empirical macroeconomics - universidade nova de...

Empirical Macroeconomics

Francesco Franco

Nova SBE

April 9, 2015

Francesco Franco Empirical Macroeconomics 1/38

Growth

Questions:

• In 1988 output per worker in the United States was more than35-40 (PPP) times higher than output per worker in Niger.

• From 1980 to today the USA output per worker in PPP asincreased 1.6 times (60%).


Growth

Quantitative implications of Solow

The Solow model identifies identifies two possible sources ofvariation in the time series and cross-section in output per worker:k = K/L and A.If capital markets are competitive and there are no externalities

–K (k) = kf Õ(k)/f (k) = 1/3

sy

ˆyˆs =

–K (kú)

1 ≠ –K (kú)= 0.5

Furthermore the speed of convergence

⁄ = [1 ≠ –K (k)] (n + g + ”) = 0.04

Threfore a change in k has modest and slow e�ects on y .


Growth

Quantitative implications of Solow

• Using di�erences in k across countries to explain di�erences iny does not work neither for the same reason: di�erences in kare far smaller than those required by di�erences in y

• implied di�erences in marginal return of capital are giganticand not observed f Õ(k) = –k–≠1 = –y –≠1

–

• the other factor A is a black box: education, skills, rights,infrastructure, organisation,...


Growth

Growth accounting

Start with the production function

Y (t) = F (K (t), A(t)L(t))

totally di�erentiate it and divide it by Y (t), define gX (t) = X/X

gY (t) ≠ gL(t) = –K (t) [gK (t) ≠ gL(t)] + S(t)

where S(t) = –A(t) ú gA , –A(t) the elasticity of output wrt to Acalled the Solow residual and measures the contribution of allsources of growth other than the contribution of capital via itsprivate return. To obtain it the assumptions are perfectcompetition (Long Run) but can be enhanced with imperfectcompetition, etc etc (medium run, short run).


Growth

Convergence1140 THE AMERICAN ECONOMIC REVIEW DECEMBER 1988

S3 2.8 o J~apan

c3J2.6 pSweden ?C 2.4 Finland + Germany S

+~Nr Canada 2 Austria + + United States

enmark *Q 1. 8 Italy + Switzerland - etherlands egm ()

1.4 % 12 France United Kingdo

0 Australia 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6

Log Per Capita Income in 1870

FIGURE 1. PER CAPITA GNP REGRESSION FOR MADDISON'S SIXTEEN

opposite errors in 1870-1979 growth and bias the regression slope toward -1. As Baumol notes, such errors can produce the illusion of an inverse relationship between income in 1870 and growth since.

The unbiased sample used here meets three criteria. First, it is made up of nations that had high potential for economic growth as of 1870, in which modern economic growth had begun to take hold by the middle of the nineteenth century. Second, inclusion in the sample is not conditional on subsequent rapid growth. Third, the sample matches Baumol's as closely as possible, both because the best data exist for Maddison's sixteen and because analyzing an unbiased sample close to Baumol's shows that different con- clusions arise not from different estimates but from removing sample selection and errors in variables' biases.

Per capita income in 1870 is an obvious measure of whether a nation was sufficiently technologically literate and integrated into world trade in 1870 to be counted among the potential convergers. Nations with high incomes in 1870 were nations with the material and human resources to industrialize. Mod- ern economic growth had already pushed real incomes far above the levels of the pre- industrial world. And such a sample does not exclude nations which had good in-

dustrialization prospects in 1870 that have not since fulfilled their potential.7

The construction of this sample requires judgment. Per capita income in 1870 must be estimated for nations in the extended sample but not in Maddison's sixteen. The estima- tion of 1870 income is discussed in the Ap- pendix.8 Changes in national boundaries must be dealt with; this paper uses modern boundaries throughout. The level of 1870 income to serve as a cutoff for inclusion in the sample must be set. The choice of cutoff level itself requires balancing three goals: including only nations which really did in

Alternative measures of prospects for development in 1870, such as per capita industrial production or the proportion of the labor force in agriculture, would serve as well but would make little quantitative difference. The correlations for the sample of Maddison's sixteen between 1870 per capita GNP and 1870 labor productivity and share of the labor force in agriculture are .98 and .84, respectively.

8The estimates of 1870 per capita income arrived at in the Appendix are not precise enough to be used for assessing the history and development of any individual country. They do, however, serve adequately as the raw material for a comparative exercise like that carried out here in which explicit econometric correction is made for errors in variables and in which errors in measuring nineteenth century per capita income for any one nation can have only a limited effect.

This content downloaded from 193.136.112.46 on Wed, 3 Apr 2013 05:44:32 AMAll use subject to JSTOR Terms and Conditions

Figure : Beaumol original sample


Growth

Convergence

Figure : DeLong sample


Level

Hall & Jones

We saw that capital share is an important parameter. What if weare underestimating capital, maybe because of human capital. Infact rewrite the production function as

Y = K– (AH)1≠–

andH = LG(E )

where G(E ) is a function giving human capital per worker as afunction of years of education per worker. The rest is as in theSolow Model. G specific functional form comes frommicroeconomic studies

G(E ) = e„(E), „Õ > 0


Level

Hall & Jones

The model is isomorphic to the Solow if you definek = K/ [AG(E )L]. The presence of human capital a�ects the levelof y but not the e�ect of K on y . Now level accounting:

Y = K– (ALG(E ))1≠–

that can be expressed as

KL =

3KY

4 1

1≠–

AG(E )

andy =

YL =

3KY

4 –1≠–

AG(E )


Level

Hall & Jones

Decomposition in terms of K/Y and not K/L:• along BGP K/Y is proportional to investment• increases in A a�ect K and not L

Data:• Penn World Tables for National Income and Labour Force• Physical capital stock: from investment, but depreciation and

initial K0

are an issue• Human capital: Hall and Jones, years of schooling from

Barro-Lee with „ piece-wise linear function: 13% for 1y-4y,10.1% for 5y-8y, 6.8% after.


Decomposition

Hall & Jones

Consider Niger-USA di�erence (35 times y in 1988):• capital intensities in the two countries contributed a factor of

1.5 to the income di�erences,• educational attainment contributed a factor of 3.1• the remaining di�erence a factor of 7.7 remains as the

productivity residual


Decomposition

Hall and Jones

Figure : Hall and Jones analysis


Cross-country correlation

Output per capita and A

Figure : Hall and Jones analysisFrancesco Franco Empirical Macroeconomics 13/38

Level

Hall & Jones

Figure : Hall and Jones analysis


Social Infrastructure

Fundamental cause ?

ln (Y /L) = – + —SI + ‘

• social infrastructure: the institutions and government policiesthat provide the incentives for individuals and firms in aneconomy: measurement?

• endogeneity problem: feedbacks from income to socialinfrastructure, is social infrastructure correlated with otherdeterminants of income.



Measurement

Hall and Jones measure SI with an index based on two variables:1 index of government anti-diversion policies: GADP:

1 Government against private diversion:1 law and order,2 bureacratic quality

2 government as a diverter:1 corruption2 risk of expropriation3 government repudiation of contracts.



Measurement

Hall and Jones measure SI with an index based on two variables:1 index of openess or market-orientation (Sachs and Werner):

fraction of years 1950-1995 that an economy has been open:1 NTB cover <40% of trade2 average tari�<40%3 black market premium <20%1970-19804 not socialist (Kornai)5 government does not monopoliza major exports



Identification

The complete model:

ln (Y /L) = – + —SI + ‘

SI = “ + ”ln (Y /L) + X◊ + ÷

The identifying assumption is EX Õ‘ = 0Mismeasurement:

SI = ÂSI + ‹

you can normalize Â = 1.

ln (Y /L) = – + —SI + ‘

where ‘ © ‘ ≠ —‹.The identifying assumption is EX Õ‘ = 0


Instruments

History and Geography

The instruments are:1 fraction of pop native English speaker2 fraction of pop native European Language speaker3 distance from the equator4 measure of geographic influences and openess to trade

(Krenkel and Romer)


Results

Instrumenting Social Infrastructure

Figure : Results


Results

Interpreting the Results

The point estimate indicates that a di�erence of 0.1 in SI iaassociated with a di�erence in output per worker of 5%. What isthe e�ect of mismeasurment?

ln (Y /L) = – + —SI + ‘ ≠ —‹

SI = “ + ”ln (Y /L) + X◊ + ÷

thereforeSI = “ + ”– + ”‘ + X◊ + ÷

1 ≠ ”—+ ‹

both positive (‘) and negative coorelations (‹). Net e�ect is seenwith OLS:measurement is more important.


Results

Reduced form

Figure : Results


Results

Robustness

Figure : Robustness


Further Literature

Colonial origins of institutions

Acemoglu, Johnson and Robinson: mortality rates by settlers incolonies.


Stata Tutorial

Introduction

• Stata is statistical package with• data management capabilities• frontier statistical techniques• graph publication system

• IC: 2047 vaiables, SE: 32766 variables


Stata Tutorial

Interface

Figure : Interface


Stata Tutorial

Interface

• Command is where you type your commands• Results is where stata print the results• Review keeps track of the command history• variables lists the variables in your dataset• GUI vs language


Stata Tutorial

Commands

Using the display command you can use stata as a calulator.Commands are case sensititive and can be abbreviated.

display 17*2To get help just type

help reg


Stata Tutorial

Commands

Let’s load a file that ships with stata and see what it containssysuse lifeexp

descnotes


Stata Tutorial

Commands

to run simple descriptive statisticssummarize lexp gnppc

list country gnppc if missing(gnppc)action of any command can be restricted to a subset of the data


Stata Tutorial

Commands

Let us draw a scatter plot but before that let’s take the natural logof gdppc

g ln_gnppc = ln(lgnppc)scatter lexp ln_gnppc


Stata Tutorial

Commands

We now run a linear regression of life expectancy on gnp per capitaregress lexp ln_lgnppc

The ln of gnp per capita explains 62% of the variation in lifeexpectancy in these countries. 1% increase in ln gnp pc isassociated with an increase in 0.0277 years of life expectancy


Stata Tutorial

Commands

We can generate fitted values or residuals and plot thempredict plexpscatter lexp ln_gnppc || lfit lexp ln_gnppc


Stata Tutorial

Commands

Let us spot the outlierlist country lexp plexp if lexp <55list gnppc ln_gnppc lexp plexp if country ==

“Portugal”, clean


Stata Tutorial

Commands

you can create a log of your sessionlog using filename, text replace

capture log close


Stata Tutorial

Do file

gen one = 1 // is a constantscatter lexp ln_lgppc || ///

lfit lexp ln_gnp#delimit ;#delimit cr


Stata Tutorial

EXAMPLE

Let us go over our Dataset1


Readings

Why Do Some Countries Produce So Much More Output PerWorker Than Others? Author(s): Robert E. Hall and Charles I.Jones Source: The Quarterly Journal of Economics, Vol. 114,No. 1 (Feb., 1999), pp. 83-116

The colonial origins of comparative development: an empiricalinvestigation. Acemoglu, Johnson and Robinson. AER 91 n52001.


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