Growth theory

Terms, definitions, basics

 * Growth comes from capital accumulation, technological progress and savings rate
 * Capital accumulation by itself cannot sustain growth because of decreasing returns to capital (i.e. sustaining a steady increase in output per worker will require larger and larger increases in the level of capital per worker)
 * Increasing saving rate can also only transitorily raise growth rate until we are back to steady-state growth
 * Steady-state: output per worker and capital per worker are no longer changing
 * Fully funded security system: Tax workers, investing in financial assets, and paying back the principal plus the interest to the workers when they retire. At any time, the system has funds equal to the accumulated contributions of workers, from which it will be able to pay benefits to these workers when they retire → pension depends on the rate of return on the financial assets held by the fund
 * Pay-as-you-go social security system: Tax workers and redistribute the tax contributions as benefits to the current retirees → pension depends on demographics (ratio of retirees-to-workers) and tax progressivity
 * Endogenous growth models: generate steady growth even without technological progress. Reflect the fact that in those models the growth rate depends, even in the LR, on variables such as the saving rate and the rate of spending on education

Capital accumulation, and Output

 * The amount of K determines the amount of Y being produced
 * The amount of Y being produced determines the amount of S and, in turn, the amount of K being accumulated over time
 * Effect of capital on output depends on what aggregate production function we have
 * The aggregate production function F tells us how much output is produced for given quantities of capital and labor. If we take the production function per worker and assume
 * Constant returns to scale: $$ \frac{Y}{N} = F(\frac{K}{N}, \frac{N}{N}) = F(\frac{K}{N}, 1)$$ → the amount of output per worker depends on the amount of capital per worker (but we have decreasing returns to capital → more capital = more output but decreasingly so)
 * New capital stock is: Kt+1 = (1-&delta;)Kt + It → new capital stock is whatever old capital stock we still have after we subtracted depreciation and added any new addition of capital
 * Evolution of capital per worker is: $$\frac{K_{t+1}}{N} – \frac{K_t}{N}= \Delta \frac{K}{N} =sf(\frac{Y_t}{N}) – \delta(\frac{K_t}{N})$$ → in words, the change in the capital stock is whatever part of output (per worker) not consumed but instead saved (i.e. invested) less what is needed to reproduce capital stock, i.e. change in capital per worker is given by the difference between investment per worker and depreciation per worker. For the no growth steady-state: $$\frac{K*}{N}$$ investment is just enough to cover depreciation
 * An economy in which output per worker grows at a constant rate is represented by a line with slope equal to that growth rate.

Technological progress

 * Shifts the production function: technological progress means more output per worker given capital per worker
 * In SS, the rate of growth of output per person is simply equal to the rate of technological progress.

Neoclassical view

 * There must be some value of the saving rate between 0-1 that maximizes the steady-state level of consumption → Golden-rule level of capital: The level of capital associated with the value of the saving rate that yields the highest level of consumption in steady state
 * Increases in the saving rate below this value lead to a decrease in consumption initially, but lead to an  increase in consumption in the long run. Increases in the saving rate beyond this value decrease consumption not only initially but also in the long run.
 * Saving rate can affect not the SS rate of growth but the level of output

Theories

 * In the neoclassical growth model and in the full employment version of the Classical growth model, the ultimate constraint on growth is the effective labor force, that is, the labor force taking into account the role of technical progress.

Classical views

 * Smith
 * Smith, e.g., thought that (à la trickle-down) the free pursuit of maximum profit would foster capital growth, which in turn creates a demand for labor and thus raises also wages. While population will grow along with capital in the process of growth, Smith thought that it would lag enough to assure a long period of higher wages → increasing returns to scale
 * Malthus
 * Over most of human history technological progress caused larger population growth but had no impact on income per capita in the long run: significant positive effect of the technological level on population density and an insignificant effect on income per capita significantly over the years 1–1500
 * Malthus reasoned that an ↑real wage → ↑workers’ standards of living → marry earlier/reduce infant mortality → ↑population → depress real wage until the (demographic equilibrium) point where infant mortality/later marriage stabilize population growth. The equilibrating real wage = natural wage around which actual wages fluctuate
 * Ricardo
 * Took up Malthus’s ideas about population and the real wage and combined them with his own theory that rent arises from the limited supply of fertile land. In Ricardo’s view, Smith’s virtuous cycle was doomed to extinction as capital accumulation and population growth eventually used up all the fertile land, food prices rose, and proﬁt rates declined to zero in what he called the stationary state → diminishing returns
 * Emphasis on class division: Workers, with wages depressed to the minimum compatible with reproduction by Malthusian forces, had no surplus available to save. As proﬁt rates fell as a result of rising rents and wages with population growth, however, Ricardo argued that the capitalist engine of growth would be choked off by a falling rate of proﬁt
 * Marx
 * Disagreed with Ricardo’s view that diminishing returns to capital and labor (b/c limited land) would eventually bring capital accumulation to a halt through rising rents and wages
 * More Smithian view: historical genius of capitalism is its technological progressivity (enforced by pressure to ﬁnd cost-reducing technical innovations)
 * What would lead to a fall in the rate of proﬁt, Marx argued, was that these cheaper technologies would use more and more capital per worker, thus driving down the rate of proﬁt

CWSM

 * In the conventional wage share version of the Classical growth model the rate of capital accumulation is free to vary because the rate of growth of the labor force can adapt → an endogenous growth model because the rate of capital accumulation is a variable determined within the model itself.

Neoclassical

 * Turning away from the explosive social and political issues that the Classical theory of growth seemed to lead to, marginalist economists focused their attention on the static efﬁciency of economic allocation, and the tendency for markets to equalize marginal costs and marginal beneﬁts across society

Demand-constrained (Keynesian)

 * Endogenous growth
 * Path dependence/hysteresis: the shock itself alters potential GDP; under path dependence, temporary shocks have permanent effects
 * Path dependence with respect to capital and employment because these variables do not return to a preexisting path after a temporary shock.
 * For example, an extended period of unemployment may discourage workers from participating in the labor force, convince immigrant workers to return home, or result in a deterioration of workers’ skills, so that when the economy recovers, it achieves an equilibrium level of employment and output that is lower than it would have been in the absence of the demand shock.