Lecture 2 - Growth Accounting

Question 1

The Production Function & Constant Returns to Scale

Accepted Answer

The production function represents the transformation of inputs (labor (L), capital (K), production technology) into outputs (final goods and services). The algebraic representation is: zY = F ( zK ,z L ) Y = Output K = Capital L = Labour Key Assumption: The Production Function has constant returns to scale. This assumption lets us analyze all quantities relative to the size of the labor force. Set z = 1/L. Y/ L = F ( K / L , 1 ) <-- This is a constant that can be ignored. Y/ L = Output Per worker is come function of K / L = the amount of capital per worker Constant returns to scale imply that the size of the economy as measured by the number of workers does not affect the relationship between output per worker and capital per worker. So, from now on, et’s denote all quantities in per worker terms in lower case letters. Here is our production function: y = f( k) where f(k) = F(k,1).

Question 2

The Solow growth model

Accepted Answer

Output (GDP) driven by K = Kapital L = Labor TFP = Total Factor Productivity Assumptions: 1. Diminishing marginal product of capital - Return on an extra machine always positive - Output is always increasing in capital but at a declining rate If firm/economy has very few machines return on extra machine very high If firm/economy has many machines then return on extra machine very low Proof: German GDP and capital growth 1936-1955 Much higher incremental capital-output ratio after 1945 offers support for diminishing marginal product in 1945 & 1946 negative change in Capital Stock and very negative GDP Growth Graph: y-axis: Output-labour ratio (y=Y/L) x-axis: Capital-labour ratio (k=K/L) 2.At high k, growth is through TFP: OECD TFP EM L All K Changes in Productivity Shifts the curve up Graph: y-axis: Output-labour ratio (y=Y/L) x-axis: Capital-labour ratio (k=K/L)

Question 3

Consumption and Investment

Accepted Answer

The saving rate s determines the allocation of output between consumption and investment. For any level of k, output is f(k) investment is i= sy = s f(k), and consumption is f(k) – sf(k). Two forces influence the capital stock: Investment: expenditure on plant and equipment. Investment causes capital stock to increase Recall investment per worker i = s*y = s f(k) Depreciation: wearing out of old capital. Depreciation causes capital stock to fall. Depreciation is –δk (proportional to the capital stock)

Question 4

Dynamics of the capital stock

Accepted Answer

Two forces influence the capital stock (1) Investment: expenditure on plant and equipment. ---> Investment causes capital stock to increase Recall investment per worker i = s y = s f(k) (2) Depreciation: wearing out of old capital. --->Depreciation causes capital stock to fall. Depreciation is –∂k (is always proportional to the capital stock) Impact of investment and depreciation on the capital stock: Δk = i –∂k Δk = Change in Capital Stocki = investment∂k = Deprectiation

Question 5

Steady State: long run equilibrium & Implications

Accepted Answer

Investment equals savings--> so the law of motion of capital is :Δk = s f(k) – ∂k The steady state is reached when the capital stock does not change: Δk =0 i.e. when capital depreciation is exactly compensated by investment Production function y = f(k) depreciation = ∂k savings = s*f(k) Saving per worker depends on y (output per worker) that depends upon k (capital per worker) Scenario: (1) At k1, ∂k < s + f(k) ---> f(k) and k will rise. When Investment greater than depreciation, Output will move toward the steady state (2) At k1, ∂k > s ---> f(k) and k will fall When Investment smaller than depreciation, Output will move toward the steady state However, Growth slows as economy approaches steady state Key Implications: Countries always eventually reach their steady state In the steady state/long run growth only comes from TFP. Countries at their steady state no longer grow from capital accumulation. Can think of the OECD economies as those at their steady state Richer countries should grow slower than poorer ones: Higher returns on investment in poorer countries. Emerging markets are moving towards a steady state and growing fast According to this story we would expect countries to “catch up” with economically most advanced nations

Question 6

Do countries converge?

Accepted Answer

•Solow Growth model with decreasing returns predicts that poorer economies grow faster than wealthier ones. Proof 1: Growth explained by TFP OECD 1947-1973 Latin America 1940-1980 East Asia: 1966-1990 --> Leas to catch up amongst Europe's big 4 in Output per head (USD) France Germany Italy UK

Question 7

Estimating the steady state (Barro with 100 countries from 1965)

Accepted Answer

Positive Factors: Secondary Schooling Life Expectancy / Health Public Sepnding on Education Terms of Trade Spillover from neighbours Negative Forces: Government consumption Black market premiums / market imperfection Political instability Trade tariffs Other studies suggest results not robust and other variables key - but education, health, investment are robust across studies Always significant in over 4 mn regressions: Education - Primary School Investment Health - Life Expectacy Frequently significant Regional dummies (Latin America, Sub Saharan Africa) Rule of Law Political Rights Religious Dummies (Muslim, Protestant) Openness Degree of Capitalism Sometimes significant: Government Consumption (neg) Financial Sophistication Inflation (negative) Ethnic Diversity (Negative) Civil Liberties Revolutions, Coups, Wars Religious dummies (Buddhism) Public Investment

Question 8

Solow Model of Growth

Accepted Answer

Δk > 0 - economy is accumulating capital -> growing Δk < 0 - depreciation higher than investments, destroy capital -> declining c = (1-s) y -> we care about consumption because the agent has a utility function and he wants to consume marginal utility is declining, concav, trick: log function, 1st derivation = 1/x the marginal utility will approach infinity if x=0 u=log(x) ....u'(x)=1/x. if x---> 0, marginal utility α In order to grow, Δk must be positive. - If depreciation is high, you have to save more. - If saving is too high, s is too high and consumption os too low, as x+(1-s)*y utility function: log -> first deviation 1/x (marginal utility)

Question 9

growth

Accepted Answer

Start-ups: fast growth due to marginal returns of captital small countries grow faster than big countries large capital countries: Japan, negative growth (0 or negative growth) fast growth we will never achieve strady state we care about the progress ocmpared to last state saving is a fraction of production functin, delta is consumption if x between 0 and 1, a steady state exists when depreciation = savings

Question 10

Technological progress

Accepted Answer

Assumption: steady state is reached production function can shift upwards if you achieve technological breakthrough this will shift the production function --> Shifter "A" Productivity Shock y = A * F(K,L) -> for the same no of inpute you can double your output - in the baseline A is equal to 1. in the data, it will be a share of TFP -> that can deliver a positive technology shock? Patents, Idea Generation, Risk Aversion of Entrepreneurs, Consition: Having Entrepreneurs BUT: Innovation is costly (whats why large corporationg innovate more, you dont invent when you can import, you do not have scale and scientists yet. usually u take what is out there and divert the scale), Misallocation (often: Olymic Stadiums shut down because depreciation eats up growth) or : educational quality: Y = F (K,LA) corruption: Y= F(AK,L) Result: We will produce more, which is good because we care about consumption. higher consumtpion is good, because there is a Utility function that depends on c Developed country: Invest in R&D to shift the production function upwards Undeveloped country: Invest in factility that generate growth in the next period Tech nprogress has a double-dividend feature relative to the output effects of an increase in the saving rate which only affects output through the increase in the capital stock China, India: shift from capital accumulating economy to a consuming economy US: consumption country

Question 11

Double-Dividend of TFP

Accepted Answer

Increases in TFP boost GDP through two channels: (1) the direct effect of the upward shift in the production function so that, for given capital, firms can produce more output (2) an indirect effect whereby, for the same investment rate, an increase in TFP leads to an increase in steady state capital and output (investment with new technology)

2 The Global Macroeconomy (Fach) / Lecture 2 - Growth Accounting (Lektion)