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Fertility and the Real Exchange Rate. Andrew K. Rose and Saktiandi Supaat with Jacob Braude. Andrew K. Rose and Suktiandi Supaat. Simple Intuition: What effect should fertility have on real exchange rate?.

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Fertility and the real exchange rate l.jpg

Fertility and the Real Exchange Rate

Andrew K. Rose

and Saktiandi Supaat

with Jacob Braude

Andrew K. Rose and

Suktiandi Supaat


Slide2 l.jpg

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 l.jpg
    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 l.jpg
    Why Should We Care? Motivation 1 on real exchange rate

    • 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 l.jpg
    The Negative Results Continue on real exchange rate

    • 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 l.jpg
    … through the present … on real exchange rate

    • Rogoff (2007) commenting on Engel, Mark and West:

      • “Is the glass ten percent full or ninety percent empty?”


    Motivation 2 l.jpg
    Motivation 2 on real exchange rate

    • Demographic Transition an Enormous Pending Economic Phenomena

      • Large across Time


    Fertility decline large over time l.jpg
    Fertility Decline Large over Time on real exchange rate


    Large variation across countries l.jpg
    Large Variation across Countries on real exchange rate


    Ldc examples l.jpg
    LDC Examples on real exchange rate


    Oecd examples l.jpg
    OECD Examples on real exchange rate


    Slide12 l.jpg

    Quick Survey of the Literature on real exchange rate

    • 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 l.jpg
    Simple Theoretical Framework on real exchange rate

    • 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 l.jpg
    Income and Consumption on real exchange rate

    • Workers earn after tax wage (w – τ)t

      • Children earn nothing

    • Two Consumption Goods:

      • Tradeables (CT)

      • Non-tradeables (CN)


    Workers optimization problem l.jpg
    Workers’ Optimization Problem on real exchange rate

    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 l.jpg
    Parameterized Utility Function on real exchange rate

    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 l.jpg
    Notes on real exchange rate

    • 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 l.jpg
    Problem for Retired on real exchange rate

    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 l.jpg
    Production on real exchange rate

    • 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 l.jpg
    Equilibrium on real exchange rate

    • Price of tradeables given exogenously to small open economy

    • Price of non-tradeables determined domestically:

      YNt = CNWt + μtCNCt + φtCNRt


    Change in fertility rate l.jpg
    Change in Fertility Rate on real exchange 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 l.jpg
    Effect of Retired Dependency Ratio on real exchange rate

    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 l.jpg
    Main Theoretical Implications on real exchange rate

    • 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 l.jpg
    What Do We Search For? on real exchange rate

    • 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


    Slide25 l.jpg

    Default Estimating Equation on real exchange rate

    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 l.jpg

    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 l.jpg
    More REER Determinants Determination

    • 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


    Slide28 l.jpg

    Data Set Determination

    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, …)


    Slide29 l.jpg

    Country List Determination




    Slide32 l.jpg

    Descriptive Statistics Determination


    Slide33 l.jpg

    Simple Bivariate Correlations  Determination

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


    Slide34 l.jpg

    Benchmark Results Determination


    Slide35 l.jpg

    Sensitivity Analysis Determination



    Slide38 l.jpg

    Simultaneity/Measurement Error and the real exchange rate

    • 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:

      • the percentage of 15+ females without schooling;

      • the percentage of 15+ females who attained secondary school; and

      • the average years of school for 15+ females.


    Deeper iv rationalizations l.jpg
    “Deeper” IV Rationalizations and the real exchange rate

    • 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 l.jpg
    Instrumental Variable Results and the real exchange rate


    Wls results l.jpg
    WLS Results and the real exchange rate


    Slide42 l.jpg

    Sensitivity Analysis: Key Regressor and the real exchange rate


    Slide43 l.jpg

    Adding Different Age Cohorts and the real exchange rateto the RER Equation


    Slide44 l.jpg

    Fertility, and Savings, Investment and the real exchange rateand Current Account

    • This all bivariate

      • No model/control variables at all for Savings, Investment, or current account; just FE

      • Essentially a “sniff test”


    Slide45 l.jpg

    Summary: 1 and the real exchange rate

    • 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 l.jpg

    Summary: 2 and the real exchange rate

    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 l.jpg
    Conclusion and the real exchange rate

    • 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


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