ECON 450 Development Economics - publish.illinois.edu · The Model Predictions Convergence of...

The Model PredictionsConvergence of Living Standards

ECON 450Development Economics

Classic Theories of Economic Growth and DevelopmentThe Empirics of the Solow Growth Model

University of Illinois at Urbana-Champaign

Summer 2017

Henrique Veras de Paiva Fonseca ECON 450 Development Economics


Introduction

This lecture continues the discussion of the Neoclassical GrowthModel.We now look at how the model works in practice.The next step is to introduce the Augmented Solow Model bymaking explicit another type of capital: Human Capital.Finally, we study the convergence in income across countries.



Outline

1 The Model Predictions

2 Are Living Standards of Developing and Developed NationsConverging?



The Syrian Crisis

Shocks to an economy, such as wars, famines, or the unificationof two economies, often generate large one-time flows ofworkers across borders.One recent example is the increasing number of Syrian refugeesin western European countries, such as Germany.What are the short-run and long-run effects on an economy of aone-time permanent increase in the stock of labor? Use adiagram to guide your arguments.



The Production Function Revisited

Let’s take a close look at the production function one more time:

Y = F (K ,L) = Kα(AL)1−α

It exhibits constant returns to scale.It also exhibits diminishing returns on each factor. How?

What does the second derivative tell us?



Solow’s Surprise

What does the diminishing returns assumption imply for thequest of sustained economic growth?

It simply cannot be achieved! (Why?)



Solow’s Surprise

What does the diminishing returns assumption imply for thequest of sustained economic growth?

It simply cannot be achieved! (Why?)



Solow’s Surprise

How did we observe sustained growth of output per worker whensuch sustained growth is not logically possible?

Solow’s solution to this paradox was technological change.Technological progress increases labor productivity. It is "as if"there were more workers in the labor force.The "effective number of workers" keeps up with the increasingnumber of machines, so diminishing returns never sets in.



Solow’s Surprise

How did we observe sustained growth of output per worker whensuch sustained growth is not logically possible?Solow’s solution to this paradox was technological change.

Technological progress increases labor productivity. It is "as if"there were more workers in the labor force.The "effective number of workers" keeps up with the increasingnumber of machines, so diminishing returns never sets in.



Solow’s Surprise

How did we observe sustained growth of output per worker whensuch sustained growth is not logically possible?Solow’s solution to this paradox was technological change.Technological progress increases labor productivity. It is "as if"there were more workers in the labor force.The "effective number of workers" keeps up with the increasingnumber of machines, so diminishing returns never sets in.



Discussion on Technological Progress

Is this "labor-saving" technology progress bad for development?

Unemployment caused by new machines taking over the jobs ofthe population



Discussion on Technological Progress

Is this "labor-saving" technology progress bad for development?Unemployment caused by new machines taking over the jobs ofthe population



The Luddite Fallacy

The Luddites were 19th-century English textile workers whodestroyed machines which embodied the labor-savingtechnology introduced during the Industrial Revolution.English government officials, after careful study, addressed theLuddites’ concern by hanging fourteen of them in January 1813.



The Luddite Fallacy



The Luddite Fallacy

The reason why the argument made by the Luddites is fallaciousis that labor-saving technology is another term foroutput-per-worker-increasing technology.Although some temporary unemployment is inevitable, workersas a whole are better off with more powerful output-producingtechnology available to them.



The Luddite Fallacy

Therefore, technological advance translates into higher outputper worker, which means more goods and services to all workers.Moreover, economies experiencing technological progress do notshow any long-run trend toward increasing unemployment; theydo show a long-run trend toward increasing income per worker.



Solow in the Tropics

What does the Solow model have to say about cross-countrydifferences in economic growth?

Economists in the 1960s applied the Solow framework toexplaining a wide variety of growth experiences, including thepoor tropical countries.Given the reasonable assumption that technology is availablethroughout the world, different countries would have the samerate of technological progress.Therefore, the only difference between poor and rich countrieswould be in levels of investment in physical capital.




What does the Solow model have to say about cross-countrydifferences in economic growth?Economists in the 1960s applied the Solow framework toexplaining a wide variety of growth experiences, including thepoor tropical countries.Given the reasonable assumption that technology is availablethroughout the world, different countries would have the samerate of technological progress.Therefore, the only difference between poor and rich countrieswould be in levels of investment in physical capital.




Poor tropical countries would catch up to the rich temperate zonewith very high returns to capital.But obviously, this Capital Fundamentalist view of countryconvergence has failed to explain why we cannot observerelative convergence in income levels of different countries.We’ll discuss the convergence predictions of the Solow modellater on.



Solow Model Predictions

The central predictions of the Solow model concerns the impactof saving and population growth on real income.Recall the Steady State condition:

k∗ =

(s

n + g + δ

)1/1−α

Substituting it into the production function and taking logs, wefind that steady-state income per capita is

logY (t)L(t)

= log A(0) + gt +α

1 − αlog s − α

1 − αlog(n + g + δ)




Let’s assume g and δ are constant.Moreover, assume

log A(0) = a + ε

where a is constant and ε is a country-specific shock.




Thus, at time 0:

logY (t)L(t)

= a + gt +α

1 − αlog s − α

1 − αlog(n + g + δ) + ε

The above equation should remind you of a certain statisticsconcept! Which is it?




If your answer was "Regression analysis", you are right!Remember that in the linear regression framework, we canestimate the parameters of the equation

y = α+ β1x1 + β2x2 + . . .+ βpxp + ε

by OLS.




On average, we can assume α = 1/3. That is, capital’s share inincome is roughly one third.Therefore, the model predicts an elasticity of income per capitawith respect to the savings rate of approximately 0.5.Moreover, the elasticity of income per capita with respect ton + g + δ should be close to -0.5.



Solow Model PredictionsFirst Results



Solow Model PredictionsFirst Results

The model explains a large fraction of income variation (AdjustedR2 = 0.59 for two of the samples).However, the estimated impacts of savings and labor forcegrowth are much larger than the model predicts. (Why?)One possible explanation for this result is that the proposedspecification ommits one important component of the growthprocess: human capital accumulation.



Solow Model PredictionsAdding Human Capital to the Solow Model

At the theoretical level, including human capital may add someinsights on how differences in human capital stock affects thegrowth process.At the empirical level, human capital enters the first specificationon the error term. Expliciting it might lead to different results.




Now consider the following production function

Y (t) = K (t)αH(t)β(A(t)L(t))1−α−β

We have now two equations representing the change in the stockof capital per effective unit of labor over time:

k(t) = sk y(t)− (n + g + δ)k(t),

h(t) = shy(t)− (n + g + δ)h(t)




We can obtain steady state values by making k(t) = h(t) = 0.

k∗ =

(s1−β

k sβhn + g + δ

)1/1−α−β

h∗ =

(sαk s1−α

hn + g + δ

)1/1−α−β




Substituting the previous equation into the production functionand taking logs we have

logY (t)L(t)

= log A(0) + gt − α+ β

1 − α− βlog(n + g + δ)+

+α

1 − α− βlog sk +

β

1 − α− βlog sh + ε







Now the results in Table II strongly support the augmented Solowmodel.The model explains almost 80% of the cross-country variation inincome per capita in two of the samples.The last lines of the table give the values of α and β implied bythe coefficients.



Outline

1 The Model Predictions

2 Are Living Standards of Developing and Developed NationsConverging?



Are Living Standards of Developing and DevolvedNations Converging?

At the dawn of the industrial era, average real living standards inthe richest countries were no more than three times as great asthose of the poorest. Today, the ratio approaches 100 to 1.




If the growth experience of developing and developed countrieswere similar, there are two important reasons to expect thatdeveloping countries would be "catching up" by growing faster onaverage than developed countries.The first reason is due to technology transfer. Today’s developingcountries do not have to "reinvent the wheel".




This should enable developing countries to "leapfrog" over someof the earlier stages of technological development, movingimmediately to high-productivity techniques of production.




As a result, they should be able to grow much faster than today’sdeveloped countries are growing now or were able to grow in thepast, when they had to invent the technology as they went alongand proceed step by step through the historical stages ofinnovation.




The second reason to expect convergence if conditions aresimilar is based on factor accumulation.In traditional neoclassical analysis, the marginal product ofcapital and the profitability of investments would be lower indeveloped countries where capital intensity is higher, providedthat the law of diminishing returns applies.




Given one or both of these conditions, technology transfer andmore rapid capital accumulation, incomes would tend towardconvergence in the long run as the faster-growing developingcountries would be catching up with the slower-growingdeveloped countries.




Whether there is now convergence in the world economydepends on two levels of how the question is framed:

whether across average country incomes or across individuals(considering the world as if it were one country);whether focusing on relative gaps or absolute gaps.



Relative Country Convergence

The most widely used approach is simply to examine whetherpoorer countries are growing faster than richer countries.In the meantime the relative gap in incomes would be shrinking,as the income of poor countries would become an increasinglylarge fraction of income of rich countries.But globally, evidence for relative convergence is weak at best,even for the most recent decades.



Relative Country Convergence: World, DevelopingCountries, and OECD



Relative Country Convergence: World, DevelopingCountries, and OECD



Absolute Country Convergence

In the 1990-2003 period, while income grew 24% in high-incomeOECD countries, it grew 56% in South Asia and 196% in China.But due to their relatively low starting income levels, despitehigher growth, income gains were still smaller in absoluteamount than in the OECD.



Growth Convergence versus Absolute IncomeConvergence



Absolute Country Convergence

That is, even when the average income of a developing countryis becoming a larger fraction of developed country averageincomes, the difference in incomes can still continue to widen forsome time before they finally begin to shrink.



Population-Weighted Relative Country Convergence

The high growth rate in China and India is particularly importantbecause more than one-third of the world’s people live in thesetwo countries.This approach frames the question so as to weight theimportance of a country’s per capita income growth rateproportionately to the size of its population.



Country Size, Initial Income Level, and EconomicGrowth



Population-Weighted Relative Country Convergence

Although it is true that conditions have remained stagnant oreven deteriorated in many of the least developed countries,because of their smaller population sizes with the population-weighted approach this divergence effect is more thancompensated for by growth in countries with large populations.


Date post:	22-Jul-2018
Category:	Documents
Upload:	doannguyet
View:	213 times
Download:	0 times

ECON 450 Development Economics - publish.illinois.edu · The Model Predictions Convergence of...

Documents