The Baby Boom and Baby Bustecon.ucsb.edu/~mkapicka/RG/bb.pdf · The Baby Boom and Baby Bust By JEREMY G REENWOOD,ANANTH S ESHADRI, AND G UILLAUME V ANDENBROUCKE * What caused the

The Baby Boom and Baby Bust

By JEREMY GREENWOOD ANANTH SESHADRI AND GUILLAUME VANDENBROUCKE

What caused the baby boom And can it be explained within the context of thesecular decline in fertility that has occurred over the last 200 years The hypothesisis that

(a) The secular decline in fertility is due to the relentless rise in real wages thatincreased the opportunity cost of having children

(b) The baby boom is explained by an atypical burst of technological progress inthe household sector that occurred in the middle of the last century Thislowered the cost of having children

A model is developed in an attempt to account quantitatively for both the babyboom and bust (JEL E1 J1 03)

The fertility of American women over the last200 years has two salient features portrayed inFigure 11 First it has declined drastically Theaverage white woman bore 7 children in 1800By 1990 this had dropped to just 2 This declinein fertility ran unabated during the 140-yearperiod between 1800 and 1940 Second fertilityshowed a surprising recovery between the mid-1940s and mid-1960s The upturn was large aldquobaby boomrdquo2 Just how large depends upon theconcept of fertility used For example the num-ber of births per fecund woman increased by 41percent between 1934 and 1959 Alternativelythe number of realized lifetime births per femalewas 28 percent higher for a woman born in 1932(whose average child arrived in 1959) vis-a-vis

one born in 1907 (whose average child was bornin 1934)3 The difference between these twonumbers suggests that the rise in fertility wascompressed in time for two reasons First olderwomen had more children Second so didyounger women But the high rates of fertilitythat younger women had early in their liveswere not matched by higher rates of fertilitylater on This leads to the last point After themid 1960s fertility reverted back to trend or theldquobaby bustrdquo resumed

Conventional wisdom links the baby boomwith the end of the Great Depression and WorldWar II The popular view is that these traumaticevents led to a drop in fertility Part of thedecline in fertility was due to economic hard-ship or a gloomy outlook about the futurewhich made it difficult to start a family Part ofit was due to the absence of so many youngmen who had gone off to fight the war AfterWorld War II fertility bounced up as the menreturned the economy boomed and a generalfeeling of optimism prevailed Fertility rose toabove-normal levels to make up for lost fertilityduring the Depression and war years4 This

Greenwood Department of Economics University ofRochester Rochester NY 14627 (e-mail greetroiccrochesteredu) Seshadri Department of Economics Uni-versity of Wisconsin-Madison 1180 Observatory DrMadison WI 53706 (e-mail aseshadrsscwiscedu) Van-denbrouke Department of Economics University of SouthernCalifornia 3620 S Vermont Ave KAP 324F Los AngelesCA 90089 (e-mail vandenbruscedu) The authors expresstheir appreciation to two referees for useful advice They alsothank Michael Haines Karen Kopecky Lee Ohanian MichaelRolleigh Aloysius Siow Nancy Stokey and Ming Hon Suenfor their help Financial support from the National ScienceFoundation (award number 0136055) is gratefully acknowl-edged

1 The source for the data used is Donald J Hernandez(1996 Tables 9 and 10)

2 The baby boom in the United States is conventionallydated as occurring between 1946 and 1964 These dates willbe questioned in Section V

3 Note that the average childbearing age was 27 roughlythe horizontal distance between the two curves

4 Surprisingly there is a dearth of economic theoriesexplaining the baby boom One well-known theory connect-ing the Great Depression and World War II to the babyboom is by Richard A Easterlin (2000) His theory is basedon the concept of ldquorelative incomerdquo Fertility is high (low)when familiesrsquo material aspirations are low (high) relativeto their projections about their lifetime income On

183

explains the baby boom according to conven-tional wisdom

Conventional wisdom is often wrong It ishere too or so it will be argued in Section VSpecifically the pattern and timing of fertilitydo not support the belief that the baby boomwas the outcome of World War II and the GreatDepression In particular

(a) It is highly unlikely that the baby boom canbe the result of delayed fertility from theGreat Depression and World War II Figure1 shows completed lifetime fertility for thewomen who gave birth during the babyboom A pure catch-up effect should havehad no influence on lifetime fertility since

one less child today would just be made upfor by having one more child tomorrowYet lifetime fertility rose

(b) Take the peak of the baby boom for theUnited States or the year 1960 As will bediscussed in Section V the cohort ofwomen contributing the most to the babyboom then (those in the 20- to 24-year-oldage group) were simply too young for eitherthe Great Depression or World War II tohave had much of an impact on them Theywere not alive during the Great Depressionand were under nine years of age at the endof World War II

(c) The data show that the baby boom actuallystarted in the 1930s in the United States andmany OECD countries This will be de-tailed in Section V Furthermore for manycountries fertility grew throughout WorldWar II Additionally the neutral countriesIreland Sweden and Switzerland all hadbaby booms Also itrsquos hard to detect aprecipitous drop in US and many otherOECD country fertility rates due to theGreat Depression

So what could have caused the baby boomTurn attention then to the hypothesis enter-

tained here For the journey through the baby

the one hand consumption plans are based on materialaspirations The latter are formed very early in life whilegrowing up with onersquos parents On the other hand youngadults base their fertility decisions on projections aboutlifetime income The generation that spawned the babyboomers had low material aspirations and hence modestdesires for consumption since they were both born in theGreat Depression and experienced World War II Theboomersrsquo parents entered the labor force in the late 1940s to1960s economically speaking a good time Therefore theyhad low material aspirations relative to their expected life-time income The surfeit wealth was channeled into familyformation and high fertility resulted

FIGURE 1 FERTILITY IN THE UNITED STATES 1800ndash1990

184 THE AMERICAN ECONOMIC REVIEW MARCH 2005

boom and baby bust a vehicle is constructedusing conventional macroeconomic theory Tobegin with an off-the-shelf overlapping gener-ations model of population growth is used as thechassis for the analysis The chassis is basedupon Assaf Razin and Uri Ben-Zionrsquos (1975)well-known model of population growth An-other classic paper on population growth takinga different approach but still close to the anal-ysis undertaken here is by Gary S Becker andRobert J Barro (1988) Next Oded Galor andDavid N Weil (2000) in important work haveexplained the -shaped pattern of fertility thathas been observed over epochs in the Westernworld The United States experienced only theright-hand side of the The engine in theGalor and Weil (2000) analysis for the declinein long-run fertility is technological progressThis engine is dropped onto the chassis hereSpecifically over the period in question realwages rose at least tenfold due to technologicaladvance (see Figure 1)56 Since raising childrenrequires time this represents a tremendous in-crease in the (consumption) cost of kids7 Therest of the vehicle is built from household pro-duction theory a la Becker (1965) and MargaretG Reid (1934) The idea here is that the suc-cessful production of kids is subject to techno-logical progress just like other goods It will be

argued that technological advance in the house-hold sector due to the introduction of electricityand the development of associated householdproducts such as appliances and frozen foodsreduced the need for labor in the child-rearingprocess This lowered the cost of having chil-dren and should have caused an increase infertility other things equal This led to the babyboom

I The Economy

A The Populace

The economy is populated by overlappinggenerations An individual lives for I J peri-ods I as a child and J as an adult Suppose thata person is fecund only in the first period ofadult life

An age-1 adultrsquos preferences are given by

(1) j 0

J 1

jUct jj 1

1 J

1 Qnt

1

j 0

J 1

j lnct jj 1 c)

1 J

1 1

nt11 1

1

where c t jj1 represents period-(t j) consump-

tion by an age-(j 1) adult and nt1 is the number

of children that he chooses to have (in the firstperiod of adult life) The sustained descent infertility that occurred over the last 200 yearsprovides an interesting backdrop for the babyboom The constant c is an elementary yetpowerful device for generating a secular de-cline in fertility It can be thought of as a simplenonhomotheticity in tastes As will be seen thisresults in a demand for kids that decreases inwages Alternatively the constant c can bethought of as representing the household pro-duction of (some fixed amount of) consumptiongoods8 The simplicity of this device is a greatvirtue for the quantitative analysis undertakenThere are other mechanisms for generating this sec-ular decline To illustrate this an example using

5 The source for the real wage data is Jeffrey G Wil-liamson (1995 Table A11)

6 The relationship between long-run growth and fertilityhas been investigated by Matthias Doepke (2004) JesusFernandez-Villaverde (2001) examines the ability of tech-nological advance to explain quantitatively the fall inBritish fertility A similar exercise for the United States isconducted by Greenwood and Seshadri (2002) Over timechild mortality has also declined This has been analyzedwell by Zvi Eckstein et al (1999) who conclude that this isthe major factor in explaining the fall in Swedish fertilityFor the United States (unlike Sweden) infant mortality didnot unambiguously begin to drop until 1880 at which pointit fell sharply As Figure 1 shows the decline in USfertility was already under way by then Still the decline inchild mortality undoubtedly did play a role in explaining thedecline in US fertility For the purposes at hand thoughabstracting from this issue probably does little harm to theanalysis

7 Part of this increase in wages is due to the fact that thelabor force has also become more skilled Over time parentshave chosen to educate their children so that the latter canenjoy the higher wages associated with skill They havetraded off quantity for quality in children While this chan-nel is absent in the baseline model it is discussed in Sec-tion IV 8 For the details see footnote 10

185VOL 95 NO 1 GREENWOOD ET AL BABY BOOM AND BABY BUST

Beckerrsquos (1960) famous quantity-quality modelis presented in Section IV

An adultrsquos income derives from two sourcesFirst he can use his time for either working orraising kids Market work in period t is remu-nerated at the wage rate wt Second an individ-ual can borrow or lend on a loan market wherethe gross interest rate prevailing between peri-ods t and t 1 is denoted by rt1 Hence anindividual earns income on past saving

Kids are costly In particular children areproduced in line with the household productionfunction shown below

(2) nt1 Hlt

1 xt xt lt11

where lt1 is the input of time and xt is the state of

household technology9 The household produc-tion technology can be purchased in period t forthe time price gt The cost function for havingkids is therefore given by

Cnt1 xt wt gt

minlt1

wtlt1 wtgt nt

1 Hlt1 xt

wtnt1

xt11

wtgt

Note that this cost function is homogenous ofdegree one in the wage rate wt

A young adultrsquos goal in life is to maximizehis well-being This translates into solving thefollowing maximization problem for an age-1adult

(P1) maxct j

j 1nt1

j 0

J 1

jUct jj 1

1 J

1 Qnt

1subject to

(3) j 0

J 1

qt j c t jj 1

j 0

J 1

qt j wt j qt Cnt1 xt wt gt

where the j-step-ahead present-value priceqtj is defined by qtj qtj1rtj with q1 110

This problem will have a solution characterizedby

(4) U1 c t jj 1 rt j1 U1 c t j1

j 2

for j 0 J 2

and

1 J

1 Q1 nt

1 U1 ct1C1 nt

1 xt wt gt

or

(5)1 J

1 1

1

nt1

1

ct1 c

1

1wtnt

1

xt11 1

nt1

9 The classic references on household production theoryare Becker (1965) and Reid (1934) The concept was intro-duced into macroeconomics by Jess Benhabib et al (1991)who studied its implications for business cycle analysis Seealso Paul Gomme et al (2001) Jose-Vıctor Rıos-Rull(1993) uses this notion to study the time allocations ofskilled versus unskilled workers between the home and themarket Stephen L Parente et al (2000) employ the conceptto analyze cross-country income differentials Last in West-ern economies there has been a secular shift in employmentout of manufacturing and into services The growth of theservice sector in several European countries however hasbeen encumbered by institutional rigidities These serviceshave been provided by the household sector instead Thisphenomena is analyzed by Richard Rogerson (2002)

10 It can now be seen that the constant c can be thoughtof as representing some fixed amount of home productionWrite momentary utility as U(c t j

j1) ln(c t jj1) where

c t jj denotes period-(t j) consumption by an age-j adult

Note that U(c t jj1) U(c t j

j1 c) Let the individualproduce at home a constant amount of consumption goodsc each period His budget constraint will now appear asj0

J1 qt jc t jj1 j0

J1 qt j(wt j c) qtC(nt1 xt wt gt)

Rewrite the budget constraint as j0J1 qt j(c t j

j1 c) j0

J1 qt jwt j qtC(nt1 xt wt gt) Next define c t j

j1 c t j

j1 c so that c t jj1 c t j

j1 c Use this to substitute outfor c t j

j1 in U(c t jj1) U(c t j

j1 c) and the above budgetconstraint This setting has transformed into the one pre-sented in the text Note that with the home productioninterpretation c t j

j1 can be negative in (1) so long as c t jj1

c remains positive In this situation the individual is sellingor devoting some of his home production to other uses


Let s t j1j2 denote the optimal level of savings

connected to this problem that the agent will doin period (t j) for period (t j 1) whenthe agent will be age j 2

B Firms

Market goods are produced in line with theconstant-returns-to-scale production technology

yt Fkt et zt zt ktet

1

where yt denotes period-t output zt is total fac-tor productivity (TFP) in this period and kt andet are the inputs of capital and labor Marketgoods can be used for nondurable consumptionand capital accumulation The aggregate stockof capital kt1 evolves according to

kt 1 kt it

where it is gross investment and is the factorof depreciation

Firms desire to maximize profits as summa-rized by

(P2) maxkt et

Fkt et zt rt kt wtet

Note that the rental rate on capital rt isequal to the net interest rate on loans rt 1plus depreciation 1 The efficiency condi-tions associated with this problem are

(6) F1 kt et zt rt

and

(7) F2 kt et zt wt

C Equilibrium

How will the population evolve over timeTo answer this let p t

j denote the period-t size ofthe age-j adult population The laws of motionfor the population are

(8) p t 1j 1 p t

j for j 1 J 1

and

(9) pt i1 pt iI

1 nt iI1 for i 1 I

The first equation simply states that the numberof (j 1)-period-old adults alive in period t 1 equals the number of j-period-old adultsaround in period t The second equation saysthat the number of age-1 adults around in periodt i equals the size of their parentsrsquo generationtimes the per-capita number of kids that thisgeneration had in period t i I Note that Iis the gestation lag in the model or the timefrom conception to adulthood

To complete the model several market-clearing conditions must hold First the goodsmarket must clear This implies that

(10) pt1ct

1 pt2ct

2 ptJct

J it yt

Second period-t savings must equal investmentso that

(11) pt1st 1

2 pt2st 1

3 ptJ 1st 1

J kt 1

Start the economy off at a certain time sayperiod 1 To do this some initial conditionsneed to be specified At this time there will be Jgenerations of adults around The initial popu-lation structure of adults will therefore be de-scribed by the J-vector ( p1

1 p1J) All but the

youngest generation will have savings denotedby (s1

2 s13 s1

J) The economy will beginperiod 1 with some level of capital k1 Thiscapital was funded by the savings of the oldestJ 1 generations Therefore the initial distri-bution of wealth must satisfy the start-up re-striction that

(12) p12s1

2 p1Js1

J k1

There will also be I 1 generations of chil-dren around waiting to mature This is capturedby the (I 1)-vector (p0

1n01 pI2

1 nI21 )

which starts with the youngest generation andgoes to the oldest11

It is time to take stock of the discussion sofar

Definition A competitive equilibrium is a time

11 If I 1 then this vector is void ie define (p01n0

1p1

1n11) to be empty since the youngest generation or the first

element is older than the oldest generation or the secondelement


path for interest and wage rates rt wtt1 a

set of allocations for households c tj ntt1

for j 1 J and a set of allocations forfirms kt ett1

such that for some given ini-tial state (k1 s1

2 s1J p1

1 p1J p0

1n01

pI21 nI2

1 ) satisfying (12) the following istrue

(a) The allocations c tj nt

1t1 solve the house-

holdrsquos problem P(1) given rt wtt1 12

(b) The allocations kt ett1 solve firmsrsquo

problems P(2) given rt wtt1

(c) The population obeys the laws of motion (8)and (9)

(d) The goods and asset markets clear or (10)and (11) hold

II Theoretical Analysis

Recall that the pattern of US fertility dis-played in Figure 1 has two distinct featuresFirst fertility shows a secular decline Secondthere is a temporary boom in fertility in themiddle of the twentieth century Two ingredi-ents are incorporated into the framework tocapture these features First it will be assumedthat there is technological progress in the mar-ket sector This will propel the secular declinein fertility Second it will be presupposed thatthere is technological advance in the householdsector This will cause the baby boom Willthese two ingredients be sufficient to accountfor the observed pattern of US fertility Whilethe resolution to this question is ultimately aquantitative matter the following propositionsuggests that theoretically speaking the answeris yes

PROPOSITION For a given interest ratepathrtt1

(a) A rise in household-sector productivity xt causes fertility nt

1 to increase(b) A fall in the time price of the household

technology gt leads to a rise in nt1

(c) An increase in market-sector productivityzt causes nt

1 to decline

PROOF See Appendix

The intuition for the above proposition can begleaned from the first-order condition govern-ing fertility (5) The left-hand side of this equa-tion gives the marginal benefit from having anextra child The marginal cost of having anextra kid is given by the right-hand side Theconsumption cost of having an extra child isC1(nt

1 xt wt gt) [1(1 )]wt[nt1xt]

1(1)

(1nt1) To get the utility cost this must be

multiplied by the marginal utility of currentconsumption U1(ct

1) (ct1 c)

Now consider the impact of technologicalprogress in the market sector This will increasewages wt Consequently the cost of havingchildren rises ceteris paribus because the timespent raising extra kids could have been usedinstead to work and purchase consumptiongoods The increase in wages will also make theadult wealthier Hence he will consume moreconsumption goods and this will decrease hismarginal utility This effect will operate to re-duce the utility cost of having children Along abalanced growth path wages and consumptionmust grow at the same rate If c 0 then thetwo effects above would cancel out and the costof having children would remain constant Therewould be no change in fertility a fact evident from(5) The marginal utility of consumption will dropslower than the increase in wages when c 0 Inthis situation the cost of having kids will riseand fertility will fall In other words c operatesto lower the marginal utility of consumptionand mitigate its decline with growth The im-pact of c is larger at low levels of ct

1 so this termworks to promote fertility at low levels ofincome

Technological advance in the household sec-tor operates to reduce the cost of children otherthings equal It is readily seen from (5) that anincrease in xt lowers the cost of kids Wheninterest rates are held fixed a change in xt hasno effect on wt

13 It may transpire that an in-crease in xt leads to a change in ct

1 but thiseffect is of secondary importance given theadopted functional forms for tastes and house-hold production Therefore technological pro-

12 There will be J 1 households older than age 1 atdate 1 These households will solve their analogues toproblem P(1) given their initial asset holdings 13 See equation (16) in the Appendix


gress in the household sector promotes fertilityLast when the time price gt for the householdtechnology drops consumers have more dispos-able income This income effect increases theconsumption of market goods other thingsequal and consequently reduces their marginalutility Hence the utility cost of having childrenfalls and higher fertility results14

To carry the inquiry further the model must besolved numerically for two reasons First the anal-ysis above presumes that technological progress inthe market and household sectors has no effect onthe equilibrium time path for interest rates Ingeneral equilibrium this is unlikely to be true It isdifficult to say much about the general equilibriumimpact of technological progress using pencil-and-paper techniques alone To analyze the effectsthe model must be solved numerically Secondthe question of whether or not the proposed frame-work can account for the observed pattern of USfertility is quantitative in nature

III Quantitative Analysis

A Technological Progress

To get the model up and running informationis needed on the pace of technological progressin the market sector over the last 200 yearsTotal factor productivity (TFP) grew at an an-nual rate of 055 percent between 1800 and1840 according to Robert E Gallman (2000Table 17) He also estimates its growth rate to

be 071 percent between 1840 and 1900 Be-tween 1900 and 1948 total factor productivitygrew at an annual rate of 141 percent (USBureau of the Census 1975 Series W6) Nextthe growth rate in TFP jumped up to 168 per-cent between 1948 and 1974 (Bureau of LaborStatistics) Note that the growth rate of TFPseems to have accelerated from 1800 to 1974The period after 1974 is problematic This pe-riod is the productivity slowdown TFP grew apaltry 057 percent per year between 1974 and1995 Casual empiricism suggests that this wasa period of rapid technological progress associ-ated with the development of information tech-nologies If this is true then the productivityslowdown is basically a mirage There is agrowing literature suggesting that this is indeedthe case In fact measured TFP growth seems tohave slowed down at the dawning of both theFirst and Second Industrial Revolutions From1995 to 2000 TFP growth seems to have re-bounded growing at an annual rate of 12 per-cent The bottom line is that it is hard to knowwhat to do about the productivity slowdownyears A conservative approach would take theproductivity numbers as given This is what willbe done here

The productivity data between 1800 and1900 are sparsemdashonly three points To make upfor the missing observations a trend line is fittedover the entire 1800ndash2000 sample This is doneby estimating the following statistical model

lnTFPt a bt dt2 t

where

t 1 t t with t N0 13

14 What about the substitution effect from a decline in gtNote that in the analysis gt is modeled as a fixed cost So aslong as the individual has any kids he must incur this costThus the substitution effect will be (potentially) operationalonly in influencing the decision of parents who would havechosen not to have kids in the absence of the price decline

TABLE 1mdashPARAMETER VALUES

BaselinemdashunweightedTastes 09810 083 c 049 000Market technology 030 (1 005)10

Home technology 020 gttT 0 x1800 253 x1950 283 x1960 284Generational structure I 2 J 4

Preferredmdashequally weightedTastes 09810 084 c 040 000Market technology 030 (1 005)10



The results of the estimation are

a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102

where the numbers in parentheses are t statis-tics Observe that the trend rate of TFP growthincreases over time The trend line that resultsfrom this estimation is shown in Figure 2 theinitial level for TFP is normalized to unityMarket sector TFP increased slightly more thansevenfold over the 200-year time period inquestion

B Calibration and Estimation

Take the length of a period in the model to be10 years Let I 2 and J 4 so that anindividual lives for 20 years as a child and for

40 years as an adult Between 1800 and 1990(the length of the data series on fertility) therewill be 20 model periods

The task at hand is to pick values for theparameters governing tastes and technologyThis will be done in two ways

(a) A priori information zrsquos Someparameters are common to a wide variety ofmacroeconomic models and can be pinneddown using a priori information Laborrsquosshare of income is roughly 70 percent Inline with this set 030 On the basis ofinvestment and capital stock data takenfrom the national income and product ac-counts the (annualized) depreciation ratefor private nonresidential equipment andstructures is estimated to be 47 percent15

For (the equally weighted version of) the

15 Specifically given data on investment and the capitalstock the period-t depreciation factor t can be estimatedfrom the formula t (kt1 it)kt The depreciation rateobtained is close to the 48 percent that Thomas F Cooleyand Edward C Prescott (1995) back out from their calibra-tion procedure

FIGURE 2 US TOTAL FACTOR PRODUCTIVITY 1800ndash2000


model this results in a steady-state investment-to-GDP ratio of 121 percent very close tothe US postwar average of 11 percent Thediscount factor is chosen so that the(annualized net) interest rate in the modelrsquosfinal steady state is 69 percent16 This in-terest rate coincides with the average returnon capital for the US postwar economy asestimated by Thomas Cooley and EdwardPrescott (1995) Last for the zrsquos the ob-served levels for economy-wide TFP will beinputted into the model For the years be-tween 1800 and 1900 the missing observa-tions will be read off of the estimated trendline Specifically the circles in Figure 2 in-dicate the data points for TFP that are usedin the analysis

(b) Estimation c xrsquos Other parametersare specific to the analysis at hand Little isknown about their magnitudes Thereforevalues for these parameters will be esti-mated using the US fertility data LetnttT denote the US time series for fer-tility where T 13 1800 1810 1990In order to estimate the model a simplifiedprocess for technological progress in thehousehold sector will be assumed Specifi-cally let x1800 x1810 x1940 x1950 x1960 x1970 x1990 That istechnological progress in the householdsector is allowed to occur only in 1950 and1960 The realism of this assumption isdiscussed in Section V Additionally it isassumed that technology can only advanceNow for a given set of parameter values themodel will generate a series for fertilitydenoted by nt

1tT Describe the mappingfrom the modelrsquos parameter values to pre-dicted fertility by nt

1 N(t c x1800x1950 x1960)17 The function N correspondsto the solution to the nonlinear differenceequation system that describes the modelrsquosgeneral equilibrium It should be noted thatthe model is not stable for all possible com-binations of parameter values Let S denotethe set of parameter values for which the

model is stable The estimation procedurecan be described by1819

mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S

Note that the first constraint restrictstechnological change in the household sec-tor to advance only The second constraintdemands that the parameter estimates yielda stable solution for the model

Table 1 lists the parameter values that resultfrom the baseline estimation procedure above20

The modelrsquos ability to match the time path ofUS fertility will now be examined

C The Baby Boom

The Computational ExperimentmdashImaginestarting the economy off in 1800 The level ofTFP or z is low Over the next 200 yearstechnological progress occurs In particular lettwo things happen First presuppose that TFPgrows in line with the US data Second after140 years assume that there is a burst of tech-nological progress in the household sector say

16 This amounts to a (nonlinear) constraint on the esti-mation scheme discussed below

17 In the analysis the technology variables gt xt zt aretaken to be functions of time t For simplicity set gt 0 forall t

18 The estimation procedure employed is similar to thatused by David Andolfatto and Glenn M MacDonald(1998) Note that given the length of a time period in themodel (10 years) there are only 20 data points Hencegiven the paucity of observations there is little point addingan error structure to the estimation

19 Some constraints on parameters values also had to besatisfied 0 1 and 0 Recall that ischosen as a function of c x1800 x1950 and x1960 sothat the net interest rate in the modelrsquos final steady state is69 percent per year

20 The numbers in the table are rounded to the seconddecimal


due to the introduction of modern appliancesmdashwashing machines dryers dishwashers and thelikemdasharising from the Second Industrial Revo-lution What is the outcome of this experiment

The pattern of fertility arising from the base-line model is shown in Figure 3 This derivesfrom the solution at the estimated set of param-eter values to the nonlinear difference equationsystem that characterizes the modelrsquos equilib-rium This figure also shows the number of kidsper parent in the US data over the period 1800to 1990 as taken from Micheal R Haines(2000 Table 4)21 Qualitatively speaking thepattern of fertility generated by the baselinemodel matches the US data fairly well Thereis a secular decline in fertility punctuated by atemporary rise spawned by technologicalprogress in the household sector The modelunderestimates the size of the baby boom Thiscan easily be rectified by allowing household-sector TFP to grow at a slightly faster rate This

creates a problem though with the decline infertility after 1960 when the baby bust resumes

To see this reestimate the model placingequal weight on the baby boom and baby bustsegments of the fertility time path22 Figure4 shows the upshot Note that the baby boom isnow much more pronounced It can be madeeven more pronounced by placing a 75-percentweight on the baby boom segment as can beseen Measured market-sector TFP does notgrow fast enough however to generate the ob-served rapid decline in fertility after the babyboom The estimation routine must trade off anygain in improved fit before 1960 obtained byincreasing the amount of technological progressin the household sector against the loss in fitafter this date Overall the equally weightedestimation scheme seems to give the preferredresults for the issue at hand Last it may bepossible to account for the rapid decline infertility after the baby boom by modifying the

21 The Haines (2000) figures have been divided by two toget the number of children per parent (as opposed to thenumber of kids per woman) In the model each child hasonly one parent not two as in the real world Therefore theUS fertility data should be divided by two otherwise therate of population growth in the model will be far too high

22 This estimation scheme weights the years 1940 1950and 1960 more heavily to put a greater emphasis on thebaby boom Specifically in the baseline estimation each ofthese years gets a 5-percent weight (since there are 20observations) as opposed to the 167-percent weight in thenew procedure

FIGURE 3 FERTILITY 1800ndash1990 US DATA AND BASELINE MODEL


model to incorporate such factors as a quantity-quality tradeoff in fertility public educationand a female labor-force participation decisionin addition to adjusting upward the rate of TFPgrowth to correct for the inflation bias in aggre-gate prices indices23

Technological Progress in the HouseholdSectormdashHow much technological progress wasthere in the household sector The equallyweighted estimation scheme suggests that be-tween 1800 and 1990 TFP in the home sectormust have risen by a factor of 12 In particularx is estimated to rise by a factor of 113 between1940 and 1950 and by an additional factor of106 between 1950 and 1960 Are these num-bers reasonable TFP in the market sector in-creased by a factor of about 7 between 1800 and1990 The assumed rise in household-sectorTFP lies considerably below this number Fig-ure 4 also illustrates the decline in time spent onchild rearing in the model given the indicatedpatterns of market and (normalized) household

productivity The estimated increase in house-hold TFP implies that the time spent on childrearing should decline by a factor of 122 hold-ing the number of kids constant The number ofchildren declines secularly and with it so doesthe time spent on child rearing Stanley Leber-gott (1993 Table 8) reports that time spent onhousework fell by a factor of 3 between 1900and 1975 The time spent on raising children inthe model drops by a factor of 4 over the periodin question

IV The Quantity-Quality Model An Example

A The Setup

The framework described above has littletrouble generating the observed 200-year secu-lar decline in fertility A simple nonhomothetic-ity in tastes does the trick Specifically themarginal utility of market consumption declinesat a slower rate than the increase in wages wtdue to the presence of a simple constant term cin tastes (1) Thus the marginal cost of an extrakid in terms of forgone consumption rises overtime While the simplicity of the setup is a bigvirtue for both the theoretical and quantitative

23 The quantity-quality tradeoff and female labor-forceparticipation are discussed in Sections IV and V D

FIGURE 4 FERTILITY 1800ndash1990 US DATA AND WEIGHTED MODELS


analysis it may seem a bit mechanical The gistof the analysis is likely to carry over to somericher models of fertility however for examplea Beckerian (1960) style quantity-qualitymodel operationalized here along the lines ofGalor and Weil (2000)

To see this suppose a workerrsquos endowmentof labor is made up of two components brawnand brain Brawn earns w for each unit suppliedon the labor market while brain receives v Anage-1 parent living in period t must now chooseboth the quantity of kids that he desires nt

1 andthe quality of each child or the fraction of thekidrsquos labor endowment that will be skilledhtI

1 [0 1]Change the specification of preferences to

(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I

1 wt Ij vt Ij qt Ijj 0J 1

j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1

with sgn (1 ) sgn(1 ) This utilityfunction is similar to (1) with three modifica-tions First the childrsquos skill level now enterstastes In the formulization adopted the parentcares about this because it will determine howmuch the child earns when he grows up orj0

J1 qtI j [wt I j (1 htI1 ) vtI jhtI

1 ]Second the utility function for market con-sumption is now of the more general constant-relative-risk-aversion variety Third the constantterm c has been dropped

There are now two types of costs associatedwith raising children The first is associatedwith producing them In particular let the quan-tity of kids be once again produced in line with

(2) The second cost is tied to educating themSpecifically let the quality of each child bedetermined in line with

ht I1 at mt

11

where mt1 is the input of time connected with

educating the child and at is the state of theeducational technology For simplicity thesecosts are borne in the first period of an adultrsquoslife

Now in period-t an age-1 adult will have askill endowment ht

1 that was determined by hisparent I periods ago The young adult mustchoose c t j

j1j0J1 nt

1 and htI1 so as to maxi-

mize his lifetime utility as given by (13) sub-ject to the budget constraint shown below

j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11

Market goods are now produced in line withthe CES production technology

(14) yt zt kt 1 ut

et1

where ut and et denote the quantities of brawnand brains hired The parameter controls thedegree of substitutability between capital andbrawn in production It plays an important rolein the analysis Suppose that 0 so that theelasticity of substitution between capital andbrawn 1(1 ) is bigger than one To com-plete the setup note that as before all marketsmust clear Now the demand and supplies forbrawn and brain must be equalized so that

ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1

Can a version of the quantity-quality modelmimic the observed pattern of US fertility overthe last two centuries To demonstrate the po-tential of the framework above to address thisquestion a numerical example will now be pre-sented The example is intended for illustrativepurposes only it should not be construed as aserious quantitative analysis It does suggesthowever that the quantity-quality model haspromise

B Numerical Example

To see whether the framework presentedabove can potentially replicate the US data themodel will be solved for and compared acrossfour steady states Think about each steady stateas giving a snapshot of the United States at apoint in time The first steady state will repre-sent the country in 1800 The United States in1940 or at the dawn of the baby boom will bedepicted by the second steady state The peak ofthe baby boom or the year 1960 will be em-blematized by the third steady state The fourthsteady state will denote the year 1990 which isthe end of the baby bust

The parameter values used in the example arepresented in Table 2 These parameter valueshave not been chosen to satisfy any calibrationor estimation scheme They have been picked sothat the example replicates in a loose sense theUS fertility and GDP data As one movesacross time or steady states the levels of tech-nology in the market and household sectorschange Specifically in the analysis the move-

ment in the level of the market technology z ispicked to match the growth in GDP for the USeconomy Note that given the form of (14) move-ments in z now represent capital-embodied tech-nological change and not neutral technologicalchange as before Thus changes in z are nowdifficult to obtain directly from the data In linewith the earlier analysis the movement in thelevel of the household technology x is chosento generate the baby boom

The upshot of the analysis is depicted inFigure 5 In the first steady state fertility is 35kids per person which exactly matches the USdata for 1800 Now move forward in time to1940 Between 1800 and 1940 US GDP grew74 times In the model GDP grows 72 timesThis is obtained by letting the level of technol-ogy in the market sector rise 3820 19times The example is fairly successful in rep-licating the drop in fertility observed in the dataModel fertility drops to 16 children per personas compared with 11 in the data When there istechnological progress in the market the capitalstock rises Fertility will drop faster the moresubstitutable capital and brawn are in produc-tion (ie the bigger is) As the skill premiumrises parents will substitute away from quantitytoward quality of children The drop-off in fer-tility will also be larger the more concave utilityis in child quality and the less concave it is inthe consumption for market goods (ie the big-ger is and the smaller is ) This transpiresbecause along with economic development thevalue of an extra child will decrease relative toan extra unit of consumption Next advance intime from 1940 to 1960 This is the baby boomperiod GDP in the United States rose by afactor of 16 This is achieved in the model byletting z increase 14 times As in the earlieranalysis technological advance in the house-hold sector promotes fertility By letting x risefrom 36 to 260 a baby boom is generated in

TABLE 2mdashPARAMETER VALUES QUANTITY-QUALITY MODEL

Tastes 09510 071 120 350 050Market technology 040 040 (1 009)10 050

z1800 20 z1940 38 z1960 52 z1990 58Home technology 050 gttT 0 05 attT 36

x1800 360 x1940 360 x1960 260 x1990 260Generational structure I 2 J 4


the model Specifically model fertility rises to20 kids per person vis-a-vis 18 in the dataLast GDP rose 21 times between 1960 and1990 To attain this z is set at 58 Fertility inthe model is now 104 which matches the data

In summary the numerical example illus-trates that the quantity-quality model has thepotential to match the time series on US fer-tility quite well In particular the example haslittle trouble matching the secular decline infertility observed over the last two centuriesRefinements of the theoretical setup togetherwith a serious quantitative analysis could un-doubtedly match the exact features of the fer-tility time series better still Such an analysisshould take account of the rise of publicly avail-able free education This lowered the privatecost of having children just as technologicaladvance in household sector did Ideally onewould also like to match the model up with theUS data on the skill premium and educationalattainment24

V Historical Discussion

A Technological Progress in the HouseholdSector

Direct evidence on the increase in the effi-ciency of raising children does not seem to beavailable Economic history unequivocally doc-uments however that the twentieth century wasa time of rapid and unparalleled technologicaladvance in the household sector Prior to 1860the household sector in the American economywas basically an arts-and-crafts industry Thesame forces propelling the mechanization andrationalization of production in the market sec-tor at that time were also at operation in thehousehold sector

The mechanization of household tasks beganin the latter half of the 1800s The vacuumcleaner made its first appearance in 1859 the

24 A consistent high-quality time series for the skill pre-mium is not currently available for the 200-year periodunder study From the fragmentary evidence available it ishard to detect any trend in the skill premium for the ante-bellum period The skill premium may have declined be-tween 1914 and 1924 This coincided with a rapid rise in the

amount of schooling When travelling through the modelrsquosfour steady states the skill premium rises modestly by afactor of 14 Note that technological advance in the educa-tional technology measured here by an increase in a willlead to a fall in the skill premium So without doing morerigorous analysis it is hard to know if the predictions of thequantity-quality model would contradict the data on thisdimension

FIGURE 5 FERTILITY AND GDP 1800ndash1990 US DATA AND QUANTITY-QUALITY MODEL


dishwasher in 1865 and the washing machinein 1869 The initial incarnation of an idea into aproduct often does not meet with great successThese inventions were mechanical in naturethey had to bide their time until the coming ofelectricity The fully automated washing ma-chine did not appear until the 1930s Itrsquos acomplicated machine involving several pro-cesses that must be regulated inserting andextracting water from the tub washing and rins-ing and spin drying Refrigerators enteredhousehold service in the 1920s They replacedthe icebox Clarence Birdseye patented the ideaof flash freezing in 1925 Frozen foods whichchanged the way of life appeared only in theearly 1930s and began to take off in the 1940s Be-tween 1929 and 1975 the household appliance-to-GDP ratio increased by a factor of 2525

After 1975 the stock of appliances relative toGDP levels off or even declines The increase inthe stock of appliances was undoubtedly pro-pelled by the rapid decline in their price

While the development of new consumer du-rables was important in liberating women fromthe shackles of housework so too was the ra-tionalization of the household The principles ofscientific management were applied to thehome just as in the factory Domestic taskswere studied with the aim of improving theirefficiency Christine Frederick (1912) was anearly advocate of applying the principals ofscientific management to the home She wascaptivated by the fact that a man named FrankB Gilbreth had been able to increase the outputof bricklayers from 120 to 350 bricks per hourby applying the principals of scientific manage-ment He did this by placing an adjustable tableby bricklayersrsquo side so that they wouldnrsquot haveto stoop down to pick up a brick He also hadthe bricks delivered in the right position so therewould be no need for the bricklayer to turn eachone right-side up He taught bricklayers to pickbricks up with their left hands and simulta-neously take trowels full of mortar with theirright hands Frederick applied the idea to dish-washing first and then to other tasks She brokedishwashing down into three separate tasksscraping and stacking washing and drying and

putting away She computed the correct heightfor sinks She discovered that dishwashingcould be accomplished more efficiently by plac-ing drainboards on the left using deeper sinksand connecting a rinsing hose to the hot-wateroutlet she estimated that this saved 15 minutesper dinner In 1913 she wrote ldquoDidnrsquot I withhundreds of women stoop unnecessarily overkitchen tables sinks and ironing boards as wellas bricklayers stoop over bricksrdquo26 Frederickand others in the home economics movementhad a tremendous impact on the design of ap-pliances and houses Take the kitchen forexample The kitchen of the 1800s was charac-terized by a large table and isolated dresser Anorganized kitchen with continuous working sur-faces and built-in cabinets began to appear inthe 1930s after a period of slow evolution Inthe 1940s the kitchen became connected withthe dining room and other living areas endingthe housewifersquos isolation

B The Timing of the Baby Boom UnitedStates United Kingdom France and

Switzerland

The analysis above suggests that it is notunreasonable to conjecture that the impact oftechnological advance in the household sectorbegan to gather steam in the 1930s and 1940sHow does this match up with the pattern offertility displayed in the US data as shown inFigure 6 Observe that fertility fell continu-ously from 1800 to about 1936 It then began torise One interpretation of the graph is that thebaby boom started in the 1930s The upwardtrend suffered a slight drop from 1943 to 1945during World War II Note that fertility fellduring World War I and then rebounded Notealso that there is no unusual decline in fertilityassociated with the Great Depression In factone could argue that the baby boom might havestarted earlier if the Great Depression hadnrsquothappened A non-demographer eyeballing thisgraph might date the baby boom as occurringfrom 1936 to 197227 Last observe that it would

25 For more detail see Greenwood et al (2005) espe-cially Figures 1 2 and 7

26 As quoted by Siegfried Giedion (1948 p 521)27 The model which has a time period of ten years is

matched up with the Haines (2000) fertility series shown inFigure 3 which uses decennial data Hence the first jump inthe series associated with the baby boom is 1950 This is


be hard to build a model explaining the babyboom on the basis of movements in marketTFP wages or GDP2829

Could the baby boom be some sort ofcatch-up effect associated with World War II

First if the baby boom was merely the result ofcouples postponing family formation during thewar years then there should be no increase inlifetime births for a woman Yet lifetime birthsdid increase for fecund women during the babyboom years as Figure 1 shows Second manyof the women giving birth during the babyboom were simply too young for such acatch-up effect to be operational Figure 7 plotsthe fertility rates for various age groups of whitewomen30 These fertility rates are weighted bythe relative size of each group Therefore thediagram provides a measure of the contributionof each group to the baby boom Take the 20- to

why estimated household productivity jumps in 1950 TheHernandez (1996) series shown in Figure 6 uses annualdata Here the baby boom starts earlier in 1936 (An unpub-lished annual series by Haines starting in 1933 also showsthe baby boom as starting in 1936) If a higher-frequencyversion of the model was matched up with this seriesinstead then estimated household productivity would startto rise in 1936 In a higher-frequency model women shouldbe allowed to bear children in more than one period Whilethis would introduce a nontrivial complexity into the anal-ysis it should not change the gist of things

28 The fertility series plots the general fertility rate and istaken from Hernandez (1996 Table 9) The GDP data aretaken from Brian R Mitchell (1998a Table J1) They aredeflated by Hainesrsquos (2000 Table 41) population seriesThe dates for the Great Depression shown in Figures 6 8 9and 10 are based on the timing procedure of Harold L Coleet al (2003)

29 Note that fertility appears to decline faster between1917 and 1936 than it does between 1800 and 1917 Butalso observe that real wages grow faster from 1917 on Infact they grow much faster as the following regressionanalysis using data from 1830 to 1972 (or to the start of theproductivity slowdown) shows

ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

t 1 t with t N0 0053

with R2 099 and DW 172 In the above regressiond is a dummy variable which takes the value one from 1917on and assumes the value zero otherwise The numbers inparenthesis are t statistics As can be seen real wages growat about 15 percent a year faster after 1917 than beforeHence the accelerated decline in fertility between 1917 and1936 is consistent with the story being told here

30 This diagram is based on unpublished data kindlysupplied by Michael R Haines

FIGURE 6 US FERTILITY 1800ndash1990


24-year-old age group They contribute themost to the baby boom This series peaks in1960 But at the peak the members of thisgroup were somewhere between 1 and 5 yearsold in 1941 and between 5 and 9 years old in1945 Hence a catch-up effect is impossible forthem Itrsquos implausible that the Great Depressionaffected their fertility decision either Fertilityfor the 25- to 29-year-old age group rises untilabout 1952 levels off until 1957 and declinesthereafter A strong catch-up effect is not veryplausible for this group Those giving birth in1952 would have been in the 14- to 18-year-oldrange in 1941 and in the 18- to 22-year-oldrange by 1945 while those having kids in 1957would have been somewhere between 9 and 13years of age in 1941 and between 13 and 17 in1945

Having said this some evidence of delayedfertility can be gleaned from the diagram but itlooks small For example note that the fertilityrate for the 20- to 24- year-old age group startsto fall in 1942 (this is marked by point A) In1947 these women would have been in the 25-to 29-year-old age group Note the small peak in1947 for the latter age group (marked by pointA) Similarly the fertility rate for the 15- to19-year-old age group begins to fall in 1943

(point B) The majority of this group wouldhave been in the 20- to 24-year-old age grouparound 1948 Note the spike in 1947 for this agegroup (point B)

UK fertility dropped more or less unabatedfrom 1876 to 1940 with one exception (seeFigure 8)31 There was a sharp decline andrebound associated with World War I TheUnited Kingdom suffered a prolonged depres-sion during the interwar years Again it wouldbe hard to argue that there was an unusualdecline in fertility during these years Interest-ingly fertility rose throughout World War IIThe non-demographer might date the babyboom as occurring between 1941 and 1971France shows a similar pattern with fertilityrising throughout World War II (see Figure9) One might date the French baby boom be-tween 1942 and 1974 Last even neutral coun-tries such as Switzerland had a baby boom (seeFigure 10) Observe that Swiss fertility rosethroughout World War II Reasonable dates forthe Swiss baby boom are 1937 to 1971

31 The birth rate data for France and the United Kingdomare from Mitchell (1998b Table A6)

FIGURE 7 US FERTILITY BY AGE GROUP 1933ndash1997


FIGURE 8 UK FERTILITY 1838ndash1993

FIGURE 9 FRENCH FERTILITY 1801ndash1993


C The Size and Start of the Baby Boom inOECD Countries

In line with the previous argument house-holds living in richer countries should on aver-age have been better able to afford labor-savinghousehold goods A question arises Was thebaby boom bigger in richer countries To an-swer this question data on income and fertilityare collected for 18 OECD countries (all theOECD countries for which data are available)32

The birth rate data are obtained from BrianMitchell (1998a Table A6 pp 68ndash83 1998bTable A6 pp 93ndash119 1998c Table A6 pp69ndash79) For each OECD country a graph simi-lar to Figures 8 to 10 is constructed The babyboom is measured by the area below the fertilitycurve and above the horizontal line connectingthe dates for the beginning and the end of thebaby boom as shown in Figure 10 for Switzer-land The income data come from the PennWorld Tables 56 and measure a countryrsquos realGDP in 1950

The results of this exercise are plotted inFigure 11 As can be seen there is a positiverelationship between the size of the baby boomand a countryrsquos income The Pearson correla-tion coefficient between the two series is 068which is significantly different from zero at the95-percent confidence level There is no reasonto presume that the relationship between the twovariables is linear Kendallrsquos gives a nonpara-metric measure of the association between twoseries33 A value of 048 is obtained for Ken-dallrsquos By either measure the two series arepositively related to one another

Likewise one would expect that the babyboom should have started earlier in richer coun-tries This appears to be true Figure 12 shows

32 Data are missing for Japan for the years between 1943and 1947 It fits in well though with the story told belowNo data were available for Turkey

33 Kendallrsquos is a measure of the degree of order betweentwo series xii1

n and yi11n Consider the case where

the two variables are positively associated with each otherCount the number of times when xj xi and yj yi Call thenumber of times the series are congruent C There are atotal of n(n 1) comparisons to do Kendallrsquos is given by

C nn 1 C

nn 1

Essentially Kendallrsquos is the probability of congruence lessthe probability of incongruence

FIGURE 10 SWISS FERTILITY 1870ndash1993


FIGURE 11 THE CROSS-COUNTRY RELATIONSHIP BETWEEN THE SIZE

OF THE BABY BOOM AND INCOME

FIGURE 12 THE CROSS-COUNTRY RELATIONSHIP BETWEEN THE START OF THE BABY BOOM

AND INCOME


that there is a negative relationship between thestart of a baby boom and a countryrsquos income34

The Pearson correlation coefficient between thetwo series is 062 and it is significant at the95-percent confidence level Similarly the Ken-dall rank correlation coefficient is 031 Fi-nally for a very limited set of countries it ispossible to plot the relationship between the sizeand start of the baby boom on the one hand anda measure of modern household technologiesadoption on the other35 Figure 13 shows thescatters As can be seen the size of the babyboom appears to be positively correlated withthe diffusion of household technologieswhile the start of the baby boom is negativelyassociated with it This is what the theorysuggests

D Fertility and Female Labor-ForceParticipation A Suggestion for Future

Research

Before concluding a suggestion for futureresearch is offered Female labor-force partici-pation rose continuously over the last centuryIn 1890 only 4 percent of married womenworked By 1980 this figure had risen to 50percent The number of married women in thelabor force rose from 15 to 40 percent over thesubperiod 1940 to 1970 that is female labor-force participation grew over the baby boomyears What could have accounted for the factthat women chose both to work and to havemore children The answer here is that techno-logical innovation in the household sector madethis possible by freeing up womenrsquos timeWomen who chose to labor in the market havealways had fewer children than those who choseto labor at home Yet in the baby boom years itwas working women who showed the biggestpercentage rise in fertility

Table 3 should not be construed as implyingthat the baby boom was caused by a rise in thefertility of working women it was not Most

34 Italy and Spain are now omitted since they did notexperience a baby boom Hence there is no starting date forthese countries

35 The data are from Lebergott (1993 Table II17) Foreach of the six countries reported a simple average is takenacross the diffusion rates for hot running water washingmachines refrigeration sewing machines stoves (exceptthe United States) and automobiles

FIGURE 13 THE CROSS-COUNTRY RELATIONSHIP BETWEEN THE SIZESTART OF THE

BABY BOOM AND THE DIFFUSION OF HOUSEHOLD TECHNOLOGIES


women didnrsquot work at the time The increase infertility between 1940 and 1960 can be decom-posed into three factors the change in fertilityfor homemakers the change in fertility forwomen in the labor force and the change infemale labor-force participation The results ofthis decomposition are given in Table 436

Working women have a lower fertility ratethan homemakers (about 03 kids versus 30 in1940 and 18 versus 47 in 1960) Hence anincrease in female labor-force participation willoperate to lower fertility as the table showsEmployed women accounted for 162 percent[19(1998) percent] of the increase in fer-tility between 1940 and 1950 This jumped to

352 percent for the 1950ndash1960 period versus aparticipation rate of 31 percent The peak of thebaby boom was 1957 Therefore a significantproportion of the increase in fertility during thebaby boom years is accounted for by a rise infertility for working women Again why didthese women choose to have more kids

It would be interesting to develop a model toaddress the facts given above Imagine whatsome of the ingredients in such a model mightbe There could be two sexes with some spe-cialization in labor by sex Males do solelymarket work Females can split their time be-tween market work and non-market work Sup-pose that there is some indivisibility in marketeffort say a fixed work week and that (as in thereal world) the number of children in a familymust be a natural number Now let familiesdiffer according to some characteristics such astheir desire for children the ability of the fe-male or the ability of the male Then somefemales will work more than others The moremarket work a female does the fewer childrenthe family will have given the time cost ofraising them Some women may choose to haveno children In such a framework a once-and-for-all decline in the cost of having childrencould lead to the findings presented in Table3 A challenge would be to match these factsagainst the backdrop of a 200-year decline infertility and a 100-year rise in female laborforce participation37

36 The decline in fertility is decomposed as followsTotal fertility n is a weighted average of the fertility forworking women w and homemakers h where the weightsf and 1 f are the fractions of women who are in and outof the labor force Thus n fw (1 f )h The change infertility between any two dates can then be written as n n [ f f ](w w)2 [(1 f ) (1 f )](h h)2 [(w h) (w h)]( f f )2 The first term gives thecontribution of the increase in the fertility of workingwomen to the total increase in fertility the second measuresthe amount arising from the increase in homemaker fertilitywhile the third shows the amount due to changes in laborforce participation The data used for these calculations aretaken from Cho et al (1970 Tables 61 to 63) A workingwoman is defined as any woman who is in the labor forceand a homemaker is one who is outside of the labor force

37 One way of doing this could be to combine somefeatures of the current analysis with aspects of Galor andWeil (1996) andor Greenwood et al (2004)

TABLE 4mdashDECOMPOSITION OF THE INCREASE IN FERTILITY

(Percentage)

Period Employed Homemakers Participation

1940ndash1950 19 98 171950ndash1960 44 81 25

TABLE 3mdashFERTILITY AND FEMALE LABOR-FORCE PARTICIPATION

Percentage change

1940ndash1950 1950ndash1960 1940ndash1960

Total fertility rateHomemakers 29 21 56Employed 269

Children per married womanHomemakers 27 57 100Employed 38 127 214

Source Lee-Jay Cho et al (1970 Table 65 p 193)


VI Conclusions

The mystery of the baby boom has not beencracked in economics The fact that the babyboom was an atypical burst of fertility thatpunctuated a 200-year secular decline adds tothe enigma Conventional wisdom ascribes thebaby boom to the effects of the Great Depres-sion andor World War II This story has severalshortcomings First for the US and manyOECD countries it is hard to detect a strongstructural break in fertility due to the GreatDepression Second fertility in the US andmany OECD countries started to rise beforeWorld War II Third at the peak of the USbaby boom the most fertile cohort of womenwas just too young for the Great Depression or

World War II to have had a direct effect onthem

The story told here attributes the secular de-cline in fertility to the tenfold rise in real wagesthat occurred over this time period This in-creased the cost in terms of forgone consump-tion of raising children The baby boom isaccounted for by the invention of labor-savinghousehold capital or other labor-saving house-hold products and management techniqueswhich occurred during the middle of the lastcentury The analysis suggests that the increasein the efficiency of the household sector neededto explain the baby boom is not that large Infact the 12-fold increase estimated here ismuch smaller than the documented sevenfoldimprovement in market productivity

APPENDIX PROOF OF PROPOSITION

PROOFBy using the first-order condition for consumption (4) in conjunction with the budget constraint

(3) the following permanent-income type equation can be obtained

(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt

where i10 rt i 13 1 This equation states that an age-1 agent will consume the fraction (1 )(1

J) of the present value of his income net of the cost of rearing his kids Using equation (15) inconjunction with the first-order condition for fertility (5) allows for a single implicit equation in nt

1

to be obtained Specifically one obtains

nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt

By totally differentiating this condition it is easy to deduce that

dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0

Note the last result obtains even if all of the wt irsquos (for i 0) rise by the same proportion ieeven when technological progress is permanent so that dwt i wt i dwt wt for all i 0 Using theefficiency conditions (6) and (7) it is easy to show that

(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0

Again note that the result in the Proposition is true even if all of the zt irsquos (for i 0) rise by thesame proportion

REFERENCES

Andolfatto David and MacDonald Glenn MldquoTechnology Diffusion and Aggregate Dy-namicsrdquo Review of Economic Dynamics1998 1(2) pp 338ndash70

Becker Gary S ldquoAn Economic Analysis of Fer-tilityrdquo in Ansley J Coale ed Demographicand economic change in developed countriesPrinceton Princeton University Press 1960pp 209ndash31

Becker Gary S ldquoA Theory of the Allocation ofTimerdquo Economic Journal 1965 75(299) pp493ndash517

Becker Gary S and Barro Robert J ldquoA Refor-mulation of the Economic Theory of Fertil-ityrdquo Quarterly Journal of Economics 1988103(1) pp 1ndash25

Benhabib Jess Rogerson Richard and WrightRandall ldquoHomework in MacroeconomicsHousehold Production and Aggregate Fluctu-ationsrdquo Journal of Political Economy 199199(6) pp 1166ndash87

Cho Lee-Jay Grabill Wilson H and BogueDonald J Differential current fertility in theUnited States Chicago University of Chi-cago Press 1970

Cole Harold L Ohanian Lee and Leung Ron-ald ldquoDeflation Real Wages and the Interna-tional Great Depression A Productivity Puz-zlerdquo Unpublished Paper 2003

Cooley Thomas F and Prescott Edward CldquoEconomic Growth and Business Cyclesrdquo inThomas F Cooley ed Frontiers of businesscycle research Princeton Princeton Univer-sity Press 1995 pp 1ndash38

Doepke Matthias ldquoAccounting for Fertility De-cline during the Transition to Growthrdquo Jour-nal of Economic Growth 2004 9(3) pp 347-83

Easterlin Richard A ldquoTwentieth-CenturyAmerican Population Growthrdquo in Stanley LEngerman and Robert E Gallman eds TheCambridge economic history of the United

States Volume 3 The Twentieth CenturyCambridge Cambridge University Press2000 pp 505ndash48

Eckstein Zvi Mira Pedro and Wolpin KennethI ldquoA Quantitative Analysis of Swedish Fer-tility Dynamics 1751ndash1990rdquo Review of Eco-nomic Dynamics 1999 2(1) pp 137ndash65

Fernandez-Villaverde Jesus ldquoWas MalthusRight Economic Growth and PopulationDynamicsrdquo Penn Institute for Economic Re-search Working Paper 01ndash046 2001

Frederick Christine ldquoThe New HousekeepingHow It Helps the Woman Who Does HerOwn Workrdquo Ladies Home Journal 191213(Sept) pp 70ndash71

Gallman Robert E ldquoEconomic Growth andStructural Change in the Long NineteenthCenturyrdquo in Stanley L Engerman and RobertE Gallman eds The Cambridge economichistory of the United States Volume 2 TheLong Nineteenth Century Cambridge Cam-bridge University Press 2000 pp 1ndash55

Galor Oded and Weil David N ldquoThe GenderGap Fertility and Growthrdquo American Eco-nomic Review 1996 86(3) pp 374ndash87

Galor Oded and Weil David N ldquoPopulationTechnology and Growth From MalthusianStagnation to the Demographic Transitionand Beyondrdquo American Economic Review2000 90(4) pp 806ndash28

Giedion Siegfried Mechanization takes com-mand A contribution to anonymous historyNew York Oxford University Press 1948

Gomme Paul Kydland Finn E and Rupert Pe-ter ldquoHome Production Meets Time-to-Buildrdquo Journal of Political Economy 2001109(5) pp 1115ndash31

Gordon Robert J The measurement of durablegoods prices National Bureau of EconomicResearch Monograph Series Chicago Uni-versity of Chicago Press 1990

Greenwood Jeremy and Seshadri Ananth ldquoTheUS Demographic Transitionrdquo American


Economic Review 2002 (Papers and Pro-ceedings) 92(2) pp 153ndash59

Greenwood Jeremy Seshadri Ananth andYorukoglu Mehmet ldquoEngines of LiberationrdquoReview of Economic Studies 2005 72(1) pp109-33

Haines Michael R ldquoThe Population of theUnited States 1790ndash1920rdquo in Stanley L En-german and Robert E Gallman eds TheCambridge economic history of the UnitedStates Volume 2 The Long Nineteenth Cen-tury Cambridge Cambridge UniversityPress 1994 pp 143ndash205

Hernandez Donald J Trends in the well-beingof Americarsquos children and youth 1996Washington DC US Department of Healthand Human Services 1996

Lebergott Stanley Pursuing happiness Ameri-can consumers in the twentieth centuryPrinceton Princeton University Press 1993

Mitchell Brian R International historical statis-tics the Americas 1750-1988 4th Ed NewYork Stockton Press London Macmillan1998a

Mitchell Brian R International historical statis-tics Europe 1750-1993 4th Ed New YorkStockton Press 1998b

Mitchell Brian R International historical statis-tics Africa Asia amp Oceania 1750-1993 3rdEd New York Stockton Press 1998c

Parente Stephen L Rogerson Richard andWright Randall ldquoHomework in Develop-ment Economics Household Production andthe Wealth of Nationsrdquo Journal of PoliticalEconomy 2000 108(4) pp 680ndash87

Razin Assaf and Ben-Zion Uri ldquoAn Intergenera-tional Model of Population Growthrdquo Ameri-can Economic Review 1975 65(5) pp 923ndash33

Reid Margaret G The economics of householdproduction New York John Wiley amp Sons1934

Rıos-Rull Jose-Victor ldquoWorking in the MarketWorking at Home and the Acquisition ofSkills A General-Equilibrium ApproachrdquoAmerican Economic Review 1993 83(4) pp893ndash907

Rogerson Richard ldquoThe Evolution of OECDEmployment 1960ndash2000 The Role of Struc-tural Transformationrdquo Unpublished Paper2002

US Bureau of the Census Historical statistics ofthe United States Colonial times to 1970 3rdEd Washington DC US Bureau of theCensus 1975

Williamson Jeffrey G ldquoThe Evolution of Glo-bal Labor Markets since 1830 BackgroundEvidence and Hypothesesrdquo Explorations inEconomic History 1995 32(2) pp 141ndash96


explains the baby boom according to conven-tional wisdom

Conventional wisdom is often wrong It ishere too or so it will be argued in Section VSpecifically the pattern and timing of fertilitydo not support the belief that the baby boomwas the outcome of World War II and the GreatDepression In particular

(a) It is highly unlikely that the baby boom canbe the result of delayed fertility from theGreat Depression and World War II Figure1 shows completed lifetime fertility for thewomen who gave birth during the babyboom A pure catch-up effect should havehad no influence on lifetime fertility since

one less child today would just be made upfor by having one more child tomorrowYet lifetime fertility rose

(b) Take the peak of the baby boom for theUnited States or the year 1960 As will bediscussed in Section V the cohort ofwomen contributing the most to the babyboom then (those in the 20- to 24-year-oldage group) were simply too young for eitherthe Great Depression or World War II tohave had much of an impact on them Theywere not alive during the Great Depressionand were under nine years of age at the endof World War II

(c) The data show that the baby boom actuallystarted in the 1930s in the United States andmany OECD countries This will be de-tailed in Section V Furthermore for manycountries fertility grew throughout WorldWar II Additionally the neutral countriesIreland Sweden and Switzerland all hadbaby booms Also itrsquos hard to detect aprecipitous drop in US and many otherOECD country fertility rates due to theGreat Depression

So what could have caused the baby boomTurn attention then to the hypothesis enter-

tained here For the journey through the baby

the one hand consumption plans are based on materialaspirations The latter are formed very early in life whilegrowing up with onersquos parents On the other hand youngadults base their fertility decisions on projections aboutlifetime income The generation that spawned the babyboomers had low material aspirations and hence modestdesires for consumption since they were both born in theGreat Depression and experienced World War II Theboomersrsquo parents entered the labor force in the late 1940s to1960s economically speaking a good time Therefore theyhad low material aspirations relative to their expected life-time income The surfeit wealth was channeled into familyformation and high fertility resulted

FIGURE 1 FERTILITY IN THE UNITED STATES 1800ndash1990




I The Economy

A The Populace



(1) j 0

J 1

jUct jj 1

1 J

1 Qnt

1

j 0

J 1

j lnct jj 1 c)

1 J

1 1

nt11 1

1











(2) nt1 Hlt

1 xt xt lt11



Cnt1 xt wt gt

minlt1

wtlt1 wtgt nt

1 Hlt1 xt

wtnt1

xt11

wtgt



(P1) maxct j

j 1nt1

j 0

J 1

jUct jj 1

1 J

1 Qnt

1subject to

(3) j 0

J 1

qt j c t jj 1

j 0

J 1




(4) U1 c t jj 1 rt j1 U1 c t j1

j 2

for j 0 J 2

and

1 J

1 Q1 nt

1 U1 ct1C1 nt

1 xt wt gt

or

(5)1 J

1 1

1

nt1

1

ct1 c

1

1wtnt

1

xt11 1

nt1







J1 qt jc t jj1 j0



j1 c) j0


j1 c t j










B Firms



1


kt 1 kt it



(P2) maxkt et



(6) F1 kt et zt rt

and

(7) F2 kt et zt wt

C Equilibrium



(8) p t 1j 1 p t

j for j 1 J 1

and

(9) pt i1 pt iI

1 nt iI1 for i 1 I



(10) pt1ct

1 pt2ct

2 ptJct

J it yt


(11) pt1st 1

2 pt2st 1

3 ptJ 1st 1

J kt 1


1 p1J) All but the


2 s13 s1


(12) p12s1

2 p1Js1

J k1


1n01 pI2

1 nI21 )





1p1








2 s1J p1

1 p1J p0

1n01

pI21 nI2
















1 to decline

PROOF See Appendix



1(1)



1) (ct1 c)















lnTFPt a bt dt2 t

where










a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES









































I The Economy

A The Populace



(1) j 0

J 1

jUct jj 1

1 J

1 Qnt

1

j 0

J 1

j lnct jj 1 c)

1 J

1 1

nt11 1

1











(2) nt1 Hlt

1 xt xt lt11



Cnt1 xt wt gt

minlt1

wtlt1 wtgt nt

1 Hlt1 xt

wtnt1

xt11

wtgt



(P1) maxct j

j 1nt1

j 0

J 1

jUct jj 1

1 J

1 Qnt

1subject to

(3) j 0

J 1

qt j c t jj 1

j 0

J 1




(4) U1 c t jj 1 rt j1 U1 c t j1

j 2

for j 0 J 2

and

1 J

1 Q1 nt

1 U1 ct1C1 nt

1 xt wt gt

or

(5)1 J

1 1

1

nt1

1

ct1 c

1

1wtnt

1

xt11 1

nt1







J1 qt jc t jj1 j0



j1 c) j0


j1 c t j










B Firms



1


kt 1 kt it



(P2) maxkt et



(6) F1 kt et zt rt

and

(7) F2 kt et zt wt

C Equilibrium



(8) p t 1j 1 p t

j for j 1 J 1

and

(9) pt i1 pt iI

1 nt iI1 for i 1 I



(10) pt1ct

1 pt2ct

2 ptJct

J it yt


(11) pt1st 1

2 pt2st 1

3 ptJ 1st 1

J kt 1


1 p1J) All but the


2 s13 s1


(12) p12s1

2 p1Js1

J k1


1n01 pI2

1 nI21 )





1p1








2 s1J p1

1 p1J p0

1n01

pI21 nI2
















1 to decline

PROOF See Appendix



1(1)



1) (ct1 c)















lnTFPt a bt dt2 t

where










a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES










































(2) nt1 Hlt

1 xt xt lt11



Cnt1 xt wt gt

minlt1

wtlt1 wtgt nt

1 Hlt1 xt

wtnt1

xt11

wtgt



(P1) maxct j

j 1nt1

j 0

J 1

jUct jj 1

1 J

1 Qnt

1subject to

(3) j 0

J 1

qt j c t jj 1

j 0

J 1




(4) U1 c t jj 1 rt j1 U1 c t j1

j 2

for j 0 J 2

and

1 J

1 Q1 nt

1 U1 ct1C1 nt

1 xt wt gt

or

(5)1 J

1 1

1

nt1

1

ct1 c

1

1wtnt

1

xt11 1

nt1







J1 qt jc t jj1 j0



j1 c) j0


j1 c t j










B Firms



1


kt 1 kt it



(P2) maxkt et



(6) F1 kt et zt rt

and

(7) F2 kt et zt wt

C Equilibrium



(8) p t 1j 1 p t

j for j 1 J 1

and

(9) pt i1 pt iI

1 nt iI1 for i 1 I



(10) pt1ct

1 pt2ct

2 ptJct

J it yt


(11) pt1st 1

2 pt2st 1

3 ptJ 1st 1

J kt 1


1 p1J) All but the


2 s13 s1


(12) p12s1

2 p1Js1

J k1


1n01 pI2

1 nI21 )





1p1








2 s1J p1

1 p1J p0

1n01

pI21 nI2
















1 to decline

PROOF See Appendix



1(1)



1) (ct1 c)















lnTFPt a bt dt2 t

where










a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES









































B Firms



1


kt 1 kt it



(P2) maxkt et



(6) F1 kt et zt rt

and

(7) F2 kt et zt wt

C Equilibrium



(8) p t 1j 1 p t

j for j 1 J 1

and

(9) pt i1 pt iI

1 nt iI1 for i 1 I



(10) pt1ct

1 pt2ct

2 ptJct

J it yt


(11) pt1st 1

2 pt2st 1

3 ptJ 1st 1

J kt 1


1 p1J) All but the


2 s13 s1


(12) p12s1

2 p1Js1

J k1


1n01 pI2

1 nI21 )





1p1








2 s1J p1

1 p1J p0

1n01

pI21 nI2
















1 to decline

PROOF See Appendix



1(1)



1) (ct1 c)















lnTFPt a bt dt2 t

where










a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES











































2 s1J p1

1 p1J p0

1n01

pI21 nI2
















1 to decline

PROOF See Appendix



1(1)



1) (ct1 c)















lnTFPt a bt dt2 t

where










a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES














































lnTFPt a bt dt2 t

where










a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES








































a 04611172

b 00045418

d 000002200

097665375

13 00299

with R2 09960 DW 225 obs 102
















mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES












































mincx1800 x1950 x1960 )

t T

nt

Nt c x1800 x1950 x1960]2

subject to

0 x1800 x1950 x1960

and

c x1800 x1950 x1960S




C The Baby Boom




















A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES



















































A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES











































A The Setup









(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES











































(13) j 0

J 1

jUct jj 1

1 J

1

Qnt1 ht I


j 0

J 1

jct j

j 11

1

1J

11

nt11

1

j 0

J 1

qt Ijwt Ij1 ht I1

vt Ijht I1 ]1






ht I1 at mt

11





j1j0J1 nt



j 0

J 1

qt j ct jj 1

j 0

J 1

qt j1 ht1wt j ht

1vt j

wt1 ht1 ht

1vtnt1

xt11

wt1 ht1 ht

1vtnt1ht I

1

at11


(14) yt zt kt 1 ut

et1


ut pt11 ht

11 lt1 mt

1

pt21 ht 1

1 ptJ1 ht J1

1


and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES







































and

et pt1ht

11 lt1 mt

1

pt2ht 1

1 ptJht J1

1


B Numerical Example

























Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES






















































Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES












































Switzerland












ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES













































ln wt 13282624

30273673

dt 00094831

t 0015675

dtt t

where

t 08101599

























C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES


























































C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES



















































C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES
















































C nn 1 C

nn 1







AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES










































AND INCOME





Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES










































Research















(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES














































(Percentage)


1940ndash1950 19 98 171950ndash1960 44 81 25


Percentage change






VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES







































VI Conclusions







(15)ct

1 cwt

1

1J j 0

J 1 wt jcwti 1

j rt i

Cnt1 xt wt gt

wt



1


nt11 1 1 1

1

1 xt

11 j 0

J 1 wt j cwti 1

j rt i

Cnt1 xt wt gt

wt


dnt1

dxt 0

dnt1

dgt 0 and

dnt1

dwt 0


(16) wt 1 1 zt11 rt 1


Thus

dnt1

dzt 0


REFERENCES







































Thus

dnt1

dzt 0


REFERENCES























































Documents

The Baby Boom and Baby Bustecon.ucsb.edu/~mkapicka/RG/bb.pdf · The Baby Boom and Baby Bust By JEREMY G REENWOOD,ANANTH S ESHADRI, AND G UILLAUME V ANDENBROUCKE * What caused the