Malgosia Madajewicz
U6602 Economic Development for International Affairs
Spring 2001
Part II: Aggregate perspectives: growth and structural change
A. Growth
1. Introduction: some empirical patterns
Country Time period Average annual growth rate of real percapita income
Netherlands 15801820 0.2%
U.K. 18201890 1.2%
U.S.A. 18901989 2.2%
Note: at a 2% rate of growth, percapita income doubles in 35 years
· per capita GDP in OECD countries 1870-1978 increased sevenfold (on ave for all OECD); such an increase cannot but transform societies completely
· takeoff into sustained growth (W. W. Rostow) has occurred only in the last century, and only in a handful of countries; in most developing countries, process of growth began only postWWII and even since then has been quite erratic
· between 19601985 annual growth rate of real percapita income averaged 1.9%, but there were tremendous disparities in the growth experiences of individual nations:
- E.Asian and S.E. Asian economies, excluding China, averaged 5.5% per year between 19651990
- China averaged 8.2% between 19801993
- average percapita income in Latin America fell by 11% during the 1980s
- similar declines in Africa
(show table 3.2 from Ray)
· the implications of these stark differences in growth performance are tremendous, and raise the basic question: what explains these differences?
· Robert Lucas: “Rates of growth of real per-capita income are … diverse even over sustained periods … Indian incomes will double every 50 years, Korean every 10. An Indian will, on average, be twice as well off as his grandfather; a Korean 32 times … I do not see how one can look at figures like these without seeing them as representing possibilities. Is there some action a govt of India could take that would lead the Indian economy to grow like Indonesia’s or Egypt’s? If so, what exactly? If not, what is it about the “nature of India” that makes it so?
· economic models of growth attempt to provide a framework for thinking about this question; the models are highly aggregative (in some ways, simplistic?), reflecting the methodological bias of economics towards beginning with abstract simplified models and introducing complications as necessary
2. Review of basic concepts
a. macroeconomic accounting identities
· at simplest level economic growth is the result of abstention from current consumption. To understand this, need to understand macroeconomic balance.
(figure 3.1 from Ray as a macroeconomic balance story – inflows = outflows)
· macroeconomic balance implies the following accounting identities (assuming a closed economy and ignoring government spending):
the first equation must be true as a matter of accounting – national income is divided between C and S
Y(t) = C(t) + S(t)
Value of produced output must match goods produced for C and I
Y(t) = C(t) + I(t)
But what is income – consumption?
S(t) = I(t)
where:
Y(t) = total output (income) of the economy at time t
C(t) = total consumption (expenditure on consumption goods) at time t
S(t) = total savings at time t
I(t) = total investment (expenditure on capital goods) at time t
· this is a static equilibrium at each point in time. We’re interested in the dynamic story – how an economy changes (grows) from period to period.
· to describe the dynamic evolution of the economy, we also need to track K(t), the capital stock of the economy at time t, which evolves according to:
K(t + 1) = (1-d) K(t) + I(t)
· the evolution of the economy can then be schematically represented as:
· the rate of growth of aggregate output, i.e., , therefore depends on:
- how the capital stock K(t) is translated into output, Y(t) (production function)
- how income Y(t) is allocated between C(t) and S(t) (household or individual utility maximization)
- how S(t) is translated into I(t) (firm profit maximization)
· for most purposes we will be interested in the rate of growth of percapita output or income, and to think about that we also need to consider the rate at which the population is growing. Let N(t) be the size of the population in the country at time t. Let denote the population growth rate. Then, the rate of growth of percapita output or income, i.e., , will be given by:
Note: for small changes.
b. Production functions
· to capture how capital and labor are combined to produce output, we need the concept of a production function (how much output will increase if number of spindles or of workers goes up given amount). Production functions are mathematical relationships characterized by the assumptions we make about what the relevant inputs are, the degree of substitutability across inputs and returns to scale. Can be defined for given output or at more aggregate level, firm or country. Two simple production functions that have been widely used in the growth literature are the fixedcoefficients (also called the Leontief) production function, and the neoclassical production function
· the fixedcoefficients production function is represented in the following way:
where L is the amount of labor available in the economy. At the efficient amount of K and L, Y=aK=bL, so K/L=b/a (i.e. capital labor ratio is constant), a is the inverse of the capital-output ratio (i.e., the number of units of capital required to make 1 unit of output), and b is the inverse of the labor-output ratio. Note that if we assume a fixedcoefficients production function we are assuming:
- no substitutability across inputs (factors of production) – e.g. person mowing a lawn, however is it still the appropriate representation over the long term (e.g. size of lawn mower)?
- capitaloutput ratio fixed
- constant returns to scale
· under the neoclassical production function output is given by , where the function F(.) is characterized by:
- diminishing marginal returns to both capital and labor, which implies, in particular, that the capitaloutput ratio increases as the capitallabor ratio increases
- the possibility of factor substitution
- e.g. Cobb-Douglas:
- returns to scale depend on the assumptions we make regarding a and b; for instance:
< 1 decreasing returns to scale
a + b = 1 constant returns to scale
> 1 increasing returns to scale
3. HarrodDomar growth model
· developed independently in 1940s by Roy Harrod (England) and Evsey Domar (MIT).
· main assumption – output of any economic unit depends on amount of capital invested in that unit. Essentially assumption that in a poor, laborsurplus economy, the binding constraint is likely to be the stock of physical capital.
(growth as abstention from current consumption, figure 3.1 from Ray again as a growth story – how growth happens, savings as leakage out of system which allows investment and therefore growth, system in balance when S=I; ec expands when I > than needed to replace depreciated capital, allowing next period’s cycle to recur on larger scale)
· basic equations/assumptions:
S(t) = sY(t)
I(t) = K(t + 1) – (1-d)K(t) = S(t)
where s is economywide savings rate (total savings divided by total income), i is the economywide capitaloutput ratio, j is the economywide laboroutput ratio,
- we’ve assumed all three are fixed and exogenously determined
- we've assumed that the binding constraint is the stock of physical capital, i.e. the economy has a surplus of labor
· the rates of growth of aggregate output, , and percapita output, , can then be determined:
K(t + 1) = (1-d)K(t) + I(t) Þ
iY(t + 1) = (1-d)iY(t) + sY(t) Þ
Þ
Þ
· to increase growth, raise s and accumulate capital, lower i, lower n
· comments/criticisms:
- combines fundamental features underlying growth: ability to save and invest, ability to convert capital into output, rate at which capital depreciates, population growth
- capital created by investment in plant and equipment is the main determinant of growth and savings determine this investment
- basis for Soviet planning, Indian fiveyear plans and other planned industrialization strategies; estimate i, then choose g and model will tell you s and therefore I, or choose s and model will tell you g; for whole country or by sector, especially useful if can affect s or i
- the Leontief production function assumes a fixed i, however this is likely to vary over time and to be susceptible to policy intervention. In general, capital-output ratio rises as ec grows, savings increase and surplus labor diminishes. However, it also depends on efficiency with which inputs used.
- assumption that s, i, and n are exogenous in the sense that there are no endogenous feedback mechanisms from the variables being determined within the model, i.e., K, Y, S, and I, to these "parameters"; hence, presumption that these parameters, can be directly manipulated by governments within a planned/command economy
- think through example in which savings rate endogenous – increases and then decreases as ec grows (and ec growth rate with it)
4. Neoclassical/Solow growth model
· developed by Robert Solow and others. Endogenizes i by introducing law of diminishing returns.
· basic assumptions/equations:
S(t) = sY(t)
· assumptions about F(K, L):
- diminishing marginal returns to each input
- input substitution possible, hence capitaloutput ratio endogenous
- constant returns to scale
· constant returns to scale allows us to rescale (ratio of marginal productivities depends only ratio of inputs, not on scale):
For example:
· fundamental equation of the Solow model:
· figure below depicts the longrun equilibrium of the Solow model
· the steadystate or longrun equilibrium is defined by:
where * denotes the steady state quantity of the variable
· comments/criticisms:
- key to difference with Harrod-Domar is diminishing marginal returns
- in the longrun, y is constant, i.e., in the steady state, unless there is technological progress, i.e., increases in q; in other words, technological progress is the only source of sustained growth in y (can be put into model as efficiency units of labor, then SS growth of per capita income at rate of tech progress)
- but note that even in the steady state, Y continues to grow at a rate of n
- longrun level effects: ;
- longrun growth effects:
- therefore in the longrun, three sources of variation in y, all of which are taken to be exogenously determined:
Ø population growth rates
Ø savings rates
Ø rates of technological progress
- thus if these three features are similar across economies, in the longrun we expect to see convergence, i.e., countries that start off with lower levels of k (and hence y) will exhibit higher growth rates in the transition to the longrun equilibrium. This is the hypothesis of unconditional convergence. Predicts convergence irrespective of historical starting point (i.e. two countries with similar parameters will end up in same place regardless of where started).
- hypothesis of conditional convergence admits that countries may differ in these parameters and emphasizes instead convergence to a countryspecific steady state y
- a lot of empirical research using crosscountry data has been done on this; evidence still inconclusive; some evidence for conditional convergence, i.e. convergence to same per capita growth rate (if tech progress same across countries), but still much more variation than in per capita income than theory predicts (can exaggerate theoretical predictions only at cost of ascribing a constancy of ec returns to physical capital which physical capital does not possess, it needs labor to be productive)
- also empirical research raises questions: why do saving rates and pop growth rates remain so different across countries, if tech progress drives all growth, what drives tech progress, diffusion etc
5. Endogenous growth models
· in Solow model, growth of y cannot be sustained in the longrun because of diminishing returns to K, except through technological progress, which is left unmodelled (modeled in black box way)
· endogenous growth models build upon Solow model by addressing these shortcomings:
- some models introduce human capital, H, as an additional form of capital that can be deliberately accumulated and assume that F(.) displays constant returns to scale when both factors, K, and H are included:
e.g.
Note: the omission of labor, L, here is intentional; what makes this model qualitatively different from the Solow model is the fact that the production function displays constant returns to scale in all the factors that can be deliberately accumulated; to the extent that the labor force grows exogenously, introducing L into the production function would make this model essentially equivalent to the Solow model.
Note: conditioning on human capital shows conditional convergence and divergence due to human capital
- other models have explicitly introduced investments in R&D that contribute to technological progress –who chooses the level of R&D? if individual then issue of appropriability of returns, need some degree of monopoly
- still other models have focused on increasing returns to scale, externalities and spillovers in the process of growth and capital accumulation such as those that might arise from learningbydoing, or from knowledge spillovers across firms, or complementarities such as will choose to save and invest more if expect overall ec investment to be higher in a way which affects my productivity
· Comments:
- all of these models have the implication that growth in y can be sustained in the longrun
- these models predict divergence in y across countries over time
- these models have focused the policy discussion on the importance of accumulating human capital and of increasing the knowledge base of an economy
6. Sources of growth analysis/growth accounting
· economists have attempted to determine the respective contributions of physical and human capital and tech progress to growth
· tech progress, or productivity growth, calculated as residual after all measurable inputs accounted for
· results very sensitive to procedure. Have to be very careful to properly measure measurable inputs, since TFP is residual. E.g. WB study finding that 1/3 of growth of rapidly growing E. and S.E. Asian economies due to TFP. Result wiped out by Alwyn Young’s careful study (TFP growth varying from .2% in Singapore to 1.7% in S. Korea): overest TFP growth if proxy L force with pop growth since L force participation increased hugely, if looking for TFP in manufacturing have to account for rural-urban migration in calculating L force, have to account for changes in K and L, particularly changes in quality, e.g. education of L (more educated L is more L)