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**Chapter 13 The Determinants of Economic Growth: An Empirical Overview**

© Pierre-Richard Agénor The World Bank

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Growth Accounting The East Asian “Miracle” Growth Regressions and convergence Testing the Mankiw-Romer-Weil Model The Empirics of Growth: Econometric Issues The Econometric Evidence: An Overview Catching Up or Falling Behind?

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Growth Accounting

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Two main types of empirical studies on the determinants of economic growth: growth accounting and cross-country regressions. Growth accounting: consists of adding contributions of growth of basic factor inputs (labor and capital) to an unexplained (exogenous) residual that captures improvements in technology.

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**Y = AF(K, L). (1) gY = gA + KgK + Lg (2)**

Basic Growth Accounting Equation Suppose output is described by, Y = AF(K, L). (1) A is Hicks neutral: An increase in technological progress raises the level of output without effecting marginal product of inputs. Differentiating with respect to time yields, gY = gA + KgK + Lg (2) K = FKK/F; L = FLL/F.

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L and K are equal, respectively, to the share of labor and capital income in total output, and, by Euler’s Theorem add up to 1. Using above information, (2) can be written as, gY/L = gA + KgK/L, gY/L : growth of output per worker; gA : Solow residual or rate of growth of total factor productivity, TFP; KgK/L: rate of growth of capital per worker.

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**gA = gY/N - KgK/N + (1 - K)gL/N .**

With Cobb-Douglas specification (Y = AK L(1-)), and K = , L = 1 - , TFP growth, gA = KgK/Y + (1 - K)gY/L . In per capita (rather than per worker) terms, TFP, gA = gY/N - KgK/N + (1 - K)gL/N .

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Framework has been extended to include not only investment in physical and human capital, but also variables such as changes in the composition and quality of factor inputs, economies of scale in domestic markets, government regulations, labor hoarding, and changes in rates of capacity use. Nevertheless, land is still ignored, with the potential of thus overstating capital’s share in the production function and understating the rate of TFP growth.

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**Basic Growth Accounting Limitations**

No standard measurement method for estimating growth rates of capital and labor. Capital: Typically constructed using perpetual inventory method: cumulating data on investment flows at constant prices from sources such as the Penn World Tables and assuming a constant depreciation rate (4-6%). Quality-adjusted measures of capital: Roldos (1997), for example, looked at relative rental rates in Chile as proxy of capital quality. Most adjustments are ad hoc.

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Labor: Measured using participation rates and work hours. Differences among types of workers and data reliability across countries create problems for comparative analysis. Quality adjusted labor: adjusting for different levels of education with weights given to relative wages. Such adjustments may underestimate true TFP by attributing a larger part of output increase to more educated labor force (Sarel, 1997).

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**Estimation of Factor Shares**

Factor shares, e.g. K , , estimated from national accounts data. Assumes perfect competition: each factor’s income contribution will equal its marginal product. Monopoly profits tend to overstate elasticity of output with respect to capital. Subsidies to capital-intensive industries may lead to an overestimation of the share of capital in the production process. Positive externalities, particularly increasing returns to scale may underestimate the contribution of capital and overestimate the true degree of total productivity growth (see Barro,1998).

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**The East Asian “Miracle”**

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Some Facts: Growth in some East Asian Countries averaged 6% between Output per worker increased by more than 5% per annum from in Korea, Singapore, Thailand, and Taiwan. From , Indonesia, Malaysia, Singapore, and Thailand more than doubled their real income per capita, compared with an increase of only 20% in the United States (Sarel 1997, p. 369). Rapid pace of physical investment resulted in a tenfold increase in the capital-labor ratio in Singapore between

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Explanations: Young (1995): nothing miraculous, rising investment, increasing labor-force participation and quality--not TFP, nothing exogenous. Collins and Bosworth (1996): From , average growth of output per worker equaled 4.2% for East Asia Only 1.1% due to TFP growth. 2.5% from high rate of physical capital accumulation per worker

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Something miraculous Sarel (1997): Found that TFP growth in East Asia was much higher than Young’s results would have suggested. Sarel attempted to capture the structure of production across countries in estimating input factor shares. Obtained capital shares, , ranging from .28 for Thailand to .34 for Singapore. (by contrast, Young had a capital share of .5 for Singapore) : TFP estimates very strong for Singapore (2.2%), Malaysia and Thailand (2%), and much less so in Indonesia (1.2%). By contrast, the U.S. had a TFP growth of .3% during this period.

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Growth Regressions and Convergence

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**Diminishing Returns and Convergence**

Do poor countries tend to grow faster than rich countries? Solow-Swan: Countries with same rate of technological progress, , will all converge to a balanced growth path in which the rate of growth of income per capita is equal to . If production technologies, saving rates, and population growth rates are the same across countries, they will all converge to the same level of income per capita as well.

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Diminishing returns to factor inputs imply that poor countries (with a smaller base of capital and labor) will grow at a faster pace than richer countries faced with identical technology, saving rates, and population growth rates.

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**Convergence and Cross-Section Regressions**

and convergence: Absolute -convergence or mean reversion: occurs if poor economies tend to grow faster than richer ones. convergence: requires that the distribution of world income become more equitable over time.

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**lnyht = a0 + (1 - )lnyht-1 + uht, h = 1,…,N.**

-convergence: Consider the following regression model, lnyht = a0 + (1 - )lnyht-1 + uht, h = 1,…,N. For h = N different countries. a0: constant term.

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**ln(yht/yht-1) = a0 - lnyt-1 + uht, h= 1,…N. (6)**

Equation can also be rewritten as, ln(yht/yht-1) = a0 - lnyt-1 + uht, h= 1,…N. (6) In (6), > 0, implies mean reversion. In the long run, with yht - 1 = yht, expected real income per capita is, Elnyh = a0 / .

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** 1 (lnyht - t)2 t2 = N - 1 -convergence:**

Requires a measure of the dispersion of income. Consider the sample variance of lnyht , N - 1 t2 = 1 N h = 1 (lnyht - t)2 t : sample mean of lnyht. With N sufficiently large, sample variance can be viewed as an accurate measure of the population variance.

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**t2 (1 - )2 t-12 + 2 2 (9) 2 = 1 - (1 - )2**

Equation (5) can be used to calculate the process driving t2 over time, t2 (1 - )2 t-12 + 2 solution of which is given by, (9) 1 - (1 - )2 2 = ~ If < 0 in (9), process driving t2 will be unstable. Thus, absolute convergence is necessary for convergence to take place.

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**Solution to (8) can also be written as, **

~ ~ (10) shows that if absolute convergence holds in the sample t2 will approach its long run value monotonically. -convergence is a necessary but not sufficient condition for -convergence. Figure 13.1.

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**Testing the Mankiw-Romer-Weil Model**

Core of model: differences in population growth and capital accumulation account for variations in incomes across countries. Income per capita equation, as before is, + ln sK + ln y = ln sH - ln (n + + ) ~ with = 1/(1 - - )

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**Mankiw-Romer-Weil use following measures to test model:**

y: logarithm of output per person in the population of working age; n: average population growth rate; sK: ratio of gross savings to GDP; sH: average fraction of the population of working age that is enrolled in secondary school over the period ; + : set to 0.05 for all countries.

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**The Empirics of Growth: Econometric Issues**

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Much of the empirical literature has focused on cross-country regressions plagued by methodological problems: measurement, specification errors, simultaneity bias. Other Difficulties: Heterogeneity between developing countries. Variations in data definitions across countries. Difficulty in separating trend component of output growth from cyclical component. Mixing stationary and nonstationary variables can lead to spurious results. Averaging implies that cross-country regressions do not represent typical behavioral equations.

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**Problems with linear models and ordinary least squares (OLS):**

Omitted variable (or specification) bias. Endogeneity bias: failure to account for the endogenous nature of some of the explanatory variables. Alternatives approaches to cross-country regressions: Quah, (1996a,1996b, 1997): jointly analyzed - and -convergence using stochastic kernels. Others suggested time series regressions for individual countries.

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Arestis and Demtriades (1997): used a cointegration approach to analyze determinants of growth in an individual context.

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**The Econometric Evidence:**

An Overview

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**Selective overview of literature on cross-country growth regressions.**

Motivated by the results of Levine and Renelt (1992), emphasizing the fragility of many of the cross-country regression results they reviewed. Many recent studies have used improved econometric methods.

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**Saving and Physical and Human Capital**

Levine and Renelt (1992): both saving and physical investment rates positively and significantly correlated with average growth rates. Few have tried to account for the quality of investment--Asia crisis demonstrated that high rates of investment not a panacea for sustained growth. Barro (1991, 1997), Benhabib and Spiegel (1994): the initial level of education was an important determinant of subsequent growth. In contrast to Levine and Renelt (1992): suggested that the significance of human capital indicators in growth regressions was not always robust to the inclusion of other variables.

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**Saving and Physical and Human Capital**

Recent evidence less conclusive: Pack and Page (1994): argued that part of the growth effects attributed to investment and education may reflect ensuing changes in the sectoral structure of production. Bils and Klenow (1998): expected growth causes an increase in enrollment rates rather than causality running from schooling to growth.

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Fiscal Policy Recent evidence on relationship between government expenditures and growth mixed. Devarajan, Swaroop, and Zou (1996): no relationship between growth and the level of expenditures. Barro (1997): Government consumption expenditures--calculated by deducting defense and education expenditures from general consumption spending--measured in proportion of GDP negatively correlated with growth.

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Devarajan, Swaroop, and Zou (1996), in contrast, found a positive relationship between public consumption expenditures (as measured by current outlays as a share of total expenditures) and economic growth. Caselli, Esquivel, and Lefort (1996) also found a positive effect on growth of government expenditure (net of military and educational spending) as a share of output. Easterly, Loayza, and Montiel (1997) found no significant effect of the share of government consumption in GDP on growth in Latin America.

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**Role of public and private investment in growth:**

Public Investment as, Complementary to private investment: infrastructure improvements can increase the marginal product of private capital. Competitive with private initiative: substitution causes a crowding out of private capital with adverse effects on growth. Evidence ambiguous. : Khan and Kumar (1997): private investment consistently more productive than public investment. Knight, Loayza, and Villanueva (1993) and Nelson and Singh (1994): Level of public investment in infrastructure significant positive effect on growth.

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**Easterly and Rebelo (1993):**

Public investment, in transportation and communications positively related to growth, in state-owned enterprises had no effect on growth, in agriculture had a negative effect. Devarajan, Swaroop and Zou (1996): Inverse relationship between public investment and growth. This suggests that governments may have been misallocating expenditures in favor of capital expenditures (as opposed to outlays on, say, infrastructure maintenance).

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**Inflation and Macroeconomic Stability**

Fischer (1993) positive link between growth and macroeconomic stability. De Gregorio (1992, 1993) negative relationship between level of inflation, variability of inflation, and growth in Latin America. Sarel (1996); relationship between growth and inflation nonlinear: changes in inflation are significant (insignificant) when it is high (low).

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Sarel (1996): High inflation (above 8% per annum) has a negative and statistically significant effect on growth. Doubling in the rate of inflation (e.g. 20 to 40%) reduces economy's growth rate by 1.7%. Barro (1997): Inflation has negative effect but smaller. Increase in average inflation by 10% per year lowers the growth rate by %. Relationship only exists with annual inflation over 40%. Bruno and Easterly (1998): No robust relationship with inflation less than 40%.

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**Other measures of macroeconomic policy uncertainty:**

Simple crude indicator of instability: unweighted sum of the mean inflation rate, the standard deviation of inflation, mean budget and external current account deficits as a percentage of GDP, and mean terms-of-trade changes. More precise measure of policy variability (Aizenman and Marion, 1993): used standard deviation of the real exchange rate, standard deviation of inflation and domestic credit growth, and composite indicators using foregoing variables.

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**More precise measure of policy variability proposed by Aizenman and Marion (1993):**

standard deviation of the real exchange rate, inflation, domestic credit growth, as well as composite indicators including all of the foregoing variables; negative relationship between policy variability and growth, although not robust for some indicators. Bleaney (1996): cross-sectional study.

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Macroeconomic instability (measured by the fiscal balance and the degree of volatility of the real exchange rate) had a significant negative effect on the rate of economic growth and possibly also a negative effect on investment.

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**Financial Factors Causality difficult to establish.**

Demetriades and Husein (1996) studied 16 countries: 4 displayed causality from financial depth to growth. 7 countries displayed a feedback relationship between finance and growth. 4 displayed causality from growth to financial depth.

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**Financial Repression and Growth**

Roubini and Sala-i-Martin: Negative effect of the bank reserve ratio on growth. However, reserve ratios can be a poor proxy for repression. Arestis and Demetriades (1997): used a weighted index of five principal controls on banking sector; actually found a mildly positive effect of financial repression on economic growth in Korea.

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**Openness and External Trade**

Benefits of trade openess: technology spillovers, access to specialized inputs etc. Sachs and Warner (1997a): Classified 117 countries as either open or closed. Constructed index of openess, based on five criteria: non-tariff barriers, average tariff levels, the parallel market exchange rate, existence of monopolies for major exports and political regime. More open countries grew by 2 to 2.5% more than others.

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**Greenaway, Morgan, and Wright (1998):**

Cross-country regression covering 73 countries. Measured openness along with other control variables---initial income per capita, the ratio of domestic investment to output, and an index of the terms of trade. Used a dynamic regression framework to investigate potential lagged effects. Results: Trade openness has an identifiable impact on growth. However, the growth effect had a J-curve feature: only over time did impact becomes positive.

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**Has implications for the sustainability of trade reforms.**

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**Political Variables and Income Inequality**

Political and civil liberties; not only desirable in themselves but also, by providing a foundation for imposing the rule of law, may play an important economic role. Dasgupta 1995: liberties are positively and significantly correlated with improvements in income per capita, life expectancy at birth, and the infant survival rate. Growth effects of political factors have been the subject of a variety of cross-country empirical studies.

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Brunetti (1997): Five groups of political variables Measures of democracy, including the Gastil index. Measures of government (or institutional) instability. Indicators of political violence, including measures of political strikes, protest demonstrations, riots, armed attacks, political assassinations, and executions. Subjective political indicators. Democracy indicators, measures of government stability, and indicators of political violence not robustly correlated with growth.

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**Survey-based measures of political risk appear more closely correlated with growth (Mauro, 1997).**

Evidence suggests no clear correlation between income inequality and economic growth. Studies have also found no systematic relationship and no clear causal link between income inequality and political instability.

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**Catching Up or Falling Behind?**

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Solow-Swan model: Implies convergence across countries in both growth rates and income levels if production technology, savings rates, and the rate of technological progress are the same. Convergence can be inhibited through, for example, trade barriers, that limit possible access to more advanced technologies.

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AK model: Along with other endogenous growth models, imply a sustained difference in growth and income levels. Externalities to specialized inputs remove diminishing returns characteristic of capital and thus remove the primary driver of convergence in the Solow-Swan model.

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