Fertility and the Real Exchange Rate

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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

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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.

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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

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Why Should We Care? Motivation 1

• Exchange Rates Matter, cant 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

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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

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through the present

• Rogoff (2007) commenting on Engel, Mark and West
• Is the glass ten percent full or ninety percent
  empty?

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Motivation 2

• Demographic Transition an Enormous Pending
  Economic Phenomena
• Large across Time

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Fertility Decline Large over Time
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Large Variation across Countries
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LDC Examples
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OECD Examples
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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.

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Simple Theoretical Framework

• OLG Model with 3 generations
• Children (C) of size µ
• Retired (R) of size f
• Workers (W) size normalized to1
• Dependency Ratios
• µ for children
• F for retired

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Income and Consumption

• Workers earn after tax wage (w t)t
• Children earn nothing
• Two Consumption Goods
• Tradeables (CT)
• Non-tradeables (CN)

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Workers Optimization Problem

• Maximize Utility
• Ut U(CNWt, CTWt) ßµtU(CNCt, CTCt)
• ?U(CNRt1, CTRt1)
• subject to budget constraint
• PNtCNWt PTtCTWt µt(PNtCNCt PTtCTCt)
• (1/(1r))(PNt1CNRt1 PTt1CTRt1)
• (wt-tt) b/(1r)

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Parameterized Utility Function

• U(CNit, CTit) ailogCNit (1-ai)logCTit
• i W, C, R
• If aC, aR aW 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

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Notes

• Workers discount kids consumption by ß, and
  utility in retirement by ?
• World interest rate (r) given exogenously
• Government finances transfer payments (b) via
  lump-sum tax (t)
• Government Budget Constraint tt ftb

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Problem for Retired

• Maximize Utility
• aRlogCNRt (1-aR)logCTRt
• Retired have income from predetermined foreign
  assets a and government transfer payments (b)
• Total income ft(rat b)

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Production

• Cobb-Douglas Production Functions
• YTt LTt?TKTt1-?T
• YNt LNt?NKNt1-?N
• Capital Stock and Sectoral Allocation given
  exogenously at t (could add dynamics)
• Perfect Competition
• Full Employment implies LTt LNt 1

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Equilibrium

• Price of tradeables given exogenously to small
  open economy
• Price of non-tradeables determined domestically
• YNt CNWt µtCNCt ftCNRt

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Change in Fertility Rate

• Solve Model, use Implicit Function Theorem
• Effect on Real Exchange Rate of Child Dependency
  Ratio
• ?PNt/?µt 0 if (aC aW) aC? 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

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Effect of Retired Dependency Ratio

• Relative Price of Non-Tradeables rises with
  Elderly Dependency Ratio
• ?PNt/?ft 0 if
• at(1r)aR(1ßµt?) b(aRaW)(aRaC)aR? 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

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Main Theoretical Implications

• Model quite stylized (no uncertainty many
  exogenous constraints on capital, production,
  utility implicitly assume LOOP for tradeables,
  )
• Dont take structure of model too literally
• Instead, focus on key predictions

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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

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Default Estimating Equation

• log(reer)it ßfertit ?1PPPit ?2y/yusit
  ?3openit
• ?4TLit ?5G/Yit ?6growthit
  ?7log(pop) it
• ?8log(y) it Stft Si?i eit
• Fixed time- and country-specific effects
• So dont have to worry about relative vs absolute
  fertility, time- or country-specific shocks
• Often augment with 1) NFA and 2) current account
  (reduced observations)

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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!

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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

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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, )

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Country List
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Real Effective Exchange Rates against Fertility
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Log REER against Fundamentals
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Descriptive Statistics
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Simple Bivariate Correlations 
Approximate standard error for default
(augmented) sample correlations .05 (.06).
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Benchmark Results
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Sensitivity Analysis
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(No Transcript)
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No evidence of non-linearity relationship between
fertility and the real exchange rate
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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
• 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.

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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?

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Instrumental Variable Results

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WLS Results
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Sensitivity Analysis Key Regressor
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Adding Different Age Cohorts to the RER Equation
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• 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

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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)

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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?)

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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