Stay at School or Start Working? - The Human Capital Investment Decision under Uncertainty and Irreversibility

Transcription

1 Stay at School or Start Working? - he Human Capital Investment Decision under Uncertainty and Irreversibility Prepared for the 44 th Annual Conference of the Canadian Economics Association N. BILKIC,. Gries and M. Pilichowski University of Paderborn, Germany

2 1. Motivation 1.1 Income, education and earning profiles Connection between income and education: male college graduate some college high school graduate some high school Education is a major determinant of income generates income profiles Educational choice may be a choice of an income profile is a sequential decision

3 1. Motivation 1. Income, education and estimations Some key elements in the traditional approach are critical: "Our sheepskin analysis points effects to according a need for more to graduation empirical studies that incorporate additional theelements sequential determine nature of education individual choice: schooling decisions taxes, and tuition uncertainty costs (+ about psychic education costs) costs and future earnings to help determine their importance. We uncertainty about educational achievements report evidence on estimated option values from the recent empirical uncertainty literature using about rich earnings panel data sources that enable Heckman analysts to et answer al. (008, questions 003, that 006), could not Cunha be answered et al. (005), with Cunha the cross and section Heckman data available (007), to Carneiro Mincer in et. the al. 1960s. (003), Hartog (Heckman, (00, Lochner, 007) and odd (006), p.6) 3

4 1. Motivation 1. Essential elements of the education decision Elements which have to be accounted for: Sequential education decision Uncertainty about education costs and future earnings Option value of being in school extensions of theoretical models extensions of estimation models 4

5 1. Motivation 1.3 HC-theory including uncertainty Levhari, Weiss (AER1974) Williams (Journal of Business, 1978) Groot, Oosterbeek (Economics of Education Review 199) Hanchane, Lioui and ouahri (WP 006) 5

6 1. Motivation 1.3 HC-theory including uncertainty Jacobs (Labor Economics 007) Real option approach, but the decision to start learning is irreversible, option to wait with higher education Hogan, Walker (Labor Economics 007) ransfer of real option theory to human capital (option for further education) he decision to leave school is irreversible, schooling is the waiting time 6

7 . Model of optimal timing of market entry Elements of the decision problem: 1. schooling costs. Earning profile 3. Option value all elements depend on the time when the market entry is reached Optimal human capital investment: 1. Derive the required income threshold to leave school. hrough the motion leading to this trigger point derive the time of schooling 7

8 . Model of optimal timing of market entry.1 Schooling costs Schooling costs are continuous investments for a number of periods : constant costs for a successful year of C schooling : cost of market entry C It I( r( t) ) Ce dt C 0 : accumulated schooling costs with each additional year of schooling t 0 : starting time of the planning process : time of terminating school and market entry r : risk free interest rate 8

9 . Model of optimal timing of market entry. Uncertain earnings profile A profile is characterized by: - an entry-level wage at market entry -adynamic income path Source: Ehrenberg, Smith, (006 ) Modern Labour Economics, p Age 9

10 . Model of optimal timing of market entry. Uncertain earnings profile 1. Entry-level wage at market entry Education improves the productivity It increases with time of education Y follows a stochastic process, described by a geometric Brownian motion dy Ydt YdW constant drift constant volatility 10

11 . Model of optimal timing of market entry. Uncertain earnings profile Entry-level wage: lny ln EY 3 ln EY dy Yd YdW ln EY t, 11

12 . Model of optimal timing of market entry. Uncertain earnings profile. Dynamic development of the earning path after market entry: Once working life has started, earnings will follow a stochastic earning dynamics Development of earnings follows a stochastic process, described by a geometric Brownian motion dy Ydt YdW constant drift constant volatility 1

13 . Model of optimal timing of market entry. Uncertain earnings profile Earning profile: entry-level wage + income path ln EY lny 3 ln EY dy Yd YdW ln EY 1 dy Ydt YdW t, 13

14 . Model of optimal timing of market entry. Uncertain earnings profile Both components of the earning profile are summarized in the expected lifetime income V ( ) E Ye dt Y ( r a r( t ) ) he expected lifetime income provides a base for th evaluation of the earning profile 14

15 . Model of optimal timing of market entry.3 Option value of schooling (time for education) he option value is the value of waiting because waiting and schooling is an option on an uncertain but potentially higher market entry waiting opens additional opportunities generated by the hope for a better income track due to more education waiting can postpone the irreversible market entry 15

16 3. Expected time of market entry 3.1 Conditions Conditions for an optimal decision Hamilton-Jacobi-Bellman equation and Ito s Lemma: 1 rf E( df) dt F F df Y t Y E( df) F t Boundary conditions F(0) 0 F( Y df( Y dy ) V ( Y ) ) dv ( Y dy 1 Y F Y Y I( ) ) Hamilton-Jacobi-Bellman F F dt Y dw Y Y 1 Y value smooth F Y dt matching pasting condition condition 16

17 3. Expected time of market entry 3. hreshold Determining the threshold that triggers the market entry Proposition: For constant costs per additional year of schooling C and an earning process following a Brownian motion dy Ydt YdW there exists a threshold Y ( ) that would trigger the market entry. Y with ( r 1 1 C ) r e r 1 1 C r 17

18 3. Expected time of market entry 3. hreshold lny Determining the threshold that triggers the market entry threshold ln Y ( ) threshold is the required entry-level wage/income level at market entry t 0 t 18

19 3. Expected time of market entry 3.3 Expected income at market entry Determine the expected first-time realization of the entrylevel wage Proposition: From the Brownian motion we can derive the expected time of first realization of the entry-level wage and hence determine the expected time until any initial income level Y is reached for the first time E 1 1 Y ln. Y 0 19

20 3. Expected time of market entry 3.4 Expected time of market entry Determining the expected time of market entry Proposition With Y i and the expected value of the earnings at market entry EY ( ) for each time, we can approximate the expected optimal time E of market entry and show that is an implicit function of the vector. (,, C, C, Y(0),, r) (,, C, C, Y(0),, r) ( r ) C 1 Cr C C Y (0) 0

21 3. Expected time of market entry 3.4 Approximate time of market entry Approximate the expected time of market entry lny i expected first time realization of wage E B entry level C threshold ln Y ( ) A earning stream t t 1

22 4. Determinants of expected market entry 4.1 Effects of schooling costs lny 0 C expected first time realization of wage E A threshold ln Y ( ) entry level ' A' t Proposition C threshold Intuition: Higher costs drive up the threshold Market must compensate for higher costs Improvement in initial wage at market entry is required

23 4. Determinants of expected market entry 4. Effects of income risk lny 0 C expected first time realization of wage E A threshold ln Y ( ) entry level ' A' t Proposition: threshold Intuition: Higher risk shifts the threshold up he investors needs a compensation for the higher risk He will get a compensation since further investments improve the market value at market entry and the total value of the project. 3

24 4. Determinants of expected market entry 4.3 No-education minimum wage income lny 0 exp ected first time realizationof entry level wage E Y (0) A A' ' threshold ln Y ( ) t Proposition Y(0) E Intuition: A rise of the minimum wage indicates that no education achieves a higher level in income a higher no-education wage path decreases the attractiveness of a long education a quick market entry becomes more attractive. 4

25 5. Conclusion he model takes human capital decision as sequential decision integrates all relevant components of the human capital decision: Complete uncertain earning profile Education costs Option on a better earning profile explicitly determines the expected time of schooling provides the comparative static for all relevant variables analytically all in all provides a basis for future theoretical and empirical examinations, which includes sequential timing, uncertainty, irreversibility and option values 5

26 Stay at School or Start Working? by N. Bilkic,. Gries, and M. Pilichowski hank you for your attention! University of Paderborn, Germany 6