Labor Supply for Norwegian Lottery Winners

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Labor Supply for Norwegian Lottery Winners

Sander Rivø Aslesen

Master in Economics

Department of Economics University of Oslo

Norway 20^thof May 2021

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Abstract

I use the Norwegian lottery combined with the Norwegian tax report and data from A- meldingen to derive the marginal propensity to earn (MPE) out of unearned income for Nor- wegian individuals. This is done by doing a difference-in-differences analysis using all lottery winners between 2010 and 2018. The software package used is STATA.

The main findings is that the MPE is -2.19 NOK per 100 NOK won in the lottery. Most of the reduction in labor supply takes place on the intensive margin, where individuals adjust the number of hours worked. As the winnings increase in size, so does the contribution of the extensive margin, where the winners choose to exit the labor market. Furthermore, the MPE shows little persistence.

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Preface

This master thesis is the conclusion of my degree at the University of Oslo, and after 5 years as a student, several people deserves recognition and gratitude.

First and foremost, I would like to thank my supervisor, Martin BlomhoffHolm, for great help with this thesis. He has helped me in all stages, from planning the subject of the thesis all the way to the finished product. He has always been available and helped me by discussing issues that have occurred.

Secondly, I would like to thank all my fellow students from our time at the University. They have made the five years here both fun and a great place to learn. I would also like to thank all professors and seminar teachers, all of whom have been helpful and exiting to learn from.

Elise Øie deserves some recognition for helping me with proofreading and helping me when I have been stuck with the thesis.

To make it clear, all errors or inaccuracies in this thesis are fully my own.

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1 Introduction

How individuals adapt their labor supply following an increase in wealth is of interest for economists and policymakers. For policymakers the labor supply elasticity is important when assessing new policies such as e.g. tax reforms. The labor supply elasticity also has an important role in the literature of optimal taxation. It plays a key role in theories regarding intertemporal substitution, and in theories regarding the trade-offbetween consumption and leisure.¹ The wealth effect also plays an important role in the theory of business cycle fluctuations.² Due to its implications for economic theory, it exists a large literature field on this subject, but there seems to be little agreement about the size of the effects following an exogenous increase in wealth.³ Furthermore, Kimball and Shapiro (2008) suggests that it is important to obtain credible estimates for the size of the income and substitution effect. This leads to the investigation of the intensive and extensive margin. The intensive margin captures how intense individuals work (measured in the number of hours), and the extensive margin captures the decision to work. Estimating the intensive and extensive margin have proven to be difficult due to data limitations, and there seem to be little consensus about what margin (intensive or extensive) that is the main driver behind empirical results of wealth effects.⁴

I investigate how Norwegian individuals react to an unexpected and transitory increase in wealth. This is done by taking advantage of the randomization of lottery prizes and estimating how this exogenous and idiosyncratic increase in wealth affect the individuals labor decisions.

The thesis estimates the marginal propensity to earn out of unearned income (MPE) to be -2.19 NOK per 100 NOK in lottery winnings.

Next, I estimate a model to shed some light on how the intensive margin plays out. The findings suggests that the reduction is mainly driven by reducing the numbers of hours worked, and not reducing the hourly wage. Afterwards, the results implies that there is an effect on the extensive margin, in the form of a higher probability of exiting the labor market following a lottery win.

I also investigate how size matters for the reduction in labor earnings, and how the effects on the margins develop as the lottery prize size increases. The findings suggests that winners of larger prizes are more prone to reduce their hourly wage than winners of smaller prizes. There is implications that the extensive margin increases with the size of the lottery win. Lastly, I find an indication that the reduction in labor earnings is transitory with the effect being depleted after 2 periods. The effect on annual hours worked shows more persistence, and actually increase in period t+3, before reverting back to zero in period t+4.

1See for instance Keane (2011) Saez, Slemrod and Giertz (2012) Saez (2001). Keane (2011) has an overview paper of the existing literature. See also Whalen and Reichling (2015) for an overview of the estimates for the intertemporal elasticises.

2See for instance Prescott (1986), Rebelo (2005) or Amu et al. (2021)

3See for example Pencavel (1986), Keane (2011), Evers, De Mooij and van Vuuren (2008), Blundell and Macurdy (1999), Blundell, Bozio and Laroque (2011), Golosov et al. (2021), Cesarini et al. (2017) or Mirrlees (1971)

4See for example Blundell, Bozio and Laroque (2011) Bengtsson (2012) for papers suggesting the extensive margin to be substantial, and see for example Cesarini et al. (2017) for a paper suggesting the intensive margin to dominate.

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This thesis is closely related to the work of Cesarini et al. (2017), they find that Swedish lottery winners have a MPE of -1.1 SEK per 100 SEK won in the lottery. Furthermore, they state that the effect is largest on the intensive margin. Golosov et al. (2021) find that Americans had a MPE of -2.2$ per 100$ won in the lottery. Imbens, Rubin and Sacerdote (2001) finds Massachusetts lottery winners to increase their leisure by 11% in response to an exogenous increase in wealth. I find results that are consistent with these estimates. The main advantage of the data I use is that the number of hours worked is a reported size from the employers. Since I can estimate on observed hours, I may be able to shed some more empirical light on the intensive margin.

I use the same type of data set as Fagereng, Holm and Natvik (2021) used when estimating the Marginal Propensity to Consume (MPC) of Norwegian lottery winners. I follow their setup closely by using similar methods when estimating the MPE as they did when estimating the MPC.

The rest of the thesis is outlined as follows. Section 2 presents the data, and the basis for the following analysis. Section 3 explains the empirical approach and presents the main results.

Section 4 looks at the importance of the size of the lottery win. Section 5 looks at the dynamics of the shock. Section 6 concludes.

2 Data

The study is based on Norwegian administrative data on individuals collected for tax purposes.

From these tax records, I observe salary and lottery prizes from the Norwegian gambling monopoly (Norsk Tipping). I use data from A-meldingen to collect information regarding the job status and annual hours worked for individuals. This section first describes the data sources in detail.

Afterward, the sample selection and descriptive statistics is presented.

2.1 Administrative data, the tax record and A-meldingen

The data forming the basis of the analysis in this thesis is a combination of Norwegian tax-report and A-meldingen. This is combined with individual fixed information on the level of education.

The Norwegian tax report contains information about several financial aspects of every individual, including their salary and lottery prizes. When a Norwegian wins any amount above 100,000 NOK in the lottery she is legally demanded to include this in the tax report. This means that the tax report not only contain information about whether an individual wins the lottery or not, but also the size of the lottery prize.

A-meldingen is a Norwegian system that was introduced in 2015. Every month employers who have payed out more than 1,000 NOK in salary must fill out A-meldingen and send it to the authorities.⁵ A-meldingen contains information about the employment conditions, including employment status and hours worked each month. The introduction of A-meldingen gives the thesis an advantage of being able to estimate on observed hours worked. A-meldingen includes

5Seeweb page with more information about A-meldingen, including who must send it in, limits before triggering the form, sole proprietorship etc.

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both the contracted weekly hours worked, and the overtime hours for the full month. When estimating the hours worked, I will use the annual hours worked, meaning the contracted hours plus overtime hours worked for a full year.⁶

There was a shift in Norwegian law regarding the minimum amount demanded to be included in the tax-report occurring in 2010. The new law stated that all winnings above 100,000 NOK were legally demanded to be reported in the tax report. The lower boundary was previously 10,000 NOK.⁷The shift in law implies two things for the data set: (i) the year limit will go from 2010 and onwards, and (ii) the smallest amount won is limited to 100,000 NOK. All the data from the tax records and A-meldingen are combined into a panel data set. With each individual being tracked from the start of the period (2010) through the end (2018). When estimating the marginal propensity to earn out of unearned income, the full sample (2010 - 2018) is included.

Since A-meldingen starts in 2015, the data sample will naturally shrink to a subsample including only winners in the years 2015 - 2018 when estimating on hourly data. The data is further limited to individuals in working age, i.e. between 25 and 67. 67 is the retirement age in Norway, and by setting the lower bound at 25 it is ensured that most of the population have finished their highest education. Because I want to look at a random and transitory increase in wealth, I exclude individuals who win more than once as these individuals may perceive the lottery prizes as a part of their income.⁸ I will also exclude all winnings above 1,500,000 NOK.⁹When imposing all these limitations on the data sample, we are left with 6,496 lottery winners for the full sample, and 1,879 lottery winners for the subsample of 2015 - 2018.

2.2 Gambling in Norway

Only Norsk tipping and Norsk Rikstoto are allowed to arrange lottery and gambling activities in Norway.¹⁰ A large part of the Norwegian population participates in gambling activities through these channels. In 2019 roughly 2 million Norwegians participated in gambling activities through one of the Norsk Tipping or Norsk Rikstoto games.¹¹ This is about 60% of the adult population in Norway.

6When the panel data was created, the weekly contractual hours worked where kept intact, and there was also made a new variable called total hours worked in a year. Total hours worked in a year was constructed by taking the contractual hours worked and multiplying this by 47, since there is 47 working weeks in a full year in Norway, then adding on the overtime hours worked for the full year.

7Seehome side of Norwegian tax authoritiesfor the laws on reporting gambling winnings to the tax authorities.

8The reason being that people who win multiple years in a row are more likely to be participating in a gambling activity that includes skill, and in such a way the increase in disposable income cannot be viewed as neither random, nor transitory.

9The exclusion of winners above 1,500,000 NOK is done to make the shock a meaningful economical size.

10In recent years, the introduction of internet gambling have of course come in play. However, there is still a substantial part of the Norwegian population that partakes in gambling activities through Norsk Tipping and Norsk Rikstoto.

11Seehome page of Norsk Tippingfor more information regarding the statistics from Norsk tipping and reports regarding Norwegian gambling activities.

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2.3 Summary statistics

Table 1 shows the summary statistics comparing the lottery winners in the data set with the non- winners. The reported statistics for the winners are data collected from the winning year. When reporting the statistics for non-winners, a random year between 2010 and 2018 is drawn.

Table 1: Summary statistics

Non-winners Winners

(N=3,930,217) (N=6,496)

Variable Mean St.dev Mean St.dev

Age 43.9 (13.4) 50.4 (11.3)

Year of education 14.0 (2.8) 13.7 (2.5)

Pre-tax salary (lagged) 358,383 (353,130) 399,799 (359,381) Annual hours worked (lagged) 1,489 (448.9) 1,554 (403.8)

Fraction male 0.50 - 0.58 -

The table reports the mean value of all characteristics. Standard deviations reported in the parenthesis. Winners characteristics are from the year they won and non winners have a randomly drawn year representing in the statistics. All monetary values are stated in NOK adjusted to 2014 levels.

Table 1 shows that the lottery winners tend to be slightly older, slightly less educated, earn a bit more, and work more hours annually, there is also a higher fraction male among lottery winners.¹² Appendix A tests the assumptions that winning the lottery is an exogenous and idiosyncratic shock. This is done by (i) testing if the observations of a lottery win is increasing with some observable traits, and (ii) testing if the size of the lottery win is increasing with some observable traits, conditioned upon winning.

Figure 1 shows the distribution of lottery winnings. The x-axis is the size of the lottery win, and the y-axis is the fraction of winners in the bin. The bars represents bins of the lottery prizes, with each bin containing 10,000 NOK. Since the least amount legally required to report in the tax-reports is 100,000 NOK the lowest bin is 100,000 - 110,000 and so on. There is some observable clustering around 100,000 NOK won. There is also some clustering around 1,000,000 NOK.¹³

12Because it is not observable when in the year the lottery win occurs, the summary statistics includes the lagged values for labor earnings and total hours worked.

13Note that this is CPI-adjusted values, there would be more clustering around 1,000,000 NOK if the reported values were nominal prize sizes.

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0.02.04.06.08.1Fraction

100 300 500 700 900 1100 1300 1500

Size of lottery winnings (1,000, 2014 NOK)

Lottery winnings size and fraction

Figure 1: Distribution of lottery winnings. The figure shows the distribution of the lottery winnings, adjusted to 2014 NOK. Each bin represent a win interval of 10,000 NOK. All sizes on the y-axis is divided by 1,000.

3 Main results

This section presents the estimations and results. The section begins with a dummy estimation of the propensity to earn out of unearned income, and a dummy estimation for the reduction in annual hours worked following a lottery win. I then move on to estimating the marginal effects of a lottery win on the labor earnings. Thereafter, I use an inverse hyperbolic specification to break the reduction in labor earnings into two parts. Lastly, the extensive margin is looked at in two ways. The set up of the estimations follows closely the set up of Fagereng, Holm and Natvik (2021), who used a difference-in-differences setup when estimating the MPC for Norwegian lottery winners. All estimations in this part uses lottery winners who have not yet won the lottery as a control group. All individuals are removed from the control group after winning the lottery.¹⁴ 3.1 Winning the lottery as a dummy estimation

I start the estimation by looking at the propensity to earn and work for lottery winners. This is done to check if there is some observable adjustment in the labor supply in the year following a

14Since including winners who have already won could lead to downwards bias. If the treated individuals were still included in the controlling sample, the MPE could be downwards biased.

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lottery win. Equation 1 estimates the average impact of being a lottery winner on the labor supply in the following year.

Y_i_,_t₊₁ =β0+β1X_i_,_t+β2Z_i_,_t−1+λi+δt+εi,t (1) In equation 1, Y_i,t+1 can be interpreted as either the labor earnings or the hours worked for individualiin periodt+1. Xi,tis a dummy variable that is equal to 1 if individualiwon the lottery in periodt. Z_i,t−1is a vector containing a set of control variables.¹⁵ λicaptures the individual fixed effects andδtcaptures time fixed effects. The coefficient of interest isβ1, as this coefficient captures the average effect that winning the lottery has on labor earnings or annual hours worked.

In table 2 there are three specifications. The first specification is equation 1 without any control variables. The second specification includes control variables. The third specification is the same as specification 1, but the estimation is done for the sub-sample of 2015 - 2018.¹⁶ Table 2 shows that the average lottery winner reduce their labor earnings with 24,555.8 NOK in the year following the lottery win. The coefficient value is reduced when including the control variables to 18,640.9 NOK. When the dummy estimation is done for the sub-sample 2015 - 2018, the coefficient value increases to 42,267.8 NOK. All the results are significant at a 95% significance level.

Table 2 also gives information about the response in hours worked. Suggesting that winning the lottery is related to reducing the number of hours worked by about 28.8 hours without any control variables, and reducing the annual hours worked with 10.1 hours when including control variables. There are two things that are important to notice about the estimations for hours worked.

First, the number of winners are reduced when estimating the response in hours worked. Second, the reduction in hours is only significant in the case without control variables. It is important to notice the large standard error when estimating with control variables. This may imply that the data from 2015 - 2018 is sensitive to outliers due to the sample size.

Table 2 implies that winning the lottery, and receiving a large windfall of money affect the labor earnings and hours worked for individuals in the following year. The results in this section can be hard to interpret because it does not say anything about marginal effects of winning the lottery.

The results only tells us that if individualiwins the lottery in periodt, she will on average reduces her labor earnings and hours worked in the following year. It does not contain any information about how one extra NOK of winnings affect the reduction in labor earnings. The next section dissect the marginal response of winning the lottery closer.

15The control variables included are lagged wage, age,age², gender and education level.

16Notice that when estimating for the hours worked there is only 2 specifications, namely specification 1 and 2. The reason for this is because only the subsample of 2015 - 2018 has hourly data, so that all estimations with annual hours worked are done with the subsample.

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Table 2: Effect of winning the lottery Specifications

(1) (2) (3)

Labor earnings_i,t+1

X_i,t -24,555.8 -18,640.9 -42,367.8 (8,103.6) (7,044.7) (9,122.3)

N 12,400 11,253 3,661

Time fixed effects Yes Yes Yes

Additional controls No Yes No

Subsample No No Yes

Hours worked_i,t+1

X_i,t -28.83 -10.12 -

(14.5) (16.09)

N 3,661 3,476

Time fixed effects Yes Yes Additional controls No Yes

Subsample Yes Yes

Specification 1 is the simple estimation of equation 1, without any control variables. Specification 2 contains control variables, and is the estimation of equation 1. The control variables are: lagged wage, age, age², gender and education level. Specification 3 is the estimation with sub-sample from 2015 - 2018.

Note that the sample size decreases from estimating the labor earnings to estimating the hours worked. This is expected and is due to the fact that the data set only contains numbers on hours worked for the time period 2015 - 2018, meaning that all observations pre-2015 will be excluded when estimating for hours worked.

Clustered robust standard errors reported in parenthesis.

3.2 Marginal responses following a lottery win

To dissect the results on labor earnings in section 3.1, a new model is estimated. This model does not contain a dummy variable for winning the lottery. Instead, it uses the size of the winnings to estimate the response in labor earnings in the following year. This allows for an estimation of the Marginal Propensity to Earn (MPE). This estimation gives a more interpretable result. The attention now shifts to equation 2.

Yi,t+1=β0+β1lotteryi,t+β2Zi,t−1+λi+δt+εi,t (2) Similarly to above, the estimation looks atY_i,t+1, and in this case it should be interpreted as the labor earnings. The vectorZi,t−1still contains the same control variables as in section 3.1. λiis

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still individual fixed effects, andδtis still time fixed effects. From equation (1) to (2), the dummy variable for winners (X_i,t) is substituted with the variablelottery_i,t.lottery_i,tis the size of the lottery winnings. The coefficient of interest is againβ1, but the interpretation ofβ1 changes. β1 is now interpreted as: ”Increasing the size of the lottery winnings by 1 NOK accompanies a reduction in labor earnings byβ1”.

Table 3: Marginal effect of 100 NOK extra won Specifications Labor earnings_i,t+1 (1) (2) (3) lotteryt -2.19 -1.57 -0.035

(1.08) (0.92) (0.25) Time fixed effects Yes Yes Yes Additional controls No Yes No

Subsample No No Yes

N 12,400 11,253 3,661

All levels of the marginal response of lottery have been multiplied by 100 NOK.

Specification 1 is the simple estimation of equation 2 without any control variables. Specification 2 contains control variables. The control variables are: lagged wage, age, age², gender and education level. Specification 3 is the same as specification 1, but the estimation is done on the subsample 2015 - 2018.

Clustered standard errors reported in parenthesis.

Table 3 includes the same three specifications as table 2 and shows that winning an extra 100 NOK reduces the labor earnings by 2.19 NOK when control variables are not included. The coefficient value is reduced when including control variables to -1.57 NOK. The MPE for the subsample of 2015 - 2018 is -0.035 NOK per 100 NOK won, and is non-significant, this may indicate that there is a small sample problem with the sub-sample of 2015 - 2018. As some estimations later in this thesis is based on the subsample 2015 - 2018, one must keep in mind that the estimated MPE for this subsample is small, and non-significant. As this implies that the results based on the 2015 - 2018 subsample must be interpreted carefully, and that the estimated values are mainly meant to be indicative.

Specification 1 and 2 are fairly similar to earlier estimate of the MPE. Cesarini et al. (2017) found a MPE of -1.1 SEK per 100 SEK won. The findings are about the same as the findings of Golosov et al. (2021), who found a MPE of -2.2$ per 100$ won.

It is not known what drives the results in table 3. It could be the case that the intensive margin is the main driver. This would imply that the lottery winners will choose to work less hours, or

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choose a job with a lower wage.¹⁷ Section 3.3 takes a closer look at how the winners reduce their labor earnings, and whether this is done by reducing hours worked or reducing their hourly wage.

It could also be the case that lottery winners have a tendency to stop working at all, and that the extensive margin is the main contributor to the MPE. Section 3.4 takes a look at the extensive margin.

3.3 Dissecting the reduction in labor earnings

To further look at how the reduction in labor earnings is done, equation 3 is estimated. This specification is an inverse hyperbolic model of the reduction in labor earnings. sinh(Y_i,t+1) is the inverse hyperbolic rescaling of the labor earnings in the year following the lottery win, and sinh(lotteryi,t) is the inverse hyperbolic rescaling of the lottery prize size.¹⁸ The coefficient of interest is stillβ1, but the interpretation is now that a 1% increase in the size of the lottery winnings affects the labor earnings byβ1%.

sinh (Y_i,t+1)=β0+β1∗sinh (lottery_i,t)+λi+δt+ε_i,t (3) The reason that the inverse hyperbolic sine of the labor earnings is estimated is because of the additive qualities of the inverse hyperbolic. Because the labor earnings compose of two factors, hours worked and hourly wage, we can rewrite the dependant variable to:

sinh(Y_i,t+1)=sinh(H_i,t+1∗W_i,t+1)≈sinh(H_i,t+1)+sinh(W_i,t+1)

With Y_i,t+1 being the labor earnings in the period following the lottery win. H_i,t+1 is the

hours worked in the period following the lottery win, andW_i,t+1is the hourly wage in the period following the lottery win.

This decomposition allows us to break down the reduction in labor earnings to reduction in hours worked and reduction in hourly wage. This could give us some insight into how the individuals choose to reduce their labor earnings. Three variations of equation 3 are estimated, one for each of the dependant variables. Table 4 gives the results. Theβ1values of the dependent variable for hours worked (H_i,t+1) and hourly wage (W_i,t+1) should approximately add up to the β1value for the estimation for labor earnings (Y_i,t+1). .

Table 4 suggests that a 1% increase in the size of the lottery win is accompanied by a 0.0368%

reduction in the labor earnings.¹⁹ The reduction in labor earnings is done both by reducing the hours worked, and by reducing their hourly wage. With coefficient values of -0.0348 and -0.0050, respectively. The reduction in hours worked seems to be a stronger driver of the total reduction

17Even though the intensive margin is mainly captured by the hours worked, it could be the case that the winners choose to take a more pleasurable job.

18Inverse hyperbolic is a logarithmic rescaling of the variable. The function for the inverse hyperbolic sin is sinhx= ln (x+√

1+x²). The advantage of the inverse hyperbolic is that as the value for the variable goes to zero, so does the inverse hyperbolic. See Bellemare and Wichman (2020) for more information regarding the inverse hyperbolic sine.

19Because of the small sample size that yields non significant results, this size must not be emphasized too much.

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Table 4: Estimation of equation 4 Dependent variable

sinh(Y_i,t+1) sinh(H_i,t+1) sinh(W_i,t+1) sinh(lottery_t) -0.0368 -0.0348 -0.0050

(0.0684) (0.0427) (0.0316)

N 3,486 3,486 3,486

The table gives the results of estimating equation 3 with three different dependant variables. One for labor earnings, one for hours worked and one for hourly wage.

Robust and clustered standard errors reported in parenthesis.

in labor earnings. As the reduction in hours worked is about 7 times larger than the reduction in hourly wage. This helps to give some indications regarding the mechanisms behind the reduction in labor earnings, implying that the winners reduce their hours worked more than their hourly wage. It is important to note the large standard errors. None of the values for any of the coefficients are significant. The results are mainly meant to be indicative, showing that the non-significant reduction found in part 3.2 is mainly due to a reduction in hours worked, and not due to a reduction in hourly wage.

3.4 Probability of working following a lottery win

Since the previous sections have focused on the intensive margin, the attention now shifts to the extensive margin. I look at the extensive margin by estimating the probability of exiting the labor market following a lottery win. There are two possible ways of defining unemployment in my data. The first is most strict and is to define an individual as unemployed in year t+1 if that individual has no labor income in period t+1. This approach is taken in this section and table 5.²⁰ The alternative is to define an individual as unemployed if that individual is not registered with a job in A-meldingen for six months or more in year t+1.²¹

To get an estimate of the extensive margin I estimate equation 4. In equation 4, Job_i,t+1 is a dummy variable that equals 1 if individualigot a job in periodt+1. X_i,tis a dummy variable that equals 1 if the individualiwon in periodt. λicaptures individual fixed effects andδtcaptures time fixed effects. The coefficient of interest isβ1, as this captures how winning the lottery affects the probability of being employed. The model is also conditioned upon the fact that winners have a job in the period before they win the lottery, so the model captures those who change employment status following a lottery win.

Job_i_,_t₊₁=β0+β1X_i_,_t+λi+δt+εi,t (4)

20This approach is also used in section 4.3

21The results with this alternative approach are very similar and are presented in appendix B and table 14.

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Table 5 shows the results and suggests that winning the lottery reduces the chances of being employed by 2.30%. This is statistically significant at a 5% level. This implies that there is an effect taking place on the extensive margin. However, the table tells us nothing about how much of the previous results on labor earnings that are driven by the extensive margin. Section 3.5 attempts to shed some light on this.

Table 5: Estimation of probit model for quitting the labor market

Job_i,t+1 Coefficient value SE N

Winneri,t -0.0230 0.00943 12,400 The table shows the estimation of the excess probability of exiting the labor market in period t+1, given that the individual wins in period t.

3.5 Reduction in labor earnings by separated results

As the results in previous sections implies that there exists both an intensive and an extensive margin, this section attempts to derive what margin that contributes the most to the MPE. This is done by estimating the MPE again, but separating the winners into two groups. One group containing the individuals who stays in the labor market and one group containing the individuals who exits the labor market. Equation 5 is the same as equation 2, but with an additional condition.

This condition states that the individual must have some labor earnings in the year following the lottery win. ²²

Y_i_,_t₊₁=β1+β2lottery_i_,_t+β3Z_i_,_t−1+λi+δt+εi,t|Y_i_,_t₊₁,0 (5) Table 6 suggests that the effect of an extra 100 NOK winnings is accompanied by a reduction in the labor earnings by 1.84 NOK, when including the control variables the coefficient value is reduced to -1.52 NOK. Both coefficients are significant at a 10% significance level.

These results are mainly interesting when they are looked at in the light of the full sample.²³ If we compare the findings in table 6 with the findings in table 3, some meaningful insight may be derived. The MPE of 100 NOK for the full sample that was found in table 3, had a coefficient value of -2.19 NOK, this is reduced to -1.84 NOK when conditioning upon the continuation of working.

Comparing these two results we see that the reduction for individuals who choose to stay in the

22When separating the two subsamples, the number of winners who quit their job is only 606. Since the sample of quitters is so small, the estimation chooses to focus on the subsample of stayers.

23The full sample meaning the sample that includes both the winners who stay in, and winners who exit the labor market. I.e., the estimated values in section 3.2.

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labor market is 85% of the MPE for the full sample. This percentage is even larger when including control variables. As the coefficient in table 3 is -1.57, and the coefficient value in table 6 is -1.52, the MPE for the individuals who choose to stay in the labor market is about 97% of the MPE of the full sample. Since the difference between the MPE in table 6 and 3 is so small, this may imply that the intensive margin is the main contributor in the MPE, with the extensive margin playing a minor role.

Table 6: Estimating the MPE for stayers Specifications Labor earningsi,t+1 (1) (2)

lottery_i,t -1.84 -1.52

(0.98) (0.86) Time fixed effects Yes Yes Additional controls No Yes

N 11,821 10,840

Specification 1 is the simple estimation of equation 5 without any control variables. Specifi- cation 2 is now the estimation with additional controls. The control variables are: lagged wage, age, age², gender and education level.

The estimation tells us the marginal effect of winning 100 extra NOK in the lottery for winners who stay in the labor market.

Clustered standard errors reported in parenthesis.

4 Heterogeneous effects by lottery prize size

The previous sections have only focused on the winners as a whole, and not differentiated by lottery prize size. As winning 1,000,000 NOK is a larger part of the lifetime earnings than 100,000 NOK, it may be the case that winning a large prize induce a larger, and just as important, different response than small winnings.²⁴ Therefore, it is intuitive to think that there is a possibility for large heterogeneous effects across the distribution of the lottery prize size. In this part the heterogeneous effects are put under the microscope. The section discusses how the lottery prize size matters for the MPE and for the effect on the extensive and intensive margin. The section starts by estimating the MPE within each quartile of the lottery prize size. Thereafter, the inverse hyperbolic specification

24Different in the sense that it may alter the response on the intensive and extensive margin. The argument being that when winning a large prize, one may actually want to change or even quit their jobs, but they are not willing to do this if they win a smaller prize.

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is repeated to dissect the reduction in labor earnings into reduction in hours and hourly wage by quartiles. Lastly, the quartiles are used to check if the probability of exiting the labor market increases with the size of the lottery prize.

4.1 MPE by quartiles

To check for heterogeneous effects, I start by estimating how the MPE varies between each quartile of winning. This is done by estimating equation 2 again. However, the estimation is now done four times, one for each quartile.²⁵

Equation 6 is the specification that is now estimated and table 7 shows the results of the estimation. When estimating the MPE for each quartile, the control group includes all winners from every quartile before they win.²⁶

Y_i,t+1=β0+β1lottery_i,t+β2Z_i,t−1+λi+δt+εi,t











Quartile1 Quartile2 Quartile3 Quartile4

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Table 7 shows that the marginal effect of an extra 100 NOK is decreasing with the size of lottery prize. The reason for this may be purely mechanic as the MPE measures the size of the reduction in labor earnings as a part of the winnings. As the winnings increase, the MPE may be smaller simply because there is a limitation to how much the individuals may be able to cut.²⁷ Table 7 gives valuable insight because it tells us that there is a statistically significant effect for all quartiles.

Showing that even small winnings trigger a response in labor earnings.

25Table 14 in Appendix C contains the table for quartile limits of prize sizes for the full sample.

26This is done to get a larger control group than what would have been if I had estimated using only individuals within the same quartile as the winner.

27The limitation is imposed by the size of the labor earnings. Considering the fact that the marginal reduction is found as _lottery^Yⁱ^,^t

i,t, the MPE is limited by the labor earnings as a fraction of the lottery prize size and as the lottery prize size increase, the fraction must, purely mechanical, become smaller.

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Table 7: MPE by quartiles (per 100 NOK) Quartile Labor earningsi,t+1 Coefficient N

1 lottery_i,t -20.94 9,191

(9.92)

2 lottery_i,t -15.81 9,004

(8.25)

3 lottery_i,t -7.31 9,089

(3.69)

4 lotteryi,t -3.16 9,104

(1.21)

The table shows the marginal effect of winnings 100 NOK in the lottery, separated by quartiles of prize size.

4.2 Dissecting the heterogeneity

As the previous section showed heterogeneous tendencies, it may be worth to look at how the mechanisms behind the reduction varies between each quartile. To look at this closer, I repeat the decomposition in part 3.3 while separating into quartiles. ²⁸

The attention now shifts back to the equations from section 3.3, but with the estimations limited to the quartiles of winnings. In the equation below,Y_i,t+1is either the labor earnings, hours worked or hourly wage depending on the specification. The parameter of interest is still theβ1coefficient.

sinh (Y_i,t+1)=β0+β1∗sinh (lottery_i,t)+ε_i,t

Table 8 shows the results of estimating the equation above with the dependent variable being either labor earnings, hours worked or hourly wage. The results presented in the table suggests that larger lottery winnings trigger a larger response in labor earnings. With the coefficient value for the labor earnings being larger in quartile 4 than in quartile 3, and both quartile 3 and 4 being larger than quartile 1.²⁹ As previously mentioned, these sizes are meant to be indicative, and to shed some light on how the different quartiles differ in their response. The first quartile mainly respond by reducing their hours, as the part of the reduction in labor earnings accounted for by the reduction in hours is nearly 3 times as large as the reduction in hourly wage. The second quartile seems more prone to adjust their hourly wage. However, the reduction in hours worked is still about 1.3 times the response in hourly wage. The third quartile seems to show the same size proportions as the second quartile. The main reduction happening on hours worked, but still

28The quartiles that are used for this estimation are listed in table 15 in appendix C. The quartile limits are now different, as the data is only from 2015 - 2018.

29The outlier of course being quartile 2, which shows a much larger reduction than the rest of the quartiles. This may be due to the small sample size.

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some effect on the hourly wage. The reduction in hours worked is about 1.9 times the reduction in hourly wage. Also the last quartile does the main part of the reduction on the hours worked.

The reduction in hours worked is about 1.9 times the size of the reduction in hourly wage. Notice however, that none of the reported values in the table are significant.³⁰

This suggests that larger winnings trigger different responses. As the size of the lottery prize increase, so does the reduction in hourly wage.³¹ This may indicate that as the lottery prize increases, the response changes in such a way that a reduction in hourly wage is more prone to happen.³² This increasing effect seems to be diminishing. As soon as the lottery prize size is in quartile 2, the size proportions of hours worked compared to hourly wage is fairly similar.

Table 8: Dissecting the inverse hyperbolic reduction Dependent variable

Quartile sinh (Y_i,t+1) sinh (H_i,t+1) sinh (W_i,t+1) N 1 sinh (lottery_i,t) -0.0248 -0.0194 -0.0067 2,039

(0.0248) (0.0177) (0.0166)

2 sinh (lottery_i,t) -0.0617 -0.0369 -0.0287 1,922 (0.0513) (0.0309) (0.0236)

3 sinh (lottery_i,t) -0.0345 -0.0243 -0.0130 1,988 (0.0538) (0.0368) (0.0227)

4 sinh (lottery_i,t) -0.0505 -0.0348 -0.0185 2,016 (0.0472) (0.0313) (0.0204)

The table shows the inverse hyperbolic rescaling estimation on labor earnings (Y_i,t+1), hours worked (H_i,t+1) and hourly wage (W_i,t+1). Showing the response in labor earnings divided into the response in hours worked and hourly wage.

30The large clustered standard errors occurring within each quartile implies that none of the values are significant.

However, the decomposition is mainly meant to be indicative and an attempt to look at the decomposition in part 3.3 within each quartile. The large standard errors could be a result of the small sample within each quartile.

31Again, the exception being quartile 2.

32How the reduction in hourly wage happens is not know. One theory may be that as the lottery prize size increase, the lottery winners are more prone to change job or similar activities.

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4.3 Probability of working

The previous sections shows heterogeneous tendencies on the intensive margin. It could be interesting to see if these heterogeneous effects also exists on the extensive margin. To check how the effect on the extensive margin changes as the winnings increases, equation 4 is now estimated for the four quartiles of the size of lottery winnings.³³³⁴

Job_i_,_t₊₁=β0+β1X_i_,_t+λi+δt+εi,t











Quartile1 Quartile2 Quartile3 Quartile4

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In equation 7, Job_i_,_t₊₁is a binary variable that equals 1 if individualigot a job in periodt+1.

X_i,t is a dummy variable that equals 1 if the individualiwon in periodt. λi captures individual fixed effects andδtcaptures time fixed effects. The coefficient of interest isβ1, as this captures how winning the lottery affects the probability of being employed.

Table 9:Probability of exiting labor market by quartiles

Quartile Job_i,t+1 Coefficient N 1 Winner_i,t -0.0175 9,191

(0.0137)

2 Winner_i,t -0.0181 9,004 (0.0169)

3 Winneri,t -0.0285 9,089 (0.0167)

4 Winner_i_,_t -0.0260 9,104 (0.0165)

The table gives the probability of exiting the labor market after a lottery win separated by quartiles.

33As before there are two ways to identify the extensive margin. One stricter identification of no labor income in the year following the lottery win, and one looser identification with the job status from A-meldingen. The results presented in this section takes advantage of the first identifying assumption, and appendix B.2 takes a closer look at the second identifying assumption.

34The quartile distribution is listed in table 14 in appendix C

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Table 9 shows that the coefficient value increase for the three first quartiles from 1.75% to 2.85%.

This suggests that the extensive margin is increasing with the size of the lottery winnings. The observed increase in the three first quartiles seems to stop when moving from quartile 3 to quartile 4. With the probability of exiting the labor market being 2.85% for quartile 3 and 2.60% for quartile 4. This results suggest that the extensive margin is ”concave” in the sense that it is increasing with the size of the lottery win, but as the lottery win increases, the probability of exiting the labor market flattens. These results may be explained by the intuitive reasoning that winning a larger prize may trigger a larger response. If the lottery prize size gets large enough, the extra money will be used to exit the labor market in full. However, this effect seems to be diminishing as the lottery prize size reach a certain threshold.

5 Dynamic labor supply responses

The previous sections have focused solely on the effect lottery prize has on the labor supply in the t+1 period. I now shift the focus to the following periods. It is important to understand to what extent the shock in wealth affect labor supply in the short and long term. Figure 2 shows the dynamic response of winning the lottery in year t for the following years.

The effect on labor earnings is largest int+1, and seems to be going back to zero in period t+2 and staying at zero in periodt+3.³⁵ The reduction in MPE is only significant in the period t+1, but the response is somewhat apparent in period t, with a coefficient value below zero. The reason for the low persistence in the MPE is of course not known, but some theories regarding the mechanism is worth mentioning. This may indicate that the winners reduce their labor earnings in the year following the win by simply taking more days offor similar short-term and non-persistent adjustments. This extra leisure is then assumed to be financed by the lottery winnings, and as soon as the extra money is spent, the MPE returns to zero.

The estimation on hours worked only stretches from the t-1 period to the t+4 period.³⁶ In periodt+1 the winners reduce their hours worked some, this effect seems to be enlarged in period t+2. Between periodt+2 andt+3 there seem to be a reverting effect, as the annual hours worked increase substantially. This increase dies out in the following period. This implicates that the winners work less in the two periods following the win. But in the t+3 period they compensate for the extra leisure by working more. The effect of hours worked show some persistence in the shock, but also large standard errors.³⁷

35Note the increasing size of the confidence intervals as the simulation moves in time.

36The reasons is because of the small sample set, so I do not have any numbers in period t-2 or t-3.

37Because the data sample is smaller for this estimation, the increase in hours may be due to some large outliers that affect the result in a big way.

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-3 -2 -1 0 1 2 3

Time period relative to winning

-10 -5 0 5 10

MPE (per 100 NOK)

Marginal response in labor earnings

-1 0 1 2 3 4

Time period relative to winning

-300 -200 -100 0 100 200

Hours worked

Response in hours worked

Figure 2:Dynamics of the shock in labor earnings and hours worked

6 Conclusion

This master thesis aimed to give some new insight on the intensive and extensive margin of labor supply. This was done by estimating the MPE and finding similar results as existing literature.

When decreasing the sample size to the sample including hours data, the MPE was shown to be small and insignificant. After finding the MPE, the thesis moves on to decomposing the reduction into two parts, and showing that the main reduction in labor earnings stems from reducing the hours worked. Due to the reduction in the sample size, the decomposition has to be interpreted indicatively. The extensive margin is then introduced, indicating that there is an increased probability of exiting the labor market following a lottery win. I then investigate the intensive margin by separating the winners into two subsamples. The sample containing lottery winners who continue to work have a MPE close to the MPE of the full sample. This indicates that the MPE is mainly driven by the intensive margin. I then use the prize size distribution to show that there are heterogeneous effects for the MPE and the effect on the intensive and extensive margin. In the last part of the thesis, the dynamics of the shock is looked at, showing that the effect on labor earnings are transitory, with the MPE being close to 0 after 2 periods. The effect on hours worked seem to be more persistent, but with a counter intuitive result in the t+3 period, where the winners actually increase their annual hours worked, before reverting back to zero in the t+4 period.

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References

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Oxford Bulletin of Economics and Statistics, 82, 50–61.

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Blundell, R., A. Bozio,andG. Laroque(2011): “Labor Supply and the Extensive Margin,”The American Economic Review, 101(3), 482–486.

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A Randomness in the lottery

This appendix tries to estimate if winning the lottery can be interpreted as an exogenous and idiosyncratic shock. The reason that this is important is because of the identifying assumption of an exogenous and idiosyncratic increase in wealth. To look at how the lottery prize is distributed, I first estimate a probit model that shows that a binary variable for winning, is not predicted by any observable traits. Secondly, the size of the lottery prize is estimated to show that there is no significant variables when attempting to predict the size of the lottery prize. All estimations are done on the pre-trend, meaning the year before the lottery winners actually win the lottery.

A.1 Randomness of winning

Equation 8 is a model laying out the probability of winning the lottery. The dependant variable isWin_i,t, this is a binary variable that is equal to 1 if individualiwins the lottery in periodt. The Xi,tcontains a series of control variables, namely age, lagged wage, lagged hours worked, gender and education. The coefficient of interest is the vector coefficientβ1, which captures the coefficient value for all the control variables.

Win_i,t=β0+β1X_i,t−1+ε_i,t (8) Table 10 shows the results of estimating equation 8, both in the multivariate and the univariate case. With the univariate being the estimation of equation 8 with only one control variable, and the multivariate including all the control variables. The table shows that the only variable that have a correlation with winning the lottery is the age of the individual. However, the pseudoR² is below 1 percentage point and the model have little goodness of fit.³⁸. Indicating that non of the observable traits increases the chance of winning the lottery. This implies that the shock is exogenous.

38The reported pseudoR²is the McFaddenR²

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Table 10: Randomness of winning the lottery

Univariate Multivariate

Control variable Value SE pseudoR² Value SE pseudoR²

Age_t−1 0.011^∗∗∗ 0.00097 0.0062 0.010^∗∗∗ 0.0016 0.0057

Wage_t−1 −2.16∗10⁻⁸ 2.36∗10⁻⁸ 0.0000 −5.88∗10⁻⁸ 4.84∗10⁻⁸ 0.0057 Hourst−1 −3.2∗10⁻⁵ 3.7∗10⁻⁵ 0.0001 −2.86∗10⁻⁵ 4.17∗10⁻⁵ 0.0057

Gender -0.00032 0.2122 0.0000 -0.0173 0.0345 0.0057

Education -0.0032 0.0044 0.0000 0.0082 0.0067 0.0057

Note: *,**,*** states a significance level of 10, 5 and 1 percent, respectively. Standard errors reported as robust and clustered errors on individuals.

A.2 Randomness of size

A similar exercise is needed for the size of the lottery winnings, as the shock must be interpreted as idiosyncratic. I now estimate equation 9. The equation is an estimation done for only the lottery winners, and should be interpreted as: Given that individualiwins in periodt(Win_i,t =1), what predicts the size of the winnings. Xi,tis the same control variables as in appendix A.1.

E[lotterysize_i,t|Win_i,t=1]=β0+β1X_i,t−1+ε_i,t (9)

Table 11: Randomness of winning the lottery

Univariate Multivariate

Control variable Value SE R² Value SE R²

Age_t−1 -298.39 533.03 0.0000 −1,632.08^∗∗ 757.74 0.0007

Wage_t−1 0.04 0.02 0.0001 0.061 0.048 0.0007

Hours_t−1 13.39 10.72 0.0001 -1.37 14.52 0.0007

Gender -4,247.66 13,274.10 0.0000 -13,934.28 11,959.99 0.0007 Education -1,810.66 1,883.92 0.0000 −5,402.67^∗ 2,876.22 0.0007 Note: *,**,*** states a significance level of 10, 5 and 1 percent, respectively. Standard errors reported as robust and clustered errors on individuals.

Table 11 shows the results of estimating equation 9. The results are presented in an univariate and multivariate case. With the univariate being the estimation of equation 9 with only one control variable, and the multivariate including all the control variables. In the univariate case, none of the coefficients are significant, and theR²is below 1% for all the specifications, implying a very low goodness of fit. In the multivariate case the variables for age and education are significant at

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a 5 and 10 percent significance level, respectively. However, as theR²is also below 1 % the model has a very low goodness of fit. The estimation and results in table 11 implies that the shock is indeed idiosyncratic.

Table 10 and 11 combined implies that the threat to identification can be assumed to be minimal, as the shock can be interpreted as both exogenous and idiosyncratic.

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B Probability of working following a lottery win revisited

In section 3.4, I mention that there is another identification possible for estimation of the extensive margin. The estimation of the probability of exiting the labor market can be done by using data from A-meldingen. This may be interesting as A-meldingen tracks the individuals employment status through every month. In this appendix the estimations done in section 3.4 and 4.3 is revisited. Doing the estimation for the probability of exiting the labor market with another identifying assumption. Since A-meldingen is a monthly data set, an assumption must be made about whether or not the individual is working in any given yeart. The identifying assumption is that if individualiwas employed for 6 months or more in periodt, the individual will be counted as employed in periodt.

B.1 Probability of working for full sample

The estimation for the probability of exiting the labor market is the same as the model in section 3.4. The only change is the identifying assumption for who is registered as employed.

In equation 10,Job_i,t+1is a dummy variable that equals 1 if individualigot a job in periodt+1.

X_i_,_t is a dummy variable that equals 1 if the individualiwon in periodt. Z_i_,_t−1 is a set of control variables, namely age, wage, gender and education. λi captures individual fixed effects and δt

captures time fixed effects.

Job_i,t+1=β0+β1X_i,t+β2Z_i,t−1+λi+δt+ε_i,t (10)

Table 12: Estimation of probit model for quitting the labor market

Job_i,t+1 Coefficient value SE N

Winner_i_,_t -0.0274 0.0095 3,488 The table shows the estimation of the excess probability of exiting the labor market in period t+1, given that the individual wins in period t.

Table 12 shows the results of estimating equation 10. The table suggests that winning the lottery reduces the chances of being employed by 2.74%. This is statistically significant at a 5%

level. The results are fairly similar to the ones that are found in section 3.4, as the results in section 3.4 was that winning the lottery increased the chance of being employed in year t+1 by 2.30%. This shows that loosening the identifying assumption gives a higher probability of exiting the labor market, but not by a large margin.

Labor Supply for Norwegian Lottery Winners