Growth and Ideas. Martin Ellison, Hilary Term 2017

Transcription

1 Growth and Ideas Martin Ellison, Hilary Term 2017

2 Recap of the Solow model 2 Production function is Cobb-Douglas with constant returns to scale in capital and labour - exponent of 1/3 on K Goods invested for the future determine the accumulation of capital The amount of labour in the economy is given exogenously at a constant level Output can be used for consumption or investment Relationship Equation Production function 1/3 2/3 YY tt = AAKK tt LLtt Capital accumulation KK tt+1 = II tt ddkk tt Labour supply LL tt = LL Resource constraint CC tt + II tt = YY tt Allocation of resources II tt = ssyy tt Agents consume a fraction of output and invest the rest

3 Data through the lens of the Solow model 3 Recall the steady state ssyy = ddkk The steady state capital-output ratio is the ratio of the investment rate to the depreciation rate KK YY = ss dd Investment rates vary across countries It is assumed that the depreciation rate is relatively constant

4 Differences in steady state output per worker 4 The Solow model gives more weight to TFP in explaining per capita output than the production model We can use this formula to understand why some countries are so much richer Take the ratio of yy for two countries and assume the depreciation rate is the same yy rrrrrrr = yy pppppppp yy YY LL = AA rrrrrrr AA pppppppp ss dd 3/2 1/2 AA 3/2 ss rrrrrrr ss pppppppp 1/2 108 from Figure 3.7 in lecture from Figure 5.3 in previous slide Assuming that countries are in steady state, the factor of 108 that separates rich and poor income per capita is decomposable into TFP and investment rate differences

5 Growth in the Solow model 5 There is no long-run growth in the Solow model Empirically, economies appear to continue to grow over time Can growth in the labour force lead to overall growth? It can in the aggregate It cannot in output per person The presence of diminishing returns leads capital per person and output per person to approach the steady state This occurs even with more workers The principle of transition dynamics If an economy is below steady state then it will grow If an economy is above its steady state its growth rate will be negative The farther below (above) its steady state the faster (slower) an economy will grow Allows us to understand why economies grow at different rates

6 South Korea and the Phillippines 6 South Korea 6 percent growth a year Increase income from 10 percent of US income to 75 percent Phillippines 1.6 percent growth a year Stayed at 10 percent of US income Transition dynamics predict South Korea must have been far below its steady state Phillippines already at steady state

7 Increased saving in South Korea 7 Assuming equal depreciation rates yy KKKKKKKKKK yy UUUU = AA KKKKKKKKKK AA UUUU 3/2 ss KKKKKKKKKK ss UUUU 1/2 by multiple of 7.5 by multiple of 2

8 Understanding differences in OECD growth rates 8 Empirically, transition dynamics hold for OECD countries Countries that were poor in 1960 grew quickly Countries that were relatively rich in 1960 grew slower

9 Understanding differences in world growth rates 9 Looking at the world as a whole, on average rich and poor countries grow at the same rate Two implications: most countries have already reached their steady states countries are poor not because of a bad shock but because they have parameters that yield a lower steady state

10 Strengths and weaknesses of the Solow model 10 Strengths It provides a theory that determines how rich a country is in the long run long run = steady state The principle of transition dynamics allows for an understanding of differences in growth rates across countries a country further from the steady state will grow faster Weaknesses It focusses on investment and capital the much more important factor of TFP is still unexplained It does not explain why different countries have different investment and productivity rates a more complicated model could endogenise the investment rate The model does not provide a theory of sustained long-run growth

11 Growth and ideas 11 Objects are finite and rivalrous one person s use reduces their inherent usefulness to someone else capital and labour from the Solow model Ideas are virtually infinite and nonrivalrous one person s use does not reduce their inherent usefulness to someone else nonrivalry implies we do not need to reinvent ideas for additional use items used in making objects may be excludable through legal restrictions, e.g. patents The distinction between ideas and objects forms the basis for modern theories of economic growth

12 The economics of ideas 12 YY tt = AA tt KK tt 1/3 LL 2/3 technology = ideas A doubling of all inputs (including ideas) will result in a more than doubling of output increasing returns to scale e.g. firms pay initial fixed costs to create new ideas but don t need to reinvent the ideas again later

13 Challenges with ideas in perfect competition 13 Perfect competition results in Pareto optimality because price = MC Fixed initial costs will never be recovered If P=MC under increasing returns, no firm will do research to invent new ideas Prices must be above marginal costs in order for firms to recoup the fixed cost of research Increasing returns imply that Adam Smith s invisible hand may not lead to the best of all possible worlds Patents Grant monopoly power over a good for a period Generate positive profits Provide incentive for innovation However, P>MC results in welfare loss Other incentive for creating ideas may avoid welfare loss, e.g. government funding and prizes

14 Growth accounting 14 Growth accounting determines the sources of growth in an economy how they may change over time Consider the production function that includes both ideas and capital YY tt = AA tt KK 1/3 tt LL 2/3 The stock of ideas AA tt is referred to as Total Factor Productivity (TFP) Take logarithms and differentiate* log(yy tt ) = log AA tt log(kk tt) log( LL) 1 dd(yy tt ) YY tt dddd = 1 AA tt dd(aa tt ) dddd dd(kk tt ) dd( LL) KK tt dddd 3 LL dddd Growth rate of GDP = Growth rate of TFP Growth rate of capital Growth rate of labour * Use the chain rule and the rule for the derivative of the logarithmic function

15 Growth accounting in the 20 th century Output growth Contribution of TFP Contribution of capital Contribution of labour Japan 2.2% 0.7% 1.2% 0.3% UK 1.3% 0.4% 0.8% 0.1% US 2.8% 1.3% 0.9% 0.6% Germany 1.3% 0.3% 0.6% 0.4% Output growth Contribution of TFP Contribution of capital Contribution of labour Japan 9.2% 3.6% 3.1% 2.5% UK 3.0% 1.2% 1.6% 0.2% US 3.9% 1.6% 1.0% 1.3% Germany 6.0% 3.3% 2.2% 0.5% Output growth Contribution of TFP Contribution of capital Contribution of labour Japan 3.8% 1.0% 2.0% 0.8% UK 1.6% 0.7% 0.9% 0.0% US 2.4% 0.2% 0.9% 1.3% Germany 2.3% 1.5% 0.9% -0.1% N. Crafts (2000), Globalization and Growth in the Twentieth Century, IMF WP/00/44

16 Growth accounting in emerging markets, Output growth Contribution of TFP Contribution of capital Contribution of labour Hong Kong 7.3% 2.4% 2.8% 2.1% Indonesia 5.6% 0.8% 2.9% 1.9% Korea 8.3% 1.5% 4.3% 2.5% Philippines 3.8% -0.4% 2.1% 2.1% Singapore 8.1% 1.5% 4.4% 2.2% South Asia 4.2% 0.8% 1.8% 1.6% Latin America 4.2% 0.2% 1.8% 2.2% Africa 2.9% -0.6% 1.7% 1.8% Middle East 4.5% -0.3% 2.5% 2.3% N. Crafts (2000), Globalization and Growth in the Twentieth Century, IMF WP/00/44

17 Growth accounting for the UK Output growth Labour Capital TFP Average UK growth of 2.1% decomposes into contributions of 0.4% from TFP, 1.2% from capital and 0.5% from labour Office for National Statistics, May 2016

18 Further growth accounting 18 The input of labour to production can be decomposed into number of production workers LL yy total number of workers* LL Production function is YY tt = AA tt KK 1/3 2/3 tt LL yy Output per capita is yy tt YY tt LL = AA tt KK tt LL 1/3 LL yy LL 2/3 Take logarithms and differentiate Composition effect log(yy tt ) = log AA tt log KK tt log( LL) log( LL yy ) log( LL) 1 dd(yy tt ) = 1 dd(aa tt ) + 1 YY tt dddd AA tt dddd 3 1 dd(kk tt ) 1 dd( LL) KK tt dddd LL dddd dd( LL yy ) 1 dd( LL) LL yy dddd LL dddd Growth rate of GDP per capita = Growth rate of TFP Growth rate of capital to labour ratio Growth rate of ratio of production workers to total workers * Includes workers engaging in research and development

19 Growth accounting in the US 19 Composition effect is due to changes in the ratio of production workers to total workers

20 Next lecture 20 Modelling ideas as a source of economic growth The Romer Model