ECON2915 Economic Growth Lecture 4 : Human capital. Productivity - - PowerPoint PPT Presentation

ECON2915 Economic Growth

Lecture 4 : Human capital. Productivity measurement. Andreas Moxnes

University of Oslo

Fall 2016

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Human capital and income

So far: Workers assumed to be identical over time and across countries. How can differences in human capital explain cross-country income differences? Human capital: Factors that influence the productivity of the worker, e.g. education & health. Production function with human capital: Y = F (K,hL), where h is effort/quality per worker.

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Human capital characteristics

1 A productive input : Increased HC −

→ increased output.

2 Can be produced (as opposed to e.g. natural resources) 3 Its value depreciates over time. 4 Yields a return, e.g. investment in education increases the wage. 5 Cannot be rented, as opposed to physical capital. 3 / 40

Human captial: Health

We’ll focus on two determinants of human capital: Health & education. Better health: Improves productivity - increase output by working more or improving quality. Brings more people into the workforce.

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Nutrition vs GDP/capita

UK: Better nutrition estimated to raise output by 95% over 200 years (0.3% per year). Output growth over the same period was 1.15%.

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Life expectancy vs GDP/capita

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Health and income

Two-way causality.

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An exogenous shift in income

A − → B − → C

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HC : Education

Education & skills also human capital.

◮ Boost productivity & wages ◮ Intrinsic value, higher utility. 9 / 40

Changes in the level of education 1975-2010

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Norway, 1970-2014

0% ¡ 10% ¡ 20% ¡ 30% ¡ 40% ¡ 50% ¡ 60% ¡ 70% ¡ 80% ¡ 90% ¡ 100% ¡ 1970 ¡ 1980 ¡ 1981 ¡ 1982 ¡ 1983 ¡ 1984 ¡ 1985 ¡ 1986 ¡ 1987 ¡ 1988 ¡ 1989 ¡ 1990 ¡ 1991 ¡ 1992 ¡ 1993 ¡ 1994 ¡ 1995 ¡ 1996 ¡ 1997 ¡ 1998 ¡ 1999 ¡ 2000 ¡ 2001 ¡ 2002 ¡ 2003 ¡ 2004 ¡ 2005 ¡ 2006 ¡ 2007 ¡ 2008 ¡ 2009 ¡ 2010 ¡ 2011 ¡ 2012 ¡ 2013 ¡ 2014 ¡ University ¡> ¡4 ¡years ¡ University ¡<= ¡4 ¡years ¡ High ¡school ¡ Primary ¡

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Education : Costs and benefits

Costs:

• Tuition. 6.2% of GDP in the U.S.

The opportunity cost. Benefits: The return to education.

◮ e.g. % increase in wage for an additional year of schooling. 12 / 40

Returns to schooling

Hall and Jones (1999). 13.4% per year for years 1-4, 10.1% for next 4 years, 6.8% for 8+ year. Both developing and developed countries.

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Decomposing wages

We know that capital’s share of income is around 1/3 (the α). For the remaining 2/3, how much is due to human capital and how much is “raw labor”.

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Share of HC in wages

For complete higher, raw labor is 1/4 of wages. For the economy as a whole, the HC share is larger in advanced countries.

◮ Higher wages for more education. ◮ Larger share of population with more education. ◮ HC share 59% in developing, 68% in advanced. 15 / 40

Education and income

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Education and income

Higher education − → higher income. Higher income − → spend more on education. 3rd factors that affect both income and education.

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The Solow model with HC

Let’s introduce HC in the Solow model: Y = AK α (hL)1−α = h1−αAK αL1−α, where h is effort/quality per worker.

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Intensive form

Y = h1−αAK αL1−α

• r

y = h1−α AK αL1−α L = h1−αAkα Change in capital stock: ˙ k = ∂ (K/L) ∂t = ˙ KL−K ˙ L L2 = ˙ K L − K L ˙ L L = γY −δK L −kn = γf (k)−(δ +n)k (as before).

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Steady state

Steady state defined by ˙ k = 0: γh1−αAkα = (δ +n)k kss = Aγh1−α δ +n 1/(1−α) = h Aγ δ +n 1/(1−α) And output yss = h1−αAkα = h1−αA

• h

Aγ δ +n 1/(1−α)α = hA1/(1−α)

• γ

δ +n α/(1−α) Compared to Solow model without h?

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Predictions

Two countries i and j, with hi and hj, all else equal. Then yss

i

yss

j

= hi hj Income per capita proportional to HC. E.g. twice as high h in i yields twice as high y.

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A numeric example

12 years of schooling in i and 2 in j. What is human capital h in the two countries?

◮ Recall wage increase per year of additional schooling (13.4% for grades

1-4, etc).

◮ Assume human capital h proportional to wages.

Then hi = 1.1344 ×1.1014 ×1.0684 ×h0 = 3.16×h0 hj = 1.1342 ×h0 = 1.29×h0 And yss

i

yss

j

= 3.16h0 1.29h0 = 2.47.

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Predicted vs actual GDP per worker

Calculate h for every country and use the formula to predict y: Positive correlation but too few poor countries in model. Why?

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The quality of education

It’s not only years of schooling that matters. E.g. student-teacher ratio, teacher quality, access to teaching materials. Test scores capture both quantity and quality.

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Externalities

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Externalities

Externalities: An incidental effect of economic activity for which no compensation is provided. The Solow model could not generate sufficient income inequality coming from human capital.

◮ One reason could be externalities.

Education: Additional schooling for individual x − → private return to x but also returns for y.

◮ E.g. x adopts new technologies that y also will use. 25 / 40

Next topic: Productivity measurement

Productivity is how efficient we use the factors of production. The Solow model: A.

◮ Knowledge ◮ Organizing production ◮ Effort

Over the long run, productivity growth is considered the major factor behind income growth.

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Recall

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Identification

What’s productivity and/or factor accumulation?

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Development accounting

Can we identify the 3rd case? Consider 2 countries with production function Yi = AiK α

i (hiLi)1−α

⇐ ⇒ yi = Aikα

i h1−α i

Then yi yj = Ai Aj kα

i h1−α i

kα

j h1−α j

⇐ ⇒ Ai Aj = yi yj kα

j h1−α j

kα

i h1−α i

• Yes. Intuition: Given same α, we adjust GDP/capita ratio with factor

accumulation ratio to infer A ratio.

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An example

Given α = 1/3, we get A1 A2 = y1 y2 kα

2 h1−α 2

kα

1 h1−α 1

= 24 1 11/312/3 271/382/3 = 2.

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Cross-country evidence

Enormous differences in the A’s. Where do A differences come from? Measurement issues?

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Productivity or factor accumulation?

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Productivity or factor accumulation?

Both - surprisingly similar plots.

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Measurement

Productivity A is the residual, after having removed h and k. Maybe we are capturing differences in

◮ the quality of capital. ◮ unobserved worker differences. ◮ other factors of production. 34 / 40

Growth accounting

The previous decomposition was in levels. Here, ask the question: is growth coming from factor accumulation or productivity?

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From levels to growth

Define ˆ x = ˙ x x We know ∂ lny ∂t = ˙ y y = ˆ y Then we have

• xy = ∂ ln(xy)

∂t = ∂ lnx ∂t + ∂ lny ∂t = ˆ x + ˆ y

• x/y = .. = ˆ

x − ˆ y

• xa = .. = aˆ

x E.g. if x and y grow by 2% and 4%, then xy grows by 6%.

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Growth accounting

Production function again y = Akαh1−α Growth rates: ˆ y = ˆ A+α ˆ k +(1−α)ˆ h ⇐ ⇒ ˆ A = ˆ y −α ˆ k −(1−α)ˆ h Productivity growth = output growth - growth in inputs.

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Example

Set α = 1/3. Then ˆ A = ˆ y −α ˆ k −(1−α)ˆ h = 0.04− 1 30.02− 2 30.02 = 0.02

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Historical data

Following countries over time, does factor accumlation (FA) or productivity explain growth?

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Historical data

Appears that ˆ A is more important - more variation in ˆ A than ˆ FA.

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