, not too much too complicate the model yet)
View Video Playlist (9 vids 1:55:00)

  1. Introduction and Motivation for the Model
  2. Solow Model Set-up & Assumptions
    Set-up model, discuss assumptions, notation and key variables & parameters. We also start working toward the steady state level of capital.
  3. Solow Diagram
    It’s useful to convert the solow model’s equations into a diagram. For many, the model’s insights become much more apparent.
  4. Solow Model Transition Dynamics
    The Solow model is a dynamic model, meaning we can plot how our variables of interest evolve through time. This helps us better understand convergence to the steady state and the effect of shocks to the model economy.

Applications and Example Problems of Simple Solow Model

Working with the very simple model: Shocks to the solow model plus their effect via solow diagram and time-series. Some intuition.

Solow Model with Population Growth

Adding in exogenous population growth doesn’t change the model much, but some steady states become balanced growth paths. I walk through the extended model below.
View Video Playlist (2 vids 36:55)

Solow Model with Technology Growth and Population Growth

Applications of extended solow model

Working with the solow-swan model with technology growth and population growth. Given the following shocks, we look at the effect on the solow diagram, and show time series analysis on the major economic variables.

Additional Content

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