1. Problems with the OLS Estimation of Labour Supply Functions

Transcription

1 Fortin Econ 561 Lecture 1B I. Labour Supply 1. Problems with the OLS Estimation of Labour Supply Functions 1. Econometric Issues 2. Extensive vs. intensive margin responses 3. Non-hours responses 2. Using Tax and Transfer Programs to Estimate Labour Supply 1. Field Experiments and Randomized Trials 2. Tax (and Transfer) Reforms

2 Fortin Econ 561 Lecture 1B 2.1 Problems with the OLS Estimation of Labour Supply Functions 1) Econometric issues [potential solutions] a) Unobserved heterogeneity/endogeneity of wage rate [tax instruments] b) Measurement error in wages and division bias [tax and other instruments] c) Selection into labor force/unobserved wage rate for non-labour market participants [selection models] d) Endogenous tax rates [non-linear budget set methods] 2) Extensive vs. intensive margin responses With fixed costs of work, individuals may jump from non-participation to part time or full time work, this requires discrete choice models of participation 3) Non-hours responses or non-wage responses Productivity responses beyond the simple labour supply model Workers may work longer hours to get promotion Focus on subgroups of workers for whom hours are better measured or more flexible, e.g. taxi drivers, courriers

3 Source: Mroz (1987)

4 Source: Mroz (1987) TABLE IV CHOICE OF BASELINE SPECIFICATION (Standard Errors in Parentheses. Common Instrument Sets: B, C, 1. Estimation Method: Two-Stage Least Squares.) Nonwife Young Older Addtitional Instruments and Comments In(w,,) Income/tODD Children Children (R 2 : R 2 in reduced form wage equation) In( w w ), OLS, R 2 = 1.0 (81) (3.1) (131) (29) E, R 2 =.17 (461) (4.6) (182) (49) E, F2, R 2 =.18 (312) (3.8) (155) (39) E, F3, R 2 =.21 (217) (3.6) (147) (36) E, F3, H3, R 2 =.23 (171) (3.4) (138) (33) E, F4, R 2 =.22 (197) (3.5) (145) (35) F2, R 2 =.15 (355) (3.5) (138) (33) F3, R 2 =.18 (220) (3.3) (131) (30) F3, H3, R 2 =.20 (174) (3.3) (129) (29) F4, R 2 =.19 (201) (3.2) (130) (30) 7 All standard errors reported in this study are corrected for arbitrary forms of heteroscedasticity. None of the tables report the intercept or the coefficients on age and education in the labor supply equation. See Mroz (1984, Appendix 2), for several estimates of the complete labor supply function and reduced form wage equation.

5 Source: Borjas (1980) Communications TABLE 3 WAGE ELASTICITIES, STRAIGHT-TIME SAMPLE Dependent = ln(hu) Dependent = ln(hw) Step ln(e/hu) ln(eihw) ln(eihu) ln(e/hw) (.95) (3.38) (3.05) (-.70) (.96) (3.40) (3.14) (-.59) (- 1.10) (1.62) (1.66) (-2.55) (-1.97) (.92) (.56) (-3.68) (-2.37) (.63) (.09) (-4.30) (-1.18) (1.86) (.67) (-3.98) Note: Step 1 regresses hours on wages. Step 2 adds nonwage income. Step 3 adds time remaining in the labor force, years of experience, number of children, and whether job information refers to current or last (if not currently working) job. Step 4 adds health and marital status. Step 5 adds education. Step 6 adds 11 one-digit industry dummies. t-ratios in parentheses, NLS 71 (Mature Men)

6 Source: Barrett and Hammermesh (2016) Table 2. Labor Supply Elasticities, Hourly Paid Women, and Men, CPS/ATUS * Dep. Var.: Usual hours ATUS Total ATUS Working WOMEN (h CPS ) (h A1 ) (h A2 ) Married (N = 3925) (0.0137) (0.0212) (0.0221) R t-statistic: α CPS = α A Unmarried (N = 4262) (0.0156) (0.0221) (0.0228) R t-statistic: α CPS = α A MEN Married (N = 3840) (0.0094) (0.0188) (0.0199) R t-statistic: α CPS = α A Unmarried (N = 3086) (0.0156) (0.0216) (0.0232) Adj. R t-statistic: α CPS = α A *The equations also include a quadratic in age, indicators of race and ethnicity, and indicators for day of week, state and year.

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8 Fortin Econ 561 Lecture 1B Issues: Desired hours of nonparticipant not observed Wage of non-participant not observed Endogeneity of wage rate/ Selection bias Estimation Procedure First-generation studies Procedure I Set to zero Use imputed wages Use predicted wage OLS Procedure II Use only workers Use only workers Use predicted wage OLS Second-generation studies Procedure III Use Tobit Use imputed wages Use predicted wage Tobit on hours Procedure IV Set to zero Use only workers Use reduced form OLS Procedure V Use Tobit Use predicted wage with selection correction from Tobit Tobit on hours and OLS on wages Procedure VI Joint ML of hours and wages Procedure VII Estimate LFP with Probit Use only workers with selection correction Use reduced form for wages with selection correction Heckit Procedure VIII Estimate LFP with Probit Use only workers with selection correction Use predicted wage from wage equation with selection correction Heckit

9 Source: Manning E333e Figure 6 A scatterplot of desired hours against x

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12 Source: Manning E330 Appendix B The Truncated Normal Distribution Some Preliminaries Suppose Z is a standard normal random variable i.e. Z N(0,1). Its density function is given by: 1 φ(z) =.e 2π 1 - z 2 2 (68) Let us denote the distribution function by Φ(z). For future use it is helpful to note that: z z φ (z) = -. e 2 = - z φ(z) (69) 2π The Truncated Standard Normal Distribution Now suppose that we know that z z 0 so that the distribution is truncated at z 0. Denote by f(z) the truncated density of z. We must have that: φ(z) f(z) =, z z 1- Φ( z0 ) 0 (70) We are interested in E(z z z 0 ). This is given by: z0 z0 0 E(z z ) = zf(z)dz = = = = z 0 z 0 z φ(z)dz - φ (z)dz - φ( )+ φ( z ) φ( z0) 1- Φ( z0) 1- Φ( z0) 1- Φ( z0) 1- Φ( z0) (71) It is simple to check that this is increasing in z 0. Now suppose that ε N(µ,σ 2 ). Suppose that ε ε 0. We can show that: ε 0 - µ σφ σ E( ε ε ε 0 ) = µ µ 1- ε Φ σ (72)

13 184 AmerICAN EconomIC JourNAL: EConomIC policy AUgUST 2010 Panel A. Indifference curves and bunching Individual L indifference curve Individual H indifference curves After-tax income c = z T(z) Slope 1 t Slope 1 t dt Individual L chooses z* before and after reform Individual H chooses z*+ dz* before and z* after reform dz*/z* = e dt/(1 t) with e compensated elasticity Source: Saez (2010), p. 184 z* z*+ dz* Before tax income z

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18 Source: Borjas (2012)

19 Source: Borjas (2012)

20 0 C0 0)V 0 ~~~~~~?t0* cd (n M CZ.00) Lr V I " o 0.0. ~~~~V V *0 0-~~~0 qj-tl -o~~~~~~~~~0 )000~~ ~~ 0 0 ~~~~z 0 U 0 Oo U o V ~ ~.. Ln.-I:$ 0 U ' U >* U~ f &..~~~~ ~ ~ o U 0 * V00V oo - ~~ ~~ Q?.Y ~~~.~~~09 LtoUoB a,- - V~~~~~~~~~~~~~~*-,zC 0~~~~~~~~~~~~~~ > U. Lr) VI~~~~~~~~~ C M0 M V C VI 0~~~~~~~~~ CZ M 0 X CN 00 V U C) 'C.. '~~~., 0 U VVV U 3 u o0 0 0 U '~~. V 000..Oo -01-en0 4.o ~ ~ ~ ~~ 0O V V II~~~~~~~~~~~0~~14 oe Source: Hum and Simpson (1993) V000 Zo~~~-oV S -0iiM 0~~~~~ 00 ~ ~ ~ ~ ~ ~ ~ ~. V - V 0 00~~~~0e

21 Source: Moffit (2003) Other Possible Negative (2) and (3) Labour Supply Responses Income F 3 D 2 D 1 C Hours worked A Figure 2. Effect of a Negative Income Tax on Labor Supply

22 Source: Hum and Simpson (1993) Table 2 Nonstructural Labor-Supply Response Estimates from the Five Experiments (in Annual Hours Worked) Single Female Husbands Wives Heads Experiment/Author Estimates % Estimates % Estimates % New Jersey: Keely (1981) Robins (1985) Burtless (1986) Rural: Keeley (1981)? 9? 29*... Robins (1985) Burtless (1986) Seattle-Denver: a Keeley (1981) * * * Robins (1985) * * * Burtless (1986) Gary: Keeley (1981) Robins (1985) Burtless (1986) All U.S. experiments: Robins (1985) Burtless (1986) Mincome: Appendix b a 3-year experiment only. bincludes single individuals (21% of all men in sample). * Statistical significance at the 5% level or lower. In some cases, statistical significance is not reported or is mixed (the result is an average of several results, some of which are significant). Burtless (1986) does not report statistical significance.

23 S282 Hum/Simpson Table 3 Structural Labor-Supply Response Estimates from the Five Experiments Substitution Income Experiment/Group Elasticity Elasticity Husbands: New Jersey Rural Seattle-Denver Gary All United States Mincome Wives: New Jersey Rural Seattle-Denver Gary All United States Mincome Single female heads: New Jersey Rural Seattle-Denver Gary All United States Mincome SOURCES.-Robins (1985) for the U.S. experiments; the Appendix (table A3) for the Canadian experiment.

24 Source: Card and Hyslop (2005) TABLE II CHARACTERISTICS OF SSP EXPERIMENTAL SAMPLEa Program Group, by SSP Eligibility Status Controls Programs Eligible Ineligible In British Columbia (%) Male (%) Mean age Age 25 or less (%) Never married (%) Average number kids < Average number kids Immigrant (%) Grew up with two parents (%) High school graduate (%) Means years work exp Working at random assignment (%) Months on IA last 3 years IA continuously last 3 years (%) Percent on IA by months since random assignment Month Month Month Month Month Month Month Month Number of observations 2,786 2, ,874 asample includes observations in the SSP Recipient Experiment who were on IA in the month of random assignment and the previous month. Eligible program group is the subset who received at least one SSP subsidy payment.

25 Source: Card and Hyslop (2005) =~~c ;^^^^~ -- Control ~ Group? Program Group v?c;1~~~~~~~~ -*- Difference Months Since Random Assignment FIGURE 3.-Monthly employment rates.

26 Source: Card and Hyslop (2005) TABLE III SUMMARY OF LABOR MARKET OUTCOMES 52 MONTHS AFTER RANDOM ASSIGNMENTa Both British New Provinces Columbia Brunswick Control group outcomes in month 52 Percent employed (1.02) (1.41) (1.48) Percent with reported wage (1.01) (1.38) (1.46) Mean log hourly wage (0.01) (0.02) (0.02) Cumulative employment since random assignment (in years) (0.03) (0.04) (0.05) Program group outcomes in month 52 Percent employed Percent with reported wage (1.00) (1.36) (1.47) (0.99) (1.34) (1.47) Mean log hourly wage (0.01) (0.02) (0.02) Cumulative employment since random assignment (in years) (0.03) (0.04) (0.05) Difference: Program group - Control group Percent employed Percent with reported wage (1.43) (1.96) (2.08) Mean log hourly wage (1.41) (1.92) (2.07) Cumulative employment since random assignment (in years) (0.04) (0.06) (0.07) (0.02) 0.28 (0.03) 0.22 (0.02) 0.33 Continues the estimated marginal wage is roughly constant over the entire 52-month period suggests that any impact on wages of those who would have worked regardless of SSP is small. 23Wages for the labor market as a whole are 20-30% higher in Vancouver than in the areas included in the New Brunswick sample. The minimum wage varies by province and is typically 25% higher in British Columbia than New Brunswick; e.g., $5.00 per hour in New Brunswick in 1993 versus $6.00 per hour in British Columbia.

27 Source: Card and Hyslop (2005) EFFECTS OF A SUBSIDY FOR WELFARE-LEAVERS 1739 TABLE III-Continued Both British New Provinces Columbia Brunswick Regression models for outcomes in month 52 Reduced form equations (a) Program group effect in model for log wage (0.02) (0.03) (0.02) (b) Program group effect in model for cumulative work (fitted to subsample with reported wage) (0.05) (0.08) (0.07) Effect of cumulative work on wage in month 52 (c) Estimated by OLS (0.007) (0.012) (0.009) (d) Estimated by IV, using program group status as instrument (0.045) (0.099) (0.046) astandard errors in parentheses. The sample includes 2,339 in the control group and 2,418 in the program group with complete employment data for 52 months after random assignment. Regression models in the bottom panel are fitted to subgroups of 895 control group members and 954 program group members with reported wage in month 52. Other covariates in regression models include year dummies, education, experience, high school completion dummy, immigrant status, age, indicators for working or looking for work at random assignment, and indicators for physical or emotional problems that limit work (measured at random assignment). See text.

28 Source: Zabel et al. (2004) Figure 1: Median Wages for British Columbia and New Brunswick Program and Control Groups From Month 2 to Month Median Wage BC Control Group BC Program Group NB Control Group NB Program Group Month Since Random Assignment As Table 1 clearly indicates, program group members could qualify for the earnings supplement if they found a full-time job within one calendar year of the point of random assignment. 8 From Figure 1, we see that the median wages of the program group actually fell during that first year as program group members found full-time jobs to qualify for the supplement. After this, there is a slow catch-up of the wages of the program group relative to the control group. Thus, between the beginning and the end of the 51-month follow-up period, Figure 1 provides no evidence of relative full-time wage progression for the program group in either British Columbia or New Brunswick.

29 Source: Riddell and Riddell (2006) Figure 1: Employment Rates, High School Upgrading Sample Upgraders Non-upgraders Month Figure 2: Hourly Wages, High School Upgrading Sample Upgraders Non-upgraders Month

30 Employment Rate Figure 1a: 1987 Tax Holiday in Iceland 95% 90% 85% 80% 75% Year Empirical (Bianchi et al. 2001)

31 The interaction of WFTC with other benefits in the UK Example: Budget Constraint for Single Parent Source: Blundell (2015)

32 Universally Available Tax and Transfer Benefits (US Single Parent with Two Children, 2008) Source: Urban Institute (NTJ, Dec 2012). Notes: Value of tax and value transfer benefits for a single parent with two children.

33 Source: Federal Govt

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35 Differences-in-Differences Before reform After reform Treated Control Step 1: Simple Difference Outcome (example): LFP (female labor force participation) Two groups: Treatment group (T) which faces a change and control group (C) which does not Simple Difference estimate: D = LFP T - LFP C captures treatment effect, if in the absence of treatment, LFP equal across 2 groups Note: this assumption always holds when T and C status is randomly assigned. To test for this assumption, we can compare LFP before the treatment: D B = LFP B T LFP B c.

36 Differences-in-Differences Step 2: Difference-in-Difference (DD) If D B 0, we can estimate DD: DD = D A D B = [LFP A T LFP A c ] [LFP B T LFP B c ] where A = after reform, B = before reform DD is unbiased if the parallel trend assumption holds: absent the treatment, the difference across T and C would have stayed the same before and after

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39 Source: Eissa and Hoynes (2008) Figure 8 Stylized EITC Budget Constraint After Tax Income D Phase-out w(1-τ p ) C Flat w No EITC w B Phase-in w(1+τ s ) A Hours of Work 0

40 EITC Amount as a Function of Earnings EITC Amount ($) Subsidy: 40% Subsidy: 34% Phase-out tax: 16% Married, 2+ kids Single, 2+ kids Married, 1 kid Single, 1 kid No kids Phase-out tax: 21% Source: Federal Govt Earnings ($)

41 Explaining EIC: 4 steps 10,000 4, Fill in earnings, EIC amount 4.Take-home Message increasing 2. Explain and dot graph 3. Table Source: Chetty and Saez (2009)

42 Vol. 2 No. 3 saez: do taxpayers bunch at kink points? 191 Panel A. One child 5,000 Earnings density ($500 bins) Density EIC Amount 4,000 3,000 2,000 1,000 EIC amount (2008 $) 0 Source: Saez (2010), p ,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 Earnings (2008 $) B. Two children or more 5,000 Density EIC Amount y ($500 bins) 4,000 3,000 ount ($)

43 192 American Economic Journal: economic policy AUgust 2010 Panel A. One child 5,000 Earnings density Source: Saez (2010), p. 192 density Wage earners Self-employed 4,000 EIC amount 3,000 2,000 1, ,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 Panel B. Two or more children Earnings (2008 $) Wage earners Self-employed EIC amount 5,000 4,000 3,000 unt ($) EIC amount ($)

44 Source: Eissa and Liebman (1996), p. 631

45 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o a'booz.. 0. O O o C) A O0O O O O O C O l ) 0 t C 0 0 C 0 e- q O cq c O CO O ~~~~~C o o :=.0 z 0 00 O O C) C)~~~~~~~~~0 >z D O O o o ~ ~~~~~~~~~~~~o ~ ~ oto ~ ~ ~ O '-i ~~~~~~~~~~~~~~~~0 0~~~~~~~~~~~~~~~~ 0 ' z OO C0 oo C CO 10 o0 > X t > H O 0 ; O O O O O 0 Ot- m O 0 ; 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' X 4 l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 4~~~~~~~~~~~~~~ C> o ou O 0? U 0 0 E* Cz CS s 10 H :H^A 04' ~ 0 '- co 'm '-4 c 0 0 Q~~~~ o ow O~~~~~~~~~~O Source: Eissa and Liebman (1996) - oc 0 0 C 0 0~~~~~ ~~ 0 0-' 0 0~ 0

46 I Source: Blundell and Hoynes (2004) Has In-Work Benefit Reform Helped the Labor Market? E tnm 0 v g 2000 El 0 m 1500 i c E n 500 Maximum EITC Difference,---.,, Difference I.- Employment Rate d L P) 5 E W c I g Year Fig Maximum EITC and difference in annual employment rates (comparison: single women with children to single women without children) Source; Liebman (1998) figure 6. Notes; Updated through 1998 using unpublished data from Liebman. The employment rate figure is based on a CPS sample of single women aged sixteen-forty-five who are not disabled or in school. Employment rate difference is the difference between the annual employment rate of single women with children and the annual employment rate of single women without children.

47 A. Top 1% Income Share and Marginal Tax Rate 60% 18% 50% 16% 14% Top 1% Marginal Tax Rate 40% 30% 20% 10% Top 1% Marginal Tax Rate Top 1% Income Share 12% 10% 8% 6% 4% 2% 0% Top 1% Income Share 0% Source: Saez (2004) B. Next 9% Income Share and Marginal Tax Rate

48 US Top 0.01% Income Share and MTR (Piketty-Saez and Landais) 100% 5.0% 90% Top 0.01% MTR 4.5% Top.01% MTR (Federal Income Tax) 80% 70% 60% 50% 40% 30% 20% 10% Top 0.01% Share 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0% Top 0.01% Income Share 0.0% log(share)=a (0.077)*log(1-MTR)+e log(share)=a+b*t (0.071)*log(1-MTR)+e Source: Saez (2004)