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Chapter_5_Solow_Growth_Model_II

# Chapter_5_Solow_Growth_Model_II - Calibrating the Solow...

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1 Calibrating the Solow Growth Model 1. Chapter overview The purpose of this chapter is two- fold. First, we shall try to make clear the reason why the Solow Growth Model is a good measuring device for a number of relevant and important macroeconomic questions. Second, we shall demonstrate the calibration procedure in the simplest way possible. Recall the five steps of the calibration process: 1. Pose a Question 2. Choose a good measuring device 3. Define Consistent Measures 4. Assign Parameters 5. Comparison of Model Predictions to Data 2. Good Measuring Device The reason why the Solow growth model is a good measuring device for addressing a host of questions is that its balanced growth path is both qualitatively and quantitatively consistent with the experience of the US economy over the 20 th Century. This makes the model attractive for analyzing the business cycles, international income differences, and for evaluating the effects of alternative government policies.

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2 2.a Review of Balanced Growth Path Properties of the Model In Chapter 3, we solved for the balanced growth path equilibrium of the Solow Growth Model. We showed that along the Balanced Growth Path Equilibrium, γ + = = = = + + + + 1 1 1 1 1 t t t t t t t t w w c c k k y y and . 1 1 = + t t r r Additionally, it is easy to verify that capital’s share of income and labor’s share or income are constant over time. Capital’s share of income is defined as t t t Y K r / and labor’s share of income equals t t t Y N w / . In any equilibrium, t t t N Y w ) 1 ( θ - = . (1) t t t t t k y K Y r = = (2) Multiplying both sides of the profit maximization condition by N t /Y t yields - = 1 t t t Y N w . (3) Applying a similar algebraic multiplication to the capital profit maximization condition, yields = t t t Y K r (4) Thus, not only are the capital and labor shares of income invariant over time, but they are equal to their respective exponents in the production function. This relation will be particularly useful when we assign values of the parameters in step 4 of the calibration procedure.
3 2.b US Long Run Growth Facts The reason that the Solow model is a good measuring device is that it accounts for the long run performance of the US economy. The stylized growth facts of the US economy are as follows: (Real) per capita GDP has grown at roughly 2 percent per year on average Real wage growth of roughly 2 percent per year on average A constant real return to capital A constant consumption to output, and investment to output ratio. A constant capital share of income equal to roughly 1/3 and a constant labor share of income equal to 2/3 A constant capital to GDP ratio of 2.5 on a yearly basis. Population growth of roughly 1 percent per year over.

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Chapter_5_Solow_Growth_Model_II - Calibrating the Solow...

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