Explaining Educational Attainment across Countries and over Time

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1 Explaining Educational Attainment across Countries and over Time D. Restuccia 1 G. Vandenbroucke 2 1 University of Toronto 2 University of Southern California Review of Economic Dynamics Vol. 17, No. 4, October 2014, pp

2 Introduction

3 Back 3/44 Facts: Schooling across Countries, Schooling differences across countries are large 2. Schooling increased in all countries 3. Schooling differences smaller in 2005 than in 1950 Schooling increased faster for poor True even if poor s GDP/cap. did not catch up

4 Back 4/44 Years of Schooling and GDP per capita (U.S. = 1) Decile y 50 s 50 y 05 s 05 s 05/s R 10/ R 9/ See data

5 Back 5/44 Income Elasticity of Schooling across Countries Holding income differences constant, the differences in years of schooling have decreased 0.9 Cross country income elasticity of schooling Year

6 Back 6/44 Questions What accounts for schooling differences across countries? patterns of schooling changes through time?

7 Back 7/44 Strategy A model of schooling based on Bils and Klenow (2000) Exogenous productivity and life expectancy Non-homothetic preferences income effect Endogenous time allocation Home production

8 Back 7/44 Strategy A model of schooling based on Bils and Klenow (2000) Exogenous productivity and life expectancy Non-homothetic preferences income effect Endogenous time allocation Home production Fit U.S. time series of schooling and time allocation

9 Back 7/44 Strategy A model of schooling based on Bils and Klenow (2000) Exogenous productivity and life expectancy Non-homothetic preferences income effect Endogenous time allocation Home production Fit U.S. time series of schooling and time allocation Cross-country experiment Economies differ in Productivity Life expectancy Ask What % of schooling diff. with U.S. accounted for in 1950? What % of changes in schooling over time accounted for?

10 Back 8/44 Findings Cross Section: Model accounts for 90% of differences in schooling between U.S. & poor countries in 1950 Time Series: Model accounts for 64% of changes in schooling over time in poor countries Schooling increases faster in poor economies relative to rich even if their income does not Emphasize role of productivity improvements for schooling in poor countries

11 Back 9/44 Model

12 Back 10/44 Environment Preferences: market & nonmarket cons., leisure time, schooling time Human capital inputs of time (schooling) and goods Finite lives, perfect foresight, perfect credit market Exogenous variables Productivity (market and nonmarket) Life expectancy

13 Back 11/44 Preferences Lifetime utility, generation τ where τ+tτ c > 0 : constant τ e ρt [U (c τ,t ) + αv (l τ,t )] dt + βw (s τ ) U (c τ,t ) = ln (c τ,t c) V (l τ,t ) = l1 µ τ,t 1 1 µ W (s τ,t ) = ln (s τ,t )

14 Back 12/44 Technology Human capital technology (from Bils and Klenow, 2000) where x τ,t : goods s τ,t : time (schooling) H (s τ,t, x τ,t ) = x γ τ,th (s τ,t ) ( ) θ h (s τ,t ) = exp 1 ψ s1 ψ τ,t

15 Back 13/44 Technology Household technology (from McGrattan et al., 1997) c τ,t = [ φ ( cτ,t m ) σ ( ) + (1 φ) c n σ ] 1/σ τ,t where c n τ,t = z n τ n τ,t cτ,t m : market goods cτ,t n : nonmarket goods n τ,t : nonmarket, nonleisure time zτ n : household productivity

16 Back 14/44 Optimization We impose c i τ,t = c i τ (i = m, n), l τ,t = l τ, and n τ,t = n τ

17 Back 14/44 Optimization We impose c i τ,t = c i τ (i = m, n), l τ,t = l τ, and n τ,t = n τ Optimization problem becomes: Tτ max e ρt [U(c τ ) + αv (l τ )] dt + βw (s τ ) cτ m,cτ n,l τ,x τ,s τ 0 subject to c m τ Tτ 0 Tτ e ρt dt+x τ = zτ m (1 n τ l τ ) H(s τ, x τ ) e (g m ρ)t dt s and technologies zτ m : market productivity g m : rate of growth of zτ m

18 Back 15/44 First Order Condition for s τ βw (s τ ) = φ ( { [ }}{ c }{{} 1 γ a τ U m (c τ ) c τ h (s τ ) τ c τ h(s τ ) + d ] τ (s τ ) d τ (s τ ) marg. benef. }{{} marg. cost ) σ A τ (s τ ) where a τ = T τ 0 e ρu du and d τ (s) = T τ s e (g m ρ)u du

19 Back 15/44 First Order Condition for s τ βw (s τ ) = φ ( { [ }}{ c }{{} 1 γ a τ U m (c τ ) c τ h (s τ ) τ c τ h(s τ ) + d ] τ (s τ ) d τ (s τ ) marg. benef. }{{} marg. cost ) σ A τ (s τ ) where a τ = T τ 0 e ρu du and d τ (s) = T τ s e (g m ρ)u du If β = 0 maximize lifetime income: A τ (s τ ) = 0 s τ independent of productivity

20 Back 15/44 First Order Condition for s τ βw (s τ ) = φ ( { [ }}{ c }{{} 1 γ a τ U m (c τ ) c τ h (s τ ) τ c τ h(s τ ) + d ] τ (s τ ) d τ (s τ ) marg. benef. }{{} marg. cost ) σ A τ (s τ ) where a τ = T τ 0 e ρu du and d τ (s) = T τ s e (g m ρ)u du If β = 0 maximize lifetime income: A τ (s τ ) = 0 s τ independent of productivity If β > 0, c > 0 Schooling depends upon productivity through c τ, c m τ U (c τ ) c τ decreasing c τ holding c m τ /c τ constant s τ

21 Back 16/44 First Order Conditions for l τ and n τ First order conditions for l τ αv (l τ ) = φ ( 1 c U m (c τ ) c τ τ 1 γ 1 n τ l τ c τ ) σ First order conditions for n τ (1 φ) (z n τ ) σ (n τ ) σ 1 (1 n τ l τ ) = φ 1 γ (cm τ ) σ

22 Back 17/44 Calibration

23 Back 18/44 Calibration Fit model to U.S. time series of Schooling Workweek Average 2 percent growth in income per worker Nonmarket hours data

24 Back 19/44 Calibration Schooling data from Goldin and Katz (2008) See Years of school completed at age 35 for to 1975-generation Market hours data from Kendrick (1961), McGrattan and Rogerson (2004) and Whaples (1990) See Hours worked per worker Nonmarket hours from Aguiar and Hurst (2007) Transform hours per person into hours per worker 25.6 hours per worker in 1965 and 22.5 in 2005

25 Back 20/44 Calibration ρ = 0.04 ψ = 0.3, γ = 0.1 (Bils and Klenow, 2000) σ = 0.4 (McGrattan et al, 1997)

26 Back 20/44 Calibration ρ = 0.04 ψ = 0.3, γ = 0.1 (Bils and Klenow, 2000) σ = 0.4 (McGrattan et al, 1997) zτ m = e g m (τ 1795) zτ n = 3 i=0 a i(zτ m ) i

27 Back 20/44 Calibration ρ = 0.04 ψ = 0.3, γ = 0.1 (Bils and Klenow, 2000) σ = 0.4 (McGrattan et al, 1997) zτ m = e g m (τ 1795) zτ n = 3 i=0 a i(zτ m ) i T τ = a T + b T τ Estimate a T and b T using U.S. data on years at school + years at work (Hazan, 2009 and Goldin and Katz, 2008)

28 Back 21/44 Calibration Remaining parameters ω = ( c, φ, µ, θ, α, β, g m, a 0, a 1, a 2, a 3 ) min ω 1915 τ=1880 ( sτ s data τ 1) τ=1795 ( 1 lτ n τ 1 l data τ nτ data ) M (ω)m(ω), where See details See parameters M(ω) = y 1965 /y 1795 e n 1968 / n 1938 /25.6 1

29 Back 22/44 Calibration Results Model U.S. Data Model U.S. Data Years Weekly hours Interval used for Interval of model s calibration implications Years of schooling completed at age 35 Weekly Hours See time allocation See value of schooling See value of c

30 Back 23/44 Experiments

31 Back 24/44 Baseline Experiment Compute 10 economies that differ by Level and growth rate of market productivity z m 1795 and g m Life expectancy in 1950 and 2005 Discipline 1. Estimate cross-sectional relation between GDP & Life Expectancy in 1950 and Using step 1, find z m 1795 and g m to match dist. of GDP/cap. in 1950 and 2005

32 Back 25/44 Baseline Results for 1950 Rel Life Leis Home Mkt Schl Dec Inc Exp Hrs Hrs Hrs Yrs c/c ĉ/c Accounting Cross-Section U.S Model accounts for 90% of difference with U.S. schooling for 1st decile

33 Back 26/44 Baseline Results for 2005 Rel Life Leis Home Mkt Schl Dec Inc Exp Hrs Hrs Hrs Yrs c/c ĉ/c Accounting Time Series U.S Model accounts for 64% of observed growth rate of s in 1st decile Elasticity of schooling to gdp: 0.52 (v in data) 0.35 (v. 0.28)

34 Back 27/44 Work Hours Across Countries Annual hours per worker Gross domestic product per capita (log scale)

35 Back 28/44 Schooling Country by Country Implications Years of Schooling, Model v. Data Years, Model LUX 10 USA ISLNLDSWEDNK GBR FRA BEL NOR CHE CAN AUS IRL NZL FIN AUT 8 VEN ITA TTO HKG CHL ARG URY ISR ESP JPN PRT 6 CYPGRC SYR MEXSAU POL BRB HUN BHR TURMYS COLPER CRIZAF IRNGTM BRA BGR JORECU BOL KOR 4 TUN MLT IRQDZA ROMJAMLKA MOZ THA EGY IDN ALB CIV 2 MLI NERPAK SDN GHA SEN PHL MMRTZA BGD CMRZMB IND KENZWE UGAVNM MWI CHN KHM Years, Model MOZ MLI NER JPN HKG LUX IRL AUTNOR TTO FIN ESP ITA ISR ISL NLD FRA DNK BEL GRC PRT SWE GBR AUS CAN KOR CYP USA MLT SAU BRB CHE BGR MYS THA TUR CRI IRN MEX POL CHL HUN NZL SYR ARG BRA TUN COL URY BHR VEN JOR ECU ROMJAM GTM IDN ZAFPER EGY LKAALB CHN MMR DZA PHL MWIPAK IND VNM BOL KHM CIV SEN IRQGHA CMR SDN UGA BGD KENZWE TZA ZMB Years, Data Years, Data 1950, R 2 = 78% 2005, R 2 = 81%

36 Back 29/44 Schooling Country by Country Implications Growth Rate of Schooling by 1950 Income 6 6 IRQ Growth Rate of Schooling (Model) MWI CHN MMR KOR THA MLT KHM JPN PAK IND VNM IDN EGY ALB TUN MLI ROM JAM MYS GRC IRN BGR CYP PRT HKG TZABGD PHL CMR LKA DZAJOR BRA TUR BRB SAU ESP ISR CRI UGA KEN ZWE MOZ ECU BHR COL MEX POL HUN GTM SYR ZMB PER SDNCIVGHA ZAF BOL NER SEN IRQ IRL ITA TTO AUT CHL FIN ISL FRA BEL NOR NLD SWE DNK ARG GBR AUS CAN LUX URY NZL CHE USA VEN GDP per capita in 1950 (log scale) Growth Rate of Schooling (Data) IRN EGYTUN MLI DZA MMR SDN GHA BHR CIV CMR BGD KEN IDN MOZ CHN IND MYS BRA TUR MWI PAK ZWE TZA NER JOR SYR UGA MEX ZMB ROM BOL GTM PRT COL ESP VNM PHL MLT SEN JAM CYP ECUPER SAU AUT VEN HKG KOR GRC CRI FRA ITA THA LKA ZAF TTO CHL FINARG ISL JPN URYNLD POL ISR BEL SWE NOR GBR KHM BGR HUN CAN LUX BRB IRL DNK AUS ALB NZL CHE USA GDP per capita in 1950 (log scale) Model Data

37 Back 30/44 Experiments Experiment 1: The effect of equal productivity growth Experiment 2: The effect of equal productivity growth AND equal change in life expectancy

38 Back 31/44 Experiments Experiment 1 Experiment 2 Rel Mkt Schl Rel Mkt Schl Dec Inc Hrs Yrs Accounting Inc Hrs Yrs Accounting Cross Section U.S Time Series U.S Cross Section Time Series

39 Back 31/44 Experiments Experiment 1 Experiment 2 Rel Mkt Schl Rel Mkt Schl Dec Inc Hrs Yrs Accounting Inc Hrs Yrs Accounting Cross Section Cross Section U.S Time Series Time Series U.S

40 Back 32/44 Experiments Experiment 1: The effect of equal productivity growth Cross Section: accounts for 90% of diff. with U.S. schooling in 1950 (v. 90 in baseline) Time Series: accounts for 65% of growth rate (v. 64% in baseline) Productivity growth differences across countries are small Effect of labor margin on returns to schooling

41 Back 32/44 Experiments Experiment 1: The effect of equal productivity growth Cross Section: accounts for 90% of diff. with U.S. schooling in 1950 (v. 90 in baseline) Time Series: accounts for 65% of growth rate (v. 64% in baseline) Productivity growth differences across countries are small Effect of labor margin on returns to schooling Experiment 2: The effect of equal productivity growth AND equal change in life expectancy Cross Section: same as Exp. 1 by construction Time series: accounts for 51% of growth rate (v. 64% in baseline) Elasticity: 0.51 in in 2005

42 Back 33/44 Conclusion

43 Back 34/44 Conclusion We developed a model of human capital accumulation to assess the quantitative importance of productivity and life expectancy in explaining differences in educational attainment across countries and over time The model accounts for 90 percent of the difference in schooling between rich and poor countries in 1950 and 64 percent of the increase in schooling levels over time in poor countries The model generates a faster increase in schooling levels in poor than in rich countries, explaining the convergence in cross-country schooling levels observed in the data

44 Back 35/44 Conclusion Model implies faster increase in schooling associated with stronger decline in hours of work, hence, even though human capital increases, per capita income may or may not increase This suggest empirical relationship between schooling and per capita income growth across countries, as pioneered for example by Benhabib and Spiegel (1994), does not provide an accurate assessment of the importance of human capital for development Our results imply that improving education and welfare in poor countries hinges more on solving their productivity gap with rich countries than pursuing often emphasized educational policies aimed at solving institutional and other frictions

45 Back 36/44 Extra Material

46 Back 37/44 Schooling Across Countries and Over Time Avg. Years of School, Avg. Years of School, Avg. Years of School, GDP per capita (log scale) GDP per capita (log scale)

47 Back 38/44 Deciles 1. MWI,CHN,MMR,TZA,MLI,KHM,BGD,NER 2. PAK,IND,UGA,VNM,ZMB,CMR,KEN,ZWE 3. THA,SDN,KOR,IDN,EGY,MLT,ALB,CIV 4. GHA,PHL,TUN,MOZ,ROM,SEN,LKA,DZA,JAM 5. MYS,IRQ,IRN,JOR,BRA,BGR,TUR,CYP,ECU 6. GRC,JPN,BOL,CRI,GTM,PRT,BRB,BHR,COL 7. HKG,SAU,ESP,PER,MEX,POL,HUN,ZAF,SYR 8. ISR,IRL,ITA,TTO,AUT,CHL,FIN,ARG 9. URY,ISL,FRA,BEL,NOR,NLD,SWE,DNK 10. GBR,AUS,CAN,VEN,NZL,LUX,CHE,USA

48 Back 39/44 Calibration HP-filtered schooling and hours Years Weekly hours Years of schooling completed at age 35 Weekly hours

49 Back 40/44 Calibration Income y τ = z m τ e 35 g m (1 n τ l τ ) H(s τ, x τ ) Model s output is decision by generation Associate s τ with actual schooling of generation τ Associate n τ with actual hours at date τ + 35 Compute 171 generations from 1795 to 1965 Match to hours from 1830 to 2000 Match to schooling of generation 1880 to 1915

50 Back 41/44 Calibration Preferences ρ = 0.04, c = 0.03, φ = 0.10 σ = 0.40, α = 0.68, β = 0.71, µ = 0.23 Technology z m 1795 = 1.0, g m = a 0 = , a 1 = , a 2 = , a 3 = γ = 0.1, ψ = 0.30, θ = 0.06

51 Back 42/44 Time Allocation in Baseline Model Mkt hours Leisure Home hours 50 Weekly hours

52 Back 43/44 Consumption Value of Schooling We compute ĉ τ such that Tτ 0 e ρt [U(c τ ) + αv (l τ )] dt + βw (s τ ) = Tτ Find ĉ τ /c τ < e ρt [U (ĉ τ ) + αv (l τ )] dt + βw (s τ 1) To compensate for one less year of school, less than a 1% increase in consumption is required

53 Value of Subsistence How large is c? Subsistence can be obtained from income (market) or home production We compute c/c τ Decline from 63% (1800) to 2% (2000) Consistent with expenditure share of food: 5.2% in 1996 Back 44/44

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