Fertility and the Real Exchange Rate

Andrew K. Rose andSuktiandi Supaat

Andrew K. Rose

and Saktiandi Supaat

with Jacob Braude

Simple Intuition: What effect should fertility have on real exchange rate?

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

Fertility Decline Large over Time

Large Variation across Countries

24

68

Tota

l Fer

tility

Rat

e, U

N

1975 1980 1985 1990 1995 2000

Box covers 25-75%; bar marks median.

Worldwide Fertility Distribution

LDC Examples0

24

6

1950 1975 2000 2025year

China IndiaRussia Brazil

Fertility Rates

OECD Examples0

24

1950 1975 2000 2025year

Germany ItalyJapan USA

Fertility Rates

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 = LTt

θTKTt1-θT

YNt = LNtθNKNt

1-θN

• Capital Stock and Sectoral Allocation given exogenously at t (could add dynamics)

• Perfect CompetitionFull 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 RatioRelative 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 (1975-2005), 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

Real Effective Exchange Rates against Fertility

R

EE

R

Raw DataFertility Rate

0 2 4 6 80

200

400

600

ln

(RE

ER

)

Natural Logarithmsln(Fertility)

0 .5 1 1.5 2

4

5

6

7

re

s(R

EE

R)

Residualsres(Fertility)

-2 -1 0 1-1

-.5

0

.5

1

ln

(RE

ER

)

Trimmed ObservationsFertility Rate

0 2 4 6 84.4

4.6

4.8

5

5.2

Log REER against Fundamentals

Log REER against Fundamentals

ln

(RE

ER

)

PPP deviation0 50 100 150

4

5

6

7

Income p/c as % of US0 50 100 150

4

5

6

7

ln

(RE

ER

)

Real GDP p/c, $0 20000 40000 60000

4

5

6

7

NFA %GDP-600 -400 -200 0 200

4

5

6

7

Descriptive Statistics

Obs. MeanStd.Dev. Min Max

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

Simple Bivariate Correlations 

Sample:Default Default Augment Augment

Correlation with: Log REER Fertility Log REER Fertility

Fertility Rate .39 .48

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

Observations 332 332 282 282

Approximate standard error for default (augmented) sample correlations = .05 (.06).

Benchmark Results Default Augment Variant 1 Variant 2 Variant 3 Variant 4 Fertility Rate .15**

(.03) .15** (.02)

.16** (.02)

.13** (.02)

.17** (.02)

.11** (.02)

PPP-deviation .0089** (.0007)

.0096** (.0007)

.0093** (.0007)

.0091** (.0007)

.0081** (.0006)

.0100** (.0008)

Real Income p/c as % US Income p/c

-.002 (.002)

.004 (.002)

-.001 (.002)

-.002 (.002)

Openness %GDP

.0014** (.0005)

.0007 (.0005)

.0011* (.0005)

.0007 (.0004)

Trade Liberalization Measure

.17** (.04)

.12** (.03)

.15** (.04)

Government Spending % GDP

.002 (.003)

.008** (.003)

.005 (.003)

Growth real GDP per capita

-.010** (.004)

-.005 (.004)

Log(population) -.13 (.15)

.00 (.13)

Log(real GDP per capita, $)

.06 (.07)

-.25** (.09)

.06 (.06)

Net Foreign Assets % GDP

-.0001 (.0003)

.0001 (.0003)

Current Account %GDP

-.001 (.002)

-.002 (.002)

Observations 332 282 336 380 311 340 R2 .10 .26 .19 .20 .25 .10

Sensitivity Analysis Default Augmented Add de jure exchange rate peg dummy

.17** (.05)

.05 (.04)

Add RR de facto exchange rate peg dummy

.19** (.03)

.17** (.03)

Add LYS de facto exchange rate peg dummy

.17** (.04)

.22** (.03)

Add Polity 2 .16** (.03)

.15** (.02)

Add Executive Constraints .12** (.03)

.10** (.02)

Add lagged dependent variable .10** (.03)

.08** (.03)

Without time effects .12** (.03)

.13** (.03)

Without country-specific fixed effects

.09** (.01)

.10** (.01)

Country-Specific Random effects .12** (.02)

.12** (.02)

Level (not log) of REER as regressand

36** (5)

39** (5)

Log (not level) of fertility as key regressor

.37** (.08)

.32** (.07)

Default Augmented Decadal data .13**

(.05) [AR1].08*

(.04) Without >|2σ| outliers .15**

(.02) .16** (.02)

Drop 1975-1984 .11** (.03)

.09** (.03)

Drop 1991-2004 .16** (.03)

.15** (.03)

Drop Latin America, Caribbean .15** (.03)

.16** (.02)

Drop European developing countries, Central Asia

.14** (.03)

.16** (.02)

Drop Middle East, North Africa .07* (.03)

.10** (.03)

Drop Sub-Saharan Africa .18** (.03)

.15** (.02)

Drop East Asia .15** (.03)

.15** (.02)

Drop South Asia .14** (.03)

.15** (.02)

Drop high income countries .19** (.04)

.22** (.04)

No evidence of non-linearity relationship between fertility and the real exchange rate

Real Effective Exchange Rates and Fertility: Linear or Not?Non-Parametric estimates & +/- 2se Linear CI, default model

-1 0 1

-.4

-.2

0

.2

.4

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

IV set 1 IV set 2 IV set 3 IV set 4 Default .25**

(.07) .32** (.09)

.20* (.10)

.29** (.08)

Augmented .20** (.05)

.28** (.07)

.17* (.08)

.26** (.06)

Variant 1 .27** (.05)

.30** (.06)

.23* (.10)

.29** (.06)

WLS Results

Default Augmented

Weighted by Population

.15**(.03)

.16**(.02)

Weighted by GDP

.15**(.02)

.16**(.02)

Default Augmented Birth Rate .009

(.006) -.001 (.005)

Infant Mortality Rate -.020** (.007)

-.014** (.005)

Child Mortality Rate -.007 (.006)

-.002 (.006)

Ratio of Young (<20) to Population

.005 (.006)

.005 (.006)

Ratio of Elderly (>65) to Population

.014 (.014)

.011 (.011)

Ratio of Active (20-65) to Population

-.010 (.007)

-.009 (.006)

Life Expectancy -.009 (.005)

-.009* (.005)

Sensitivity Analysis: Key Regressor

Cohort Coefficient Std. Error . * % 0-4 .021 .013 . * % 5-9 .018 .012 . * % 10-14 .015 .011 . * % 15-19 .012 .011 . * % 20-24 .009 .010 . * % 25-29 .007 .010 . * % 30-34 .005 .010 . * % 35-39 .003 .010 .* % 40-44 .002 .011 * % 45-49 .001 .011 *. % 50-54 -.000 .011 *. % 55-59 -.001 .011 * . % 60-64 -.002 .012 * . % 65-69 -.002 .012 * . % 70-74 -.002 .012 * . % 75-79 -.002 .012 *. % 80-84 -.001 .012 *. % 85-89 -.001 .012 * % 90-94 .000 .013 .* % 95-99 .002 .013 . * % 100+ .003 .013 Sum .09 .22

Adding Different Age Cohorts to the RER Equation

Regressand Fertility Effect Observations Savings Rate, % GDP (PWT)

-1.67* (.75)

452

Investment Rate, % GDP (PWT)

2.41** (.43)

452

Current Account, % GDP (WDI)

-.21 (.67)

393

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”

Summary: 1

• Use quinquennial data set: 87 countries, 1975-

2005 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