Production and Growth August 24 2016 1 91 What do we want to explain 2 91 The importance of small differences I Di erent growth rates lead to big di erences in income levels 3 91 Roadmap I Assume you are the president I You want to increase growth I It s costly I How do you do it I What s the best use of resources 4 91 A simple production model I Now that we have some data in mind we want to construct a model that may be consistent with these observations I A natural place to start is asking how is output produced I What are the factors of production Which ones are we going to focus on I What assumptions do we want to make on a functional form I What is the productivity component I Then we ll compare the production model to the data I This production model is central to almost everything we ll do in this course 5 91 The Production Function I GDP is produced using many factors machines labor energy land raw materials and more I Focus on Capital K Labor N and Technology A I Technology I reflects the idea that more productive economies produce more with the same K N I depends on actual technology management efficient allocation of resources human capital other institutions etc I we will see how to read it from existing data but still hard to assign exact weights for the di erent components of productivity 6 91 The Production Function A production function translates a given level of capital labor and productivity into output Yt At F Kt Nt I Yt is aggregate physical output or GDP Price index produced during period t a month quarter year I Kt is the stock of capital available during period t I Nt is the labor input or total hours of work during period t I At is Total Factor Productivity a variable that captures productivity elements we discussed I F is a time invariant function Inputs change 7 91 Marginal Products MPN MPK Y F K N A AFN N N Y F K N A AFK K K 8 91 Properties of the production function Here are four assumptions that we ll keep throughout our analysis 1 Marginal products are positive M P N 0 I MPK 0 Everything else equal more input more output 2 Diminishing marginal products M P N N M P K K 2Y 2 F K N A AFN N 0 2 N N 2 2Y 2 F K N A AFKK 0 K 2 K 2 9 91 Properties of the production function The first two properties result in production functions that have this graphical representation I Assumption 1 positive slopes I Assumption 2 diminishing slopes 10 91 Properties of the production function 3 Complementarity I More N higher marginal product of capital M P K 2Y 2 F K N A AFKN 0 N K N K N I More K higher marginal product of labor M P N 2Y 2 F K N A AFN K 0 K N K N K I Intuition provides competitive forces to balance inputs towards an optimal ratio of capital to labor 11 91 Properties of the production function 4 Constant Returns to Scale CRS I I Double the inputs double the output More precisely if we multiply both K and N by some factor 0 we get times the output AF K N A F K N Y I The ratio of capital to labor becomes the key K K N N 12 91 The Cobb Douglas Production Function Yt At Kt Nt 0 I Heavily used I Satisfies the four properties I Elasticities 1 for CRTS ln Y ln K I Y K I is the elasticity of output with respect to capital is the elasticity of output with respect to labor I I Y K K Y 1 We ll derive this later on 13 91 Development Accounting I Does the production model provide a good account for data I Assume a Cobb Douglas prod function AK N 1 I Divide by N to make it per capita 14 91 Development Accounting I Does the production model provide a good account for data I Assume a Cobb Douglas prod function AK N 1 I Divide by N to make it per capita Y AK N 1 y N N I I y is output per worker and k A K N K N Ak is the capital labor ratio Assume 0 333 and A 1 normalization I Use data k for di erent countries and calculate predicted di erences in y across countries I Compare to actual data on y I Does the model provide a good fit 15 91 Development Accounting I With our assumptions the model is inconsistent with the data I Should we dismiss it Not necessarily let s look at a related exercise 16 91 Development Accounting I Allow A Total Factor Productivity TFP to di er I Use data on y and k to find the implied di erences in A across countries y A k 17 91 The Importance of TFP I We just learned that TFP A is responsible for at least some of the observed income di erences between countries I How important Let s look at an example assuming model correct yUS yIndia 1 0 089 yUS yIndia AUS kUS AIndia k1 3 India 3 95 2 845 log 3 95 log 11 24 log 2 845 log 11 24 1 3 1 I I I 11 24 57 43 TFP is responsible for 57 of income di erences Capital is responsible for 43 of income di erences Repeating for di erent countries results in di erent numbers but A is still important 18 91 Summary of Development Accounting I A simple production model allows to account for some fraction of income di erences across countries I The large part is due to an unknown component that we call Total Factor Productivity TFP I Responsible for at least 50 of income di erences I Includes many dimensions that are crucial for growth some are easier to quantify than others 19 91 So What s in TFP I Technology accumulated knowledge I Institutions and culture I Infrastructure I Natural resources Climate and Geography I Efficient allocation of resources see next slide 20 91 Misallocations I Recent studies identified misallocations as quantitatively important I What is it Easy to illustrate with our production model I Assume two firms that have the same production function same A and same N I However firm 1 has more capital K1 K2 I Implication M P K1 M P K2 why I Let s reallocate a unit of K from 1 to 2 I I I I we lose M P K1 units of output we gain M P K2 units of output the gain is greater than the loss We can max output by reallocating K until the marginal products are equal 21 91 Misallocations I This is not the only way we can also reallocate N from firm 2 to firm …