MIT Spring 2018: Lecture 2 The Canonical Model of Skill Differentials

Transcription

1 MIT Spring 2018: Lecture 2 The Canonical Model of Skill Differentials David Autor, MIT and NBER February 12, 2018

2 Agenda 1 Some Motivating Figures 2 The Canonical Model 3 International Comparisons of Wage Inequality: Supply, Demand and Institutions

3 Earnings Differentials between College and High School Young Adults in OECD Countries, 2005 Country Differential Country Differential Denmark 22% Sweden 22% Spain 30% Australia 34% Belgium 34% Finland 38% Italy 43% Netherlands 47% Austria 48% France 48% Korea 48% Germany 50% Ireland 59% UK 61% OECD (2007): Education at a Glance

4 Tertiary Education Completion in OECD Countries as of 2012 by Age Groups, and Population with tertiary education Percentage, by age group % year-olds year-olds Korea Canada Japan Denmark England/N. Ireland (UK) Cyprus¹ Poland Ireland Finland Flanders (Belgium) Estonia Norway Australia Average United States Netherlands France Sweden Spain Germany Czech Republic Slovak Republic Italy Austria 1. See notes at the end of this chapter. Countries are ranked in descending order of the percentage of year-olds with tertiary education. Source: Survey of Adult Skills (PIAAC) (2012), Table B2.2 in Annex B. OECD Skills Outlook 2013

5 Distribution of Educational Attainment of the U.S. Workforce, : So Low in 1915! Goldin and Katz 2008

6 College Share of U.S. Hours Worked, College share of hours worked (%) Autor 2014

7 Indexed Real Full-Time Wages in U.S. by Sex and Education, Changes in real wage levels of full-time U.S. workers by sex and education, Real weekly earnings relative to 1963 (men) A Real weekly earnings relative to 1963 (women) B Some college > Bachelor's degree Bachelor's degree High school dropout High school graduate Autor, 2014

8 Agenda 1 Some Motivating Figures 2 The Canonical Model 3 International Comparisons of Wage Inequality: Supply, Demand and Institutions

9 Building blocks The simplest framework for interpreting skill premia 1 Competitive supply-demand framework 2 Closed economy setting 3 Factors are paid their marginal products 4 Economy operates on its supply and demand curves This model is a workhorse... It s as common as livestock Can carry a big load Often a bit tired and overburdened

10 The CES Model: Setup Two types of workers, skilled and unskilled (or high and low education, college and non-college, etc.) Types are imperfect substitutes. Why is imperfect substitutability crucial? Suppose that there are L(t) unskilled workers and H(t) skilled workers supplying labor inelastically at time t. The production function for the aggregate economy takes the constant elasticity of substitution (CES) form: Y (t) = [(A l (t)l(t)) ρ + (A h (t)h(t)) ρ ] 1/ρ where ρ 1 [i.e., ρ (, 1)] Ignore capital for now and drop time subscripts

11 The CES Model Aggregate production function: Y (t) = [(A l (t)l(t)) ρ + (A h (t)h(t)) ρ ] 1/ρ where ρ 1 [i.e., ρ (, 1)] Elasticity of substitution is given by σ 1/(1 ρ), ρ (, 1) Reminder: σ is % in relative demand for low (high) skill workers per % in relative wage of high (low) skill workers.

12 The CES Model Aggregate production function Three cases Y (t) = [(A l (t)l(t)) ρ + (A h (t)h(t)) ρ ] 1/ρ 1 σ 0 (or ρ ): Skilled and unskilled workers are Leontief. Fixed proportions. Perfect complements 2 σ (or ρ 1): Skilled and unskilled workers are perfect substitutes. Changes in aggregate supplies affect the price of skill overall. Relative wage of skilled vs. unskilled (w H /w L ) is constant. 3 σ 1 (or ρ 0): Production function is Cobb Douglas, with fixed shares paid to each factor

13 The CES Model Aggregate production function Key distinction Y (t) = [(A l (t)l(t)) ρ + (A h (t)h(t)) ρ ] 1/ρ σ < 1: Gross complements. A reduction in supply of one input reduces demand for the other σ > 1: Gross substitutes. A reduction in supply of one input raises demand for the other

14 A More General Production Function with Skill-Replacing Technologies Y (t) = K α {(1 b (t)) [A l (t)l(t) + B l (t)] ρ + b (t) [A h (t)h(t) + B h (t)] ρ } (1 α)/ρ In prior setup, only factor augmenting technologies Here, B l, B h are directly skill-replacing technologies Intensive versus extensive technical changes b t a technology that shifts the allocation of tasks among factors A l, A h terms are intensive technical changes, augmenting without reallocating K is capital: enters in Hicks-neutral form above, no bearing on skill premium Note that if σ 1, the b (t) terms limit to the exponents in the Cobb-Douglas production function

15 The CES Model Three interpretations of this aggregate model 1 Only one good, skilled and unskilled workers are imperfect substitutes in its production 2 Two-good economy: Consumers have utility function [Y ρ l + Y ρ h ]1/ρ with elasticity of substitution σ = 1/ (1 ρ) Good Y h is produced with Y h = A h H Good Y l is produced with Y l = A l L 3 A mixture of these two where different sectors produce goods that are imperfect substitutes, and high and low education workers are employed in all sectors

16 Wage Setting Given competitive labor markets, wages are set according to marginal products and Two immediate results w L = Y L = Aρ l [Aρ l + A ρ h (H/L)ρ ] (1 ρ)/ρ w H = Y H = Aρ h [Aρ h + Aρ l (H/L) ρ ] (1 ρ)/ρ 1 First w H / (H/L) < 0. Why? 2 Second w L / (H/L) > 0. Why?

17 The CES Model Combining the wage equations to get skill premium π π = w H w L = ( Ah A l ) ρ ( ) (1 ρ) H = L ( Ah A l ) (σ 1)/σ ( ) 1/σ H L Taking logs Notice that ( ) σ 1 ln π = ln σ ( Ah A l ln π ln(h/l) = 1 σ < 0 ) 1 ( ) H σ ln L Relative demand curve for H vs. L is downward sloping (recall that σ 0) For given skill bias, A h /A l, an increase in relative supplies H/L lowers relative wages with elasticity σ (except when?)

18 The CES Model Seriously, WTF is σ? Aggregate production function is an abstraction Not intended to correspond to production function of any given firm Combines substitution in production and consumption across consumers, industries, firms, plants within firms, etc Would expect factors to be less substitutable at the firm level than at the aggregate level Where to aggregate production functions come from? See Jones 2005 QJE, Houthakker 1955 ReStud What are plausible values of σ? Surprising degree of consensus: σ [1, 2]

19 Technical change and the skill premium How does the skill premium respond to a shift in A h /A l? Differentiating ( ) σ 1 ln π = ln σ yields ( Ah A l ln ω ln(a h /A l ) = σ 1 σ, ) 1 ( ) H σ ln L Why would an increase in the productivity of more skilled workers, that is a rise in A h /A l, cause their wages to fall?

20 Summary of key relationships: Skill supplies An exogenous rise in H/L 1 The skill premium π = W H /W L falls 2 Wages of unskilled workers rise 3 Wages of skilled workers decrease 4 Average wages rise provided the skill premium is positive w = LW L + HW H L + H = [(A l) ρ + (A h H/L) ρ ] 1/ρ, 1 + H/L Increasing in H/L provided the skill premium is positive (π > 0 or A ρ h (H/L)ρ A ρ l > 0)

21 Summary of key relationships: Factor-biased technical change An increase in A h, holding A l and L/H constant 1 ω = W H /W L rises if σ > 1, falls if σ < 1, and is unchanged if σ = 1 2 Average wages rise if σ > 0. Why not if σ = 0? 3 Wages of L workers rise if σ <. Why not if σ =? 4 Both W H and W L rise if σ 1. Why not if σ < 1? General takeaway: It s hard for factor-augmenting technical change to lower wages (though of course π may rise)

22 The long term skill bias of technical change Key implication: As H/L increases, the skill premium (π) falls In every advanced country the supply of educated workers has risen dramatically in the past seven decades Yet relative wages of better educated workers have remained consistently above those of less educated U.S. college-educated share rose from 6.4 to 29.7 percent from 1940 to High school dropout share fell from 68 to 9 percent of the workforce Yet, the skill premium in 2000 (measured in a variety of ways) was at or above that of in 1940 (though not above that in 1915 If we believe this model at all, suggests that relative demand for skilled workers must have risen practically everywhere

23 Tinbergen: Education race Jan Tinbergen, 1975 The two preponderant forces at work are technological development, which made for a relative increase in demand and hence in the income ratio... and increased access to schooling, which made for a relative decrease. Translation Long term trend increases towards greater relative demand and greater supply of skilled workers Bursts of supply and/or technologically-induced demand accelerations/decelerations that cause demand to temporarily move out more rapidly than supply or vice versa in some eras.

24 Wages by Skill Group: (Katz-Murphy 1992) Katz and Murphy 1992

25 Katz-Murphy 92: Evolution of College Premium Katz and Murphy 1992

26 Bringing the model to the data Relative productivity of skilled workers ( ) σ 1 ln π = ln W h /W l = ln σ ( Ah A l ) 1 ( ) H σ ln L The technological parameter is σ 1 σ ln (A h/a l ) or simply (σ 1) ln (A h /A l ) since denominator just a scalar Must have increased considerably since 1939 (i.e., first representative data on skill supplies and wages) How much has (σ 1) ln (A h /A l ) increased? We can observe H/L and π = ln W h /W l If we knew σ, could infer ln (A h /A l ) This approach pioneered by Katz and Murphy 1992

27 If we wanted to estimate this model with time-series data Structural equation ln π = σ 1 σ ln ( Ah A l ) 1 ( ) H σ ln L Add time subscripts to everything except for σ ln π t = γ 0 + γ 1 t + γ 2 ln(h/l) t + e t. We observe (H/L) t and π t Unknowns are σ and (A h /A L ) t γ o is a constant, γ 1 gives the time trend on ( σ 1 σ ) ln(a ht/a Lt ), and ˆγ 2 is an estimate of 1/σ Identification assumptions: (1) ln(h/l) t is exogenous or quasi-fixed; (2) ln(a h /A L )/ t is approximately linear

28 Data to be Explained: Katz-Murphy 1992 Katz and Murphy 1992

29 Model Fit: ˆσ = (1/0.71) = 1.41 [R 2 = 0.52] log (w1/w2) = log (x1/x2) time + constant, (0.150) (0.007) Katz and Murphy 1992

30 Implied Demand Series: Alternative Values of σ Katz and Murphy 1992

31 Acemoglu-Autor Replication/Update: Supply Series!"#$%&'('! )*$%+&,' -.%+/' 01)' 2.3.' 4*%' &.%5"5#6' 7&.%6' 6$BBC7' "6' +.C+$C.3&2' $6"5#'.CC' B&%6*56'.#&6' 8:<:D' E/*' %&B*%3&2'/.F"5#'E*%G&2'.3'C&.63'*5&'E&&G'"5'3/&'&.%5"5#6'7&.%6H'&I+C$2"5#'3/*6&'"5'3/&'J"C"3.%7?'K/&'2.3.'.%&'6*%3&2'"53*' 6&I<&2$+.3"*5<&IB&%"&5+&'#%*$B6'*4'3E*'6&I&6'LJ.C&M4&J.C&NH'4"F&'&2$+.3"*5'#%*$B6'L/"#/'6+/**C'2%*B*$3H'/"#/'6+/**C' Acemoglu-Autor 2011

32 Acemoglu-Autor Replication/Update to 2008!"#$%&'('! &.+/' 7&.%' *5' 4*$%' &2$+.3"*5' 2$DD"&6' F/"#/' 6+/**C' 2%*G*$3E' 6*D&' +*CC&#&E' +*CC&#&' #%.2$.3&E' #%&.3&%' 3/.5' +*CC&#&HE'.' I$.%3"+'"5'&JG&%"&5+&E'"53&%.+3"*56'*4'3/&'&2$+.3"*5'2$DD"&6'.52'&JG&%"&5+&'I$.%3"+E'.52'3A*'%.+&'+.3&#*%"&6'FKC.+BE' 5*5;A/"3&' *3/&%H?' L/&' +*DG*6"3"*5;.2M$63&2' D&.5' C*#' A.#&' "6' 3/&' G%&2"+3&2' C*#' A.#&' &N.C$.3&2' Acemoglu-Autor 4*%' A/"3&6'.3' 3/&' 2011

33 Detrended Supply and Demand Series: !"#$%&'()'! 40&'%&7"3$/B7'5%+D'7&A/%/4&'EF*'%&#%&77"+67'+5'40&'%&B/4"G&'7$AAB8'/63'%&B/4"G&'C/#&'D&/7$%&7'+6'/',+674/64'/63'/'B"6&/%' 4"D&'4%&63?'! Acemoglu-Autor 2011

34 KM Model Fit , Out of Sample ! Acemoglu-Autor 2011

35 KM Model Fit: Regression Version, Table 8 Regression models for the college/high school log wage gap, CLG/HS relative supply (0.128) Time (0.005) (1) (2) (3) (4) (5) (0.043) (0.001) (0.066) (0.002) Time X post (0.002) (0.112) (0.006) Time 2 / (0.006) (0.094) (0.006) (0.012) Time 3 / (0.002) Constant (0.134) (0.039) (0.066) (0.122) Observations (0.103) R-squared Source: March CPS data for earnings years See notes to Figs 2 and 19. Acemoglu-Autor 2011

36 KM Fit: in Sample, using Quadratic Cheat College versus High School Wage Gap (Percent) Measured Gap Predicted by Supply Demand Model Autor 2014

37 The U.S. Return to Education in the Longer Run Actual values for college wage premium Predicted college wage premium, col. (2) Predicted wage premium, col. (3) Goldin and Katz, 2007

38 The U.S. College/High-School and High-School/Dropout Wage Premiums over the Long Run Figure 1 College Graduate and High School Graduate Wage Premiums: 1915 to College graduate wage premium High school graduate wage premium Sources and Notes: Goldin and Katz 2008 College Graduate Wage Premium: The plotted series is based on the log college/high school

39 Models for the High-School/Dropout Wage Premium, Table 4 Determinants of the High School Wage Premium: 1915 to 2005 (1) (2) (3) (4) (5) (High school/dropout) supply (0.059) (0.039) (0.039) (0.071) (0.137) (High school/dropout) supply post (0.054) (High school/dropout) supply time ( ) Time ( ) ( ) ( ) (0.0037) (0.0100) Time post (0.0011) (0.0029) Time post (0.0006) (0.0006) Time post ( ) (0.0026) (0.0026) (0.0029) 1949 Dummy (0.0192) Time (0.0012) Time (0.025) Time 4 10, (0.0015) Constant (0.118) (0.078) (0.077) (0.142) (0.271) R Number of observations

40 Krussell, Ohanian, Rios-Rull, and Violante, 2000: Declining Log Relative Price of Equipment Capital, Log rel. price of equip. capital Post-1974 trend Pre-1974 trend.1 Log relative price of equipment capital year Figure 6. Behavior of the Log Relative Price of Equipment Capital, Krussell, Ohanian, Rios-Rull and Violante, 2000 (reprinted in Acemoglu 2002)

41 KORRV 2000: An Alternative Explanation, Declining Log Relative Price of Equipment Capital, G (k st, k et, L t, H t ) = k α st [βl δ t + (1 β) (λk ρ et + (1 λ) H ρ t ) δ/ρ] (1 α)/δ k st is structures capital, k et is equipment capital α is structure share of output (note: Cobb-Douglas) β is the extensive margin technological parameter σ e = 1/ (1 ρ) is elasticity btwn H labor and equipment capital k e σ u = 1/ (1 δ) is elasticity btwn H + K e aggregate and L Key condition: σ u > σ e If elasticity btwn H + K e vs. L greater than elasticity btwn K e and H, then K e is a relative complement to H. σ u > σ e implies equipment-skill complementarity

42 Estimation of K-S Complementarity Model (KORRV 2000) Krussell, Ohanian, Rios-Rull and Violante, 2000

43 Does this Chart Look Familiar? Katz and Murphy 1992 Krussell, Ohanian, Rios-Rull and Violante, 2000

44 Equipment Prices or Time Trend? TABLE 2 THE EFFECT OF THE RELATIVE PRICE OF EQUIPMENT ON SKILLED PREMIA Dependent variable is log college premium Relative supply (0.053) Time (0.002) (1) (2) (3) (4) (5) (0.037) Log relative price (0.024) (0.068) Relative price (0.086) (0.100) (0.007) (0.084) (0.054) (0.005) (0.167) Adjusted R Note: This table reports the regression of the log college premium on a linear time trend, the log relative supply of skilled workers and various measures of the relative price of equipment capital. For comparability, all data taken from Krusell et al. (2000). Acemoglu 2002

45 Agenda 1 Some Motivating Figures 2 The Canonical Model 3 International Comparisons of Wage Inequality: Supply, Demand and Institutions

46 Cross-National Differences in Estimated Wage Returns to PIACC (2012) Skills Figure 2. The return to skill, United States and other PIAAC countries Notes: The figure shows the coefficient on skill from a regression of log hourly wages (including bonuses) for wage and salary earners (in PPP corrected USD) on standardized numeracy scores and a quartic of experience. 3. The importance of skills: Evidence from wage simulations Broecke, Quintini and Vandeweyer 2016 In this section, we estimate the extent to which higher wage inequality in the United States is associated with differences in: (i) skills endowments; and (ii) skills prices. Our method differs from those used in the

47 Abstract: Blau and Kahn, JPE 1996

48 Does More School Equal More Skill? Leuven, Oosterbeek and van Ophem 2004

49 IALS data used by Leuven, Oosterbeek and van Ophem Prose literacy the knowledge and skills needed to understand and use information from texts including editorials, news stories, poems and fiction, Document literacy the knowledge and skills required to locate and use information contained in various formats, including job applications, payroll forms, transportation schedules, maps, tables and graphics; and Quantitative literacy or numeracy the knowledge and skills required to apply arithmetic operations, either alone or sequentially, to numbers embedded in printed materials, such as balancing a checkbook, figuring out a tip, completing an order form or determining the interest on a loan from an advertisement.

50 A Cross-National Supply Demand Analysis: Supply Index Constructing a skill supply measure: s kj Choose a baseline country b, and group workers in all countries into three skill groups k ={low, medium, high} Use as cut-points the values in country b that break the skill distribution (proxied by IALS scores) into three even parts For each country j b, LOvO form a relative skill supply index of: s kj = ln (E kj /E kb ) where E kj, E kb are the shares of total labor input supplied by skill group k in countries j and b respectively (the latter being equal to 1 3 by construction)

51 in different-sized groups of low-, medium- and high-skilled workers in each one of these countries. For example, Table 3 shows that in Japan, 47.4% of the working age population is high-skilled according to this definition, but that in both Italy and Spain more than 50% is low-skilled. Skill Tercile Shares by Country Table 3. Proportion of high-, medium- and low-skilled individuals in the labor force, by country (in %) Country Low Medium High Australia Austria Canada Czech Republic Denmark England/N. Ireland (UK) Estonia Finland Flanders (B) France Germany Ireland Italy Japan Korea Netherlands Norway Poland Slovak Republic Spain Sweden United States The next step is to construct indices which measure how the demand and supply for each skill group in the United States compare to those in the other Broecke, PIAAC countries. Quintini More andspecifically, Vandeweyer build 2016 the supply index Supply s,x so that it measures the relative supply of skills group s in the United States compared to

52 Labor Force Skill Shares by Country: PIAAC Terciles 2012 Labor Composition By Country Proportion Spain Italy Ireland U.S. France Poland Korea England/N. Ireland (UK) Canada Estonia Low Australia Czech Republic Germany Austria Slovak Republic Denmark Norway Sweden High Flanders (B) Netherlands Finland Japan Broecke, Quintini and Vandeweyer (2015)

53 A Cross-National Supply Demand Analysis: Demand Index Demand index d kj : Let c ok be base emp share in country b in skill group κ in ind-occ cell o Industries: 1) Agriculture; 2) Mining, manufacturing, and construction; 3) Transportation, communications, and public utilities; 4) Trade; 5) Finance, insurance, real estate, and services; 6) Government Occupations: 1) Managers and professionals; 2) Clerical and sales workers; 3) Craft workers, operatives, laborers, and service workers ( ) d kj = ln c ok E oj E kb where E oj is the country j minus country b in emp share in industry-occupation o E kb is emp share of skill group k in country b (equal to 1 3 )

54 Estimating Equation Regressing rel. wage gap on rel. supply-demand gap: Define w kj as the mean relative wage of skill group k relative to a base skill group in country j LOvO estimate the following model for relative wages: (w kj w kb ) = α + β [(s kj d kj ) (s kb d kb )] + ε j In fact, they do this as a diff-in-diff Let equal the difference between two skill groups k (e.g., w Hj w Lj or w Hj w Mj ( w kj w kb ) = α + β [( s kj d kj ) ( s kb d kb )] + ε j What s the expected sign of β?

55 Leuven et al: Fit Using Years of Schooling Leuven, Oosterbeek and van Ophem, 2004

56 Leuven et al: Fit Using IALS Scores Leuven, Oosterbeek and van Ophem, 2004

57 Labor Force Skill Shares by Country: PIAAC Terciles 2012 Labor Composition By Country Proportion Spain Italy Ireland U.S. France Poland Korea England/N. Ireland (UK) Canada Estonia Low Australia Czech Republic Germany Austria Slovak Republic Denmark Norway Sweden High Flanders (B) Netherlands Finland Japan Broecke, Quintini and Vandeweyer (2015)

58 LOvO Type Analysis Using PIAAC 2012 Relative wage ratio (P90/P10) JP 1. Top versus bottom 2. Top versus middle 0.5 y = -0.27x y = -0.11x DK SE R² = 0.05 NO SE R² = FI NO FI BE CZ BE DK FR CZ AT AU AT FR 0.3 NL DE AU CA NL IT UK IE IT 0.2 ES UK IE ES SK CA PL SK PL DE 0.1 EE JP EE 0 KO Relative wage ratio (P90/P50) -0.1 KO Relative net supply high- versus low-skilled Relative net supply high- versus medium-skilled Relative wage ratio (P50/P10) 3. Middle versus bottom 4. All 0.5 y = 0.03x R² = SE FR FI 0.3 NO BE AT DK AU 0.2 CZ IEUK JP ES IT PL 0.1 SK NL CA 0 EE KO -0.1 DE Relative net supply medium- versus low-skilled Relative wage ratio (all observations) y = -0.14x R² = Relative net supply (all observations) Broecke, Quintini and Vandeweyer (2015)

59 Cross-Country Regression: 90/50 (relative to U.S.) Panel (ii) Dependent variable: P90/P50 (in logs, relative to US) (i) (ii) (iii) (iv) (v) (vii) (vii) Net supply of skills (high v. medium) ** * ** *** *** ** *** Statutory minimum wage (MW dummy) a * Level of minimum wage b x MW dummy Employment protection legislation c ** Union coverage *** *** Size of public sector d *** ** Generosity of unemployment benefits e *** Constant 0.170*** 0.263*** *** 0.073* N R² Adjusted R² Broecke, Quintini and Vandeweyer (2016)

60 Cross-Country Regression: 50/10 (relative to U.S.) Panel (iii) Dependent variable: P50/P10 (in logs, relative to US) (i) (ii) (iii) (iv) (v) (vii) (vii) Net supply of skills (medium v. low) Statutory minimum wage (MW dummy) a ** Level of minimum wage b x MW dummy ** Employment protection legislation c Union coverage *** * Size of public sector d *** Generosity of unemployment benefits e Constant 0.160*** ** N R² Adjusted R² Broecke, Quintini and Vandeweyer (2016)

61 Employment Rates of Top and Bottom Skill Terciles by Country: PIACC 2012 Employment Rate of Skilled Labor Proportion Employed Korea Slovak Republic Poland Czech Republic Italy France Ireland Japan Spain Flanders (B) Low Finland PIAAC average Austria Estonia England/N. Ireland (UK) Australia Sweden Denmark High Germany Canada Netherlands U.S. Norway Broecke, Quintini and Vandeweyer (2016)

62 Employment Rates by Skill Terciles: PIAAC 2012 Employment rate Low-skilled Medium-skilled High-skilled Australia Austria Canada Czech Republic Denmark England/N. Ireland (UK) Estonia Finland Flanders (B) France Germany Ireland Italy Japan Korea Netherlands Norway Poland Slovak Republic Spain Sweden United States PIAAC average Broecke, Quintini and Vandeweyer (2016)

63 Oscars Reveal Widening Gap Between Best, Worst Dressed