Chapter_5_Solow_Growth_Model_I - The Solow Growth Model...

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1 The Solow Growth Model Step 2 of the calibration procedure is to choose a good measuring device, namely a model. The choice of model in this book is the Growth Model (referred to as the Solow Growth model in the case that saving rate is fixed, and Neoclassical Growth Model in the case in which the savings rate is not fixed). Although there is no single model in macroeconomics that can be used to address every question, the Growth Model has been used to study a number of phenomenon. The main reason why the Growth Model has been used extensively to study a wide range of phenomenon is that its equilibrium properties match the experience of the United States economy over the last century fairly well. This is not surprising since Robert Solow (1970) developed the model to capture the long run performance of the US economy. This ability to match the U.S. growth facts is the subject of Chapter 4. The subject of this chapter is the model itself, and its equilibrium properties. 1. Parameters, Endogenous and Exogenous Variables All models are abstractions of reality. All models will have some variables that are endogenous and some that are exogenous. Additionally, mathematical models will contain parameters. Definitions: An Endogenous Variable - is an element whose value is determined within the model itself.
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2 An Exogenous Variable – is a variable whose value is assumed to be determined outside the model. From the standpoint of the model, its value is taken as a given. Exogenous variables are sometimes referred to as parameters . 2. The Solow Growth Model We begin by analyzing Solow’s version of the growth model, where the savings rate of the economy is treated parametrically. When the savings rate is treated parametrically, the model is trivial to solve out. People. Initially, there are N 0 people alive. We use N t to denote the number of people in the economy at date t. People prefer more consumption to less and are assumed to save a constant fraction s of their income. Demographics: For the purpose of this and the next chapter, we assume that the population growth is exogenously determined with a constant growth rate equal to 0 n . More specifically, t t N n N ) 1 ( 1 + = + (1) Endowments: Each person in the economy is endowed with one unit of time each period which he or she can use to work. Additionally, people are endowed with some capital initially. The aggregate endowment of capital in the economy is denoted by K 0 .
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3 Production Function: The economy produces a single final good using labor and capital. The production function is given by θ - = 1 t t t N K A Y (2) The letter A is a parameter that reflects the efficiency at which a country uses its resources to produce output. We call this parameter Total Factor Productivity (TFP).
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This note was uploaded on 04/13/2011 for the course ECON 509 taught by Professor Villamil during the Fall '08 term at University of Illinois, Urbana Champaign.

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Chapter_5_Solow_Growth_Model_I - The Solow Growth Model...

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