I. Labour Supply 1. Neo-classical Labour Supply 1. Basic Trends and Stylized Facts 2. Static Model a. Decision of hether to ork or not: Extensive Margin b. Decision of ho many hours to ork: Intensive margin 3. Comparative Statics 4. Estimation of Labour Supply Functions and Elasticities
1.1 Basic Trends and Stylized Facts Labour Force Concepts: P Population Aged 15 and Older 29.7m (10 provinces) Statistics Canada, November 2016 LF Labor Force (orking or actively seeking ork) 19.5m (LFPR=65.6%) NLF Not in Labor Force (students, retired persons, household orkers, etc.) 10.2m E Employed (orking, at ork or not) 18.2m (EPR=61.2%) U Unemployed (Not employed, but looking for ork) 1.33m (UR=6.8%) Labour Force = Employed + Unemployed o LF = E + U o Size of LF does not tell us about intensity of ork Labour Force Participation Rate o LFPR = LF/P o P = civilian adult population 16 years or older not in institutions
1.1 Basic Trends and Stylized Facts Statistics Canada, November 2016 E Labour Force Concepts: P Population Aged 15 and Older 29.7m (10 provinces) LF Labor Force (orking or actively seeking ork) 19.5m (LFPR=65.6%) NLF Not in Labor Force (students, retired persons, household orkers, etc.) 10.2m Employed (orking, at ork or not) 18.2m (EPR=61.2%) U Unemployed (Not employed, but looking for ork) 1.33m (UR=6.8%) Employment: Population Ratio (percent of population that is employed) o EPR = E/P o Employed at ork and not at ork (e.g. maternity or sick leave) sometimes distinguished Unemployment Rate o UR = U/LF
8.7 Source: Fortin (2016), LFS Public use files, 1976-2015 *Labour force participants include employed (at ork or on-leave) and unemployed individuals
Source: Blau and Kahn (2016)
1.9 U.S. Male LFP over the Life-Cycle.8.7.6.5.4.3.2 20 25 30 35 40 45 50 55 60 65 Age <=1920 1921-39 1940-45 1946-52 1953-58 1959-65 1966-75 1976-88 All Source: Fortin (2015), US-GSS 1976-2008
1.9 U.S. Female LFP over the Life-Cycle.8.7.6.5.4.3.2 20 25 30 35 40 45 50 55 60 65 Age <=1920 1921-39 1940-45 1946-52 1953-58 1959-65 1966-75 1976-88 All Source: Fortin (2015), US-GSS 1976-2008
Source: Fortin (2016), Canadian Public Use Labour Force Surveys, ages 25 to 64
Source: Fortin (2016), Canadian Public Use Labour Force Surveys, ages 25 to 64
1.2. Static Model In neo-classical theory, the individuals decisions of hether or not participate in the labour market and of ho many hours to ork each eek (and eeks per year) are modeled in static frameork of consumption-leisure choice. From a policy point of vie, this model has been very important to evaluate the potentially negative effects on labour supply of tax and transfer programs. From a labour econometrics viepoint, the analysis ill provide us ith a classic example of correction for selection biases.
The estimation of the elasticity of labour supply (% h/% ) has long been an important quest for labour econometricians - differences across studies in labour supply estimates may come not only from differences in sampling or data differences but also in the underlying modeling assumptions. The more modern approaches have emphasized clearly sources of identification coming from natural and quasi-natural experiments, as ell as field experiments. - An identification strategy describes the manner in hich a researcher uses observational data to approximate a real experiment, i.e. a randomized trial.
The standard static, ithin-period labour supply model is an application of the consumer s utility maximization problem over consumption and leisure. Assume that each individual has a quasi-concave utility function: U ( C, L; X ) (1) here C, L, and X are ithin-period consumption, leisure hours and individual attributes. Then utility is assumed to be maximized subject to the budget constraint p C + L = Y + T (2) here is the hourly age rate, Y is the non-labour income, and T = + L is the total time T available, here is the number of hours of ork. - M = Y + T is sometimes called full-income. - (L),C are endogenous, - T, Y, and the preference-shifters X are exogenous in this model.
The consumer may choose his/her hours of ork (L) by selecting across employers offering different packages of hours of ork and ages. FOC: * In the case of an interior solution, the individual choose to participate in the labour market L < the first-order conditions equates the marginal rate of substitution ( MRS CL ) to the real age rate T, U U ( C, L; X ) ( C, L; X ) L * = L C p (3) It is important to distinguish the characteristics of the interior solution for hours of ork, > 0,( L < T ) from the corner solution, = 0( L = T ).
In the case of the corner solution, here the reservation age, at = 0( L = T ). * L = T, R p p U = U L C ( C, L; X ) ( C, L; X ) R, is equal to the negative of L = T MRSL (4) of orking hours for commodities Solving the FOC (3) or (4) yield the Marshallian demand functions for goods and leisure * * C = C(, Y; X ) and L = L(, Y; X ) * or equivalently the labour supply function = (, Y; X ) (5)
1.3 Comparative Statics The comparative statics of the impact of changes in income, Y, and age rate,, of the labour * supply functions = (, Y; X ) are best illustrated in a diagram of consumption-leisure choice.
The general effects are the folloing. An increase in non-labour income: An increase in non-labour income ill shift the budget line outards ithout changing the slope of the line: this is a pure income effect. The effect on the optimal amount of leisure consumed or hours orked can then be summarized as: - L ill rise and ill fall if leisure is a normal good - L ill fall and ill rise if leisure is an inferior good. There are very strong reasons to believe that leisure is a normal good, e.g. those ho in the lottery (a large increase in non-labour income) are more likely to ork less afterards than before and certainly not the other ay round. ence, it is likely that an increase in non-labour income ill reduce hours of ork. An increase in the real hourly age: An increase in the real hourly age ill pivot the budget line about the point here L=T making at the line steeper: here there are to effects: - An income effect. Individuals are better-off than before so there is a positive income effect that, because leisure is a normal good, makes individuals ork feer hours than before.
- A substitution effect. An hour of ork no buys more consumption than previously so that there is an incentive to increase consumption and reduce leisure. ours of ork ill rise as a result. ence, the impact of a change in the age on hours of ork is theoretically ambiguous. They may rise or fall. There is one exception to this: for non-participants there is no income effect as they have no labour income so nobody can be induced to reduce hours of ork to zero as a result of an increase in the age.
o can e quantify these effects? Recall that the icksian labour supply function is the solution to the expenditure minimization problem ) min( ),, ( C p U p E = subject to U C U ), ( and correspond to the folloing uncompensated labour supply function ),, ( ),, ( U p Y p C = here ),, ( U p E Y = Differentiating ith respect to and applying the chain-rule = + U C E Y
With the application of Sheppard Lemma and because is a factor (reverses the sign), e get the Slutsky equation C = + U Y (6) substitution income effect effect here the overall effect of a age change is decomposed into a substitution effect plus an income effect. Y Multiplying the entire equation (6) by and the last term (income effect) by Y = C U + Y Y Y or in terms of elasticities ε s η C = ε + L Y (7)
Thus, there are three sufficient statistics of labour supply o the uncompensated age elasticity: the % change in labour supply resulting from 1% change in the age rate; sign is theoretically ambiguous as the positive substitution effect can sometimes be dominated by the negative income effect ε = > 0 ( < 0)? o the compensated age elasticity: : the % change in labour supply resulting from 1% change in the age rate, after compensation for the age change; sign is positive as it reflects a pure substitution effect C C ε = > 0 o the income elasticity: the % change in labour supply resulting from 1% change in non-labor income; sign is expected to be negative Y η Y = < 0 Y
The simple consumption-leisure model can be extended (altered) to analyze labour supply under various conditions: o introducing the fixed (money) cost of orking or time cost (commuting) of orking o moonlighting (2 nd job) and overtime pay o should a firm offer flexible hours (part-time) or hire only full-time orkers o family labour supply (actually more than a simple extension)
1.4 Estimating Labour Supply Functions and Elasticities We can proceed by assuming that the individuals have a direct utility function of the form: U ( C, L) = C α L β, L = C β / The FOC ill become α / * * fact that = 1 L, e obtain p. Combining that equation ith the budget constraint and using the * = 1 γ γ ( Y / ) * C = (1 γ )[( + Y ) / p], here γ β /( α + β ). For example, see Abbott and Ashenfelter (1976) for the results of the estimation of a Stone-Geary utility function. See Stern (1986) for the functional forms that can be linked to a utility function.
Because of the identification problems above, many studies focus directly on the age elasticity of the Marshallian supply function and on the associated utility-constant icksian age elasticity. Suppose that e have individual data on hours of ork ii, the age rate ii, and on non-labor income YY ii, e could estimate a simple OLS regression i Y β β β + ε Then the estimated effects, (setting pi=1 as numeraire) ˆ β ill be the overall (uncompensated) effect, 1 i i = 0 + 1 + 2 i pi p (8) i ˆ β 2 ill be the income effect,, (evaluated at mean hours) ˆ β 1 ˆ2 β ill be the substitution effect,, (evaluated at mean hours) Y βˆ 2 ill be the income elasticity of labour supply,, (evaluated at mean hours and income) YY
We may control for individual attributes i Yi i = β 0 + β1 + β2 + β3x i + ε i p p (9) i and e usually assume that the distribution of the ε i ould be a normal distribution. i There have been many studies estimating labour supply and income elasticities of labour supply, and there have been many meta-analysis of these studies (e.g. ansson and Stuart (1985) Killingsorth (1983), Killingsorth and eckman (1986), Pencavel (1986), and Evers, de Mooij and van Vuuren (2008). Evers, de Mooij and van Vuuren (2008) conclude that an uncompensated elasticity of 0.5 for omen and 0.1 for men is a good reflection of hat the literature reveals, although for the US it may be negative for men, due to the income effect. o For male orkers, small age effects o For female orkers, much larger elasticities ith larger variations across studies and declining over time as omen have become more attached to the labour market
Bargain, Orsini and Peichl (2012) perform an extensive cross-country study of 17 European countries plus the US, Argue for genuine differences across countries not necessarily linked to differences in tax code o the extensive (participation) margin dominates the intensive (hours) margin o for singles, this leads to larger labor supply responses in lo-income groups o income elasticities are extremely small everyhere.
the results for cross-age elasticities in couples are opposed beteen regions, consistent ith complementarity in spouses leisure in the US versus substitution in spouses household production in Europe. Basic readings: Borjas, George J. Labor Economics. (Boston, Mass.; London: Irin/McGra-ill, 2012) sixth edition Chapter 2. pp.1-64 (see on-line papers on course eb-site)