I. Labour Supply (The Decision to Work) A. Neo-classical Approach Plan

Fortin – Econ 560 Lecture 1A I. Labour Supply (The Decision to Work) A. Neo-classical Approach Plan 1. Basic Trends and Stylized Facts 2. Static Model a. Decision of whether to work or not (extensive margin) b. Decision of how many hours to work (intensive margin) 3. Comparative Statics 4. Estimating Labour Supply Functions and Elasticities (Traditional) Fortin – Econ 560 Lecture 1A 1. Basic Trends and Stylized Facts Statistics Canada, January 2005 E Employed (working, at work or not) LF Labor Force (working or actively seeking work) 16.1m P Population Aged 15 and Older (10 provinces) U Unemployed (Not employed, but looking for work) 17.3m 25.6m NLF Not in Labor Force (students, retired persons, household workers, etc.) 1.2m 8.3m Fortin – Econ 560 Lecture 1A Labour Force Concepts: • Labour Force = Employed + Unemployed o LF = E + U o Size of LF does not tell us about “intensity” of work • Labour Force Participation Rate o LFPR = LF/P o P = civilian adult population 16 years or older not in institutions • Employment: Population Ratio (percent of population that is employed) o EPR = E/P o Employed at work and not at work (e.g. maternity or sick leave) sometimes distinguished o • Unemployment Rate o UR = U/LF Fortin – Econ 560 Lecture 1A Fortin – Econ 560 Lecture 1A Fortin – Econ 560 Lecture 1A Source: Statistics Canada, LFS and U.S. BLS, March CPS Fortin – Econ 560 Lecture 1A Source: BLS, OOchart Fortin – Econ 560 Lecture 1A Female Labour Participation and per capita GDP Fortin – Econ 560 Lecture 1A Male Labour Participation and per capita GDP Source: Alesina, Glaeser and Sacerdote (2005) Figure 1 Annual Hours Worked Over Time OECD data. Annual hours per employed person. Annual hours are equivalent to 52*usual weekly hours minus holidays, vacations, sick leave. 2200 2000 US 1800 Italy 1600 France Germany 1400 1200 1000 19 60 19 62 19 64 19 66 19 68 19 72 19 70 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 Source: Kuhn and Lozano (2008) Long Work Hours among U.S. Men Table 1 Fraction of Men Usually Working Long ( ≥ 50) Hours 1979 All men Full-time men ( ≥ 30 hours) Salaried Hourly Ages 25–34 Ages 35–44 Ages 45–54 Ages 55–64 Less than high school High school graduates Some college College graduate Average hourly earnings quintile: 1 (highest wage) 2 3 4 5 (lowest wage) .161 .164 .244 .086 .171 .185 .154 .128 .124 .137 .166 .240 .151 .137 .132 .176 .217 1989 .193 .199 .312 .094 .197 .221 .193 .154 .121 .155 .190 .303 .243 .193 .176 .202 .186 2000 .190 .207 .320 .105 .196 .222 .216 .178 .116 .149 .194 .312 .297 .214 .199 .184 .151 317 2006 .178 .195 .301 .096 .167 .208 .213 .191 .099 .153 .182 .278 .268 .219 .189 .172 .133 Note.—Sample is employed men who are not self-employed, ages 25–64. Source: Alesina, Glaeser and Sacerdote (2005) Figure 6 Weekly Hours Per Person Versus Marginal Tax Rate OECD data. Y axis shows total weekly hours worked per persons 15-64. 30 Iceland Weekly Hours Per Person 20 25 New Zealand United States Canada Austria Mexico Ireland United Kingdom Greece Norway Czech Republic Denmark Slovak Republic Sweden Finland Germany Belgium Spain Portugal France Netherlands Italy 15 .3 .4 .5 Marginal Tax Rate .6 .7 Fortin – Econ 560 Lecture 1A In the United States, more women than men work part-time, but spend more time on household work Source: BLS, TED: The Editor's Desk Fortin – Econ 560 Lecture 1A 2.Static Model • In neo-classical theory, the individuals’ decisions of whether or not participate in the labour market and of how many hours to work each week (and weeks per year) are modeled in static framework of consumption-leisure choice. - “leisure” is a terminology used to mean “non-labour market work”, - “individual” masked the fact that labour supply decisions are often “family” decisions • From a policy point of view, this model has been very important to evaluate the potentially negative effects on labour supply of tax and transfer programs. • From a labour econometrics viewpoint, the analysis will provide us with a classic example of correction for selection biases. • The estimation of “the” elasticity of labour supply (%Δhrs/%Δwage) has long been an important quest for labour econometricians bearing in mind that 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 - An identification strategy describes the manner in which a researcher uses observational data to approximate a real experiment, that is a randomized trial. Fortin – Econ 560 Lecture 1A • The standard static, within-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) where C, L, and X are within-period consumption, leisure hours and individual attributes. • Then utility is assumed to be maximized subject to the budget constraint p ⋅C + w ⋅ L = Y + w ⋅T (2) where w is the hourly wage rate, Y is the non-labour income, and T = H + L is the total time available, where H is the number of hours of work. - M = Y + w ⋅ T is sometimes called full-income. - T , Y , w are exogenous in this model, - H ( L), C are endogenous, and X are preference-shifters. • The consumer may choose his/her hours of work H (L) by selecting across employers offering different packages of hours of work and wages. Fortin – Econ 560 Lecture 1A Source: UCL Fortin – Econ 560 Lecture 1A • It is important to distinguish the characteristics of the interior solution for hours of work , H > 0, ( L < T ) from the corner solution, H = 0( L = T ). • In the case of an interior solution, the individual choose to participate in the labour market L* < T , the first-order conditions equates the marginal rate of substitution ( MRSCL ) to the real wage rate U L (C , L, X ) U C (C , L, X ) * L = w p (3) • In the case of the corner solution, L* = T , w wR U L (C , L, X ) ≤ = p p U C (C , L, X ) L =0 where the reservation wage, wR , is equal to the negative of MRS CL of working hours for commodities at h = 0( L = T ). (4) Source: Benjamin, Gunderson and Riddell (1998) Fortin – Econ 560 Lecture 1A 3. Comparative Statics • The comparative statics of the income and substitution effects are best illustrated in a diagram of consumption-leisure choice. The general effects are the following. • An increase in non-labour income: An increase in non-labour income will shift the budget line outwards without changing the slope of the line: this is a pure income effect. The effect on the optimal amount of leisure consumed or hours worked can then be summarized as: - L will rise and H will fall if leisure is a normal good - L will fall and H will rise if leisure is an inferior good. • There are very strong reasons to believe that leisure is a normal good. Hence, it is likely that an increase in non-labour income will reduce hours of work. • An increase in the real hourly wage: An increase in the real hourly wage will pivot the budget line about the point where L=T making at the line steeper: here there are two 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 work fewer hours than before. - A substitution effect. An hour of work now buys more consumption than previously so that there is an incentive to increase consumption and reduce leisure. The opportunity cost of leisure rise, so hours of work will rise as a result. Source: Benjamin, Gunderson and Riddell (1998) Fortin – Econ 560 Lecture 1A Hence, the impact of a change in the wage on hours of work 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 work to zero as a result of an increase in the wage. • Recall that the Hicksian labour supply function is the solution to the expenditure minimization problem E ( w, p,U ) = min( p ⋅ C − wH ) subject to U (C , H ) ≥ U and correspond to the following uncompensated labour supply function H ( w, p, Y ) = H C ( w, p,U ) where Y = E ( w, p,U ) • Differentiating with respect to w ∂H ∂H ∂E ∂H C + = ∂w ∂Y ∂w ∂w − U Fortin – Econ 560 Lecture 1A • With the application of Sheppard Lemma and because H is a factor (reverses the sign), we get the Slutsky equation ∂H ∂H ∂H C = − + H ⋅ (6) ∂Y ∂w U ∂w substitution income effect effect where the overall effect of a wage change is decomposed into a substitution effect plus an income effect. w Y and the last term (income effect) by Multiplying the entire equation (6) by h Y C ∂H w ∂H w w ⋅ H ∂H Y ⋅ = + ⋅ ⋅ − ⋅ ∂w H ∂w U H ∂Y H Y • or in terms of elasticities C ε Hw = ε Hw + sL ⋅η HY (7) Fortin – Econ 560 Lecture 1A • Thus, there are three “sufficient statistics” of labour supply o the uncompensated wage elasticity: the % change in labour supply resulting from 1% change in the wage rate; sign is theoretically ambiguous as the positive substitution effect can sometimes be dominated by the negative income effect ε Hw > 0(< 0) ? o the compensated wage elasticity: : the % change in labour supply resulting from 1% change in the wage rate, after compensation for the wage change; sign is positive as it reflects a pure substitution effect C ε Hw > 0 o the income elasticity: the % change in labour supply resulting from 1% change in nonlabor income; sign is expected to be negative η HY < 0 • The simple consumption-leisure model can be extended (altered) to analyze labour supply under various conditions: o introducing the fixed (money) cost of working or time cost (commuting) of working o moonlighting (2nd job) and overtime pay o should a firm offer flexible hours (part-time) or hire only full-time workers o family labour supply (actually more than a simple extension) Source: Benjamin, Gunderson and Riddell (1998)3) Source: Borjas (1996) Fortin – Econ 560 Lecture 1A 4. Estimating Labour Supply Functions and Elasticities (Traditional) • Solving the FOC (3) or (4) yield the Marshallian demand functions C * = C ( w, Y , X ) and L* = L( w, Y , X ) or equivalently H * = H ( w, Y , X ) (5) • Some empirical studies seek to estimate forms of (5). However, depending on issues with the measurement of the wage, the income variable or the demographic controls, we may find ourselves estimating different types of substitution and income effects (i.e. the identification may be muddy). • We can proceed by assuming that the individuals have a direct utility function of the form: U (C , L) = C α Lβ , β /L w • The FOC will become α / C = p . Combining that equation with the budget constraint and using the fact that H * = 1 − L* , we obtain H * = 1 − γ − γ (Y / w) C * = (1 − γ )[( w + Y ) / p ] , where γ ≡ β /(α + β ) . • For example, see Abbott and Ashenfelter (1976) for the results of the estimation of a StoneGeary utility function. Source: Abbott and Ashenfelter (1976) Source: Abbott and Ashenfelter (1976) Fortin – Econ 560 Lecture 1A • Because of the difficulties in the choice of functional form for the utility function, many studies focus on estimating directly on the labour supply elasticities. • Suppose that we have individual data on H , w, p,Y , we can regress H i = β 0 + β1 wi Y + β2 i + εi pi pi (8) ˆ • Letting β j be the estimated value of β j , then ∂H ˆ β 1 will be the overall effect , ∂w ˆ β 2 H will be the income effect (evaluated at mean hours), ˆ ˆ β1 − β 2 H will be the substitution effect (evaluated at mean hours) ˆ Y β2 will be the income elasticity of labour supply. H • Note (8) can be a seen as a reduced-form of a labour supply function derived from an indirect utility function Fortin – Econ 560 Lecture 1A • We may control for individual attributes H i = β 0 + β1 wi Y + β2 i + β3 X i + εi pi pi (9) and we usually assume that the distribution of the ε i would be a normal distribution. • There have many studies estimating labour supply and income elasticities of labour supply, and there have been many meta-analysis of these studies (e.g. Hansson and Stuart (1985) Killingsworth (1983), Killingsworth and Heckman (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 women and 0.1 for men is a good reflection of what the literature reveals, although for the US it may be negative for men, due to the income effect. • Gunderson et al. (2007) suggest the following numbers Gender Both Sexes Men Women ε Hw 0.25 -0.10 0.80 C ε Hw η HY -0.15 -0.20 -0.10 0.40 0.10 0.90 34 MICHIEL EVERS, RUUD DE MOOIJ AND DANIEL VAN VUUREN 25 20 15 10 5 0 -0.3 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Figure 1 – Distribution of elasticities for men. Note: The solid line indicates the median of the empirical distribution, and the dashed lines indicate the 95% confidence interval around the mean of the distribution 7 6 5 4 3 2 1 0 -0.3 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Figure 2 – Distribution of elasticities for women. Note: The solid line indicates the median of the empirical distribution, and the dashed lines indicate the 95% confidence interval around the mean of the distribution. The lower border of the confidence interval is smaller than the smallest value on the horizontal axis (−0.7), and is thus not shown in the figure 340 Kuhn/Lozano Table 11 Percentage of Fortune 1000 Firms Surveyed in Which Over 20% of Employees Are Covered by Selected Reward Practices 1987 Individual incentives Work group or team incentives Gainsharing Profit sharing Employee stock ownership plan Stock option plan Nonmonetary recognition awards for performance Employee security 38 22 7 45 52 NA NA 34 1990 45 31 11 44 56 NA 68 27 1993 50 NA 16 44 63 30 73 19 1996 59 41 20 52 59 41 80 17 1999 67 48 24 55 63 49 82 14 Source.—Lawler et al. (2001, tables 5.1 and 5.3). Note.—Gainsharing is a bonus based on improvements in productivity, cost effectiveness, quality, or other performance indicator at a large organizational level such as a plant. Employee security is defined as corporation policy designed to prevent layoffs. NA p not available.