Solow Model, Overlapping Growth Model, Endogenous Growth Model

Economic Growth Model Definitions

σ-convergence

σ-convergence tries to examine the cross-sectional dispersion of per capita income over time. The cross-sectional dispersion can be measured by the standard deviation of the natural logarithm of per capita income across a group of countries. The concept of σ-Convergence tries to examine whether this dispersion decreases over time or not.

β-convergence

β-convergence refers to a situation when the partial correlation between growth in income over time and its initial level is negative:

Production function is homogenous of degree one

Growth Accounting

Growth accounting is a framework that allows one to break down growth into components that can be attributed to the observable factors of the growth of the capital stock and of the labor force, and to a residual factor (the total factor productivity or the Solow residual). The last one measures the portion of growth left unaccounted for by increases in the standard factors of production.

Total Factor Productivity

TFP refers to that part of growth that is not explained by capital accumulation and labour force expansion (the part of growth which is explained by technological progress) assuming total output depends on physical capital and labour. It is also known as Solow’s Residual. This accounting exercise crucially hinges on two assumptions: perfect competition and constant returns to scale. The aggregate production function is a relationship between output Y(t) of an economy and inputs (factors of production), say capital K(t) and labour L(t) given the state of the available technology A(t). We assume that the technological progress is Hicks-neutral:

Y(t) = F[K(t), L(t), A(t)] = A(t)F₁[K(t), L(t)]

The equation that determines the TFP is given by:

Harrod-Neutral Technological Progress

If the technological progress is labour augmenting, then it is called as Harrod-neutral. We express the Harrod-neutral technological progress as:

F[K(t), L(t), A(t)] = F₁[K(t), A(t)L(t)] where production (output) depends on physical capital stock [K(t)], labour [L(t)] and the technology [A(t)].

Hicks-Neutral Technological Progress

If the technological progress is output augmenting, then it is called as Hicks-neutral. We express the Hicks-neutral technological progress as:

F[K(t), L(t), A(t)] = F₁[A(t)K(t), L(t)] where production (output) depends on physical capital stock [K(t)], labour [L(t)] and the technology [A(t)].

Solow-Neutral Technological Progress

If the technological progress is capital augmenting, then it is called as Solow-neutral. We express the Solow-neutral technological progress as:

F[K(t), L(t), A(t)] = F₁ A(t) [K(t), L(t)] where production (output) depends on physical capital stock [K(t)], labour [L(t)] and the technology [A(t)].

Ricardian Equivalence

Ricardian equivalence shows the irrelevance of the government’s financing decision between debt and taxes, as there is no impact on consumption or capital accumulation in a finite horizon model with bequest motive (like the OLG model with bequest motive) when the tax is lump-sum in nature. If the public sector borrows at the same rate of interest as the private sector and satisfies its inter-temporal budget constraint, it does not matter whether a given amount of public expenditure is financed through lump sum taxes or debt. This is because any increase in household wealth caused by a reduction in the current tax burden will be exactly offset by the decrease in wealth caused by the resulting increase in future taxes. Here, as long as the path of government spending remains unchanged, consumption is unaffected by taxes. However, in presence of distortionary taxation this may not be valid.

Fully Funded Social Security System

Social security system is a system that uses revenue from taxes on wage income to provide payments to senior citizens. One of the main goals of such a system is to ensure that elderly people have adequate incomes when they retire. If the social security system is fully funded, the government at time t collects from each young an amount T_t by compulsory contributions to pension fund, invests it the only productive asset of the economy, the capital stock, and pays the young when they are old an amount R(t + 1)T_t. In an OLG model, with the fully funded social security system, the inter-temporal budget constraint remains unaltered. The rate of return on social security is the same as that on private savings as far as the individual is concerned.

Pay as you Go/Unfunded Social Security System

Social security system is a system that uses revenue from taxes on wage income to provide payments to senior citizens. One of the main goals of such a system is to ensure that elderly people have adequate incomes when they retire. If the social security system is unfunded, the government at time t collects from each young an amount T_t by compulsory contributions to pension fund, and uses the proceeds to pay benefits to the old. Taking into account that there are more young than old because of population growth, each old gets (1 + n)T_t. Note here the rate of return on social security system is (1 + n), whereas the rate of return on private savings is (1+ R_t+1). This is accounted for in a new inter-temporal budget constraint.

Unconditional Convergence

According to the convergence hypothesis, poor countries grow faster than rich countries. Unconditional convergence looks at the income gap between two countries increases or decreases irrespective of these countries’ characteristics. This implies that without controlling for any country-specific characteristics, we inspect the relationship between the initial level of per capita GDP and the growth rate in per capita GDP for a set of countries.

Conditional Convergence

Conditional convergence means that we need to control for the individual countries’ steady states to determine how fast a country should grow. The...

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