Development and Growth Accounting

ECON 164: Theory of Economic GrowthDevelopment and Growth Accounting

Pablo Fajgelbaum

UCLA

May 13, 2015

Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 1 / 18

The Role of Productivity in Growth

These slides complement Chapter 7 of Weils textbook.

Our production function is:

y = AF (k, h)

We call A the level of productivity, or "total factor productivity" (TFP)

We saw that k (and factors that determine k, like s) and h partlyexplain dierences in y

How much does productivity A dier among countries? How much ofdierences in income per capita and growth is explained by A?Because A is not observed, its sometimes referred to as "Solowresidual" (also called a "measure of our ignorance")


Sources of Dierences in Income per Worker withProductivity Variation


Measuring Productivity Dierences across Countries

The world looks more like the 3rd panel, so we must use a productionfunction to infer dierences in A


Measuring Productivity Dierences Across Countries

We start from output in country i

Yi = AiK i (hiLi )1

Then output per worker in country i is:

yi = Aiki h1i| {z }

factors

Output of country 1 relative to country 2:

y1y2=A1A2

k1 h11

k2 h12

We can solve for (unobserved) productivity ratios as function of(observed) dierences in income and factors:

A1A2=y1y2

k2 h12

k1 h11

This exercise is called Development Accounting


Measuring Productivity Dierences Across Countries

We start from output in country i

Yi = AiK i (hiLi )1

Then output per worker in country i is:

yi = Aiki h1i| {z }

factors

Output of country 1 relative to country 2:

y1y2=A1A2

k1 h11

k2 h12

We can solve for (unobserved) productivity ratios as function of(observed) dierences in income and factors:

A1A2=y1y2

k2 h12

k1 h11

This exercise is called Development AccountingFajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 5 / 18

Development Accounting


Factors of Production Relative to the US by group ofIncome


Productivity Relative to the US by group of Income


Importance of Productivity and Factor Accumulation?

Both productivity and factor accumulation appear to be important

Accumulated factors range from 19% (poorest countries) to 94%(richest countries)Productivity factors range from 15% (poorest countries) to 94%(richest countries)

Productivity appears to be slightly more important to explain the lowrelative incomes of poorest countries

Can we obtain a precise measure?


Importance of Productivity and Factor Accumulation

Let

ry ,i = yi/yUSrA,i = Ai/AUSrf ,i =

ki h

1i /k

USh

1US

Then

ry ,i = rA,i rf ,i

in logsln ry ,i = ln rA,i + ln rf ,i

Implies

var [ln ry ,i ] = var [ln rA,i ] + var [ln rf ,i ] + 2cov [ln rf ,i , ln rA,i ]


Importance of Productivity and Factor Accumulation

We can measure each of these in the data:

var [ln ry ,i ]| {z }1.64

= var [ln rA,i ]| {z }0.49

+ var [ln rf ,i ]| {z }0.38

+ 2cov [ln rf ,i , ln rA,i ]| {z }0.39

Finally, we compute the role of our residual measure of productivity:

Productivity explains:var [ln rA,i ] + cov [ln rf ,i , ln rA,i ]

var [ln ry ,i ]= 53%

Factors explain:var [ln rK ,i ] + cov [ln rf ,i , ln rA,i ]

var [ln ry ,i ]= 47%

So, observable dierences in factors explain about half (47%) ofvariation in income


Growth Accounting

The exercise before consisted in explaining variations in levels.

What about variation in growth rates? > Growth Accounting


The Role of Factor Accumulation in Growth, 1975-2009

Ranges from 0.43% to 1.83%


The Role of Productivity in Determining Growth,1975-2009

Ranges from -1.42% to 1.33%


Growth Accounting

Can we obtain a concrete measure of how important is factoraccumulation for growth dierences?Start in general from

y = AF (k, h)

Take total derivative with respect to all factors of production andproductivity

dy = F (k, h) dA+ AFk (k, h) dk + AFh (k, h) dh

Divide both sides by Y

dyy=

F (k, h)AF (k, h)

dA+AFk (k, h)AF (k, h)

dk +AFh (k, h)AF (k, h)

dh

to reach

gy = gA +AFk (k, h) kAF (k, h)

dkk+

AFh (k, h) hAF (k, h)

dhh


Growth Accounting (Contd)

Therefore we get

gy = gA + gk + (1 ) ghOver time within a country, how important is productivity? I.e.,compute gAgy

US: g19702005A = 0.66% and g19702005y = 1.57% from 1970-2005, so

g 19702005Ag 19702005y

= 42%

Across countries between 2 periods of time, how important isproductivity? I.e., compute

var [gA (i)] + cov [gA (i) , gk (i) + (1 ) gh (i)]var [gy (i)]

= 68%


Measurement Issues

Measurement of human capital

Not only years of education but also quality (much harder to measure)mattersHuman capital is accumulated in forms other than schooling

Measurement of physical capital

Separating between investment and consumption in total expendituresGovernment spending

Measurement of number of workers

Informal sectorHome production

What do these issues imply for the gaps in our measured productivityand income across poor and rich countries?


Measurement Issues


Not only years of education but also quality (much harder to measure)matters

Human capital is accumulated in forms other than schooling







Measurement Issues









Measurement Issues




Separating between investment and consumption in total expenditures

Government spending





Measurement Issues









Measurement Issues






Informal sector

Home production



Measurement Issues









Where next?

Our analysis suggests that focusing on A in the production function isimportant (at least as important as K , L)

We will incorporate changes in A to the Solow model to studylong-run behavior of the economy

"Endogenous growth"


Development and Growth Accounting

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