1. Problems with the OLS Estimation of Labour Supply …faculty.arts.ubc.ca/nfortin/econ561/E561L171B_TF.pdf1. Problems with the OLS Estimation of Labour Supply Functions . 1. Econometric

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


2.1 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

Source: Mroz (1987)

770 THOMAS A. MROZ

are presented in Table III and a detailed description of the data set constructioncan be found in Appendix 1.

This paper contains three sections. The first examines the statistical assumptionsin the basic model. The second section presents the results with the controls fortaxes. The final section summarizes the main conclusions and uses the results ofthe empirical analysis to shed some light on the empirical discrepancies foundin previous studies in this field.

1. THE BASIC LABOR SUPPLY MODEL

1.1. Choice of Baseline Specification

The estimates presented in Table IV demonstrate the sensitivity of the wageand income coefficients to minor variations in the variables used to instrumentthe wage rate.7 In this table (and Tables VI, VII, and VIII) we use the subsampleof working women to calculate the estimates, and our estimation procedures(ordinary least squares and two stage least squares) do not control for selfselection into the labor force. Although many recent studies of female laborsupply have stressed the importance of controlling for self-selection, we find

TABLE IV

CHOICE OF BASELINE SPECIFICATION

(Standard Errors in Parentheses. Common Instrument Sets: B, C, 1. Estimation Method: Two-StageLeast Squares.)

Nonwife Young Older Addtitional Instruments and CommentsIn(w,,) Income/tODD Children Children (R 2

: R 2 in reduced form wage equation)

1. -17 -4.2 -342 -115 In( ww ), OLS, R 2 = 1.0(81) (3.1) (131) (29)

2. 1282 -8.3 -235 -60 E, R 2 = .17(461) (4.6) (182) (49)

3. 831 -7.0 -271 -78 E, F2, R 2 = .18(312) (3.8) (155) (39)

4. 672 -6.4 -283 -85 E, F3, R 2 = .21(217) (3.6) (147) (36)

5. 482 -5.8 -300 -93 E, F3, H3, R 2 = .23(171) (3.4) (138) (33)

6. 638 -6.3 -287 -87 E, F4, R 2 = .22(197) (3.5) (145) (35)

7. -182 -3.7 -356 -122 F2, R 2 = .15(355) (3.5) (138) (33)

8. 46 -4.4 -337 -112 F3, R 2 = .18(220) (3.3) (131) (30)

9. -30 -4.2 -338 -113 F3, H3, R 2 = .20(174) (3.3) (129) (29)

10. 129 -4.7 -330 -108 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 supplyequation. See Mroz (1984, Appendix 2), for several estimates of the complete labor supply functionand reduced form wage equation.

Source: Mroz (1987)

Communications 1 417

TABLE 3 WAGE ELASTICITIES, STRAIGHT-TIME SAMPLE

Dependent = ln(Hu) Dependent = ln(Hw)

Step ln(E/Hu) ln(EIHw) ln(EIHu) ln(E/Hw)

1 .0132 .0458 .0463 -.0105

(.95) (3.38) (3.05) (-.70) 2 .0133 .0463 .0479 -.0089

(.96) (3.40) (3.14) (-.59) 3 -.0168 .0243 .0280 -.0422

(- 1.10) (1.62) (1.66) (-2.55) 4 -.0307 .0140 .0096 -.0614

(-1.97) (.92) (.56) (-3.68) 5 -.0383 .0099 .0163 -.0743

(-2.37) (.63) (.09) (-4.30) 6 -.0201 .0307 .0127 -.0721

(-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.

(9) o-ro2(lnHu) = .180

Thus about 18 percent of the variance in (In) usual hours can be explained by errors of measurement. Note that even this relatively small error leads to a bias that turns a positive and weak wage elasticity (.016) to a negative and strong elasticity (-.038) of usual weekly hours with respect to the wage rate. We can carry out similar calculations in terms of hours worked last week. After making the appropriate calculations, we find that the proportion of lnHw that can be explained by errors is 23.8 percent. Again, it is important to note that this error turns the wage elasticity from positive (.01) to negative (-.074).

Table 2 also shows a remarkable similarity between the wage elasticities estimated by using equation (6) or (7). This similarity is not coincidental and, in fact, is not affected by what variables are held constant in the equation. Table 3 presents the wage coefficient on both usual hours and last week's hours using both wage constructs: usual wage rate (E/Hu) and last week's wage rate (E/Hw). The wage coefficients are shown for six steps of the estimation of the hours-of-work equation, each step adding additional variables into the regression. In step 1, the regression is a simple bivariate relationship between log hours and log wage rates. Due to the division bias,

Source: Borjas (1980)

t-ratios in parentheses, NLS 71 (Mature Men)

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Table 2. Labor Supply Elasticities, Hourly Paid Women, and Men, CPS/ATUS

2003-12*

Dep. Var.:

Usual

hours ATUS Total ATUS Working WOMEN (hCPS) (hA1) (hA2)

Married (N = 3925)

0.1158 0.0880 0.0865

(0.0137) (0.0212) (0.0221)

R2 0.0471 0.0278 0.0285

t-statistic: αCPS = αA 1.40 1.42

Unmarried (N = 4262)

0.1814 0.1455 0.1334

(0.0156) (0.0221) (0.0228)

R2 0.1312 0.0619 0.0581


MEN

Married (N = 3840)

0.0651 0.0584 0.0339

(0.0094) (0.0188) (0.0199)

R2 0.0813 0.0366 0.0292


Unmarried (N = 3086)

0.1837 0.1227 0.1039

(0.0156) (0.0216) (0.0232)

Adj. R2 0.1556 0.0751 0.0678


*The equations also include a quadratic in age, indicators of race and ethnicity, and indicators for

day of week, state and year.

Source: Barrett and Hammermesh (2016)

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Issues: Desired hours of non-

participant 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


Use predicted wage from

wage equation with


Heckit

Figure 5 The Effect of an Increase in the Real Wage on the Budget Constraint

Figure 6 A scatterplot of desired hours against x

23

Source: Manning E333e

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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:

21- z21(z) = .e2

φπ

(68)

Let us denote the distribution function by Φ(z). For future use it is helpful to note that:

21- z2z(z) = - . = - z (z)e2

φ φπ

′ (69)

The Truncated Standard Normal Distribution Now suppose that we know that z∃z0 so that the distribution is truncated at z0. Denote by f(z) the truncated density of z. We must have that:

00

(z)f(z) = , z z1- ( )zφ

≥Φ

(70)

We are interested in E(z|z∃z0). This is given by:

0 0

0

0z z0

0 0 0z

z (z)dz - (z)dz- ( )+ ( ) ( )z zE(z | z ) = zf(z)dz = = = = z 1- ( ) 1- ( ) 1- ( ) 1- ( )z z z

φ φφ φ φ

∞ ∞

∞′

∞≥

Φ Φ Φ Φ

∫ ∫∫ 0

0z (71)

It is simple to check that this is increasing in z0.

Now suppose that ε−N(µ,σ2). Suppose that ε∃ε0. We can show that:

0

00

-

E( | ) = -1-

µεσφσε ε µε µεσ

≥ + Φ

(72)

26

Source: Manning E330

184 AmErICAN ECoNomIC JoUrNAL: ECoNomIC PoLICy AUgUST 2010

elasticity e would no longer be a pure compensated elasticity, but a mix of the com-pensated elasticity and the uncompensated elasticity. Four points should be noted.

First, the larger the behavioral elasticity, the more bunching we should expect. Unsurprisingly, if there are no behavioral responses to marginal tax rates, there

Panel A. Indifference curves and bunching

Before tax income z

Slope 1− t

z* z*+ dz*

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

Individual H indifference curves

Individual L indifference curve

Panel B. Density distributions and bunching

Den

sity

dist

ribut

ion

Before reform density

After reform density

Pre-reform incomes between z* andz*+ dz* bunch at z* after reform

Before tax income zz* z*+ dz*

Afte

r-ta

x in

com

e c

=z−

T(z

)

Figure 1. Bunching Theory

Notes: Panel A displays the effect on earnings choices of introducing a (small) kink in the budget set by increasing the tax rate t by dt above income level z*. Individual L who chooses z* before the reform stays at z* after the reform. Individual h chooses z* after the reform and was choosing z* + dz* before the reform. Panel B depicts the effects of introducing the kink on the earnings density distribution. The pre-reform density is smooth around z*. After the reform, all individuals with income between z* and z* + dz* before the reform, bunch at z*, creating a spike in the density dis-tribution. The density above z* + dz* shifts to z* (so that the resulting density and is no longer smooth at z*).

Source: Saez (2010), p. 184

Raj Chetty () Labor Supply Harvard, Fall 2009 52 / 156






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Figure 2. Effect of a Negative Income Tax on Labor Supply

Income

Hours worked

Source: Moffit (2003) Other Possible Negative (2) and (3) Labour Supply Responses

Guaranteed Annual Income S279

a guaranteed-income program, the experiments are not without their own analytic headaches.

C. The Experimental Evidence for Labor-Supply Response

As discussed in Section IVA, both ANOVA and structural models provide useful information about the labor-supply response to a GAI using the experimental data. The ANOVA model gives a direct answer to the question, "Was there an experimental response (i.e., does labor supply response differ between the treatment and control groups)?" The structural model, in contrast, answers the question, "What was the experimental response in terms of conventional (substitution and income) labor-supply effects?" The models should provide similar answers concerning labor- supply response to a guaranteed-income program, but the results from the structural model may be more useful in other social policy evaluation.

In table 2 we summarize the evidence from a variety of studies on the difference in mean annual hours worked between the treatment and control groups in the five experiments. For the U.S. experiments, the surveys of

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) -116 7 -75 33 ... Robins (1985) -34 2 -56 25 ... Burtless (1986) -21 1 -56 25 ...

Rural: Keeley (1981) ? 9 ? 29* ... Robins (1985) -56 3 -178 28 ... Burtless (1986) -56 3 -178 28 ...

Seattle-Denver: a

Keeley (1981) -147 8* -139 21* -155 15* Robins (1985) -113 7* -141 21* -163 16* Burtless (1986) -144 8 -107 17 -85 9

Gary: Keeley (1981) -80 5 -9 3 -102 28 Robins (1985) -35 2 -58 20 -37 10 Burtless (1986) -114 7 +14 5 -112 30

All U.S. experiments: Robins (1985) -89 5 -117 21 -123 13 Burtless (1986) -119 7 -93 17 -133 17

Mincome: Appendix -17 1 b -15 3 -79 7

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.

Source: Hum and Simpson (1993)

S282 Hum/Simpson

Table 3 Structural Labor-Supply Response Estimates from the Five Experiments

Substitution Income Experiment/Group Elasticity Elasticity

Husbands: New Jersey .09 -.02 Rural .09 .00 Seattle-Denver .09 -.14 Gary .06 -.08

All United States .08 -.10 Mincome -.07 -.03

Wives: New Jersey -.08 -.28 Rural .28 .01 Seattle-Denver .14 -.12 Gary .37 .26

All United States .17 -.06 Mincome -.08 .07

Single female heads: New Jersey Rural Seattle-Denver .12 -.15 Gary .14 -.20

All United States .13 -.16 Mincome -.17 -.01

SOURCES.-Robins (1985) for the U.S. experiments; the Appendix (table A3) for the Canadian experiment.

Table 3 provides a summary of the evidence on labor-supply response consistent with structural models. Elasticity estimates are presented to facilitate comparison across experiments and with nonexperimental re- search and to provide the most useful information for current policy analysis. The results from the GAI experiments, in contrast with the nonexperimental literature, provide very uniform and quite low elasticity estimates of labor-supply response. The experimental evidence therefore corroborates the nonexperimental evidence of very inelastic male labor- supply response (Keeley 1981; Killingsworth 1983; Pencavel 1986; Hum and Simpson 1991). Robins's (1985) weighted average for all experiments is 0.08 for the substitution elasticity and 0.10 for the income elasticity.

Unlike the bulk of the nonexperimental evidence,'5 however, the experimental evidence for wives and single mothers indicates similarly inelastic response. Robins's estimates are 0.17 and 0.13 for the substitution elasticities for wives and single mothers and 0.06 and 0.16 for their re-

15Reviews include Keeley (1981); Killingsworth (1983); Killingsworth and Heckman (1986); and Hum and Simpson (1991).

D. CARD AND D. R. HYSLOP

of the incentive effects of SSP, however, we summarize the key experimental findings from the demonstration.

B. The SSP Sample Characteristics and Basic Impacts on Welfare

The data associated with the SSP experiment were assembled from three separate sources. Income Assistance data were obtained from provincial welfare records. The SSP participation and receipt data were collected from SSP administrative records. Demographic data and labor market outcomes were obtained from surveys conducted at 18-month intervals, starting with a baseline survey just prior to random assignment. Table II gives an overview of the characteristics of the SSP sample. Columns 1 and 2 of the table show the mean characteristics of the control and program groups of the experiment, while the

TABLE II

CHARACTERISTICS OF SSP EXPERIMENTAL SAMPLEa

Program Group, by SSP

Eligibility Status

Controls Programs Eligible Ineligible

In British Columbia (%) 52.6 53.2 50.9 54.4 Male (%) 4.7 5.2 4.6 5.5 Mean age 31.9 31.9 31.1 32.4 Age 25 or less (%) 17.8 17.1 18.5 16.3 Never married (%) 48.1 48.3 48.0 48.5 Average number kids <6 0.7 0.7 0.7 0.7 Average number kids 6-15 0.8 0.8 0.8 0.8

Immigrant (%) 13.8 13.3 12.2 13.9 Grew up with two parents (%) 59.7 59.4 62.1 58.1 High school graduate (%) 44.6 45.7 56.9 39.9 Means years work exp. 7.4 7.3 8.6 6.7 Working at random assignment (%) 19.0 18.2 31.5 11.4 Months on IA last 3 years 29.6 30.1 29.2 30.6 IA continuously last 3 years (%) 41.5 43.8 36.3 47.7 Percent on IA by months since random assignment

Month 6 90.8 83.1 62.8 93.5 Month 12 83.7 72.4 39.1 89.4 Month 18 77.9 65.9 27.2 85.6 Month 24 73.0 63.3 26.5 82.1 Month 36 65.4 58.8 27.6 74.8 Month 48 56.7 53.5 29.3 65.9 Month 60 50.6 48.4 28.5 58.5 Month 69 45.0 45.0 25.4 55.0

Number of observations 2,786 2,831 957 1,874

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.

1728

Source: Card and Hyslop (2005)

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1734 D. CARD AND D. R. HYSLOP

and control groups. Unfortunately, these data have some critical limitations relative to the administratively based Income Assistance data. Most impor- tantly, they are only available for 52 months after random assignment. Since some program group members were still receiving subsidy payments as late as month 52, this time window is too short to assess the long-run effects of the program. Indeed, looking at Figure la, there is still an impact on IA participation in month 52 that does not fully dissipate until month 69. Second, because of nonresponses and refusals, labor market information is only available for 85% of the experimental sample (4,757 people).l8 Third, there appear to be

relatively large recall errors and seam biases in the earnings and wage data.19 Nevertheless, the labor market outcomes provide a valuable complement to the administratively based welfare participation data.

Figure 3 shows the average monthly employment rates of the program and control groups, along with the associated experimental impacts. After random assignment the employment rate of the control group shows a steady

0.5

0.4 - . . .

0.3 -

=~~c ;^^^^~ ~ -- Control Group

? 0.2 - ----- Program Group

v?C;1~~~~~~~~ -*- Difference

0.1

0 6 12 18 24 30 36 42 48

Months Since Random Assignment

FIGURE 3.-Monthly employment rates.

18The distribution of response patterns to the 18-, 36-, and 54-month surveys is fairly similar for the program and control groups (chi-squared statistic = 11.4 with 7 degrees of freedom, p-value = 0.12). However, a slightly larger fraction of the program group have complete labor market data for 52 months-85.4% versus 84.0% for the controls. Moreover, the difference in mean IA participation between the treatment and control groups in month 52 is a little different in the overall sample (2.5%) than in the subset with complete labor market histories (3.3%).

"9Each of the three post-random-assignment surveys asked people about their labor market outcomes in the 18 months since the previous survey. Many people report constant earnings over the recall period, leading to a pattern of measured pay increases that are concentrated at the seams, rather than occurring more smoothly over the recall period.


D. CARD AND D. R. HYSLOP

The absence of a trend in the average marginal wage relative to the minimum wage is important because it suggests that the SSP program group experienced little or no relative gain in potential wages over the course of the experiment. This is confirmed by the analysis in Table III of labor market outcomes in the last available month (month 52). Recognizing the higher average level of wages in one of the two provinces (British Columbia), we present data for the overall sample and separately by province.23 By month 52 there is no significant gap

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 41.56 39.19 44.08

(1.02) (1.41) (1.48) Percent with reported wage 38.26 35.63 41.08

(1.01) (1.38) (1.46) Mean log hourly wage 2.17 2.36 1.99

(0.01) (0.02) (0.02) Cumulative employment since 1.41 1.33 1.49

random assignment (in years) (0.03) (0.04) (0.05)

Program group outcomes in month 52 Percent employed 41.69 37.73 46.05

(1.00) (1.36) (1.47) Percent with reported wage 39.45 35.04 44.31

(0.99) (1.34) (1.47) Mean log hourly wage 2.15 2.34 1.99

(0.01) (0.02) (0.02) Cumulative employment since 1.68 1.55 1.82

random assignment (in years) (0.03) (0.04) (0.05) Difference: Program group - Control group

Percent employed 0.13 -1.46 1.97 (1.43) (1.96) (2.08)

Percent with reported wage 1.19 -0.58 3.23 (1.41) (1.92) (2.07)

Mean log hourly wage -0.02 -0.02 -0.01 (0.02) (0.03) (0.02)

Cumulative employment since 0.28 0.22 0.33 random assignment (in years) (0.04) (0.06) (0.07)

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.

1738


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EFFECTS OF A SUBSIDY FOR WELFARE-LEAVERS

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 -0.01 -0.02 -0.002 (0.02) (0.03) (0.02)

(b) Program group effect in model for cumulative work 0.37 0.28 0.46 (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 0.049 0.046 0.051

(0.007) (0.012) (0.009) (d) Estimated by IV, using program group status -0.032 -0.088 -0.004

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.

between the program and control groups in the fraction of people working or reporting a wage. Indeed, in one province the program group has a slightly lower employment rate than the control group, while in the other the pattern is reversed, although in neither case is the difference significant. Mean wages are also very similar in the program and control groups. This may seem a little surprising given the extra work effort by the program group over the previous 51 months. Indeed, as shown in the table, we estimate that program group members worked a total of 0.28 years more than control group members between random assignment and month 52. Recall, however, that the sample had about 7 years of work experience at random assignment. Evidence on the returns to experience for less skilled female workers suggests the marginal impact of 0.2-0.3 years of work experience for such a group is small-on the order of 1-2% (Gladden and Taber (2000))-and probably undetectable.

The bottom panel of Table III presents results from a series of regression models that evaluate the impacts of being in the SSP program group on wages and cumulative work experience in the 52nd month of the experiment. These models are fitted to the subsamples of control and program group members with wage data in month 52, and include time dummies, province dummies (in the models that pool the two provinces), and a set of covariates that repre- sent pre-random-assignment characteristics. A possible concern with the models is selectivity bias, since the sample is conditioned on reporting a wage in month 52. However, given equality in the fractions of the program and control groups with a wage, and the similar characteristics of the employed subgroups, a conventional control function for selectivity bias would have the same mean

1739 Source: Card and Hyslop (2005)

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-14-

Figure 1: Median Wages for British Columbia and New Brunswick Program and Control Groups From Month 2 to Month 51

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Month Since Random Assignment

Med

ian

Wag

e

BC Control Group

BC Program Group

NB Control Group

NB Program Group

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.

We now take a closer look at the period starting in Month 14, since this is when the eligibility period has ended and all take-up group members now receive the SSP supplement for full-time work.9 This is the time period when we first expect to see evidence of relative wage progression as the supplement induces eligible individuals to work more. The additional work experience will lead to relatively higher wages as long as there is a positive return to experience. Further, using Month 14 as the baseline for comparison will help to mitigate the composition bias that is generated by comparing median wages across two time periods. Because of the structure of SSP, we expect the program group members who worked in Month 51 to be more similar to those who worked in Month 14 than to those who worked in Month 2. This should imply that the difference in median wages between months 14 and 51 is a better measure of wage progression as it is less influenced by the composition bias relative to the same comparison of median wages in months 2 and 51. This is suggested by the fact that in British Columbia only 83 program group members worked in Month 2 whereas 305 worked in Month 14 and 271 worked in Month 51. Further, a comparison of 8We actually define the incentive period to be the first 13 months. Each program group member had exactly 12 months to qualify for the earnings supplement by finding a full-time job. The employment variable measured in the surveys, however, was based on calendar months. A participant whose 12-month period started on January 21st, for example, would have until January 21st of the following year to qualify. However, “Month 1” for that person would be the January in which random assignment occurred. If he or she found a full-time job in the first three weeks of the second January, full-time employment would have been coded as starting in Month 13.

9At Month 14, all program group members who could qualify for the supplement would have qualified for it. However, only a subset of eligible program group members were typically working in any given month, since take-up group members were free to leave full-time work without forfeiting their supplement eligibility.

Source: Zabel et al. (2004)

-34-

Figure 1: Employment Rates, High School Upgrading Sample 1

0

0.1

0.2

0.3

0.4

0.5

0.6

-12 -10 -8 -6 -4 -2 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53

Month

Upgraders

Non-upgraders

Figure 2: Hourly Wages, High School Upgrading Sample 1

4

5

6

7

8

9

10

11

-12-10 -8 -6 -4 -2 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53

Month

Upgraders

Non-upgraders

Source: Riddell and Riddell (2006)

Em

ploy

men

t Rat

e

Year

Empirical (Bianchi et al. 2001)

75%

80%

85%

90%

95%

1982 1984 1986 1988 1990 1992

Figure 1a: 1987 Tax Holiday in Iceland

The interaction of WFTC with other benefits in the UK

Example: Budget Constraint for Single Parent

Source: Blundell (2015)

Universally Available Tax and Transfer Benefits (US Single Parent withTwo Children, 2008)

Source: Urban Institute (NTJ, Dec 2012).Notes: Value of tax and value transfer benefits for a single parent with twochildren.

Richard Blundell () UBC Lecture I UCL & IFS, September 2015 22 / 66

Source: Federal Govt

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Differences-in-Differences

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 = LFPT - LFPC • 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:

• 𝐷𝐵 = 𝐿𝐹𝑃𝐵𝑇 − 𝐿𝐹𝑃𝐵

𝑐 .

Before reform

After reform

Control

Treated

Differences-in-Differences

Step 2: Difference-in-Difference (DD) • If 𝐷𝐵 ≠ 0, we can estimate DD:

• 𝐷𝐷 = 𝐷𝐴 − 𝐷𝐵 =[𝐿𝐹𝑃𝐴

𝑇 − 𝐿𝐹𝑃𝐴𝑐] − [𝐿𝐹𝑃𝐵

𝑇 − 𝐿𝐹𝑃𝐵𝑐]

• 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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38

Figure 8 Stylized EITC Budget Constraint

After Tax Income

Hours of Work

D

C

B

A

0

Flat w

Phase-in w(1+τs)

No EITCw

Phase-out w(1-τp)

Source: Eissa and Hoynes (2008)

EITC Amount as a Function of Earnings

Earnings ($)

0 5000 10000 15000 20000 25000 30000 35000 40000

Subsidy: 34%

Subsidy: 40%

Phase-out tax: 16%

Phase-out tax: 21%

Single, 2+ kidsMarried, 2+ kids

Single, 1 kidMarried, 1 kid

No kids

EIT

C A

mou

nt ($

)

010

0020

0030

0040

0050

00

Source: Federal Govt

4.Take-homeMessage

1. Fill in earnings, EIC amount

10,000 4,000

increasing

ExplainingEIC: 4 steps

2. Explain and dot graph

3. Table

Source: Chetty and Saez (2009)

VoL. 2 No. 3 191SAEz: do TAxPAyErS BUNCh AT kINk PoINTS?

indexes earnings to 2008 using the IRS inflation parameters, so that the EITC kinks are perfectly aligned for all years.

Two elements are worth noting in Figure 3. First, there is a clear clustering of tax filers around the first kink point of the EITC. In both panels, the density is maximum exactly at the first kink point. The fact that the location of the first kink point differs between EITC recipients with one child, versus those with two or more children, con-stitutes strong evidence that the clustering is driven by behavioral responses to the EITC as predicted by the standard model. Second, however, we cannot discern any

5,000

4,000

3,000

2,000

1,000

0

EIC

am

ount

(20

08 $

)

Ear

ning

s de

nsity

($5

00 b

ins)

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Earnings (2008 $)

Density EIC Amount

Panel A. One child

Ear

ning

s de

nsity

($5

00 b

ins)

0 5,000 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

Density EIC Amount

5,000

4,000

3,000

2,000

1,000

0

EIC

am

ount

($)

Figure 3. Earnings Density Distributions and the EITC

Notes: The figure displays the histogram of earnings (by $500 bins) for tax filers with one dependent child (panel A) and tax filers with two or more dependent children (panel B). The histogram includes all years 1995–2004 and inflates earnings to 2008 dollars using the IRS inflation parameters (so that the EITC kinks are aligned for all years). Earnings are defined as wages and salaries plus self-employment income (net of one-half of the self-employed pay-roll tax). The EITC schedule is depicted in dashed line and the three kinks are depicted with vertical lines. Panel A is based on 57,692 observations (representing 116 million tax returns), and panel B on 67,038 observations (repre-senting 115 million returns).


192 AmErICAN ECoNomIC JoUrNAL: ECoNomIC PoLICy AUgUST 2010

systematic clustering around the second kink point of the EITC. Similarly, we cannot discern any gap in the distribution of earnings around the concave kink point where the EITC is completely phased-out. This differential response to the first kink point, versus the other kink points, is surprising in light of the standard model predicting that any convex (concave) kink should produce bunching (gap) in the distribution of earnings.

In Figure 4, we break down the sample of earners into those with nonzero self-employment income versus those zero self-employment income (and hence whose

5,000

4,000

3,000

2,000

1,000

0

5,000

4,000

3,000

2,000

1,000

0

EIC

am

ount

($)

EIC

am

ount

($)

Ear

ning

s de

nsity

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Earnings (2008 $)

Wage earners

Self-employed

EIC amount

Panel A. One child

Ear

ning

s de

nsity

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Earnings (2008 $)

Panel B. Two or more children

Wage earners

Self-employed

EIC amount

Figure 4. Earnings Density and the EITC: Wage Earners versus Self-Employed

Notes: The figure displays the kernel density of earnings for wage earners (those with no self-employment earnings) and for the self-employed (those with nonzero self employment earnings). Panel A reports the density for tax fil-ers with one dependent child and panel B for tax filers with two or more dependent children. The charts include all years 1995–2004. The bandwidth is $400 in all kernel density estimations. The fraction self-employed in 16.1 per-cent and 20.5 percent in the population depicted on panels A and B (in the data sample, the unweighted fraction self-employed is 32 percent and 40 percent). We display in dotted vertical lines around the first kink point the three bands used for the elasticity estimation with δ = $1,500.


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

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Source: Eissa and Liebman (1996)

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Has “In-Work” Benefit Reform Helped the Labor Market? 441

3000

2500

E

0 g 2000

tn m

v

El

0 m

1500

I i 1000

c .- E n

500

0

Maximum EITC Difference

,---., , ’ Difference I ‘.-’

Maximum EITC Difference

Employment Rate ,---., , ’ Difference I ‘.-’

.0.0500

-0.1000

3 d

5 E“

g

L

P)

.0.1500 2

W c I

.0.2000

.0.2500 1984 1986 1988 1990 1992 1994 1996 1998

Year

Fig. 10.17 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.

73.0 to 75.8 percent. There is also some evidence ofnegative effect on hours for those in work, but this is rather small.

Liebman (1998) and Meyer and Rosenbaum (2000) use a similar ap- proach to examine the impact of all three of the EITC reforms. The estimated behavioral responses are very similar in magnitude to those found by Eissa and Liebman (1996). The Liebman results are summarized in figure 10.17. The figure plots the difference in employment rates of single women with and without children against the difference in the maximum EITC credit in 1996 dollars.’O The figure shows that the relative increase in employment rates among single mothers tracks quite closely the expansion of the EITC. Meyer and Rosenbaum (2000) present similar calculations for several other comparison groups, including comparing single women with

10. In the early period, the difference in maximum credit is equal to the credit for families with children. Figure 10.17 takes into account that there was a small EITC for childless families starting in 1994. It is not clear whether Liebman (1998) took this into account in his cal- culation.

Source: Blundell and Hoynes (2004)

FIGURE 1Top Income Shares and Marginal Tax Rates, 1960-2006

Source: Updated version of Figure 8 in Saez (2004). Computations based on income tax return data.Income excludes realized capital gains, as well as Social Security and unemployment insurance benefits.The figure displays the income share (right y-axis) and the average marginal tax rate (left y-axis)(weigthed by income) for the top 1% (Panel A) and for the next 9% (Panel B) income earners.

A. Top 1% Income Share and Marginal Tax Rate

0%

10%

20%

30%

40%

50%

60%19

6019

6219

6419

6619

6819

7019

7219

7419

7619

7819

8019

8219

8419

8619

8819

9019

9219

9419

9619

9820

0020

0220

0420

06

Top

1% M

argi

nal T

ax R

ate

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Top

1% In

com

e Sh

are

Top 1% Marginal Tax Rate Top 1% Income Share

B. Next 9% Income Share and Marginal Tax Rate

0%

10%

20%

30%

40%

50%

60%

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

Nex

t 9%

Mar

gina

l Tax

Rat

e

0%

5%

10%

15%

20%

25%

30%

Nex

t 9%

Inco

me

Shar

e

Next 9% Marginal Tax Rate Next 9% Income Share

Source: Saez (2004)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%19

13

1918

1923

1928

1933

1938

1943

1948

1953

1958

1963

1968

1973

1978

1983

1988

1993

1998

2003

2008

Top

.01%

MTR

(Fed

eral

Inco

me

Tax)

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

US Top 0.01% Income Share and MTR (Piketty-Saez and Landais)

Top

0.01

% In

com

e Sh

are

Top 0.01% MTRTop 0.01% Share

log(share)=a+0.617 (0.077)*log(1-MTR)+elog(share)=a+b*t+0.666 (0.071)*log(1-MTR)+e

Source: Saez (2004)

Documents

1. Problems with the OLS Estimation of Labour Supply …faculty.arts.ubc.ca/nfortin/econ561/E561L171B_TF.pdf1. Problems with the OLS Estimation of Labour Supply Functions . 1. Econometric