Upload
xiao-xi
View
219
Download
0
Tags:
Embed Size (px)
DESCRIPTION
uuu
Citation preview
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")
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 2 / 18
Sources of Dierences in Income per Worker withProductivity Variation
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 3 / 18
Measuring Productivity Dierences across Countries
The world looks more like the 3rd panel, so we must use a productionfunction to infer dierences in A
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 4 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 5 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 5 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 5 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 5 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 6 / 18
Factors of Production Relative to the US by group ofIncome
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 7 / 18
Productivity Relative to the US by group of Income
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 8 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 9 / 18
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 ]
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 10 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 11 / 18
Growth Accounting
The exercise before consisted in explaining variations in levels.
What about variation in growth rates? > Growth Accounting
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 12 / 18
The Role of Factor Accumulation in Growth, 1975-2009
Ranges from 0.43% to 1.83%
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 13 / 18
The Role of Productivity in Determining Growth,1975-2009
Ranges from -1.42% to 1.33%
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 14 / 18
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
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 15 / 18
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%
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 16 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
Measurement Issues
Measurement of human capital
Not only years of education but also quality (much harder to measure)matters
Human 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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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 expenditures
Government 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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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 sector
Home production
What do these issues imply for the gaps in our measured productivityand income across poor and rich countries?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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?
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 17 / 18
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"
Fajgelbaum (UCLA) Development and Growth Accounting May 13, 2015 18 / 18