Explaining CrossCountry Income Differences

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Explaining Cross-Country Income Differences

• By
• Bao Lee
• Jiyoung Jang

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Two Approaches

• .

Growth Regressions
Quantitative Theory
Effects of Policy on Disparity
Effect of Policy on Growth
Policies Distorting Investment
Policies in a Two Sector AK Model
Other Policies
Policies in a RD Model
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• .

Two Growth Models
An Exogenous Growth Model
An Endogenous Growth Model
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Quantitative Theory

• Q How much of the cross-country differences in
  income levels and growth rates can be explained
  by differences in particular economic policies?

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• First some information
• Disparity ratio of GDP per worker of the MOST
  productive countries to the LEAST productive
  countries
• Data most productive countries are 30 times that
  of least productive

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Effects of Policy on Disparity

• Q how much of this difference is due to policies
  such as taxes on investments, inefficient
  government production, labor market restrictions,
  and granting of monopolies
• Use explicit formulas to show, under certain
  assumptions, that measured differences in
  policies imply income disparity

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Policies Distorting Investment

• Using a two-sector NGM (consumption goods and
  investment goods)
• Representative HHs maximizes
• SßtU(Ct)
• s.t. Ct ptXt rtKt wtLt, t0
• p-price of relative price of investment
• L-constant labor input

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• Law of motion
• Kt1 (1-d)Kt Xt
• Capital goods can be allocated to either sector.
• Consump. max C-rKc-wLc
• s.t.
• Investment max pX-rKx-wLx
• s.t.
  (? ?)
• AcAx

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• Thus relative productivities is (?)

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• For all values of ? and Lx/L, the ratio (?) will
  exceeds 1
• Estimates of
• suppose and
• If then

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• If then
• Q What fraction of the productivity gap should
  be attributed to this model?

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• Taking the log of productivity in model and
  divide by log of productivity in data
• ln(1.57)/ln(8) 0.22
• ln(2)/ln(8) 0.33
• Hence, under this calculation, the policy
  accounts for between 22 to 33 percent of the
  productivity gap.

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Effects of Policy Growth

• Main Question
• What are the determinants of the long-run growth
  rate ?
• The determinants can be policies of taxes on
  investment, government production, tariffs, labor
  market restrictions, granting of monopolies,
  monetary policies, and subsidies to research and
  development.
• Answer
• - The estimates found using quantitative
  theory depend in critical ways on values of
  parameter and measures of factor inputs for which
  there is a little consensus.

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Two Prototype Endogenous Growth Model

• Policies in a Two-Sector Model
• Two-Sector Model with Growth driven by Factor
  Accumulation
• Policies in a R D Model
• - The Growth driven by Research and Development

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For both models,

• Derive steady-state growth rates
• Show how they depend on economic policies

• Under certain assumptions,

Measured differences in policies
Significant differences in growth rates
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1. Policies in a Two-Sector AK Model

• - Analyze the balanced growth predictions of a
  prototype two-sector endogenous growth model.

• ? Three main differences b/w Two-Sector AK Model
  and exogenous growth model
• Constant Return to Scale in accumulable factors
• Elastic Labor Supply
• Taxes on factor incomes

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• Representative household maximizes
• ?ßtU(ct, lt)Nt
• c consumption per HH, l the fraction of time
  devoted to work
• Nt the total number of HH

• Two Sectors of Production
• Firms in sector 1 produce goods which can be used
  for consumption or as new physical capital.
• The Production Technology in this
  sector 1
• cxk y
  A(kv)ak(hlu)ah
• xk Per capita investment in physical capital, A
  Index of the technology level,
• v and u the fractions of physical capital and
  labor, k and h the per capita
• stocks of physical and human capital
• 2. The human capital investment good is produced
  in sector 2.
• xh per capita investment in human capital, B
  index of the technology level

The Production Technology in this sector 2
xh B(k(1-v)?k (hl(1-u))?h
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The Law of Motion for the per capita capital
stocks k and h

• (1n)kt1(1-dk)ktxkt
• (1n)ht1(1-dk)htxht
• HH supply labor and capital to the firms in the
  two sectors
• Their income and investment spending are taxed.
• HH BC
• Ct(1txkt)xkt(1txht)qtxht
• 
  (1-tk1t)r1tktvt (1-tk1t)r2tktvt (1-vt)
• (1-th1t)w1tlthtut(1-th2
  t)w2tltht(1-ut)Tt
• q the relative price of goods produced in
  the two sectors, txk a tax on physical capital
  investment, txh a tax on human capital
  investment, rj the rental rate on physical
  capital in sector j, wj the wage rate in sector
  j, txj a tax on income from physical capital
  used in sector j, thj a tax on income from human
  capital used in sector j, T per capita transfers.

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Steady-State Growth for a 0 Percent and 20
Percent Income Tax in the Two-Sector Endogenous
Growth Model
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• There is large difference between the predictions
  of Lucas(1990) or Kim(1992) and King and
  Rebelo(1990) or Jones et al.(1993) if growth
  rates are compounded over many years.
• The estimated impact of policy on growth varies
  dramatically in the literature.
• There is still much debate about the magnitude of
  the estimates of policy effects

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Q Why the results are so different ?

• To get some sense of this answer,
• Consider two special cases of the model
• Derive explicit formulas for the growth rate of
  productivity in the steady state.

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The First Special Case1.
Suppose that incomes from capital and labor used
in sector j are taxed at the same rateThat is,
tj tkj thj

• 2. Suppose that tax rates on physical and human
  capital investment are equal
• That is, tx txk txh
• 3. Suppose that capital shares are equal in the
  two sectors
• That is, a ak ? k
• 4. Suppose that the depreciation rates are equal
  for physical and human capital,
• That is, d dk dh

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• In this case, the steady-state growth rate for
  output per worker

g ß 1-dAa(1-t1)aB(1-a)(1-t2)1-a
l(t)1-a/(1tx)1/s -1

• Predicted effects of a tax increase depend on the
  discount factor, the depreciation rate, the
  capital share, and the elasticity of labor.

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• A Second Special Case
• Suppose that the sector for producing human
  capital uses no physical capital.

• In this case, the steady-state growth rate for
  output per worker

g ß (1-dhBl(t) (1-th2 )/(1txh)1/s -1
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Comparing Two Special Cases of the Model

• The First Case
• - WITH physical capital
• Changes in tax rates only affect growth if
  they affect supply of labor. If labor is
  inelastically supplied, the taxes levied on
  factors in sector 1 have no growth effects at
  all.

• The Second Case
• NO physical capital
• Changes in tk 2 have no effect at all
  because of no physical capital.

g ß 1-dAa(1-t1)a B(1-a)(1-t2)1-a
l(t)1-a/(1tx)1/s -1
g ß (1-dhBl(t) (1-th2 )/(1txh)1/s -1
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Policies in a R D Model

• Theoretical models of endogenous growth based on
  devoting resources to RD

New product development models Such as Romer
Quality-ladder models Such as in Grossman and
Helpman
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A Discrete-Time Version of the Model in Romer

• Technological innovation new blueprints for
  intermediate inputs- is the driving force behind
  growth in this model.
• The model implies a scale effect.
• The growth rate increases with the number of
  people working in RD.
• There is no scale effect in Jones model

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Three Production Sectors

• In the research sector, firms use existing
  blueprints and human capital to produce new
  blueprints.
• In the intermediate goods sector, firms use
  existing blueprints and capital to produce
  intermediate capital goods.
• In the final goods sector, firms use intermediate
  capital good, labor and human capital to produce
  a final good that can be consumed or used to
  produce new capital.
• ? There is a household sector.
• -HH buy consumption and investment goods with
  wages, rental earnings, and profits.

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g dH ?r ??a/(1-a)(1-a-?)
g ß(1r) 1/s -1

• G depends positively on the stock of human
  capital H.

There is a scale effect
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Main Assumption
A doubling of the number of people working on RD
A doubling of the growth rate by Nt!Nt dH?
NtNØ t
However, in the OECD countries, there has been a
dramatic increase in the number of scientists and
engineers and a dramatic increase in the
resources devoted to RD with little or no
increase in growth rates over a sustained period
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Romer Model Jones

• Jones offers a possible solution to the problem
  of the existence of a scale effect.
• Assume that the evolution of blueprints is given
  by
• Now g depends on the growth rate of the labor
  force that the total number of researchers. Thus
  the scale effect is removed.

Nt1 Nt dH?Nt NØt ,0lt ?1, Ølt1
g ?n/1-Ø
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• Q Is the relationship in this equation
  consistent with the data ?
• A It depends a lot on how the model is
  interpreted.
• Ex 1. If we interpret this model as one of a
  typical country, then the answer is NO.
• - The correlation b/w growth rates of GDP er
  worker and growth rates of the labor force over
  the period 1960-1985 is 0.12. The relationship
  in this equation implies a positive correlation.
• Ex 2. If we interpret this model as one relevant
  only for countries in which there is a lot of
  activity in RD, we still find that the
  correlation b/w the growth rates of GDP per
  worker and the labor force are around zero or
  slightly negative.

g ?n / 1-Ø
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Testing Implications against Data

• Two model will be examined
• Standard exogenous growth model
• Standard AK endogenous growth model

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• Exogenous growth maximization problem

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• AK endogenous model maximization problem
• Firms problem

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Simulation of

• Using this investment distortion as an input, we
  simulate an artificial panel data set for both
  exogenous and endogenous growth model

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Exogenous model
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data
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Exogenous

• 1820, country at 90th percentile has per capita
  GDP of 4.3 times that of country at 10th
  percentile
• 1989, it was 16.5, which is close to the data of
  16.7

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Exogenous

• Figure 18 relationship between initial incomes
  and growth rates
• Negative correlation because of transition
  dynamics of capital (s.s.) and investment
  distortion (PI/PC)

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Exogenous model
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data
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Exogenous

• Figure 19 correlation between growth rates in
  sub-periods of 1961-1972 and 1973-1985
• Weak positive correlation of 0.21
• Data shows 0.16

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Exogenous model
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data
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Exogenous

• Figure 20 plot maximum growth rate (top 2 ½
  percent) of each decades from 1880-2000
• Model is higher than data
• Model also shows no significant upward trend
• Model although a lot mobility of countries across
  income, most are above 6 percent

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Exogenous
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data
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Exogenous

• Next, s5
• Differences between s2 and s5
• Maximum growth rates are smaller when s5 (5
  compared to 10)
• Smaller range of distribution (1989) 90th per is
  only 7.1x that of 10th per when s5 (oppose to
  16.5)

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An Endogenous Growth Model (ak?k)

• Figure 25

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Figure 26
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Figure 2
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Figure 27
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Figure 28
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Figure 4
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Conclusion of both Exogenous and Endogenous

• We worked out implications of two standard growth
  models for basic facts on income
• From that we found that exogenous growth model
  does a better job simultaneously accounting for
  dispersion of income over time, lack of
  persistence in growth rates, and range in
  cross-country growth rates than the AK endogenous
  model does

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• However, more is needed before we can definitely
  say how well it do in explaining cross-country
  income differences.
• Although we found that despite their simplicity,
  do fairly well mimicking some of the basic
  features of the data.

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Conclusion

• throughout, there are still many open issues and
  unanswered questions
• Quantifying the role of economic policies for
  growth and development depends on policy
  variables that are difficult to measure and
  models that have predictions which rely on
  controversial parameterizations
• only reviews progress made thus far

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Conclusion

• leaves room for new development that can be made
  with better measures of factor inputs (especially
  human capital), better measures of policy
  variables, and greater synthesis of theory and
  data