Macroeconomics (1)MEK 781

Manoel Bittencourt

University of Pretoria

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Barro (1991)

n = 98, t = 1960� 1985, cross section of countries (data are mostlyfrom PWT, UN and World Bank)economic growth is positively determined by initial humancapital and inversely related to initial incomegrowth is inversely determined by government consumption toGDP and positively determined by political stability (andinversely related to market distortions)

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Barro (1991)

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Barro (1991)

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Barro (1991)

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Barro (1991)

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Barro (1991)

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Barro (1991)

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Barro (1991)

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Barro (1991)

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Mankiw, Romer and Weil (1992)

the paper examines whether the Solow model is consistent withinternational (cross-country) variation in income(n = 98, t = 1960� 1985 and from the PWT and UN) and it alsoexamines convergencefurthermore, they augment the Solow model with human capitaland argue that the model provides a good description of thecross-country dataand they also find that there is convergence in the data

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Mankiw, Romer and Weil (1992)

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Mankiw, Romer and Weil (1992)

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Mankiw, Romer and Weil (1992)

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Mankiw, Romer and Weil (1992)

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Mankiw, Romer and Weil (1992)

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Mankiw, Romer and Weil (1992)

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Economic endogeneity

Consider the following linear relationship,

yit = α+ βxit + uit (1)

where y is the explained variable, x is the explanatory variableand u is the residual (unobservables). α is the intercept and β theslope, or the effect of a change in x on y, and the Greek areparameters we want to estimate. If y and x are in logs, then β isthe elasticity, or the percentage changethere are assumptions about the unexplained error term u,

1 E(u) = 0, zero average, and2 E(u/x) = 0, not correlated with each other3 following from the above,

E(yit/x) = E(α+ βxit + uit/x)) α+ βxit + uit/x ) α+ βxit

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Economic endogeneity

is the above exogeneity of regressors plausible in growtheconomics? Think of institutions and growth, what is causingwhat in this case? Good institutions might cause growth, howeverricher societies might buy better institutionsif there is some sort of economic endogeneity present, then OLS isbiased. A method that is used to deal with that sort ofendogeneity is called Instrumental Variables (IV)we have to find an instrument z for the endogenous x in themodel. A good instrument must:

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Economic endogeneity

1 not be in the original equation, cov(u, z) = 02 and be correlated with x, cov(x, z) 6= 0 (the instrument is relevant,

it extracts only the variation in the endogenous x that is notcorrelated with u)

think about the following regression:

gi,t�1 = α log yi,t�1 + democracyi,tβ+ εi,t

some will argue that democracy causes growth, however otherswill argue that growth causes democracy. What is causing what inthis case? We have reverse causality, or endogeneity. We need aninstrument for democracy, which is still not in the equation, hencenot correlated with the residual, and also that is correlated withdemocracy itself

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Economic endogeneity

some people have used the natural resources as an instrument fordemocracy, it is not in the equation, and theoretically speaking,resources should be correlated with democracy (but resources canbe correlated with growth too)another possibility is to use the lags of democracy as instrumentslet’s see how it works, there are two stages:

DEMOCRACYit = αit + βRESOURCESit + uitsave the predictions from the first stage

gi,t�1 = α log yi,t�1 +DEMOCRACYi,t β̂+ εi,t

bear in mind that the instrument must be statistically significantin the first-stage regression. Moreover, if the explanatory variablesare measured with error (measurement error), or there are omittedvariables in the regression, then the use of IV is also advisable

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Economic endogeneity

Figure: Lights and development, or development and lights?

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The basicsThe basics

Economic endogeneity