Download HKMA-MAS Bilat Slides, 18 Jan 2003

Fertility and the Real
Exchange Rate
Andrew K. Rose
Andrew K. Rose and
and Saktiandi Supaat
Suktiandi Supaat
with Jacob Braude
Simple Intuition: What effect should
fertility have on real exchange rate?
•Suppose fertility rate declines exogenously (e.g., improvement in female
education, or decrease in contraception cost).
•Child-rearing associated with increased consumption. So decline in
fertility means increased savings.
•Investment may drop with decline in future equilibrium capital stock.
•If savings rise and investment falls, current account improves
•Children consume non-tradeables (education) disproportionately.
The relative price of non-tradeables should fall.
•Conclusion: real depreciation of the exchange rate part of
equilibrium response to decline in fertility.
Actual Finding: fertility has positive,
significant effect on real exchange rate
• 1-point increase in fertility rate (from say 2 to
3 children/woman) results in equilibrium
appreciation of 15%, ceteris paribus
• Consistent with theory, plausible in sign/size
• Robust results
Why Should We Care? Motivation 1
• Exchange Rates Matter, can’t be Modeled!
– Lane and Milesi-Ferretti: big impact on NFA,
international adjustment
• Exchange Rate Determination: A Literature of
Failure
– Dates back to at least Meese and Rogoff (1983):
random walk model out-forecasts structural
models, even given actual future fundamentals
– Huge Negative Implications for International
Finance as a Field
• Depressing inability to explain our most basic prices!
• Many major universities have no senior presence in
international finance
The Negative Results Continue
• Cheung, Chinn and Pascual (2005)
“Empirical Exchange Rate Models of the
Nineties: Are Any Fit to Survive?”
– “… we conclude that the answer to the
question posed in the title of this paper is a
bold ‘perhaps’ …”
• Taylor and Taylor (2005) in JEP Survey:
– “short run PPP does not hold … long run
PPP may hold …”
… through the present …
• Rogoff (2007) commenting on Engel,
Mark and West:
– “Is the glass ten percent full or ninety
percent empty?”
Motivation 2
• Demographic Transition an Enormous
Pending Economic Phenomena
– Large across Time
Global Dependency Ratios (UN)
70
60
50
40
30
20
10
0
1950
1960
1970
1980
1990
2000
Child Dependency Ratio
2010
2020
65+ Dependency Ratio
2030
2040
2050
Fertility Decline Large over Time
Global Fertility Rate
6
5
4
3
Fertility Rate
2
1
0
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
Large Variation across Countries
Worldwide Fertility Distribution
2
4
6
8
Box covers 25-75%; bar marks median.
1975
1980
1985
1990
1995
2000
LDC Examples
0
2
4
6
Fertility Rates
1950
1975
2000
year
China
Russia
India
Brazil
2025
OECD Examples
0
2
4
Fertility Rates
1950
1975
2000
year
Germany
Japan
Italy
USA
2025
Quick Survey of the Literature
•Little empirical work; much analysis theoretical/uses
simulations
•Most empirical work concerned with macroeconomic
quantities (such as the current account, or savings and
investment rates), not prices.
•Exceptions:
•Andersson and Österholm (2005) link age-distribution in
Sweden to real exchange rate.
•Helps in forecasting.
•No controls
•Andersson and Österholm (2006) extend to OECD, with
more limited success.
Simple Theoretical Framework
• OLG Model with 3 generations:
– Children (C) of size μ
– Retired (R) of size φ
– Workers (W) size normalized to1
• Dependency Ratios:
– μ for children
– Φ for retired
Income and Consumption
• Workers earn after tax wage (w – τ)t
– Children earn nothing
• Two Consumption Goods:
– Tradeables (CT)
– Non-tradeables (CN)
Workers’ Optimization Problem
Maximize Utility:
Ut = U(CNWt, CTWt) + βμtU(CNCt, CTCt)
+ ρU(CNRt+1, CTRt+1)
subject to budget constraint:
[PNtCNWt + PTtCTWt ]+ [μt(PNtCNCt + PTtCTCt)]
+ (1/(1+r*))(PNt+1CNRt+1 + PTt+1CTRt+1)
= (wt-τt) + b/(1+r*)
Parameterized Utility Function
U(CNit, CTit) = αilogCNit + (1-αi)logCTit
i = W, C, R
If αC, αR > αW consumption of children, retirees
biased towards non-tradeables (relative to
workers)
• When proportion of children (μ) rises:
– consumption per child falls
– but aggregate consumption of children rises
– resources shift from parents’ consumption and
savings
Notes
• Workers discount kids’ consumption by β,
and utility in retirement by ρ
• World interest rate (r*) given exogenously
• Government finances transfer payments (b)
via lump-sum tax (τ)
– Government Budget Constraint: τt = φtb
Problem for Retired
Maximize Utility:
αRlogCNRt + (1-αR)logCTRt
• Retired have income from predetermined
foreign assets a and government transfer
payments (b)
Total income φt(r*at + b)
Production
• Cobb-Douglas Production Functions:
YTt = LTtθTKTt1-θT
YNt = LNtθNKNt1-θN
• Capital Stock and Sectoral Allocation
given exogenously at t (could add
dynamics)
• Perfect Competition
Full Employment implies LTt + LNt = 1
Equilibrium
• Price of tradeables given exogenously
to small open economy
• Price of non-tradeables determined
domestically:
YNt = CNWt + μtCNCt + φtCNRt
Change in Fertility Rate
• Solve Model, use Implicit Function Theorem
• Effect on Real Exchange Rate of Child
Dependency Ratio:
∂PNt/∂μt > 0 if (αC – αW) + αCρ > 0
• RHS can be decomposed into two parts
– Composition of Spending Channel: children spend
more on non-tradeables
– Savings Channel: reallocation from consumption
to savings raises demand for non-tradeables
Effect of Retired Dependency Ratio
Relative Price of Non-Tradeables rises with
Elderly Dependency Ratio:
∂PNt/∂φt > 0 if
at(1+r*)αR(1+βμt+ρ) + b[(αR–αW)+(αR–αC)+αRρ] > 0
• Can Decompose into Two Effects
– Asset (first part); always positive; retired spend
without supplying labor (akin to “transfer effect”)
– Transfers (second): depends on relative demand
for non-tradeables through both composition and
savings channels
Main Theoretical Implications
• Model quite stylized (no uncertainty; many
exogenous constraints on capital,
production, utility; implicitly assume LOOP
for tradeables, …)
– Don’t take structure of model too literally
• Instead, focus on key predictions
What Do We Search For?
• Increase in fertility rate should
appreciate real exchange rate
• Ditto increase in elderly dependency
ratio
– Less time-series variation; may be more
difficult to detect
Default Estimating Equation
log(reer)it = βfertit + γ1PPPit + γ2y/yusit + γ3openit
+ γ4TLit + γ5G/Yit + γ6growthit + γ7log(pop) it
+ γ8log(y) it + Σtφt + Σiθi + eit
•Fixed time- and country-specific effects
•So don’t have to worry about relative vs absolute fertility,
time- or country-specific shocks
•Often augment with 1) NFA and 2) current account (reduced
observations)
Nests Existing Standard Models of
Real Exchange Rate Determination
•Purchasing Power Parity deviation much disputed,
important to enter for robustness
•Here included via absolute term from PWT 6.2
•Supply (“Balassa-Samuelson”) Effects of differential
productivity growth included via three common proxies
•National/American Real GDP per capita
•Growth Rate (Chinn)
•Log of Real GDP per capita
•Potential Multicollinearity with fertility!
More REER Determinants
• Demand Effects
• Government spending (mostly non-tradeables)
• Income p/c (non-homothetic demands, growing
demand for non-tradeable services)
• Openness, Degree of Liberalization
– Lower Prices, Exchange Rates
• Size
– Ease of Pursuing Mercantilist Policies
Data Set
Two Constraints
•
UN demographic data (1950-2050), quinquennial
•
•
Fertility rate, Life expectancy, age distribution
IFS data on real effective exchange rates (19752005), annual
•
CPI weighs (“rec”) for maximal coverage
•
Results in overlapping data for 87 countries, 6
quinquennial periods (1975-2005)
•
Other sources straightforward (PWT, WDI, …)
Country List
Algeria
Armenia
Australia
Austria
Bahamas
Bahrain
Belgium
Belize
Bolivia
Bulgaria
Burundi
Camer.
Canada
C.A.R.
Chile
China
Colombia
Congo
C Rica
Croatia
Cyprus
Czech
Côte d'Iv.
Denmark
Dom.Rep
Ecuador
Eq’l Guin
Fiji
Finland
France
Gabon
Gambia
Germany
Ghana
Greece
Guyana
Hungary
Iceland
Iran
Ireland
Israel
Italy
Japan
Lesotho
Luxemb.
Maced.
Malawi
Malaysia
Malta
Mold.
Morocco
Neth.
Neth Ant.
N.Z.
Nicarag.
Nigeria
Norway
Pakistan
PNG
Paraguay
Philipp.
Poland
Portugal
Romania
Russia
Samoa
S. Arabia
Si. Leone
Singapore
Slovakia
Sol. Isl.
S. Africa
Spain
St. Lucia
St.VinG.
Sweden
Switzerl
Togo
Tri&Tob
Tunisia
Uganda
Ukraine
UK
USA
Uruguay
Venez
Zambia
Real Effective Exchange Rates
against Fertility
7
ln(REER)
REER
600
400
200
5
4
0
0
2
4
6
Fertility Rate
8
0
Raw Data
.5
1
1.5
ln(Fertility)
2
Natural Logarithms
1
5.2
.5
5
ln(REER)
res(REER)
6
0
-.5
-1
4.8
4.6
4.4
-2
-1
0
res(Fertility)
Residuals
1
0
2
4
6
Fertility Rate
8
Trimmed Observations
Real Effective Exchange Rates against Fertility
ln(REER)
Log REER against Fundamentals
7
7
6
6
5
5
4
4
ln(REER)
0
50
100
PPP deviation
150
0
7
7
6
6
5
5
4
4
0
20000
40000
Real GDP p/c, $
60000
-600
50
100
Income p/c as % of US
-400
-200
0
NFA %GDP
Log REER against Fundamentals
150
200
Descriptive Statistics
Obs.
Mean
Std.
Dev.
Log(Real Effective Exchange Rate)
443
4.69
.27
3.9
6.4
Fertility Rate
522
3.36
1.86
1.1
7.6
PPP-deviation
472
66.59
34.31
15.3
195.2
Real Income p/c, % US Income
472
38.35
30.19
1.1
137.9
Openness, %GDP
472
80.24
53.93
8.9
406.7
Trade Liberalization Measure
462
.59
.48
0
1
Government Spending, %GDP
472
22.76
10.74
4.6
67.9
Growth real GDP per capita
462
1.67
3.68
-10.4
48.2
Log(population)
546
8.55
2.06
3.7
14.1
Log(real GDP per capita, $)
472
8.81
1.08
5.9
10.8
Net Foreign Assets, %GDP
387
-35.67
76.21
-980.
184.
Current Account, %GDP
409
-3.08
6.8
-30.4
21.4
Min
Max
Simple Bivariate Correlations
Default
Default
Augment
Augment
Log REER
Fertility
Log REER
Fertility
Sample:
Correlation with:
Fertility Rate
.39
PPP-deviation
.00
-.53
.00
-.50
Real Income p/c, % US Income
-.19
-.73
-.20
-.70
Openness, %GDP
.05
-.17
.06
-.14
Trade Liberalization Measure
-.31
-.60
-.34
-.55
Government Spending, %GDP
.13
.08
.17
.12
Growth real GDP per capita
-.13
-.39
-.24
-.33
Log(population)
-.02
-.06
-.01
.00
Log(real GDP per capita, $)
-.22
-.85
-.27
-.83
Net Foreign Assets, %GDP
-.08
-.50
Current Account, %GDP
-.11
-.31
282
282
Observations
332
.48
332
Approximate standard error for default (augmented) sample correlations = .05 (.06).
Benchmark Results
Fertility Rate
PPP-deviation
Real Income p/c as
% US Income p/c
Openness
%GDP
Trade Liberalization
Measure
Government Spending
% GDP
Growth real GDP
per capita
Log(population)
Log(real GDP
per capita, $)
Net Foreign Assets
% GDP
Current Account
%GDP
Observations
R2
Default
.15**
(.03)
.0089**
(.0007)
-.002
(.002)
.0014**
(.0005)
.17**
(.04)
.002
(.003)
-.010**
(.004)
-.13
(.15)
.06
(.07)
332
.10
Augment
.15**
(.02)
.0096**
(.0007)
.004
(.002)
.0007
(.0005)
.12**
(.03)
.008**
(.003)
-.005
(.004)
.00
(.13)
-.25**
(.09)
-.0001
(.0003)
-.001
(.002)
282
.26
Variant 1
.16**
(.02)
.0093**
(.0007)
-.001
(.002)
.0011*
(.0005)
.15**
(.04)
.005
(.003)
Variant 2
.13**
(.02)
.0091**
(.0007)
-.002
(.002)
.0007
(.0004)
Variant 3
.17**
(.02)
.0081**
(.0006)
Variant 4
.11**
(.02)
.0100**
(.0008)
.06
(.06)
.0001
(.0003)
336
.19
380
.20
311
.25
-.002
(.002)
340
.10
Sensitivity Analysis
Add de jure exchange rate peg
dummy
Add RR de facto exchange rate peg
dummy
Add LYS de facto exchange rate peg
dummy
Add Polity 2
Add Executive Constraints
Add lagged dependent variable
Without time effects
Without country-specific fixed
effects
Country-Specific Random effects
Level (not log) of REER as
regressand
Log (not level) of fertility as key
regressor
Default
.17**
(.05)
.19**
(.03)
.17**
(.04)
.16**
(.03)
.12**
(.03)
.10**
(.03)
.12**
(.03)
.09**
(.01)
.12**
(.02)
36**
(5)
.37**
(.08)
Augmented
.05
(.04)
.17**
(.03)
.22**
(.03)
.15**
(.02)
.10**
(.02)
.08**
(.03)
.13**
(.03)
.10**
(.01)
.12**
(.02)
39**
(5)
.32**
(.07)
Decadal data
Without >|2σ| outliers
Drop 1975-1984
Drop 1991-2004
Drop Latin America, Caribbean
Drop European developing countries,
Central Asia
Drop Middle East, North Africa
Drop Sub-Saharan Africa
Drop East Asia
Drop South Asia
Drop high income countries
Default
.13**
(.05)
.15**
(.02)
.11**
(.03)
.16**
(.03)
.15**
(.03)
.14**
(.03)
.07*
(.03)
.18**
(.03)
.15**
(.03)
.14**
(.03)
.19**
(.04)
Augmented
[AR1].08*
(.04)
.16**
(.02)
.09**
(.03)
.15**
(.03)
.16**
(.02)
.16**
(.02)
.10**
(.03)
.15**
(.02)
.15**
(.02)
.15**
(.02)
.22**
(.04)
No evidence of non-linearity relationship
between fertility and the real exchange rate
.4
.2
0
-.2
-.4
-1
0
Non-Parametric estimates & +/- 2se Linear CI, default model
Real Effective Exchange Rates and Fertility: Linear or Not?
1
Simultaneity/Measurement Error
•
Measurement error a potential issue (probably not
simultaneity)
•
•
Little seems to drive real exchange rate empirically!
Barro and Lee (“Sources of Economic Growth” 1994):
“We also find that female educational attainment has a
pronounced negative effect on fertility …”
•
Three instruments used:
1) the percentage of 15+ females without schooling;
2) the percentage of 15+ females who attained secondary
school; and
3) the average years of school for 15+ females.
“Deeper” IV Rationalizations
• Technological Progress implies Rise in
Return to, Demand for Human Capital
– Hence increased preference for offspring
quality instead of quantity?
• Knowledge of Birth Control?
Instrumental Variable Results
Default
Augmented
Variant 1
IV set 1
.25**
(.07)
.20**
(.05)
.27**
(.05)
IV set 2
.32**
(.09)
.28**
(.07)
.30**
(.06)
IV set 3
.20*
(.10)
.17*
(.08)
.23*
(.10)
IV set 4
.29**
(.08)
.26**
(.06)
.29**
(.06)
WLS Results
Weighted by
Population
Default
.15**
(.03)
Augmented
.16**
(.02)
Weighted by
GDP
.15**
(.02)
.16**
(.02)
Sensitivity Analysis: Key Regressor
Birth Rate
Infant Mortality Rate
Child Mortality Rate
Ratio of Young (<20)
to Population
Ratio of Elderly (>65)
to Population
Ratio of Active (20-65)
to Population
Life Expectancy
Default
.009
(.006)
-.020**
(.007)
-.007
(.006)
.005
(.006)
.014
(.014)
-.010
(.007)
-.009
(.005)
Augmented
-.001
(.005)
-.014**
(.005)
-.002
(.006)
.005
(.006)
.011
(.011)
-.009
(.006)
-.009*
(.005)
Adding Different Age Cohorts
to the RER Equation
.
*
.
*
.
*
.
*
. *
. *
. *
.*
.*
*
*.
*.
*.
*.
*.
*.
*.
*.
*
.*
.*
Cohort
% 0-4
% 5-9
% 10-14
% 15-19
% 20-24
% 25-29
% 30-34
% 35-39
% 40-44
% 45-49
% 50-54
% 55-59
% 60-64
% 65-69
% 70-74
% 75-79
% 80-84
% 85-89
% 90-94
% 95-99
% 100+
Sum
Coefficient
Std. Error
.021
.018
.015
.012
.009
.007
.005
.003
.002
.001
-.000
-.001
-.002
-.002
-.002
-.002
-.001
-.001
.000
.002
.003
.09
.013
.012
.011
.011
.010
.010
.010
.010
.011
.011
.011
.011
.012
.012
.012
.012
.012
.012
.013
.013
.013
.22
Fertility, and Savings, Investment
and Current Account
•This all bivariate
•No model/control variables at all for Savings,
Investment, or current account; just FE
•Essentially a “sniff test”
Regressand
Savings Rate,
% GDP (PWT)
Investment Rate,
% GDP (PWT)
Current Account,
% GDP (WDI)
Fertility Effect
-1.67*
(.75)
2.41**
(.43)
-.21
(.67)
Observations
452
452
393
Summary: 1
• Use quinquennial data set: 87 countries, 19752005 to investigate fertility - real effective
exchange rate link
• Control for host of potential determinants (PPP,
Balassa-Samuelson, etc)
Summary: 2
• Some Positive Results!
• Find statistically significant and robust link
between fertility and the exchange rate.
• No non-linearities
• Robust results
• Instrument variables just raises estimate
• Other demographic effects estimated
sensibly but with less precision (sample
variation?)
Conclusion
• Decrease in fertility rate of one child per
woman associated with 15% depreciation in
the real effective exchange rate
• Such fertility rate changes common in sample
• Enormous wealth transfers!
– Using Gourinchas and Rey (2007) estimates: 15%
depreciation results in transfer of 8% US GDP from RoW