THE ECONOMIC IN THE VERY LONG RUN Chapter 8 Economic Growth II: Technology, Empirics, and Policy 1
This Chapter is about... Incorporating technological progress in the Solow model Policies to promote growth Growth empirics: confronting the theory with facts Endogenous growth model 2
Examples of technological progress From 1950 to 2000, U.S. farm sector productivity nearly tripled. The real price of computer power has fallen an average of 30% per year over the past three decades. 1981: 213 computers connected to the Internet 2000: 60 million computers connected to the Internet 2001: ipod capacity = 5GB, 1000 songs. 2006: ipod capacity = 80GB, 20,000 songs. 3
Technological Progress in the Solow Model Technological progress: Ability to produce more output with a given amount of capital and labour (inputs). Here, technological progress works through improving the efficiency of labour input Labour augmenting technological growth: Let E be defined as the efficiency of labour as E grows, labour is more efficient. Examples of things that influence E: health, education new technology (e.g., computers) 4
Assume: Technological progress is labor augmented: it increases labor efficiency at the exogenous rate g: The production function as: where, L E = the number of effective workers Suppose, L = 100 and E = 1, then L E = 100 Technological growth gives E = 2, so L E = 200. Labour is 100 percent more efficient 5
So, the labour factor of production (effective labor, L E ) is growing at a rate (n+g) So, the break even investment is ( + n + g)k consists of: k to replace depreciating capital n k to provide capital for new workers g k to provide capital for the new effective workers created by technological progress 6
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Now the capital accumulation: In the SS, : In steady state: - y, k, and c, measured as per effective worker, are constant - Y/L, K/L, and C/L are growing at the rate of technological progress g. 8
Recall, In steady state: Since, E is growing at rate g, so is Y/L Y, K, and C are growing at rate (n+g) According to the Solow model, only technological progress can explain sustained growth and persistently rising living standards. 9
The Golden Rule: As before, the golden rule level is derived from consumption function maximization. When c* is maximized: or, 10
Model s Predictions There were two main predictions: a. Differences in the level of per capita income, explained in the model by: o differences in saving rates o differences in population growth rates o differences in technology growth rates b. Differences in the growth rates of per capita income o differences in technology growth rates 11
We can re-organize our assessment in terms of convergence. Our model makes two predictions concerning convergence of economies over time: 1. Countries with similar saving rates, technology and population growth should converge to the same steady state - output per person disparities disappear in the steady state 2. Under the same conditions, low income countries should grow faster than high income countries (in the transition to steady state) 12
But, if two economies have different rates of saving, and two have different SS, then we should not expect convergence. Instead, each economy will approach its own steady state. The Solow model predicts the conditional convergence countries converge to their own steady states, which are determined by saving, population growth, and education. This prediction comes true in the real world 13
Growth Accounting: Technological Change The production function with effects of the changing technology is: where, A is the current level of technology, called total factor productivity. For given levels of inputs, if A increases by 1 percent output increases by 1 percent. 14
Taking log and doing the first order total derivatives: 15
or, This is the central equation of growth accounting R is the growth in total factor productivity, which is not observable and cannot be explained by changes in inputs R is called the Solow residual 16
Policy to Promote Growth a. Evaluating the rate of saving Use the Golden Rule to determine whether the Canadian saving rate and capital stock are too high, too low, or about right. If (MPK ) > (n + g ), Canada is below the Golden Rule steady state and should increase s. If (MPK ) < (n + g ), the Canadian economy is above the Golden Rule steady state and should reduce s. 17
To estimate (MPK ), three factors required, and for the Canadian these are given as: 1. The capital stock is about 3 times of one year s GDP: k = 3 y 2. About 10% of GDP is used to replace depreciating capital: k = 0.1 y 3. Capital s income share to the GDP is 33%: MPK k = 0.33 y Using 1 and 2, we get =0.033, depreciation rate Using 1 and 3, we get MPK = 0.11 18
So, for the Canadian economy MPK = 0.077 Since 1950, the real GDP in Canada has grown at just under 4 percent per year. As such, (n + g)= 0.04 That is, (MPK ) > (n + g ) 7.7% 4% The capital stock in Canada is well below the Golden Rule Level Suggests saving/investment should be increased Increase capital formation has been a high priority of the Canadian economic policy 19
b. How to increase the saving and investment Reduce the government budget deficit (or increase the budget surplus). Increase incentives for private saving: reduce capital gains tax, corporate income tax, estate tax as they discourage saving. replace federal income tax with a consumption tax. expand tax incentives for IRAs (individual retirement accounts) and other retirement savings accounts 20
c. Encouraging technological progresses Patent laws: encourage innovation by granting temporary monopolies to inventors of new products. Tax incentives for R&D Grants to fund basic research at universities Industrial policy: encourages specific industries that are key for rapid technological progress (subject to the preceding concerns). 21
Endogenous growth theory Solow model: sustained growth (long-run) in living standards is due to technological progress. the rate of technological progress is exogenous. Endogenous growth theory: a set of models in which technological change is treated as endogenous. At a general level, these are theories that model the process of creating, disseminating, and using ideas (new technology) 22
Simple AK Model A Basic Model: No labour input, just capital. Let, the Production function: Y = A K where, A is the amount of output for each unit of capital (A is exogenous & constant) Key difference between this model & Solow: MPK is constant here, diminishes in Solow 23
Investment: Depreciation: Equation of motion for total capital: Dividing the capital accumulation function both side by K, and use Y=AK we get: Or, If, then income will grow forever, and investment is the engine of growth. Here the permanent growth rate depends on s. In Solow model, it does not. 24
Does Capital have diminishing returns or not? Depends on definition of capital If Capital is narrowly defined (only plant and equipment), then yes Advocates of endogenous growth theory argue that knowledge is a type of capital If so, then constant returns to capital is more plausible, and this model may be a good description of economic growth. 25