Global Divergence in Growth

Regressions

Michele Battisti University of Palermo

Gianfranco di Vaio Cassa Depositi e Prestiti - LUISS

Joseph Zeira Hebrew University of Jerusalem and LUISS, CEPR, RCEA

La Sapienza Workshop

March 7, 2014

Introduction: Main Goal

• This paper tries to reconcile growth regressions (Barro 1991 and later) with some of its critiques.

• The main result of growth regressions is ‘conditional convergence:’ each country converges to its own steady state. This means that the cross-country distribution of output converges to a limit distribution.

• But studies of this distribution (Bernard and Durlauf 1995 and more) found that it diverges.

• This paper reconciles these two findings.

Introduction: More Goals

• Another critique of growth regressions has been the use of control variables in measuring convergence.

• These control variables, sometimes called explanatory variables, are chosen somewhat arbitrarily, and their total number already passed 150.

• In this paper we succeed in estimating the dynamic parameters of the model without use of any control variables.

• The effect of the explanatory variables in standard growth regressions reflects both long-run and short-run effects. Our approach enables us to isolate the long-run effect.

Introduction: Our Approach

• We extend the growth regression model by assuming that a country’s productivity (TFP) follows the global frontier, but not necessarily fully.

• This extension of the model enables us to estimate separately two dynamic parameters.

• The parameter b measures how fast output converges to a long-run path.

• The parameter d measures by how much the long-run path follows the global frontier.

Introduction: The Open Economy

• One way to view our approach is to consider it as related to growth in small open economies.

• Most countries do not create new technologies, but use the innovations created elsewhere.

• They can either adopt an innovation, or not.

• The small open economy also affects the convergence result.

• While in a closed economy it is driven by bounded savings, in the open economy it is driven by adjustment costs to investment.

Introduction: Main Results

• We find that the parameter b is similar across countries and is similar to the convergence parameter in growth regressions.

• We find that the parameter d differs across countries and is smaller than 1 in many countries.

• Hence, there is significant global divergence.

• We then estimate the effect of standard explanatory variables, like education, geography, institutions, and more on d.

• We find that these effects are quite different from the effects of standard growth regressions.

The Growth Regressions Model

• We present our contribution with respect to the canonical Growth Regression Model as presented in the survey of Durlauf, Johnson and Temple (2005).

• Output is described by:

• The labor force grows at a rate n(i) and productivity grows at a rate g(i):

• Many studies assume that g is common to all countries.

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The Convergence Assumption

• Output per worker:

• Efficiency Output per worker:

• It is assumed that efficiency output per worker adjusts gradually to its long-run value:

• The gradual adjustment can be due to bounded savings in a closed economy, as in the Solow model, or if the economy is open, due to costly adjustment of capital.

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Convergence in an Open Economy

• If the economy is open and relatively small and if adjustment of capital is costly, we get:

• Hence, the long-run efficiency output per worker should be similar across countries.

• Another result of the adjustment cost model is:

• Hence, the parameter b is expected to be somewhere between 0.02 and 0.1.

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Cross-Country Growth Regressions

• From the convergence equation we can derive the common two forms of growth regressions. The first is a cross-section regression, where the rate of growth is over a long period:

• Initial productivity and its rate of growth are not observed. They are controlled for by various explanatory variables. That creates a number of problems. One is how to differentiate between a level effect and a rate of growth effect.

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Panel Growth Regressions

• The accumulation of data in recent years enables us to use panel growth regressions, thus adding more observations.

• The basic panel equation is derived from the convergence assumption above:

• The estimation of panels creates problems as well. The main one is that while there is high variability in output and in productivity, there is not much variability in the explanatory variables, like geography, ethnic composition, institutions, fiscal policy, education, etc.

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Extending the Model

• We extend the growth regression model by assuming instead of growing at a fixed rate g(i), the country’s productivity follows the global frontier, but not necessarily fully:

• The rate of following the frontier satisfies:

• The global frontier grows at an average rate g:

• We next embed these dynamics in the convergence model.

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The Extended Model

• The extended growth regression model is:

• After some manipulation:

• This means that output converges to a long-run path described by:

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Empirical Implications

• Growth depends not only on characteristics of the country, but on the global frontier as well.

• Convergence can no longer be measured only by b. It measures convergence of output to own long-run growth path, but the path itself might diverge if d(i) < 1. Hence, the two parameters are required in order to have a full picture.

• We can estimate the parameters b, a and d for each country directly, without controls.

• The explanatory variables may affect a and d, but we can still estimate them without using explanatory variables.

Panel Cointegration

• The empirical model is:

• Subtracting d(i)lnF(t) from each side we get:

• Where:

• Hence, output is cointegrated with F. The coefficient of cointegration is d and the error correction coefficient is b.

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Data

• We use data on output per capita, which is PPP adjusted, from the Groningen Growth and Development Centre (2013).

• Specifically, real GDP per capita, in PPP adjusted Geary-Khamis 1990 US$, for 139 countries over the years 1950-2008. We remove a few outliers (like oil producing countries) and are left with 124 countries.

• For a set of 30 countries the data are from 1870 to 2010.

• For the global frontier we use as a proxy the US output per capita. The US has a stable growth rate over the period and is the leading among large countries.

US GDP per Capita 1870-2010

Ln of GDP per Capita in Regions and

in the US

An Example of an Outlier

Panel Cointegration Regression

• To avoid cyclical high-frequency autocorrelation we use 5 year averages:

• The cointegration estimation of the parameters b and d for each country is performed for these smoothed data, on annual frequency. We find that d is below 1 for most counties.

• For robustness we have also tried other types of averages, from 10 years averages to annual data.

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Panel Cointegration: 1950-2008

Coefficient Whole Sample Without Oil & Outliers

b 0.0389***

(0.002)

0.0405***

(0.002)

d 0.688***

(0.093)

0.708**

(0.072)

Test for

d = 1

χ2=23.95

P=0.00

χ2=16.63

P=0.00

Hausman Test for

Heterogeneity

χ2=2.80

P=0.094

χ2=9.23

P=0.002

No. of Countries 139 124

1. Standard errors in parenthesis.

2. Hausman null hypothesis: difference in coefficient not systematic.

Divergence by Regions

Coefficient OECD SSA LAC SEA Other

Countries

b 0.0344***

(0.006)

0.0424***

(0.005)

0.0468***

(0.004)

0.0348***

(0.006)

0.0438***

(0.007)

d 1.060***

(0.078)

0.201*

(0.115)

0.634**

(0.098)

1.617***

(0.322)

0.623***

(0.177)

Test for

d = 1

χ2=0.59

P=0.4425

χ2=48.54

P=0.000

χ2=14.05

P=0.000

χ2=3.67

P=0.056

χ2=4.31

P=0.038

Hausman Test

for

Heterogeneity

χ2=0.54

P=0.464

χ2=1.18

P=0.277

χ2=7.33

P=0.007

χ2=-43.00

P=0.0000

χ2=9.71

P=0.002

No. of

Countries

21 42 23 13 25

b and d across Countries

b vs d 1950-2008

-0.050

0.000

0.050

0.100

0.150

0.200

-3.000 -2.000 -1.000 0.000 1.000 2.000 3.000 4.000

d

b

Convergence and Divergence

• In all regressions the coefficient b is positive and significant. This means that countries follow what is called β-convergence, or conditional convergence.

• But in our framework this is interpreted as convergence to own long-run growth path.

• But the long-run path may converge to the frontier or diverge from it, depending on whether d < 1 or equal to 1.

• We show that for most countries d < 1, so that most countries diverge from the frontier. This fits the many findings on divergence.

A Differences Estimation of b and d

• Another way to estimate the dynamic parameter is to estimate the differences of the empirical model.

• The estimation uses IV in order to cope with correlation between the error term and lagged output. The IV used are lagged growth rates of each country and of the US.

• We do not impose any structure on c, but estimate b and c directly, and then calculate the parameter d = c/b.

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Results of Difference Estimation

Coefficient Pesaran-Smith I.V. Estimates

Full Sample Without Oil and Outliers

Countries

1-b 0.890***

(0.013)

0.890***

(0.014)

c 0.075***

(0.012)

0.073***

(0.012)

1-b+c 0.965 0.963

d=c/b 0.682 0.664

Number of Countries 139 124

Correlation between Estimated d’s in

the Two Methods

-3.000

-2.000

-1.000

0.000

1.000

2.000

3.000

4.000

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Panel Cointegration Results for 30

Countries in the years 1870-2010

Parameter Coefficient z P>z Test d = 1 Hausmann Test

for Heterogeneity

b 0.0232

(0.004)

6.51 0.000

d 0.993

(0.060)

16.49 0.000 χ2 (1)=0.01

P>χ2(1):

0.908

χ2 (2)=2.86

P> χ2 (2): 0.091

Robustness Checks

• First, we check for the alternative data set of PWT and the results are unchanged (now the two data sets are merged).

• Second, we test for changes in the length of period of averaging. The d is not affected, b increases the shorter is the period.

• Third, we test possible changes in d over time. We find that after 1980 d is higher, but still significantly lower than 1.

• Finally we repeat the analysis with human capital subtracted from output and productivity. This lowers d significantly.

Effect of Explanatory Variables on d

• Next we estimate the effect of various explanatory variables on the estimated d.

• Previous growth regressions could estimate whether an explanatory variable affects output.

• The effects of these same explanatory variables on d can identify their long-run effect.

• We compare this estimation with a standard growth regression to check whether these long-run effect actually differ from the overall effect.

The Explanatory Variables I

• TROPIC is the share of land in a country that is tropical.

• COAST is the share of land in a country that is within 100 km from a coast or from a navigable river.

• ETHNIC is the measure of ethnic fractionalization in a country.

• Y_50 is the natural logarithm of the GDP per capita at 1950.

• EDU_is the average years of schooling of people above age 15 during the time of the panel.

The Explanatory Variables II

• OPEN measures openness by trade policy over the years 1965-1990. A country is closed (i) if average tariff rate exceeded 40%; (ii) if non-tariff barriers covered more than 40% of imports; (iii) if it had a socialist economic system; (iv) if it had a state monopoly of major exports; or (v) if black-market premium exceeded 20% during the 1970s or the 1980s.

• ICRG is average measure of quality of institutions during 1982-1997 (International Country Risk Guide).

• G/Y is the share of public expenditures in GDP, averaged over the years 1950-1960.

Explanatory Variables: Corr. Matrix

TROPICS COAST ETHNIC Y_50 EDU OPEN G/Y

TROPICS 1.0000

COAST -0.1794 1.0000

ETHNIC 0.5729 -0.5279 1.0000

Y_50 -0.4754 0.3517 -0.3811 1.0000

EDU -0.5709 0.4554 -0.5503 0.7405 1.0000

OPEN -0.3205 0.3301 -0.3812 0.4930 0.5353 1.0000

G/Y -0.0466 -0.2029 0.1393 -0.2273 -0.0785 -0.2162 1.0000

ICRG -0.5740 0.4079 -0.5705 0.6879 0.7884 0.7054 -0.1777

Taking Out SEA and OECD

• In the following regressions we estimate the effects of these explanatory variables for all countries and then without South East Asia and even without the OECD countries.

• Some of the South East Asian countries are in the midst of a period of catching up with the frontier so their rate of growth is very high and they appear to have d that is much higher than 1. We know that this catching up will stop some time, but the data do not know.

• The OECD countries have d = 1, which is the maximum d. Hence they are at a corner solution, so that d is less sensitive to the various explanatory variables.

A Standard Growth Regression Dependent Variable: AVG

Explanatory Variable (1)

Whole sample

(2)

Without SEA

(3)

Without SEA and OECD

TROPIC -0.704***

(0.235)

-0.938***

(0.242)

-0.906***

(0.281)

COAST 0.008***

(0.003)

0.007***

(0.003)

0.007**

(0.004)

Y_50 -0.857***

(0.178)

-0.648***

(0.194)

-0.529***

(0.222)

ETHNIC -0.766*

(0.452)

-0.569

(0.422)

-0.530

(0.574)

EDU 0.149***

(0.059)

0.123**

(0.060)

0.156**

(0.076)

OPEN 1.109***

(0.231)

0.754***

(0.234)

1.190***

(0.471)

G/Y -2.558***

(0.898)

-1.707**

(0.859)

-1.883**

(0.986)

CONST. 8.012***

(1.267)

6.527***

(1.343)

5.509***

(1.566)

R2 0.61 0.60 0.52

OBS. 90 77 57

Effect on d Dependent Variable: d

Explanatory Variable (1)

Whole sample

(2)

Without SEA

(3)

Without SEA and

OECD

TROPIC -0.287**

(0.152)

-0.389***

(0.133)

-0.459***

(0.144)

COAST 0.004**

(0.002)

0.002

(0.002)

0.003

(0.002)

Y_50 -0.468***

(0.127)

-0.240**

(0.122)

-0.225*

(0.137)

ETHNIC -0.432*

(0.282)

-0.417**

(0.218)

-0.574**

(0.304)

EDU 0.088**

(0.039)

0.053

(0.038)

0.048

(0.043)

OPEN 0.591***

(.150)

0.319**

(0.150)

0.875***

(0.291)

G/Y -1.290**

(0.578)

-0.483

(0.513)

-0.927

(.680)

CONST. 4.051***

(0.946)

2.517***

(0.835)

2.580***

(0.966)

R2 0.45 0.44 0.48

OBS. 90 77 57

Results

• The effects of explanatory variables in the standard cross-country growth regression are very different from the effects on d.

• Education has a positive and significant effect on growth, but not on d.

• The size of the public sector has a significant negative effect on output in growth regression, but its effect on d is insignificant.

• The effect of ethnic fractionalization on output is insignificant, but its effect on long-run growth is negative and significant.

Conclusions

• It is still a bit early to throw growth regressions to the dump.

• Including the global frontier can enrich the estimation of convergence and divergence of countries over time.

• It reconciles the results of growth regressions with alternative measures of convergence and divergence.

• This approach also enables us to better evaluate various explanations to growth, by separating level effects from rate of growth effects. But our results on that are still preliminary.