Does Working Overtime Under Different Culture Belief

Hurt the Labor Market? ∗

Yiqian Lu†

November, 2016

∗I am grateful to Neel Rao for his helpful comment and sincere help. Also I appreciate the commentfrom Mingliang Li, Goncalo Monteiro, Joanne Song Mclaughlin, Eric Nierenberg, Bibaswan Chatterjeeand Jinquan Gong. All errors are mine.

†Email: yiqianlu@buffalo.edu Address: 415 Fronczak Hall, Buffalo, NY 14260. Department ofEconomics, State University of New York at Buffalo.

1

Abstract

In this paper we model the work-leisure equilibrium under different culture and

social norm influence. We build a two-sector general equilibrium model and use

Panel Study of Income Dynamics (PSID) data from 1975 to 1992 to test our the-

oretical predictions. Three major findings are reported. (1) A stronger preference

on social status will make employees substitute leisure with working hours. The

working hours will increase with respect to the relative exponential ratio between

labor and capital input. And the growth rate of the economy is higher. (2) On the

contrary, the individual self-identified utility level might be lower in such society

since everyone are extremely exhausted chasing high social ranks. (3) We find no

significant evidence that strong social preference and working overtime will lead to

an increasing unemployment level. This article contributes to the literature by ex-

amining labor market outcomes under various social status preference assumptions.

JEL Classification: J22, J31, E23

Keywords: Social Status Preference, Working Overtime, Labor Market Equilib-

rium, Ability Signal

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1 Introduction

The allocation of time remains in the central topic of labor economics. Becker (1965)

pioneers the work of interpreting the time allocation decision between working and

other activities such as home production. It sheds the light for economists to study how

individuals behave in the labor market. Gronau (1976) revisits Becker’s famous result

and finds out that home production is affected differently by changes in socioeconomic

variables comparing to leisure decision. Men and women tend to obtain different specific

human capital training. For instance, married women tend to spend less effort in

the labor market competition since child care and housework carry an intensive effort

(Becker 1985). With technology progress and emancipation for the female from the

family sector, women is more willing to participate in the labor market. Consequently,

the participation rate for women increases from 21% in 1900 to 59% in 2009 (Bowen,

William G., and T. Aldrich Finegan 2015).

At the same time, we can never fail to notice that labor market behaviors vary with

ages. Young women, for instance, have the tendency to work part-time or reduce the

workload(Kunze, Astrid, and Kenneth R. Troske 2015) when entering the job market

since the duties of raising kids reduce their interests for working during the child-bearing

and child-raising age. Some young mummies even quit the labor market, which might be

temporary. However, most of them would like to return to the job market when children

grow up. This phenomenon could be explained as the domination of substitution effect

at the early stage of job market for young women. Traditionally it is believed that

homogeneous agent model ignores the heterogeneity (culture-based heterogeneity in

this paper), which could result in unreliable research conclusions. For some East Asian

countries, for example, young women enter the labor market more intensively, where

the culture could be distinct from the West (Yoon, Jayoung 2015). Particularly, the

childbearing age-cohort female labor participation rate remains at high level, displaying

a stronger income effect in Asian countries. It could be the direct result of observed

low fertility rate in the East Asian region, which could also be explained by the inverse

causal effect. In fact, the domination of income effect could be explained by low subsidy

to the childcare system or birth controlling policies (James Liang 2015, Fuxian Yi 2010).

3

Added worker effect is a plausible explanation in this situation. Female workers are

encouraged heavily by their husbands or families to join the labor market to support

the family income.

Culture and cross-industry difference is another crucial factor to explain the het-

erogeneity. Investment banks, for example, may push the employers to work 80 or 100

hours per week to satisfy the job requirement, especially for the entry-level analysts or

associates. These facts can be observed whenever you come across the Goldman Sachs

or Morgan Stanley’s offices in Manhattan. Also, most Chinese information technol-

ogy companies strongly encourage workers to follow a so-called ”996” working pattern,

which means each employers should work from 9 am to 9 pm each working day and 6

days a week. Any worker who fail to obtain such workload criteria might be considered

as ”low ability” or ”unsatisfied performance” so that she/he could be fired or lose the

promotion possibilities. It is summarized by JH Kang, JG Matusik, LA Barclay (2015)

and explained by culture difference that Asian culture requires more working effort.

HUAWEI1, the CISCO major competitor all over the world but USA, strongly

encourages every junior engineers to work and sleep in the office and never go home

but only pays them based on the 40 or 50 hours scheduled weekly working hours. In

this case, many engineers could work more than 100 hours a week but only report

40 or 50 working hours to the Taxation and Labor Department so as not to break the

worker-protection law. The co-called ”wolf-culture”, aka. working unreported overtime

with little compensation, is the key for HUAWEI to compete with CISCO. You might

wonder why the junior workers are willing to wait for 24/7 project assignments without

reasonable compensations. If a junior worker displays sufficient hard working and

loyalty by following such torturing job requirements, he/she would have a large chance

to be promoted and get an outstanding payment throughout the industry. Other under-

reported working overtime is the case in Japan. Junior workers are seldom allowed to

leave the office before their bosses, which displays disrespect in Japanese culture. Even

a low-rank employee finishes her/his job duties, she/he should wait until the direct

boss leaves (WB Schaufeli, A Shimazu, TW Taris 2009), which leads to, in a certain

extent, an excessive and compulsive working overtime. Also, coming home too early,

1you can raise a couple of other similar examples in the East Asian countries

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say 7:30 pm, could be treated as a dangerous signal of potential unemployment, which

is particularly true for young men workers. Hence, each worker in such situation works

or pretends to work hard and leaves office later and later. (Samuel, Sidney W 2015)

This phenomenon enlightens the research that I propose in this paper. We are

going to answer the following three questions. (1) Since leisure is generally considered

as normal good, why do those workers wish to give up their precious leisure time to

work for the reported or unreported excess workload? Do they work overtime in order

to increase their promotion chances by sending signal of diligence or high ability? (2)

Does the culture affect the work-leisure choices in those East Asian countries? Does

such ”leaving after the boss” belief reduce the utility and market efficiency level? If so,

how does the culture bias influence the equilibrium? (3) If most people are willing to

work overtime, will the employer decrease the labor demand by recruiting less people

to fulfill the job tasks? Will the overtime-working lead to an increasing unemployment

rate?

We are going to build a heterogeneous agent model to answer the aforementioned

questions. After calibrating various social norm or regional culture with different utility

function, we would like to discuss how equilibrium shifts under various social norm.

Finally, we would like to use the Panel Study of Income Dynamics (PSID) data to

examine our theoretical findings.

The remaining parts of this article are organised as follows. Section 2 reviews the

existing literature on similar topics. Section 3 builds the standard model and discusses

the equilibrium under various social normal assumptions. Section 4 describes the data

we use and provides estimate for the theoretical results. Concluding remarks are made

in Section 5.

2 Literature Review

There are extensive literature discussing the working hour difference between various

regions. Even among OECD countries, the annual average working hour for a full-time

worker varies. (Mexico 2,228, South Korea 2,124, USA 1,436, Japan 1,729, Denmark

1,436, Germany 1,371) (2014 OECD report). In non-OECD regions, the annual working

5

hours also distinct a lot. Hong Kongers and Singaporeans, for example, have to work

approximately 2400 hours per year while less than 1500 in some less developed regions.

We can notice that the employers in some northwest European countries only work

two-thirds of Mexicans and Koreans. It is explained by different ethic standards like

Confucian ethics, where too much leisure is considered as laziness and immorality (JH

Kang, JG Matusik, LA Barclay 2015).

Akerlof (1976) pioneers the work that labor market equilibrium could result in

inefficient long hours. It is also noticed by the academia community (Blair-Loy 2004)

that firms might reserve the best jobs and opportunities for workers who can give

long hours to their employers with very limited family responsibilities. Gicheva (2013)

documents that 5 extra hours are associated with a 1% increase in annual wage growth

but the relationship is not presents when weekly working hour is below 47, which

displays the non-linear hour-wage relationship.

Mauss, Marcel (1923) describe the labor-wage contract as a kind of gift exchange

process, where wage-payers exchange a gift of a wage premium for the expected high

effort performance. By following this framework, if workers are willing to provide ex-

cess work, they should expect to receive high payoff currently or in the future, which

is the increasing promotion chances 2 . Akerlof, George A.(1982) uses a specific utility

function to mimic the workers’ effort. Each individual preference depends on her/his

attitude towards fairness . If the employee cares nothing about fairness, the market

equilibrium in this case will be the competitive equilibrium. If the fairness (altruism)

level is positive there will be positive improvement on the wage and employment. And

vice versa, which could also be a possible reason explaining the ubiquitously observed

cross-industry wage differences(Akerlof, George A., and Janet L. Yellen 1988). Invol-

untary unemployment could be a direct result of negative fairness preference. Workers

are discouraged to provide sufficient labor supply comparing to the competitive equilib-

rium with negative fairness preference. There would exist no involuntary unemployment

when all employers are neutral (Akerlof, George A., and Janet L. Yellen 1990, Fehr,

Ernst, and Klaus M. Schmidt 1999). The existence of non-monetary motivation in the

2Treating the chances of promotion as options, the employees write the option at the early stage. Ifthe employers could survive the challenging duties in the first period, the expected return of the optionwould be high. Otherwise, the option would expire in the second period and the option value is 0.

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preference function is tested by Gneezy and Rustichini (2000a & 2000b) by examining

the performance of the parents in the daycare centers in Israel. They conclude there

indeed exists such selfish or altruism component in the utility function.

Also, there is alternative literature concluding that work-leisure choices are affected

by policies. Osuna, Victoria (2003) finds out the taxing overtime wage could greatly

reduce the observed excess overtime workings. They calibrate the model and conclude

a marginal 12% tax rate could reduce 8 hours a day (which is one hour excess work

each working day) to 7 hours 3. Nickell, Stephen, and Richard Layard (1999) discover

that union strength and social welfare system play pivotal roles in explaining the un-

willingness of working overtime for European societies. The stronger union protection

for workers and the better social welfare benefits, the less effort people would like to

supply in the labor market. They argue that increasing product market competition

could be a remedy to solve the negative influence of unions and social security, which

provides more incentive for employers to work hard.

There is an ongoing heated debate between pros and cons of working overtime. Some

scholars argue the workers who work overtime display an extraordinary effort and ef-

ficiency level comparing to those employees who do not (Machlowitz, 1980; Peiperl,

Jones, 2001). However, an opposite view is that workaholics increase the difficulties

level by themselves, adding unnecessary complexities for their colleagues (Oates, 1971,

Machlowitz, 1980, Porter, 2001), and therefore it could be problematic for the com-

panies. Especially when the accomplishment of projects relies heavily on cooperation,

such low-efficient performance could lead to excess workload to the co-workers and re-

sult a trouble-making working overtime culture. There is also some literature (Burke

2001, etc.) pointing out there is no relationship between the working overtime and the

efficiency level, contradicting the positive or negative ability signal hypothesis. The

positive outcomes could be an excess wage ratio for overtime workload while the neg-

ative could never be neglected at the same time. Researchers demonstrate there is a

negative association between working overtime and weak health level such as high levels

of stress, ill-health situation and strain (Sparks, Kate, et. al. 1997).

37-hour a day is the regular working schedule for some European countries but not for USA, Chinaand Japan

7

It could hardly be ignored that tenure structure influences the workers’ selection

on work-life balance. Robert A. Hart, Yue Ma (2013) test British plant and machine

operatives and discover workers with longer tenure are more fond of supplying excess

work. However, the marginal product during the over time is less than the wage pre-

mium, indicating potential low efficiency level when workers are fatigue. By noticing

such phenomenon, the employees could lower the base wage rate in order to set the

aggregate salary for the overtime-working staff the same level comparing to never over-

working peers. There is little evidence that demand side serves as the main driven force

for overtime working (Bell, David NF, and Robert A. Hart 2003). Usually speaking,

extensive-margin elasticities are supposed to be higher than intensive-margin predicted

by various macroeconomic models (Richard Rogerson 1988, Gary D. Hansen 1985,

Lars Ljungqvist and Thomas J. Sargent 2006). In a sense, it is the case that work-

ing overtime should not be widely observed since the intensive adjustment to a higher

compensation should be relatively small. However, recent literature(Chetty, Raj, et

al 2011) argues the intensive-margin elasticity are significantly underestimated by the

previous literature, which could possibly offer vigorous explanation for widely-existing

overtime working.

Overall speaking, there are various interpretations on the reason and influence of

overtime working and economists have not yet reached out a convincing conclusion.

3 Model Setup and General Equilibrium

3.1 Workers

We build a competitive equilibrium model in the section. Following Bakshi, Gurdip S.,

and Zhiwu Chen(1996)’s approach, we may assume a worker lives forever and maximizes

his/her lifetime utility.

max{Ct}∞t=0,{Lt}∞t=0

βtE0[U(Ct, Lt, St)] (1)

where β is the time preference parameter; U(Ct, Lt, St) denotes the utility function

of consumption level Ct, leisure Lt and social status level St. Assume U(., ., .) are

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twice differentiable with each variable and UC ,UL > 0 , indicating that additional

consumption or leisure creates positive marginal utility. We cannot assume St have

the similar characteristics at this moment. If the agent has no preference on the social

status, i.e. US = 0, then U(., ., , ) has no relationship with S.

We maximize the target function subjected to the budget constraint 4,

at+1 − at = µtat − Ct + wt(St) (2)

where µt represents the return on capital in period t and wt(St) is the wage in

period t corresponding to the social status level St. at is the asset level.

In this model, the social status variables St are not direct choices variables for

workers. The status will be determined by the employees after observing workers’

labor effort and potential influential factors (for example luck). When t increases from

0 to infinity, we assume that the social status or the rank strictly increases. In other

word, {S = 1} ≺ {S = 2} ≺ {S = 3} ≺ ... ≺ {S = t} ≺ {S = t + 1} ≺ ... and at the

initial period S0 = 1. It is assumed S ∈ Z+ is discrete without loss of generality.

We attempt to use four different models with various representative’s preferences

to explain our findings.

Model 1. (No preference on social status).

The worker has no preference on social status. In other word, there is no discrimination

against various rank or social status. In this case, US = 0 and we have U(Ct, Lt, St) =

U(Ct, Lt). A Cobb-Douglas utility function is given by

U(Ct, Lt, St) =(Cρt L

1−ρt )1−γ

1− γ(3)

This assumption is consistent with M Lettau, H Uhlig (2000), as well as Rupert,

Peter, Richard Rogerson, and Randall Wright (2000). We use this utility function since

the marginal rate of substitution is a function of consumption and leisure.

MRSt+1 = β(Ct+1

Ct)ρ(1−γ)−1(

Lt+1

Lt)(1−γ)(1−ρ) (4)

4we first assume there is no stochastic term in the budget constraint

9

Typically it is more likely to observe the utility function with US = 0 in the most

developed economies such as United States. People have no discrimination taste.

Model 2. (Utility level depends on the social status)

The representative agent’s utility depends not only on consumption and leisure but

the social status as well in Model 2 .

U(Ct, Lt, St) =(Cρt L

1−ρt )1−γ

1− γSηt (5)

where η depicts the preference level on the social status. If η = 0, Model 2 shrinks

to Model 1 automatically. η > 0 indicates a positive preference on social status. A

higher social status may provide you more power and welfare such as travel benefits

and respects. It is widely observed in most Confucian-dominated countries such as

East Asia and Singapore that people have positive preference on social status. On

the contrary, η < 0 shows a negative preference, which might result from increasing

peer pressure and responsibility. η < 0 could be observed in some European countries

thanks to the well-developed social welfare system and religious influence.

Model 3. (Utility level depends on the ratio between individual social status and

its social average)

In this case, the utility function turns into the following format.

U(Ct, Lt, St) =(Cρt L

1−ρt )1−γ

1− γ(StS

)η (6)

where S represents the average social status. If St < S, the agent is in the bottom half

while St > S indicates an above average rank. If St = S, then the agent is exactly in

the median class. You could notice if we preset S as constant, then Model 3 is exactly

Model 2.

Model 4. (Utility depends on the self-identified social status level)

U(Ct, Lt, St) =(Cρt L

1−ρt )1−γ

1− γ(St − κS)η (7)

where κ > 0 is the worker’s self-identified anti-poverty “reservation” coefficient.

10

Notice when St − κS < 0, the utility function will collapse to a negative value. As a

result, a rational employer will never attempt choose a St level below κS by supplying

sufficient labor market efforts to win higher chances of reaching positive utility(although

sometimes could potentially result in a failure) . For instance, if we set κ = 12 , a

rational agent will find the bottom 50% social status intolerable. Definitely, κ relies

heavily on the parents’ social status and educational attainment. For instance, workers

from prestigious ivy league universities are supposed to self-identify a higher level of κ

comparing to high school dropouts. Because of the national constraint of κ, κ could

never exceed the ratio of self-selected social status and the community average, and

consequently it is somehow difficult for a lower-class worker to self-identify a high κ.

During the early age of the career, given the relative low opportunities being promoted

to higher ranks, self-identified κ should be no more than during the later stage of the

career. Therefore, κ might be time-variant. Model 2. is the particular case of Model

4 when κ = 0.

Model 1 to Model 4 are inspired by the spirit of Bakshi, Gurdip S., and Zhiwu

Chen (1996) and Campbell, John Y., and John H. Cochrane (1995).

3.2 Firms

We assume the only input is labor. The firm uses heterogeneous labor inputs with

different level to maximize its profit level. The only cost is wage expenditure.

π = max∏

∑Sj=i

Sj>0

(∑Sj=i

Sj)λi −

∑∑Sj=i

Sj>0

∑Sj=i

w(Sj) (8)

In other word,

π = max{∏i

(number of employers with rank i)λi

−∑i

number of employers with rank i ∗ w(S = i)}

where π is the profit level and λi denotes the corresponding exponent for social

status S = i. If we requires constant returns to scale technology,∑λi = 1 should hold.

However, at this moment constant returns to scale is not assumed. w(Sj) is the wage

11

function for workers in rank Sj , which is constant within each rank.

It is assumed that the wage for each worker only depends on their rank but not

working hours and experience. This compensation structure is typically observed in

most high-tech companies. Google, for instance, provides a fresh master junior em-

ployer with Level 2 class with a package of approximately $ 150,000 per year (base

salary+bonus+restricted stock units) while a fresh PhD junior employer with Level 3

class a with a package of approximately $200,000 per year.

In this model, however, high class workers could be treated as durable goods that

could hardly be replaced in the short run. Low class workers are considered to be non-

durable goods which could be substituted with other competitors on the job market

without difficulties. For instance, if there are only two classes (leader with rank 2 and

worker with rank 1) in the model, we can treat leader as capital good and worker as

labor input in the Cobb-Douglas form production function.

We also assume the relative output elasticities for class i and class j should only

relate to the distance between i and j (ie. |i− j|). In particular we have

λ1

λ2=λ2

λ3= ... = λ > 1 (say) (9)

As a result we can assume λi = λ−i,∀i ∈ Z+. If the number of classes goes to infinity

and constant returns to scale is assumed, we have λi = 12i, ∀i ∈ Z+.

Assume there are ni workers in class i. Under the First Order Conditions with

respect to rank i and rank i+ 1 in the profit function and assuming the aggregate wage

packages for each class being the same, we should have

ini(i+ 1)ni+1

=λiλi+1

=1

λ, ∀i ∈ Z+ (10)

Assuming equal aggregate wage packages is consistent with widely observed wage struc-

ture in high-tech companies. Microsoft, for instance, CEO Nadella earns approximately

100 million annually while Microsoft has approximately 2,000-4,000 lowest level employ-

ers with less than $ 50,000 compensation.

The following relationship between the number of workers in each classes is obtained

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by solving (10).

ni = (1

λ)i−1 1

in1 ∀i ∈ Z+ (11)

We can easily identify that n1 ≥ n2 ≥ n3 ≥ ... ≥ nt ≥ ... ≥ 0. Assume the total number

of workers is fixed number N , there must exist a unique k ∈ Z+ such that nk > 0 and

nt = 0, ∀t > k.

Proposition 1. The overall number of classes k with the firm is decided by the

total worker number N and the relative output elasticities λ between adjacent classes.

It can be uniquely determined by solving the following simultaneous inequalities.

∑ki=1( 1

λ)i−1 1in1 = N

( 1λ)k−1 1

kn1 ≥ 1

( 1λ)k 1

k+1n1 < 1

(12)

The economic meaning of inequalities (12) is quite straightforward. The firm no

longer needs to set class k+1 to maximize the profit level. For instance, the prestigious

hedge fund Two Sigma has altogether 800 employees and 7 class level (T1 the lowest

class to T7 CEO). The following Proposition 2 is obtained the the proof is provided

in the appendix.

Proposition 2. The total number of class level k is a non-decreasing function with

respect to the total number of workers N and non-increasing function with respect to

the relative output elasticities λ between adjacent classes.

Proposition 2 is quite intuitive. The total class number should increase with the

number of employees. For instance, Baidu, the famous search engine company with

more than 20,000 staff in China, has a total 11 classes while Two sigma has 7 classes

with an approximate 800 staff. Also, it should decrease with respect to the promoting

difficulty level. Apple, with more challenging promotion criteria, has less ranking classes

comparing to Google with similar size but larger promotion chances and more classes.

We assume all workers enter the firm with S0 = 1. Outputs are hard to measure5.

5In Yang(2001), if the output are hard to measure for the firm, it is better to use the fixed wagerate for each class. For instance, research outcome is hard to measure in research universities in theshort run, so the wage rate is relatively fixed for tenure-track assistant professors, tenured associateprofessors and full professors. Research institutes will measure the publication quality to make the

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Only working time could be observed by the firm to make the final promotion decision.

Also, it is rational to assume in each period a worker can be promoted up to one class

at most and no one could be downgraded(In other word, 0 ≤ St+1 − St ≤ 1, ∀t ∈

Z+). According to Central Limit Theorem, all workers’ working hours follow normal

distribution if they are independent. The firm uses Maximum Likelihood Estimate to

finish the promotion decision.

St+1(ω) =

St(ω) + 1, with prob.

∫ lt(ω)−∞

pc√2πσ2

exp(− (ξ−lc)22σ2 )dξ

St(ω), otherwise

(13)

where lc is the average working hour for all the staff in the class of St = c and lt(ω) is

the working hour choice of person ω, where lt(ω) = 1 − Lt(ω). By revisiting (10) we

obtain

0 ≤ pc =c

c+ 1

1

λ< 1 (14)

And by setting the base wage for level 1 at w1(w(Sj = 1) = w1) we conclude the

following wage equation.

wi = w(Sj = i) = iλi−1w1,∀i ≥ 1 (15)

3.3 Equilibrium

The Bellman Equation for the employees is as follows.

V (at, St) = maxCt,Lt{U(Ct, Lt, St) + βEoV (at+1, St+1)} (16)

subject to

Ct = (1 + µt)at + wt(St)− at+1 (17)

tenure decision within the tenure clock. However, if the outcomes are easy to measure, then piece ratewage is better than fixed wage. It is rational to make the assumption that wage rate only depends onthe class in this model.

14

We eliminate the choice variable Ct by rewriting the budget constraint and get the

following Bellman Equation with choice variables at+1, Lt, and state variables at, St.

V (at, St) = maxat+1,Lt

{U((1 + µt)at + wt(St)− at+1, Lt, St) + βE0V (at+1, St+1)} (18)

We have the following two First Order Conditions.

With respect to at+1:

−U tc + βV1(at+1, St+1) = 0 (19)

With respect to Lt:

U tL − βV1(at+1, St+1)∂at+1

∂lt− βV2(at+1, St+1)

∂St+1

∂lt= 0 (20)

Also we generate two Envelope Conditions.

With respect to at:

V1(at, St) = U tc(1 + µt) (21)

With respect to St:

V2(at, St) = U tc∂wt(St)

∂St+ U ts (22)

where

∂wt(St)

∂St= λSt−1w1(1 + St lnλ) (23)

We could reach the following Euler Equations.

U tc︸︷︷︸Marginal utility of consumption in period t

= β(1+µt) U t+1c︸ ︷︷ ︸

Marginal utility of consumption in period t+1

(24)

15

Notice ∂at+1

∂lt= 0 (next period’s initial wealth level is not affected by current labor input

level). We should have

U tL

= (1− p∗)β [

MU of consumption with labor︷ ︸︸ ︷U t+1c λSt−1(1 + St lnλ)w1 +

MU of status with labor︷ ︸︸ ︷U t+1S ]

StSt + 1

1

λ

1√2πσ2

exp(−(lt − ¯lSt)2

2σ2)︸ ︷︷ ︸

marginal utility of labor if not promoted

+ p∗β [U t+1c λSt(1 + (St + 1) lnλ)w1 + U t+1

S ]St

St + 1

1

λ

1√2πσ2

exp(−(lt − ¯lSt)2

2σ2)︸ ︷︷ ︸

marginal utility of labor if promoted

(25)

where the promotion probability p∗ is

p∗ =

∫ lt

−∞

StSt+1

1λ√

2πσ2exp(−(ξ − ¯lSt)

2

2σ2)dξ (26)

Briefly speaking, Euler Equation (25) shows the representative worker will increase the

labor effort until the marginal utility from the increasing chances of promotion being

equal to the marginal utility loss with respect to leisure when providing additional unit

of labor. We will discuss the different consumption and labor choices under Model 1

to Model 4 assumptions.

For Model 1., we evaluate Ct and Lt at their steady state and the following rela-

tionship between β and µt is summarized.

β(1 + µt) ≡ 1, ∀t ≥ 1 (27)

However, it is the usual case that the return on {µt}∞t=1 fluctuates around the steady

state. Generally, during the Great Moderation economists tend to believe that the long

term rate will approach to a constant since the volatility keeps decreasing. However,

the recent Great Recession breaks the illusion of economists and consequently, the

fluctuation of Ct and Lt could be the direct result from the variation of µt.

16

Also, from (25), we should have

Le = {peβρCe ρ−1λS

e−1w1[(1− pe)(1 + Se lnλ) + peλ(1 + (Se + 1) lnλ)]

1− ρ}−

1ρ (28)

where Ce, Se, Le are the steady state of Ct, St and Lt, where

pe =Se

2(Se + 1)λ(29)

The properties of the steady state could be derived without difficulties.

Proposition 3. ∂Le

∂β < 0. It indicates the steady state working level will be higher

if the worker have an increasing preference level on the future period, which could be

expected in the infinity period problems due to income effect.

Proposition 4. ∂Le

∂ρ < 0. If the preference for consumption over leisure is higher,

then the equilibrium working level should increase, which is also quite intuitive due to

substitution effect between consumption and leisure.

Proposition 5. ∂Le

∂Se < 0. That is to say, if the equilibrium social status increases,

the leisure level at the steady state will be lower. Obviously, it is due to substitution ef-

fect such that with higher class/social status the income will be higher, which generates

a higher utility level.

Proposition 6. ∂Le

∂Ce < 0. With higher equilibrium leisure, the consumption level

will be lower, which seems to be intuitive at first glance. Notice that the representative

agent will never choose any unnecessary additional working hour since the marginal

utility loss would be higher than the marginal utility gain from the potential promotion,

given the additional working hour could not significantly enhance the belief for the firm

that this worker is indeed working hard to be promoted. In short, ”lazy” people have

with less consumption.

Proposition 7. ∂Le

∂λ < 0.The working hour will increase with respect to the relative

output elasticities between adjacent classes λ. We should also notice that λ is positively

correlative to the difficulty of promotion and negatively correlative to the number of

classes. It could also be obtained that the more difficult for each promotion and the

less classes in the hierarchy systems, the equilibrium working level should be higher as

17

well as the consumption level. For instance, when we revisit the stories of Two Sigma

and Apple, it is widely-known that Apple has a relatively stricter promotion policy

than Two Sigma for coding and machine learning group. With Proposition 7 we

shall reach the conclusion that Apple is the priority choice for hard-workers comparing

to Two Sigma, which is exactly what we observed in reality when you come across the

parking lots for both companies during weekends.

For Model 2, we evaluate the Euler Equation with respect to consumption and

evaluate the consumption, class, leisure, interest rate at their corresponding steady

state. ( ie Ct = Ce, St = Se, Lt = Le µt = µ).

Seη = β(1 + µ)Se

2(Se + 1)λ(Se + 1)η + β(1 + µ)(1− Se

2(Se + 1)λ)Seη

= β(1 + µ)Seη + β(1 + µ)Se

2(Se + 1)λ

∞∑k=1

(η

k

)Se η−k

(30)

From (30) it can be found that β(1 +µ) < 1, which indicates the preference for current

consumption is higher in Model 2 comparing to Model 1.

Proposition 8. From the (30) we should have ∂Se

∂β < 0 when η < 56β(1 + µ).

Proof is provided in the appendix. We could conclude if the preference for current

period utility is high, the employee will tend to chase for a higher level of social status.

With very similar logic, the following proposition is obtained.

Proposition 9. ∂Se

∂µ < 0 when η < 56β(1 + µ).

It is straightforward if the return on asset is low, which is similar to the effect of a low

β, the preference for current period is higher and the corresponding feedback is to hunt

for a higher social level.

Then we repeat the same procedure and gain the following expression for the steady

state of leisure.

ALe −ρ +BLe 1−ρ = D (31)

where

A = 1− ρ > 0 (32)

B = −pe(1− pe)β Ceρη

(1− γ)Se− pe 2β

Ce ρη

(1− γ)Se< 0 if γ < 1 (33)

18

D = peβρCe ρ−1λSe−1w1[(1− pe)(1 + Se lnλ) + peλ(1 + (Se + 1) lnλ)] > 0 (34)

and

pe =Se

2(Se + 1)λ(35)

We have the following important result.

Proposition 10. ∂Le

∂η < 0 when γ ≤ 1 and ∂Le

∂η is ambiguous when γ > 1 . In

particular, when η = 0 Model 2 shrinks to Model 1. Consequently the steady state

leisure level under positive preference on the social status should be higher than no

preference case if the relative risk aversion level is small (γ ≤ 1), which is still higher

than the negative preference case.

The proof is not hard, which is included in the appendix.

With no preference on social status case η = 0 when the relative risk aversion level is

low, the worker simply chooses the optimal working level where marginal consumption

benefit from working equals marginal loss from sacrificing leisure. However, in positive

preference on social status case(η > 0), the working level is chosen at the point where

marginal utility loss from decreasing leisure equals marginal consumption benefit from

working plus marginal status gain from the increasing chances of promotion. Employee

tends to work more than no preference case since working provides additional benefit

6 in class enhancement besides consumption benefit. On the contrary, when η < 0

the preference for status is negative. The working level is selected at the point where

marginal benefit from consumption less the utility loss from a higher status equals

marginal loss from a diminishing leisure level, which leads to a higher leisure level

comparing to no preference case. But when the relative risk aversion ratio γ is high

enough, it might happen that the income effect dominates the substitution effect, which

leads to an ambiguous change in the labor input level 7.

For Model 3. S is calculated as the following expression.

S =

∫SdF (S) (36)

6It could be treated as a sort of additional substitution effect because of higher ”income” from socialstatus gain.

7See Chetty Raj 2005, if γ > 1.25 in his approach, the income effect might dominate substitutioneffect, leading a potential downward sloping labor supply curve.

19

where F (S) is the cumulative distribution function of S.

The general conclusion for Model 3 would not be significantly different from Model

2 where the workers care relative social status in Model 3 while focus on absolute

class in Model 2. If the skewness of F (S) is zero (for example normal distribution),

the optimum working-leisure choice decision function will be exactly the same as the

previous case. However, it is generally believed that the class structure is right skewed

(positive skewness with some extent of income inequality). In this case S will be greater

than the equilibrium social status. Therefore, the marginal utility gain from a higher

status with more labor input will be smaller in Model 3, which leads to a higher

equilibrium leisure level in this case. In a unlikely-to-be-true negative skewness case,

the equilibrium leisure will be less than Model 2 case, encouraging each worker to work

even harder and consumes less leisure. It is observed in some Korea-culture-dominate

corporations such as Samsung.

For Model 4, let S = S − κS. When we replace S with S in the Euler Equation

of Model 2, the Euler Equation for Model 4 is therefore obtained. If κ > 0 the

equilibrium status level must be higher.

The economic explanation for κ is that it represents the self-identified ambition

level. Clearly the well-educated worker tends to have a higher κ value, chasing a higher

position in the company. In this case, the equilibrium working hour will be longer

and the corresponding consumption level is enhanced. For instance, if in a particular

society a level 1 steady state class level in never tolerated, then κ will be intentionally

selected above 1/S. Any rational worker will never stay at S = 1 for very long time

since the utility level is negative no matter how much consumption the employee could

have.

Model 4 also provides groundbreaking evidence to explaining the asset return dif-

ference among various countries. Suppose we have two economies (type H and type

L with corresponding ambition level κH and κL where κH > κL) and the observed

average social status are the same for those two economies. In other word, SH = SL.

Since κH > κL, we get

SH − κH S = SH < SL = SL − κLL (37)

20

With Proposition 9 we can conclude the µH > µL, which indicates type H economy

would have a rate of return on asset (which is an exogenous variable in my model).

With the same logic and Proposition 8, we could also conclude a higher β should be

accompanied with a higher realized rate of return on asset. However, when higher κ

leads to advanced level of economic growth, we can fail to conclude that the correspond-

ing self-identified utility level is also high. Taking Japan as an example, Japanese care

greatly on the relative social status and seldom tolerate staying on the low class within

the company. Consequently the labor hour is very high and so is consumption level.

The self-identified utility level, however, might be the lowest among OECD countries

with the highest suicide rate. A high ambition level κ greatly reduces the utility level,

pushing everyone inside the economy chasing a higher rank with more labor input and

less leisure with heavy exhaustion.

One more thing to mention is the influence of the working hour standard deviation

σ8. If the worker are approximately homogeneous, then σ would be relatively small.

As a result, a few more hours can significantly increase the promotion probability,

increasing the utility for the worker sharply without much leisure loss. On the contrary,

if σ is high, only the employee who sacrifices a considerable amount of leisure is more

likely to be promoted. Therefore, unless the positive preference over social status is

high enough (for instance, a high κ or η), the employee will be reluctant to trade more

leisure for consumption and social status.

3.4 Stochastic Case and Risk Premium

In this part we consider the general asset pricing problem. Assume there are one risk-

free asset with return µ0 and M risky assets . The price of ith risky asset in period t

Pi,t satisfies the following Geometric Brownian Motion.

dPi,tPit

= µi,tdt+ σi,tdBPi,t,∀1 ≤ i ≤M, ∀t ∈ N (38)

where µit are the expected drifts and σi,t are standard deviation. BPi,t stands for stan-

dard Brownian Motion.

8See Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2001), the standard deviation of USworking hour is quite stable comparing to non-financial income and consumption.

21

We assume the employee invests w0,t percentage of total investable asset on the

risk-free asset in period t while puts wi,t percentage on risky asset i. Definitely we

should haveM∑i=0

wi,t = 1,∀t ∈ N (39)

The new choice variables become {wi,t}Mt=0, at+1 and Lt in the original discounted utility

maximization function.

max{{wi,t}Mi=0,{Lt},{at+1}}∞t=0

βtE0[U(Ct, Lt, St)] (40)

subject to

at+1 − at = w0,tat +M∑i=1

µi,tat − Ct +M∑i=1

wi,tσi,tBPi,t (41)

Following the procedure of Bakshi, Gurdip S., and Zhiwu Chen (1996) and Grossman,

Sanford J., and Robert J. Shiller (1982), we obtain the following Euler Equation with

respect to the price of risky asset.

Pi,t = βEt{[Uc(Ct+1, Lt+1, St+1)

Uc(Ct, Lt, St)+Us(Ct+1, Lt+1, St+1)

Uc(Ct, Lt, St)]Pi,t+1} (42)

which are all evaluated on the optimal path Ct = C∗t , Ct+1 = C∗t+1, Lt = L∗t , Lt+1 =

L∗t+1, St = S∗t , St+1 = S∗t+1.

Notice when the worker has no preference on social status, the above Euler equation

(42) is exactly the same as Euler Equation (24)

We further assume Ct, Lt and St satisfy the following stochastic processes.

dCtCt

= µC,tdt+ σC,tdBCi,t (43)

dLtLt

= µL,tdt+ σL,tdBLi,t (44)

dStSt

= µS,tdt+ σS,tdBSi,t (45)

where µC,t, µL,t, µS,t are the expected drift and σC,t, σL,t, σS,t are the expected diffusion.

BCi,t, B

Li,t, B

Si,t are three different standard Brownian Motion.

22

By subtracting the risk-free component from the (42), we have

Et{[UC(C∗t+1, L

∗t+1, S

∗t+1)

UC(C∗t , L∗t , S∗t )

+US(C∗t+1, L

∗t+1, S

∗t+1)

UC(C∗t , L∗t , S∗t )

](dPi,tPi,t

− r0dt)} = 0 (46)

US(C∗t+1, L∗t+1, S

∗t+1) could be omitted when we use Taylor Series Approximation around

the point (C∗t+1, L∗t+1, S

∗t+1).

Et[(µi,t − r0)dt+dPi,tPi,t

][1 +UCCC

∗t

UC

dC∗tC∗t

+UCLL

∗t

UC

dL∗tL∗t

+UCSS

∗t

UC

dS∗tS∗t

] = 0 (47)

let

dBPi,tdB

Ci,t = VP,Cdt (48)

dBPi,tdB

Li,t = VP,Ldt (49)

dBPi,tdB

Si,t = VP,Sdt (50)

With Ito’s Lemma, we could calculate the following risk premium for Pi,t .

µi,t − r0 = −UCCVP,CUCPi,t

−UCLVP,LUCPi,t

−UCSVP,SUCPi,t

(51)

Fama-French three factor model (Fama, Eugene F., and Kenneth R. French 1993) states

that consumption risk should be compensated and included in the asset risk premium

while Zhang Lu q-Factor Model (Hou, Kewei, Chen Xue, and Lu Zhang 2015) states

investment risk should be the dominant component in the Capital Asset Pricing Model.

While in our approach, not only the consumption risk but the leisure risk and social

status risk should be compensated. For instance, if we assume ρ = 0 and η = 0 in

Model 2, our model should be very similar to the original CAPM approach. While we

only set η = 0 in Model 2, it becomes a two-factor model considering both consumption

and leisure risk. When you use the general assumption in Model 2, it turns out to

become a consumption-leisure-class CAPM approach, which definitely, deserves future

research.

23

3.5 Option Explanation

In this part, we attempt the explain the behavior of employee using an alternative

approach. Instead of the traditional Euler Equation approach, we treat the promotion

opportunity as a call option. For example, in the first period, all workers have the class

level 1 and are issued a call option with strike price ”S=2”. It is a binary call option9

with a positive probability of being promoted to the social status S = 2 through current

observed labor input l. We denote the price of such call option call(L, S = 1→ 2). At

the same time, being promoted class level 2 means the additional promotion probability

of being promoted to level 3 in the next period, which could be treated as a call on

call option. And so on. Consequently, the call option combination in period 1 not only

contains a call option of being promoted to level 2 in the next period, but contains a

call of a call option of being promoted to level 3 in the next two periods ,..., and so on.

So the overall value of such option combinations is calculated as follows.

P =∞∑i=2

1∏i−1j=1(1 + µj)

call(L, S = 1→ i) (52)

In Model 1, for example, the workers’ preference for the social status is 0. In this

case, all the benefit of promotion is pecuniary effect.

callModel 1(L, S = 1→ i) = ((i+ 1)λi − iλi−1)w1Pr(1→ i) (53)

where

Pr(1→ i) =i−1∏j=1

[1

λ

j

j + 1

∫ L

−∞

1√2πσ2

exp(−(L− L)2

2σ2)]

=1

λi−1i(

∫ L

−∞

1√2πσ2

exp(−(L− L)2

2σ2))i−1

(54)

Further if we assume µj ≡ µ, ∀j ∈ N , then the price of such option combination is

P = w1

∞∑i=2

1

(1 + µ)i−1[(i+ 1

iλ− 1)(

∫ L

−∞

1√2πσ2

exp(−(L− L)2

2σ2))i−1] (55)

9The payoff of this binary call option is either 0 or being promoted to class 2.

24

A worker will choose the when the Delta of this call option (∆P = ∂P∂L ) equals the

marginal utility of leisure.

Let us discuss the how parameters will influence the median worker’s option com-

bination value. Plug L = L into the expression of P and we can figure out

P = w1

∞∑i=2

1

(2(1 + µ))i−1((i+ 1

i)λ− 1)

= w1[−(1 + 2λµ) + 2λ(1 + µ)(1 + 2µ) ln(2+2µ

1+2µ)

1 + 2µ]

(56)

Clearly we should have ∂P∂λ > 0 and ∂P

∂µ < 0, which is consistent with the characteristics

of a call option that the Rho should be negative.

When we reconsider Model 2 to Model 4

callModel 2∼4(L, S = 1→ i) = [((i+ 1)λi − iλi−1) +MUS ]w1Pr(1→ i) (57)

where MUS is the additional marginal utility gain from the increasing of social sta-

tus, which is positive, negative or zero when the worker has positive, negative or no

preference on the social status. In this case

PModel 2∼4 >=<PModel 1 (58)

and

∆Model 2∼4P

>=<

∆Model 1P (59)

Consequently we have

LModel 2∼4 <=>LModel 1 (60)

when η>=<

0

25

4 Empirical Tests

4.1 Data Description

Obviously, we should use panel data to study the dynamic work-leisure behavior. In

this case, the Panel Study of Income Dynamics (PSID) data is selected to accomplish

our empirical test. The data range are from 1975 to 1992, which the same cohort

and their descendants are surveyed through phone call annually. The beginning year

1975 is selected in particular since it is the time points when reliable phone interviews

were used and the ending year 1992 is chosen since from 1993 computer techniques

are introduced into the survey. During this period the measurement errors could be

regarded as homogeneous.

We have approximately 7,000 effective observations for each year, where the sum-

mary statistics of age, education, hours working per year and annual before-tax income

for labor market participants are provided in Table 7. In our approach, a worker is

considered to be a labor market participant if his/her annual paid working hours are

no less than 200 and the age is between 25 and 70.

From Table 8 to Table 11 we summarize the age, education level, hours working per

year and nominal income for each year in 1975 to 1992. The educational level increases

steadily in those 18 years while the variance decreases significantly during 1984-1988.

A representative working employee increases the working hour during George H.W.

Bush presidential term. The nominal income increases sharply during 1980s. We can

notice the nominal average income for 1990 in PSID panel survey was almost 200%

of 1980, which could be majorly explained by the high inflation rate10 during that

period. Notwithstanding, the real inflation-adjusted average income is still growing

during Ronald Reagon’s presidency but becoming much slower, which is listed in Table

13.

The next very important thing in our model is to calibrate λ and the corresponding

number of classes. Since we use Cobb-Douglas form technology, we have better follow

Cobb-Douglas’s original approach (Charles Cobb, Paul Douglas & NBER 1927, Paul

Samuelson, Robert Solow 1976, Filipe, Jesus; Adams, F. Gerard 2005) to set λ = 3.

10The inflation rate during 1975-1992 is listed in Table 12

26

The effective response for each year is approximately 7,000, which leads to an estimated

7 classes altogether by following the decision rule in Proposition 2 by noticing

7∑i=1

3i−1i = 7, 108 (61)

We use the wage function to decide the class level approximately. By following (15),

the higher wage, the higher social status. By setting the living wage as the separation

line of class 1 and class 2 and following the spirit of equation (15) we use the following

rule to decide the social class level.

• class 1: if the hourly wage in year t ∈ (0, hourly wagetmax/64]

• class 2: if the hourly wage working hour in year t ∈ (hourly wagetmax/64, hourly

wagetmax/32]

• class 3: if the hourly wage in year t ∈ (hourly wagetmax/32, hourly wagetmax/16]

• class 4: if the hourly wage in year t ∈ (hourly wagetmax/16, hourly wagetmax/8]

• class 5: if the hourly wage in year t ∈ (hourly wagetmax/8, hourly wagetmax/4]

• class 6: if the hourly wage in year t ∈ (hourly wagetmax/4, hourly wagetmax/2]

• class 7: if the hourly wage in year t ∈ (hourly wagetmax/2, hourly wagetmax]

where hourly wagetmax represents the highest hourly wage in year t. It could be

found that the individual class status should be indifferent no matter if we use real

income level or not.

If the person’s observed status is increased, s/he is considered to be promoted in

our empirical analysis.

4.2 Basic Empirical Results

First, we have to test one of the most important assumption in our model, where

the promotion chances should be higher for those workaholics. We run the Linear

Probability Model, Probit Model and Logit Model separately to test the efficiency of

our assumption in Table (15).

27

In column 1 to column 3, we could find that all three models report positive in-

fluence of working hour towards to ratio of promotion. If we add education level into

our regression in column 4 to 6 , we could find out the coefficient of working hour

remain significantly positive while the effect of education, without any doubt, is posi-

tive. Finally, if we add linear and quadratic term of age into the regression, the t-stat

for working hours decreases but is still significantly positive while the rest coefficients

are exactly predicted by traditional Mincer earnings function. It is proved our general

assumption is reliable that working longer could help promotion. After considering

the age effect, an additional 1,000 working hours per year will increase the promotion

chances in the next year by 0.58%.

Then we run several Mincer-type earning equations to briefly overview the panel

data we have. The results are listed in Table 16. After controlling for the social status,

the working hour is still positively related to the hourly nominal wage . However, from

column (4) we find the effect of additional working hours on wage rate is insignificant if

we take into account the unemployment hours in the regression. We don’t run Heckman

correction in this table and the result does not depress us that much. We can only argue

that within those who suffer unemployment in one year the hardworking level has no

significant effect on wage rate. At the same time, the unemployment itself is reported

to have a negative effect on the wage ratio, which is consistent with our intuition since

unemployment could send bad signals to employers. When the real wage is used as

regressand, the working hour has a smaller positive influence on the real wage rate. We

could explain the difference of working hour effect in column (1) to (4) and column (5)

to (8) by the high inflation and the upward trend of working hours in the 1980s. That is

to say, working more time will compensate a larger nominal hourly wage increase but a

relatively smaller real wage enhancement measuring by dollars in 1975. Meanwhile, we

could never fail to notice the return on education in column (6) and (7) are significantly

negative, which could be the result of controlling for various status. Suppose person

P1 and person P2 are in the same class level C but P1 has a relatively higher education

level than P2, the education itself might send weaker signal of person P1 comparing to

P2 since the effort for P2 to reach level C is much more challenging than P1 with a low

starting point. An additional 1,000 hours per year could increase the inflation-adjusted

28

hourly compensation by 0.18 dollars measuring in 1975 dollars. The preliminary result

is subject to endogeneity challenge but still pretty useful to understand the hour-wage

relationship.

We also report the influence of working hour effect in Table (17) by using Heckman

Correction. The independent variables we use in the first step Probit selection model are

education, age (or experience), type of income and relationship to the head of the family.

The very similar result are reported in Table (16) whether we use Heckman Correction

or not, suggesting the self-selected labor market participation decision (which is decided

by education, age, type of income and family condition linearly in our approach) would

not have a significant influence on the wage ratio. Also the standard robustness check

are done by replacing age with working experience (exp) by using the following equation

exp = age− edu− 7 (62)

The result shows that although the coefficients of age and experience slightly differ,

the sign does not change. The coefficient for working hours decreases only 2 % when

the age variable is replaced by experience, indicating a strong positive effect of working

hour on the wage ratio.

4.3 Calibration for the social preference

The next step is to calibrate the parameters β, γ, η and κ. First we use only the

equation (24) to determine β and γ. First we use the Federal fund rate from 1975

to 1993 as the risk-free return on asset µt, which is appended in Table 18. With the

lack of individual consumption data in PSID, we make a plausible assumption that the

proportion of consumption in current income is steady between two continuous years.

Although there is permanent income hypothesis claiming a person’s consumption at a

point is determined not just by their current income but also by their expected income

in the future. Campbell, John Y., and N. Gregory Mankiw (1991) finds that the

fraction of income accrues to individuals who consume their current income instead of

their permanent income by testing the postwar data of US till 1990, which is consistent

with our settings and data period. In this case, we could use inter-temporal relative

29

income as a good proxy of inter-temporal relative consumption. Also, we assume the

leisure each year is calculated by the following equation by excluding 8 hours per day

resting hour from the total allocatable time. Notice 5840 = 16 ∗ 365.

leisure = 5840− working hour (63)

By using Euler Equation of consumption we can calibrate ρ and γ.

The instruments we use here in the Generalized Method of Moments is the one-

year lag risk-free interest rate and social status, which by no means correlate with the

variable we use in calibrating ρ and γ.

E[U tc − β(1 + µt)Ut+1c |rt−1] = 0 (64)

and

E[U tc − β(1 + µt)Ut+1c |St−1] = 0 (65)

Table 1: Calibration Results by Consumption EE in Model 1

GMM weight matrix: HAC Bartlett 4

Coeff. Std. Err. z p > |z| [95% confidence interval]

β 0.95 literature value

γ .2553133 .0732329 3.49 0.000 [ .1117794, .3988471 ]

ρ .9756675 .1100314 8.87 0.000 [ .76001,1.191325 ]

We could find that λ < 1. According to Raj Chetty (2005), the substitution effect

dominates income effect as λ < 1.25 threshold point, indicating a upward sloping labor

supply curve for the PSID data from 1975-1992. The existing literature suggests λ

could vary from 0.15 to 1.45, indicating no out of expectation λ value. The ρ value

here, however, is least important since the absolute weight of leisure could change with

different unit measure of relative consumption and leisure.

Then we reestimate the value of γ and ρ by taking into account the social status

influence. For Model 1, equation (28) are included in the simultaneous equations.

30

One-year and two-year lag risk-free interest rates are used as proxies for (28) to obtain

two more moment conditions. And we should decide the w1 first. We calibrate w1 in

each year from 1975 to 1992 by using the average income of the workers in first class,

just as the original setting in the firm sector .

Table 2: w1 used from 1975 to 1992w1 value for each year 1975-1992

1975 1976 1977 1978 1979 1980 1981 1982 1983

2250.141 1652.54 1551.471 2412.876 2011.671 4092.228 5017.307 4753.249 2696.743

1984 1985 1986 1987 1988 1989 1990 1991 1992

3364.369 9606.21 3295.947 5163.282 8860.022 12709.87 9515.766 7315.009 6855.409

The results obtained by the Generalized Method of Moments are

Table 3: Calibration Results by Consumption and Social Status EE in Model 1

GMM weight matrix: HAC Bartlett 4

Coeff. Std. Err. z p > |z| [95% confidence interval]

β 0.95 literature value

γ .627034 .0082546 75.96 0.000 [ .6108553 .6432128 ]

ρ .4222069 .0287144 14.70 0.000 [ .3659278 .478486 ]

Notice after we considering the embedded promotion option in equation (28), the

calibrated relative risk aversion rate will increase a lot, but still less than 1.25 threshold

indicated by Raj Chetty (2005), which points out that the substitution effect still

dominates income effect even taking into account the promotion option value but a little

bit weaker. In other word, the labor supply curve becomes even steeper, which could

have a high slope than tradition belief. It could be the case that the standard expected

utility function without promotion setup could fail to explain a higher relative risk

aversion, which is consistent with Browning, Hansen, and Heckman (1999) suggesting

λ as high as 4.

Then we shift to estimate the η in Model 2. Focusing on equation (31),

ALe −ρ +BLe 1−ρ = D (66)

Notice ALe −ρ << D and ALe −ρ << BLe 1−ρ, we should have the approximate

31

equation

BLe 1−ρ = D (67)

Together with the equation (24), we reach out the following calibration values by using

the Generalized Method of Moment. In our model here, we use the one-period lagged

interest rate, two-period lagged interest rate and one-period lagged promotion rate

as instruments for equation (64) while the one-period lagged interest rate, two-period

lagged interest rate and status are used as instruments for equation (24).

Table 4: Calibration Results Model 2GMM weight matrix: HAC Bartlett 4

Coeff. Std. Err. z p > |z| [95% confidence interval]

β 0.95 literature value

γ 1.610928 .1203562 13.38 0.000 [ 1.375034 1.846821 ]

ρ .9760741 .012142 80.39 0.000 [ .9522762 .999872 ]

ln ηγ−1 1.478234 .1202525 12.29 0.000 [ 1.242543 1.713924 ]

In this case, the estimated preference level of social status is exp(1.478234)∗(1.610928−

1) = 2.679. Interestingly we find the relative risk aversion ratio γ is quite large in this

calibrated model, which contradicts the traditional belief that γ < 1.25 in most labor

economics literature. However, the large γ does not generate a downward sloping labor

supply curve in Model 2 since there is additional utility gain from social status which

provides more incentive to substitute leisure with working hours. We could still ar-

gue the labor supply curve is upward sloping, being consistent with standard textbook

conclusion. And with the inclusion of promotion variable, the relative risk aversion

ratio could be higher than the standard assumption, which is exactly what some non-

expected-utility theories argue.(Chew and MacCrimmon 1979, Tversky and Kahneman

1992).

In the next step we calibrate η for each year during 1975 to 1992 to help us under-

stand the change of preference on social status during these two decades. The method

we use is similar but in this part each year’s data are treated as cross-sectional rather

than panel.

32

Table 5: η calibration value for each year 1975-19921975 1976 1977 1978 1979 1980 1981 1982 1983

2.425 2.301 2.268 2.472 2.701 2.736 2.708 2.799 2.808

1984 1985 1986 1987 1988 1989 1990 1991 1992

2.831 2.972 2.862 2.825 2.909 2.990 2.909 2.871 2.950

The preference on the social status varies from 2.2 to 3.0 during 1975 to 1992,

showing a relative high preference towards social status, which might contradict the

general belief. In the next figure we show the relative relationship between η and annual

working hours, nominal wage, inflation rate, real wage, respectively.

Figure 1: The relative relationship between η and annual working hours, nominal wage,inflation rate, real wage

And the correlation matrix is listed as follows.

We could find when the preference for social status increases, the annual working

hours also increases, which is consistent with our conclusion in Proposition 10. Mean-

while, the nominal wage rate increases while the real wage decreases at the same time.

33

Table 6: The correlation matrix of η, annual working hours, nominal wage, inflationrate and real wage

correlation η annual working hours nominal wage inflation real wage

η 1.0000

annual working hours 0.2995 1.0000

nominal wage 0.8952 0.5481 1.0000

inflation -0.3992 -0.3201 -0.6303 1.0000

real wage -0.0094 0.5478 0.0888 -0.2515 1.0000

It might give us hint the preference for social status would increase just because of the

high inflation. The employers are pushed to have a higher preference on status to catch

up the inflation speed during the high inflation era. The relationship between inflation

and social status preference could be a challenging research topic that deserves future

works.

It should be pointed out the approximation in equation (65) guarantees γ should be

no less than 1, indicating a higher than usual risk aversion level in the utility function.

However, it does not lead to a downward sloping labor supply curve with high γ since

in our approach the positive taste for social status generates additional incentive for

employees to work more. The existing literature in labor economics literature suggest-

ing a low risk aversion ratio could be less convincing without taking into account other

utility gains besides consumption and leisure. For instance, a higher rank in the soci-

ety/corporation may provide a employee a first-class business trip, a special assistant

and/or security service, which is never generally considered as personal consumption

and is not recorded by the standard database like PSID.

4.4 Unemployment Influence

The final thing in this section is to examine whether hard-working hurts the labor

market by generating more unemployment. It could be expected that increasing work-

ing hours could decrease a person’s unemployment time automatically. From Table

(19) and Table (20) we could indeed confirm this conclusion. However, if we run the

regression by each social class respectively, the statement that working more hours

could significantly reduce unemployment time is true only for low-rank classes but not

for high-rank employees. It might be explained that employees rely heavily on the

34

working-hour as tools of making hiring decisions for junior workers while for seniors

the self-selected hardworking level could not affect the unemployment level. That is

to say, the assumption in my approach assuming self-selecting working hour as ability

signal might not remain valid for high-rank employees. We might use other assump-

tions to depict the hiring decisions for high-rank employees and the matching model

for entrepreneurs could differ a lot.

Meanwhile we examine whether the working hour has a significant influence on

the unemployment the year after. The result is reported in Table (20) and Table

(21). Instead of the real working hour, current year’s unemployment hour could be

a good predictor of next year’s unemployment situation, which gives us hint that the

unemployment could be lasting. The rest of the result is quite similar to Table (18) and

Table (19). Therefore, we could reach an educated guess that working overtime under

various preference on social status might not increase the unemployment, which could

be inconsistent with our naive expected results. The social status preference, however,

influences the intensive margin greater than extensive margin more significantly.

4.5 Discussion of the PSID data

The biggest advantage of using PSID dataset is that it could be used as panel tracking

on the same cohort for a long time. In this case, it is possible for us the depict the

social status preference consistently. However, we could still fail to neglect the potential

weakness of using PSID database.

The first weakness is that PSID does not record the aggregate level of consumption.

It adds additional difficulty when we have to estimate the consumption in aggregation

level, which creates additional measurement errors. The first treatment is to use food

consumption/garbage generation (A Savov 2011) in some particular years as proxies of

overall consumption. However, the Engel Coefficients/garbage generation between the

poor and the rich, the person who has a high social preference and the the person with

a lower one could be totally different, which makes the consumption level estimates

unconvincing. Also PSID does not record the food consumption for each year, adding

more difficulties of using food consumption to estimate the overall consumption. Conse-

quently, we make the rational assumption that inter-temporal relative income could be

35

used a good proxy of inter-temporal relative consumption despite the widely-believed

permanent income hypothesis.

Secondly, PSID uses a top coding rule for protecting the private information of

the rich. For instance, in the year 1992 all the salary income greater than 999,999

dollars are reported as 999,999 dollars. It is a mechanism to protect the high-income

responders’ incentive to participate the survey more actively but create biases for our

conclusion. Since the top coding strategy is treated as an up-censored model, the real

incentive for promotion could be underestimate, particularly for high-rank employees.

As a result, I am strongly convinced that the preference for social-status preference

should be overestimated since the pecuniary marginal utility is underestimated by us-

ing PSID database. A possible robustness check is to use other panel database like

National Longitudinal Survey of Youth 1979 (NLSY79) to test the validity of the var-

ious preference on social status and other non-pecuniary factors, which is still beyond

current research and deserves future work.

5 Concluding Remarks

It is the time to answer the three questions raised at the beginning of this article. Indeed

different social status preference could have a significant impact on work-leisure choices.

In our benchmark model, social status is considered to be non-pecuniary normal good.

The substitution effect will dominate income effect for the employee with high rank

preference level, which leads to a longer working hour. They work more time even

overtime a lot, sending their strong-ability signals to employees not only to increase

their potential salary income after promotion but the utility level with a higher social

status. The signaling effect is tested to be weaker for high-rank positions. The working

hour will increase with respect to the relative output elasticities between labor and

capital input. As a result, it is widely observed that workers in developing economies

tend to work overtime more frequently than in developed countries. The leisure time

will be less if the median worker is fond of a higher rank position. In other word, if

the preference for social status is higher inside one corporation, the leisure time will

be occupied with working with higher probabilities. We could observe the working

36

overtime phenomenon in Asian companies since most workers are educated to surpass

others in their early age. For instance, many students are educated to be man on top of

man in those Confucian-dominated culture. In this case, the rational choice is to work

more and consume less leisure. For instance, an Asian kid is typically educated that

Peking University, Tsinghua Universiy, Seoul National University, Tokyo University,

IIT, Harvard, MIT, Stanford are the only choices of college education, which going

without saying increases the working load for teenagers. However, the utility level

might be lower with a strong preference on relative ranking11. An economy with higher

preference on relative ranking should have a faster growth rate while the self-identified

utility level of each individual could be lower. They tend to believe that the utility level

is negative no matter how high are the consumption and leisure level12 if they can fail

to surpass their peers. In other word, they become extremely exhausted chasing high

social ranks although they are compensated with higher consumption level. Finally, we

find no significant evidence that high social preference and working overtime will lead

to an increasing unemployment level. There is still a long way to go to examine the

culture’s influence on labor market decisions. For instance, we could test the validity

of our conclusion using other US or developing countries databases, which could be a

challenging topic for future research.

11In Model 4, it is depicted as a higher κ value12In Model 4, if the social status is lower than κS the utility level is negative.

37

Appendix

Proof of Proposition 2. For the simultaneous inequalities

k∑i=1

(1

λ)i−1 1

in1 = N (68)

(1

λ)k−1 1

kn1 ≥ 1 (69)

(1

λ)k

1

k + 1n1 < 1 (70)

If we assume when N increase to N + 1, kN+1 < kN . Notice k is decided by (69) and

(70) . Then n1,N+1 < n1,N . Then in (68), we should have

kN+1∑i=1

(1

λ)i−1 1

in1,N+1 ≤

kN∑i=1

(1

λ)i−1 1

in1,N+1

<

kN∑i=1

(1

λ)i−1 1

in1,N

= N

(71)

It leads to contradiction. So kN+1 ≥ kN .

Also if assume when λ increase to λ′, kλ′ > kλ. Notice k is decided by (69) and (70)

Then n1,λ′ > n1,λ. Since the promotion difficulties increases and the number of class

also increases, we should have for each rank,

(1

λ′)i−1 1

in1,λ′ ≥ (

1

λ)i−1 1

in1,λ (72)

And

kλ′∑i=1

(1

λ′)i−1 1

in1,λ′ ≥

kλ∑i=1

(1

λ′)i−1 1

in1,λ′ + (

1

λ′)kλ

1

kλ + 1n1,λ′

≥kλ∑i=1

(1

λ)i−1 1

in1,λ + (

1

λ′)kλ

1

kλ + 1n1,λ′

> N

(73)

It leads to contradiction. So kλ′ ≤ kλ.

38

Proof of Proposition 8.

Let

p =S

2(S + 1)λ(74)

Notice

∂p

∂S> 0 (75)

Take the total differential of (30), we should have

ηSη−1

β(1 + µ)dS+

Sη

1 + µ(− 1

β2)dβ =

∂p

∂S(S+1)ηdS+pη(S+1η−1)dS+(1−p)Sη−1dS− ∂p

∂SSηdS

(76)

We have

dS

dβ=

Sη

1+µ(− 1β2 )

((S + 1)η − Sη) ∂p∂S + (pη(S + 1)η−1 + (1− p)Sη−1 − ηSη−1

β(1+µ))< 0 (77)

since

((S + 1)η − Sη) ∂p∂S

> 0 (78)

thus

(pη(S + 1)η−1 + (1− p)Sη−1 − ηSη−1

β(1 + µ)) > (1− p)Sη−1 − ηSη−1

β(1 + µ)> 0 (79)

when 1− p > 56 >

ηβ(1+µ) in our later approach

Proof of Proposition 10.

Take the total differential of (31).

−ρALe −ρ−1dL+ Le 1−ρdB + (1− ρ)BL−ρdL = 0 (80)

We have

dL

dB=

Le 1−ρ

ρALe −ρ−1 − (1− ρ)BLe −ρ> 0 (81)

since A > 0 and B < 0 if γ < 1

Notice ∂B∂η < 0 we have ∂Le

∂η < 0

39

Table 7: Summary statistics for panel data

Variable Mean Std. Dev.

age 38.864 11.051educaion 13.821 10.953nominal income 18116.744 20800.172annual working hours 1877.982 722.348

N 141436

Table 8: Age summary for each year

Year Mean Std. Dev.

1975 40.683 11.8651976 40.295 11.8641977 39.897 11.8441978 39.562 11.7931979 38.906 11.7591980 38.551 11.6121981 38.383 11.4811982 38.325 11.2981983 38.206 11.1931984 38.235 11.0671985 38.261 10.9451986 38.101 10.7161987 38.222 10.5411988 38.273 10.3991989 38.922 10.4041990 39.115 10.571991 39.262 10.4541992 39.502 10.375

40

Table 9: Education level summary for each year

Year Mean Std. Dev.

1975 11.63 3.0631976 11.748 2.9951977 11.837 2.9461978 11.917 2.8611979 12.018 2.7881980 12.121 2.6831981 12.213 2.6071982 12.279 2.5691983 12.438 2.6381984 12.485 2.5881985 12.802 2.5671986 12.846 2.5211987 12.889 2.4781988 12.929 2.4051989 13.243 4.6811990 12.487 2.9191991 12.515 2.891992 12.551 2.864

Table 10: Hours working per year summary 1975-1992

Year Mean Std. Dev.

1975 1872.584 741.3121976 1851.446 749.0241977 1876.023 737.3341978 1895.655 739.7081979 1880.287 730.2061980 1854.485 722.2761981 1838.884 719.0421982 1838.35 706.3921983 1812.677 722.3611984 1828.622 712.5681985 1870.425 730.1751986 1885.719 723.1511987 1895.668 713.9171988 1915.36 712.8471989 1953.08 718.2461990 1909.997 709.1741991 1913.027 704.2581992 1905.777 712.644

41

Table 11: Nominal income summary per year 1975-1992

Year Mean Std. Dev.

1975 9366.403 8136.3331976 9741.860 8019.9611977 10807.123 8869.2211978 12047.257 10316.6741979 12684.298 10801.7731980 13748.575 11348.6491981 14799.202 12484.3251982 16105.113 13395.9771983 16923.797 16338.4471984 18052.262 17867.3691985 19535.002 26110.8281986 20162.431 20439.0091987 21215.044 24605.8121988 22359.454 26948.9221989 24184.252 27122.6381990 23003.262 27420.6281991 22491.541 22089.8721992 23230.69 24691.309

Table 12: US inflation rate 1975-19921975 1976 1977 1978 1979 1980 1981 1982 1983

11.80% 6.72% 5.22% 6.84% 9.28% 13.91% 11.83% 8.39% 3.71%

1984 1985 1986 1987 1988 1989 1990 1991 1992

4.19% 3.53% 3.89% 1.46% 4.05% 4.67% 5.20% 5.65% 2.60%

42

Table 13: Real income per year(in 1975 dollars) summary 1975-1992

Year Mean Std. Dev.

1975 9366.403 8136.3331976 9128.429 7514.9561977 9624.23 7898.4411978 10041.768 8599.2731979 9627.355 8198.5231980 9160.862 7561.761981 8817.768 7438.5021982 8853.091 7363.8611983 8970.329 8660.0671984 9183.666 9089.6071985 9599.127 12830.3631986 9536.466 9667.2821987 9889.939 11470.6331988 10017.718 12073.9391989 10351.852 11609.6011990 9359.638 11156.991991 8662.023 8507.3311992 8719.968 9268.232

Table 14: Federal Fund Rate 1975-19921975 1976 1977 1978 1979 1980 1981 1982 1983

7.13% 4.87% 4.61% 6.70% 10.07% 13.82% 19.08% 13.22% 8.68%

1984 1985 1986 1987 1988 1989 1990 1991 1992

9.56% 8.35% 8.14% 6.43% 6.83% 9.12% 8.23% 6.91% 4.03%

43

Tab

le15

:T

esti

ng

whet

her

pro

mot

ion

rate

incr

ease

sw

ith

resp

ect

tom

ore

wor

kin

gh

ou

rs

pro

mot

ion

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

LP

MP

robit

Log

itL

PM

Pro

bit

Logit

LP

MP

robit

Logit

annual

wor

kin

ghou

rs0.

0000

0542∗

∗∗0.

0000

189∗

∗∗0.

0000

330∗

∗∗0.

0000

0579

∗∗∗

0.0000205∗

∗∗0.0

000362∗

∗∗0.0

0000264∗

0.0

000114∗

∗0.0

000201∗∗

(4.6

1)(4

.70)

(4.7

2)(4

.93)

(5.0

4)

(5.0

9)

(2.2

3)

(2.6

8)

(2.6

3)

educa

tion

0.00

167∗∗

∗0.

00556∗∗

∗0.0

0897∗

∗∗0.0

0167∗

∗∗0.0

0560∗∗

∗0.0

0910∗

∗∗

(16.9

9)(1

8.9

9)

(19.1

5)

(17.0

3)

(19.0

1)

(19.2

7)

age

0.0

0238∗

∗∗0.0

0842∗∗

∗0.0

145∗

∗∗

(26.5

2)

(27.3

4)

(27.5

0)

age2

-0.0

0000222∗∗

∗-0

.00000790∗∗

∗-0

.0000136∗∗

∗

(-15.9

9)

(-18.2

5)

(-18.4

8)

const

ant

term

0.19

1∗∗∗

-0.8

74∗∗

∗-1

.443∗

∗∗0.

170∗∗

∗-0

.945∗∗

∗-1

.559∗∗

∗0.0

960∗∗

∗-1

.215∗∗

∗-2

.027∗

∗∗

(81.

97)

(-10

7.65

)(-

101.

68)

(65.

88)

(-104.7

7)

(-99.4

3)

(26.4

8)

(-90.1

3)

(-85.7

7)

N14

1436

1414

3614

1436

14143

6141436

141436

141436

141436

141436

tst

ati

stic

sin

pare

nth

eses

∗p<

0.0

5,∗∗p<

0.0

1,∗∗∗p<

0.0

01

44

Tab

le16

:R

egre

ssio

non

nom

inal

and

real

wage

per

hou

raft

erco

ntr

oll

ing

stat

us

dep

end

ent

vari

ab

le(1

)(2

)(3

)(4

)(5

)(6

)(7

)(8

)w

agep

erh

ou

rw

agep

erh

ou

rw

agep

erh

ou

rw

agep

erh

ou

rre

alw

agep

erh

ou

rre

alw

agep

erh

ou

rre

alw

agep

erh

ou

rre

alw

agep

erh

ou

r

an

nu

al

work

ing

hou

rs0.0

00419∗∗∗

0.0

00440∗∗∗

0.0

00381∗∗∗

0.0

000371

0.0

00201∗∗∗

0.0

00198∗∗∗

0.0

00183∗∗∗

0.0

0000957

(18.3

6)

(19.3

0)

(16.6

7)

(1.7

8)

(20.0

2)

(19.7

1)

(18.2

1)

(0.8

2)

(sta

tus

=1

isom

itte

d)

statu

s=2

3.5

56∗∗∗

3.4

75∗∗∗

3.4

62∗∗∗

2.0

07∗∗∗

1.6

51∗∗∗

1.6

63∗∗∗

1.6

61∗∗∗

1.6

07∗∗∗

(83.5

3)

(81.5

9)

(81.6

3)

(46.9

1)

(88.4

4)

(88.8

6)

(88.9

2)

(67.3

6)

statu

s=3

7.3

38∗∗∗

7.2

33∗∗∗

7.1

54∗∗∗

4.9

15∗∗∗

3.9

07∗∗∗

3.9

22∗∗∗

3.8

99∗∗∗

4.0

72∗∗∗

(159.2

8)

(156.8

0)

(155.5

7)

(113.4

0)

(193.4

2)

(193.5

0)

(192.5

5)

(168.5

4)

statu

s=4

14.4

0∗∗∗

14.2

8∗∗∗

14.0

6∗∗∗

9.5

00∗∗∗

8.2

82∗∗∗

8.3

00∗∗∗

8.2

28∗∗∗

8.0

77∗∗∗

(202.7

3)

(201.0

6)

(197.9

4)

(167.0

7)

(265.9

8)

(266.0

5)

(263.1

3)

(254.8

1)

statu

s=5

33.3

9∗∗∗

33.2

5∗∗∗

32.9

6∗∗∗

21.2

3∗∗∗

19.3

2∗∗∗

19.3

4∗∗∗

19.2

4∗∗∗

17.9

2∗∗∗

(185.5

3)

(185.0

9)

(183.9

4)

(169.2

4)

(244.9

4)

(245.1

5)

(243.8

8)

(256.2

4)

statu

s=6

80.3

4∗∗∗

80.2

3∗∗∗

79.9

0∗∗∗

42.2

2∗∗∗

45.4

6∗∗∗

45.4

8∗∗∗

45.3

6∗∗∗

35.2

2∗∗∗

(193.8

2)

(194.0

0)

(193.9

9)

(134.8

1)

(250.2

4)

(250.3

8)

(250.1

9)

(201.8

0)

statu

s=7

263.7∗∗∗

263.5∗∗∗

263.3∗∗∗

114.3∗∗∗

132.0∗∗∗

132.0∗∗∗

132.0∗∗∗

95.3

6∗∗∗

(284.5

8)

(284.9

8)

(286.0

2)

(102.4

0)

(324.9

9)

(325.1

4)

(325.6

0)

(153.3

2)

edu

cati

on

0.0

410∗∗∗

0.0

425∗∗∗

0.0

281∗∗∗

-0.0

0596∗∗∗

-0.0

0533∗∗∗

0.0

123∗∗∗

(26.3

5)

(27.3

2)

(15.6

5)

(-8.7

1)

(-7.7

8)

(12.2

9)

age

0.4

00∗∗∗

0.0

679∗∗∗

0.1

13∗∗∗

0.0

444∗∗∗

(33.2

2)

(6.9

0)

(21.3

6)

(8.1

0)

age2

-0.0

0434∗∗∗

-0.0

00709∗∗∗

-0.0

0119∗∗∗

-0.0

00443∗∗∗

(-31.2

5)

(-6.2

3)

(-19.4

7)

(-6.9

9)

un

emp

loym

ent

-0.0

00264∗∗∗

-0.0

00137∗∗∗

(-5.9

1)

(-5.5

0)

con

stant

term

3.6

70∗∗∗

3.1

73∗∗∗

-5.1

52∗∗∗

0.6

06∗∗

2.0

14∗∗∗

2.0

86∗∗∗

-0.3

40∗∗

0.5

63∗∗∗

(72.3

8)

(58.7

7)

(-20.9

5)

(3.0

0)

(90.5

0)

(87.8

7)

(-3.1

4)

(5.0

0)

N142964

142964

142964

41143

142881

142881

142881

41139

tst

ati

stic

sin

pare

nth

eses

∗p<

0.0

5,∗∗p<

0.0

1,∗∗∗p<

0.0

01

45

Table 17: The influence on wage rate using Heckman correction

Regressand (1) (2) (3) (4)realwageperhour realwageperhour realwageperhour realwageperhour

annual working hours 0.000271∗∗∗ 0.000267∗∗∗ 0.000270∗∗∗ 0.000267∗∗∗

(15.50) (15.49) (15.49) (15.48)

education 0.0184∗∗∗ 0.181∗∗∗ 0.0184∗∗∗ 0.181∗∗∗

(15.46) (64.20) (15.46) (64.22)

age 0.262∗∗∗ 0.262∗∗∗

(28.48) (28.49)

age2 -0.00257∗∗∗ -0.00257∗∗∗

(-24.17) (-24.17)

experience 0.118∗∗∗ 0.118∗∗∗

(64.03) (64.06)

experience2 -0.00145∗∗∗ -0.00145∗∗∗

(-54.00) (-54.00)

constant term -1.918∗∗∗ 0.684∗∗∗ -1.917∗∗∗ 0.685∗∗∗

(-10.19) (10.29) (-10.19) (10.31)selecteducation 0.000194 -0.0109∗∗∗

(0.18) (-7.16)

age -0.0111∗∗∗

(-10.61)

relation -0.0300∗∗ -0.0298∗∗

(-2.66) (-2.65)

type of income 0.101∗∗∗ 0.101∗∗∗

(6.95) (6.94)

experience -0.0111∗∗∗

(-10.61)

cons 2.863∗∗∗ 2.786∗∗∗

(53.24) (57.66)athrhocons -0.0272∗∗ -0.0267∗∗

(-2.91) (-2.88)lnsigmacons 1.608∗∗∗ 1.600∗∗∗

(859.54) (855.23)N 142881 142881 142881 142881

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

46

Table 18: The influence of working hours on unemployment for all labor market par-ticipants

Unemployment (1) (2) (3) (4) (5) (6) (7) (8)all class class=1 class=2 class=3 class=4 class=5 class=6 class=7

annual working hours -0.0818∗∗∗ -0.0785∗∗∗ -0.119∗∗∗ -0.114∗∗∗ -0.101∗∗∗ -0.0771∗∗ -0.0735 -0.119(-47.58) (-20.43) (-38.02) (-31.09) (-13.12) (-2.69) (-1.74) (-0.30)

age -0.414∗∗∗ -0.488∗∗ -0.794∗∗∗ -0.536∗∗∗ -0.357 -1.916 0.759 -19.43∗

(-4.97) (-2.99) (-5.36) (-3.62) (-1.27) (-1.00) (0.25) (-2.80)

education 0.813∗∗∗ 1.358∗∗∗ 0.188 -1.093∗∗ -7.233∗∗∗ -22.44∗∗∗ -4.067 22.71(5.11) (4.42) (0.78) (-3.20) (-7.02) (-4.41) (-0.42) (0.76)

type of income -13.82∗∗∗ -9.453 1.500 -4.106 -13.10∗ -15.86 -32.38 323.3(-7.34) (-1.52) (0.43) (-1.54) (-2.42) (-0.55) (-0.72) (1.83)

constant term 263.3∗∗∗ 271.3∗∗∗ 342.4∗∗∗ 332.0∗∗∗ 393.9∗∗∗ 655.6∗∗∗ 287.5 193.9(62.48) (28.63) (44.07) (34.27) (17.43) (6.01) (1.75) (0.49)

N 63500 13516 22320 16996 4737 647 101 14

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 19: The influence of working hours on unemployment for the labor market par-ticipants who experience unemployment during one year

Unemployment (1) (2) (3) (4) (5) (6) (7)all class class=1 class=2 class=3 class=4 class=5 class=6

annual working hours -0.438∗∗∗ -0.437∗∗∗ -0.421∗∗∗ -0.428∗∗∗ -0.506∗∗∗ -0.569∗ -1.219(-52.27) (-34.45) (-35.46) (-20.98) (-8.52) (-2.09) (-1.17)

age 0.235 -0.673 -0.225 0.806 8.750∗∗ 10.58 6.629(0.74) (-1.61) (-0.32) (1.44) (2.75) (0.70) (0.40)

education -3.850∗∗∗ -2.026∗ -2.779∗∗∗ -6.263∗∗∗ -48.65∗∗∗ -198.0∗∗∗ 17.48(-6.63) (-2.37) (-3.60) (-4.23) (-5.04) (-4.44) (0.11)

type of income -11.84 37.08 4.822 -28.61 -22.03 -69.83 -48.39(-1.39) (1.83) (0.36) (-1.87) (-0.56) (-0.31) (-0.22)

constant term 1258.3∗∗∗ 1237.5∗∗∗ 1207.9∗∗∗ 1251.5∗∗∗ 1563.1∗∗∗ 3547.4∗∗∗ 1496.5(66.98) (40.83) (39.78) (27.71) (8.73) (4.83) (0.91)

N 10825 3023 4626 2539 540 63 9

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

47

Table 20: The influence of working hours on unemployment the year after for all labormarket participants

Unemployment (1) (2) (3) (4) (5) (6) (7)in the next year all class class=1 class=2 class=3 class=4 class=5 class=6

unemployment 0.146∗∗∗ 0.174∗∗∗ 0.138∗∗∗ 0.139∗∗∗ 0.0956∗∗∗ 0.0333∗ 0.0130(35.42) (16.58) (17.85) (17.78) (10.15) (2.43) (0.19)

annual working hours -0.0193∗∗∗ 0.000433 -0.0309∗∗∗ -0.0460∗∗∗ -0.0384∗∗∗ -0.0260∗ -0.0484(-10.32) (0.09) (-8.08) (-11.76) (-7.38) (-2.58) (-1.68)

age 0.00442 -0.504∗ 1.243∗∗∗ -0.747∗∗∗ -0.231 -1.725∗ 0.865(0.05) (-2.39) (7.26) (-4.96) (-1.27) (-2.58) (0.43)

education 0.940∗∗∗ 0.764 1.014∗∗∗ 0.229 -1.949∗∗ -1.360 1.009(5.37) (1.81) (3.47) (0.66) (-2.82) (-0.76) (0.16)

type of income -20.36∗∗∗ -24.59∗∗ -21.99∗∗∗ -7.159∗ 0.856 21.53∗ -8.082(-10.06) (-3.04) (-4.93) (-2.52) (0.24) (2.13) (-0.26)

constant term 127.5∗∗∗ 140.5∗∗∗ 123.3∗∗∗ 183.0∗∗∗ 142.3∗∗∗ 133.9∗∗∗ 75.55(27.78) (11.55) (12.98) (17.84) (9.30) (3.43) (0.67)

N 53605 9701 18907 15399 4518 625 99

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 21: The influence of working hours on unemployment the year after for the labormarket participants who experience unemployment during one year

Unemployment (1) (2) (3) (4) (5) (6) (7)in the next year all class class=1 class=2 class=3 class=4 class=5 class=6

unemployment 0.0302∗∗∗ 0.0566∗∗ 0.0318∗ 0.0265 0.00560 0.000836 0.0909(3.81) (2.80) (2.44) (1.79) (0.31) (0.02) (0.48)

annual working hours -0.0589∗∗∗ -0.0402∗ -0.0388∗∗ -0.107∗∗∗ -0.108∗∗∗ 0.0446 0.345(-7.27) (-2.25) (-3.18) (-6.29) (-3.90) (0.53) (0.75)

age -0.460 -0.483 -0.487 -0.456 1.002 -1.414 3.654(-1.75) (-1.09) (-0.76) (-1.09) (0.72) (-0.30) (0.57)

education -0.417 -1.384 0.221 -0.568 -5.981 3.159 0.0752(-0.80) (-1.20) (0.31) (-0.52) (-1.41) (0.20) (0.00)

type of income 3.762 8.950 -1.461 0.710 33.75∗ 129.8 78.47(0.50) (0.36) (-0.11) (0.06) (1.97) (1.94) (0.95)

constant term 331.5∗∗∗ 308.9∗∗∗ 299.7∗∗∗ 412.1∗∗∗ 345.4∗∗∗ -2.606 -517.9(17.40) (7.03) (9.35) (10.51) (4.22) (-0.01) (-0.75)

N 9092 2137 4036 2308 519 61 9

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

48

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