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Real option, human capital investment returns and higher educational policy
Economic Modelling 31 (2013) 447–452
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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod
Real option, human capital investment returns and higher educational policy Wei-Yei Hwang a, 1, Shu-Yi Liao b, 2, Mao-Lung Huang c,⁎ a b c
Department of Marketing and Logistics Management, Chung Chou Institute of Technology, Changhua 51003, Taiwan Department of Applied Economics, National Chung Hsing University, Taichung 40227, Taiwan Bachelor's Degree Program of Hotel Management, Tainan University of Technology, Tainan 71002, Taiwan
a r t i c l e
i n f o
Article history: Accepted 30 November 2012 JEL classification: D81 J24 I21 Keywords: Real option Human capital investment Higher education Unemployment rate
a b s t r a c t This paper incorporates the concept of real option into a modified Harris–Todaro model to investigate the relationship between higher education and unemployment rates. We found that the real option value of waiting to invest in graduate school education will decrease when the expected wage rate of labors with an undergraduate degree becomes relatively lower than that with a graduate degree. As a result, more undergraduate students will decide to go to graduate schools immediately after graduation. As the supply of labors with a graduate degree increases and the job creations fail to meet the increasing demand, those who cannot get a graduate-level job will be willing to accept job offers lower than their education level. Our modified Harris–Todaro model shows that it will lead to an increase in the number of unemployed and underemployed higher educated labors. This explains why the unemployment rates for higher educated labor are relatively high in some developed countries. © 2012 Elsevier B.V. All rights reserved.
1. Introduction It is widely recognized in the economics of human capital that educational returns are positively correlated with schooling years (e.g., Denny and Harmon, 2001; Hungerford and Solon, 1987; Mincer, 1974; Park, 1999; Silles, 2008). There are basically two schools of thought about the returns to education. One considers wages as educational returns in order to identify sheepskin effects based on various step-function specifications. The other treats education as a signal for employers to recognize individual ability in the labor market. According to the screening theory, diplomas are important for primary matching labor choices in work, however, diploma effects will decline as working experience increases. That is, education demand is negatively correlated with working experience. In contrast to the screening theory, the human capital hypothesis asserts that investments in education can improve labor skills. Therefore, employers are willing to pay more for employees with a higher education diploma than those with a primary or secondary education diploma. The real options method has attracted significant interests in the fields of individual decision making for the purchase of durable goods, employee hiring, career choices, and human capital investment (see e.g., Ashenfelter et al., 1999; Card, 1999; Harmon et al.,
⁎ Corresponding author. Tel.: +886 6 2421046; fax: +886 6 2433836. E-mail addresses: [email protected] (W.-Y. Hwang), [email protected] (S.-Y. Liao), [email protected] (M.-L. Huang). 1 Tel.: +886 4 8359000x3114; fax: +886 4 8314515. 2 Tel.: +886 4 22840350x208; fax: +886 4 22840255. 0264-9993/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econmod.2012.11.061
2003; Jacobs, 2007). In comparison with the net present value (NPV) method, the real options method is more capable of incorporating return and cost uncertainties into the individual human capital investment decision-making process (Groot and Oosterbeek, 1992; Hogan and Walker, 2007). Friedman (1962) claims that human capital should be considered as non-liquid assets. That is, individuals can recover their foregone wages and schooling expenditures only after they start working. Therefore, the educational investment is considered an irreversible sunk cost. During the human capital investment decision-making process, individuals can decide when to invest in order to reduce risks in the labor market. The real options value of educational investment is mainly determined by the current average wage rates, estimated direct and indirect educational expenditures, and expected future wage rates after graduation (Jacobs, 2007; Palacios-Huerta, 2004; Palacios-Huerta and Serrano, 2006). For example, the real options value of higher education investment for an individual with a Bachelor's diploma is the educational risk premium subtracted by sheepskin effects. Because the future wage rate and the probability of obtaining a job after graduation are both uncertain, it is important to take both factors into account in an individual's human capital investment decision-making process. The issue of relatively high unemployment rate for higher educated labor in some developed countries has been widely studied since the 1990s (see e.g., Groot and van den Brink, 2000). Most previous literatures conclude that overinvestment in higher education could lead to the supply surplus of higher educated labor based on either qualitative analysis or simple quantitative models. There is still lack of a
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theoretical model to investigate the positive relationship between higher education and unemployment rates in some developed countries. In this paper, we try to resolve this important issue by incorporating the concept of real options value into a modified Harris–Todaro model. According to the Harris–Todaro migration model (Harris and Todaro, 1970), the expected wage rate in the urban modern sector plays the key role in the migration decision making process for rural labors. A similar analytical framework is developed in this paper by replacing rural and urban wage rates with undergraduate-level and graduate-level wage rates. However, in addition to expected wage rate, we further incorporate real options value in the decision making process for an undergraduate student choosing between job markets and graduate schools. This implies that the real options value of higher education investment and the re-examination rate (or reapplication rate) will affect the choice between job markets and graduate schools for an undergraduate student. While the Harris–Todaro migration model assumes that the rural labor market will be cleared with urban labor migrations, we assume that unemployment exists for labors with an undergraduate degree. Labors with a graduate degree that accept a job below their educational level are considered as underemployment. In this paper, we attempt to identify how government's higher education expansion policy affects the relationship between the unemployment rate of labors with an undergraduate degree (undergraduate-level labor), the re-examination/reapplication rate of people who have decided to go to graduate schools but failed to get accepted, and the unemployment rate of labors with a graduate degree (graduate-level labor). According to our analysis, overinvestment in higher education is very likely to cause the increase in the unemployment rate of higher educated labors and the decrease of higher educated labor wage rates. The magnitude of these negative impacts will depend upon the demand of higher educational labor markets. Therefore, our model can be used to explain why there are relatively high unemployment rates for higher educated labor in some developed countries. The remainders of this paper are organized as follows. Section 2 demonstrates how to incorporate the real options concept into the decision-making process of human capital investment. In Section 3, we develop a modified Harris–Todaro higher education investment model to explain the relationship between unemployment rate, re-examination/reapplication, and unemployment rate of higher educated labor. In Section 4, a graphical analysis is used to explain the impacts of overinvestment in higher education on the unemployment, re-examination/reapplication, and wage rate of higher educated labor. In the last section, we summarize the main conclusions and implications for higher education policy. 2. Education investment and real options Dixit and Pindyck (1994) point out that there are two strong unrealistic assumptions implicit in the traditional NPV criterion of human capital investment models: reversibility and non-postpone decision making. The former assumes that investment activities would create feedback costs or drawbacks for the individual's original investments if the market condition worsens. The latter assumes that there are only two choices for an individual. That is whether to invest right now or abandon investment forever. Several recent studies have also concluded that the above assumptions are in conflict with the investment decision making process in reality because individual higher education investment decision is deferrable but irreversible (see e.g., Hogan and Walker, 2007; Jacobs, 2007). Therefore, higher educational investment is irreversible and the schooling expenditure and forgone labor earnings should be considered as sunk costs. In general, an individual can decide to invest in higher education immediately (or at later date) or enter the labor market after completing the compulsory levels of education. The decision is highly affected by the direct and indirect costs of education and uncertainties in the labor market. More importantly, real options are present in the
irreversible and risky higher education investment because the individual can influence the timing of the investment. As a result, the higher education investment decision making process is more consistent with the concept of real options than traditional NPV method. The real options of higher education investment can be considered as a put option without a predetermined expiration date. Individuals can influence the timing of the decision and wait for more information about the costs and returns of higher education investment. Therefore, the real options value is derived from the fact that individuals can invest in higher education immediately after graduation or enter the labor market and wait until the expected return is sufficiently large to give up the valuable option. Once individuals decide to invest in higher education, they cannot recover forgone labor earnings and school tuition expenses by selling their human capital asset. As a result, the risk and illiquidity of higher education investment explain why the real option emerges. If individuals decide to give up this valuable real option to wait and decide to invest in higher education, they must be compensated with higher returns. This explains why the wage rate for labors with a graduate degree is in general significantly higher than that for labors with an undergraduate degree. To calculate the real option value of higher education investment, we assume that the annual forgone labor earnings (indirect costs) is w, the annual school expenses (direct costs) is k, and it takes T years to graduate. For simplicity, we assume that w, k, and T are known to the individual during the investment decision process. The present value of total costs I for higher education investment at the date of graduation (t = 0) can be calculated as 0 X wþk ¼ωþκ ð 1 þ r Þt t¼−T r : real interest rate w t¼0 ω≡∑t¼−T : present value of gross wages ð1 þ r Þt k t¼0 : present value of direct expenditures: κ≡∑t¼−T ð1 þ r Þt
I≡
ð1Þ
For simplicity, we assume that the retiring date after graduation is farther enough and thus the time-horizon for future labor earnings can be viewed as infinite. Assume that the expected return right after graduation (t = 0) is R0 and it will increase by v with probability q and decrease by δ with probability (1 − q) at t = 1 after all uncertainty is revealed. That is the future expected return from t = 1 to t = ∞ equals (1 + v)R0 with probability q and equals (1 − δ)R0 with probability (1 − q). The present value of total labor earnings V0 for higher education investment at t = 0 can be calculated as ∞ X V 0 ¼ R0 þ ðqð1 þ vÞR0 þ ð1−qÞð1−δÞR0 Þ
¼
R0 ð1 þ r þ qðv þ δÞ−δÞ : r
1 ð 1 þ r Þt t¼1 ð2Þ
If the individual has to decide whether to invest in higher education or not immediately after graduation, that is, without the option to postpone the decision, then the decision will be made depending on the net present value (NPV) of the investment. Let Ω0 represent the NPV of higher education investment without the option to wait, Ω0 can be defined as Ω0 ≡ maxfV 0 −I; 0g ¼
R0 ð1 þ r þ qðv þ δÞ−δÞ −ω−κ; 0 : r
ð3Þ
For simplicity, we assume that the individual will consider to invest in higher education only if Ω0 is greater than zero. The individual will never consider to enroll in higher education if Ω0 is equal to zero.
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On the other hand, the real options value emerges if the individual can postpone his/her higher education investment decision and gain more information about future expected returns. Assume that the information about the magnitudes and probabilities of the upswing (v) or the downswing (δ) will be revealed one year after graduation (t = 1). Let F0 represent the NPV of higher education investment with the real option and V 1 and V 1 denote the NPV3 of the upswing (v) with probability q and the NPV4 of the downswing (δ) with probability of (1− q) at t = 1,5 respectively. F0 can be defined as Ω0 ; qF 1 þ ð1−qÞ F 1 1þr ( ) max V 1 −I; 0 max V 1 −I; 0 ¼ max maxfV 0 −I; 0g; q þ ð1−qÞ : 1þr 1þr
F 0 ≡ max
ð4Þ The real option value of higher education investment (O) can be defined as the difference of NPV with and without the option to wait (O ≡ F0 − Ω0). 6 According to Eqs. (3) and (4), the value of the real option O will decrease as the expected return to higher education R0 increases. That is the option to delay investment becomes less valuable as the individual's loss to invest in higher education immediately increases. On the contrary, the value of the real option O will increase as the costs of higher education investment I increase. In other words, the opportunity costs of waiting decrease as the costs of investment increase, and thus the value of the option to wait increases. Therefore, the criteria for the individual to decide whether to invest in higher education immediately after graduation or wait for one year can be stated as 1 −I a. If V 0 −I > q V1þr and Ω0 > 0, the value of the option to wait equals 0 (O = 0). It is optimal for the individual to invest in higher educationimmediately. 1 −I , the value of the option to wait becomes positive b. If V 0 −Ibq V1þr (O > 0). The individual will be more reluctant to invest immediately and will wait for one year to see if the expected returns turn out to be high V 1 or low ð V 1 Þ. It is optimal for the individual to invest in higher only when the expected returns turn out education to be high V 1 . 3. Real option and modified Harris–Todaro model 3.1. Real option and modified Harris–Todaro model In this paper, we assume the higher educated labor market consists of undergraduate-level labors (u) and graduate-level labors (g). Assume capital input is fixed, a CES production function (X ρ) with higher educated labor input can be defined as ¼ α K ρ þ ∑β Lρ ; X ¼ F Li ; K i i ρ
i ¼ u; g;
α þ βu þ βg ¼ 1;
ρb1 ð5Þ
is second-order differentiable with decreasing marginwhere F Li ; K al productivity of labor. Assume that the factor markets for capital and labor are competitive, the marginal productivity of capital (MPk),
3
4
5
6
ð1−δÞR0 ð1 þ r Þ −ω−κ; 0 . F 1 ≡ maxf V 1 −I; 0g ¼ r ð1 þ r Þð1 þ vÞR0 −ω−κ; 0 . F 1 ≡ max V 1 −I; 0 ¼ r V 1 −I ð1−δÞR0 ω þ κ V 1 −I ¼ ð1 þ vÞR0 − ω þ κ ; ¼ . − 1þr 1þr 1þr 1þr r r n o 8 9 < max V 1 −I; 0 maxf V 1 −I; 0g= þ ð1−qÞ O≡F 0 −Ω0 ¼ max maxfV 0 −I; 0g; q :. ; 1þr 1þr − maxfV 0 −I; 0g
449
undergraduate labor (MPu), and graduate labor (MPg) will equal to capital price (V), undergraduate-level wage rate (wu), and graduatelevel wage rate (wg), respectively. ρX ρ−1 MP k ¼ ραK ρ−1 ¼ V ρX ρ−1 MP u ¼ ρβu Luρ−1 ¼ wu ρX ρ−1 MP g ¼ ρβg Lgρ−1 ¼ wg : 1 Let σ ¼ 1−ρ , the above three equations can be rewritten as
MP σk ¼ α σ AP k ; MP σu ¼ βσu AP u σ σ MP g ¼ βg AP g
σ¼
1 1−ρ
ð6Þ
Assume that the price of the output is P, the cost share for undergraduate-level labor input (Su) and graduate-level labor input (Sg) can be derived as wu Lu wu Lu 1 ¼ ¼ wg Lg PX V K þ wu Lu þ wg Lg VK þ1þ wu Lu wu Lu wg Lg wg Lg 1 ¼ sg ¼ ¼ : wu Lu PX V K þ wu Lu þ wg Lg V K þ 1 þ wg Lg wg Lg
su ¼
ð7Þ
For simplicity, we assume that the elasticities of the substitution between various factor inputs are the same: σ ¼ σ uk ¼ σ gk ¼ σ ug ¼ u −d log LLug =d log w wg . The output elasticity of labor can be derived as τi = − d log X/d log wi and the cross elasticity of demand for capital and labor can be derived as μK = − d log(K)/d log(wi). According to Eq. (6), the logarithmic difference between the labor wage rate log(w) and the output price log(P) can be derived as σ[log(w) − log(P)]= σ log βi + log X − log Li. Differentiating it with respect to log wi, we have σ 1− τηi ¼ λi −τ i . Therefore, the output elasticity of labor i can h i be calculated as τ i ¼ η =ðη−σ Þ ðλi −σ Þ, in which η is the elasticity of product demand and λi represents the elasticity of labor demand. The relationship between the capital–labor ratio and the factor price ratio in the above CES production function can be derived as log(K) − log(Li) = σ log(α/βi) − σ log V + σ log wi. By differentiating this equation with respect to log wi, we have λi −μ k ¼ σ μek þ σ, in which μk represents the cross elasticity of demand for capital with respect to wage rates. Let e represents the elasticity of demand for caph i ital, given μ k ¼ e =ðσþeÞ ðλi −σ Þ we have λi −μ k ¼ σσþe ðλi þ eÞ and σ ðηþeÞ τi −μ k ¼ ðλi −σ Þ ðσþe Þðη−σ Þ . After the derivations of various elasticities above, the total differentiation of output X with respect to undergraduate-level labor wage rate wu can be calculated as dLg dX dK dL dK ¼ MP k þ MP u u þ MP g ¼ 1−su −sg AP k dwu dwu dwu dwu dwu w dK dLg dL w dX u þsu AP u u þ sg AP g ⇒ u⋅ ¼ 1−su −sg dwu dwu X dwu K dwu þsu
wu dLu w dL þ sg u u : Lu dwu Lg dwu
Therefore, the output elasticity of undergraduate-level labor can be redefined as τu = (1− su − sg)μk + suλuu + sgλug where λii represents the own elasticity of labor demand and λug denotes the cross elasticity of demand for two different educational levels of labor. By combin σ ing equations τu −μ k ¼ su ðλuu −μ k Þ þ sg λug −μ k ¼ σþe ½su ðλuu þ eÞþ σ ðηþeÞ sg λug þ e and τ u −μ k ¼ ðλuu −σ Þ ðσþeÞðη−σ Þ , we can calculate the
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σ own and cross elasticity of labor demand: λuu ¼ η−σ þ ηþe1 1− ηþe su η−σ −su σ esu þ sg λug þ e , λgg ¼ η−σ þ ηþe1 esg þ su λug þ e , and 1− ηþe sg η−σ −sg n h i ηþe o ηþe 1 λug ¼ sg λuu η−σ −su þ e sg −su − η−σ σ .
For simplicity, we assume that the labor market for each individual higher educated labor is competitive. In equilibrium, marginal productivity of labor i (FiL) equals its wage rate (wi). L
L
F u ¼ wu and F g ¼ wg :
ð8Þ
Following the fundamental assumption about the expected wage rate in the Harris–Todaro migration model, the expected wage rate for graduate-level labors (wge) and for undergraduate-level labors (wue) can be defined as e
Lg Lg 1 Lu e ¼ wg ¼ wg and wu ¼ wu 1 þ ϕg Lg þ U g Dg Lu þ U u L 1 ¼ wu u ¼ wu 1 þ ϕu Du
wg ¼ wg
ð9Þ
where Lg and Lu represent the number of employed graduate-level and undergraduate-level labors; Ug and Uu represent the number of unemployed graduate-level and undergraduate-level labors; Dg and Du represent the total number of graduate-level and undergraduate-level labors that obtain their diploma from regular graduate programs and on-job graduate programs; ϕg = (Ug/Lg) and ϕu = (Uu/Lu) represent the unemployment rate of graduate-level and undergraduate-level labors. Therefore, the equilibrium condition in the Harris–Todaro migration model can be modified as e
e
wu ¼ wg ⇔wg ¼
1 þ ϕg L Dg w ¼ wu u ⋅ : 1 þ ϕu u Lg Du
ð10Þ
To account for the individuals who decided to invest in higher education but were unable to get the acceptance of a graduate school, we define the total number of individuals who decided to invest in graduate school education as Ng. In general, the gap between Ng and Dg (i.e., the number of re-examination/reapplication) will be affected by the government policy of graduate school education. More people who decide to invest in higher education will be accepted as the supply of graduate program increases. Therefore, the re-examination/reapplication rate for graduate school will be smaller. Similar to the Harris–Todaro model, we assume that higher educated labor wage rates are exogenously determined by various economic factors and government higher education policy. Suppose θ represents the total number of people who can go to graduate schools, the expected wage rate for higher educated labors (wge and wue) will be a function of θ. e wg
g ; ϕg ðθÞ; ϕu ¼f w
and
e wu
u ; ϕg ðθÞ; ϕu ¼f w
shown in Fig. 1. In Fig. 1, GG and UU curves, which are functions of market wage rates wg and wu, represent the derived demands for graduate-level and undergraduate-level labors, respectively. G′G′ and U′U′ curves represent the expected wage rate for graduate-level and undergraduate-level labors, respectively. If the magnitude of upswing (v) and its corresponding probability (q) are sufficiently large, the expected wage rate can be greater than the market wage rate. This explains why G′G′ (U′U′) curve interacts with GG (UU) curve at a relatively high wage rate level in Fig. 1. The difference between G′ G′ (U′U′) curve and GG (UU) curve can be defined as the real option value of higher education investment, that is, Oi = wie − wi. As the value of Oi decreases to less than zero (i.e., wi ≥ wie), the optimal decision for the individual is to invest immediately in higher education without waiting. Only when Oi becomes positive, it is optimal for the individual to wait and enroll in higher education at a later date. Therefore, having the option to wait will reduce the required expected return to consider the investment in higher education. As shown in Fig. 1, the segment between the intersection of G′G′ and GG curves (point Eg) and the intersection of U′U′ and UU curves (point Eu) represent the individuals who have decided to invest in higher education. The segment EuEg can be viewed as the total number of undergraduate-level and graduate-level labors when the option to postpone higher education investment is taken into account. Therefore, the modified Harris–Todaro real option model in Fig. 1 can be scaled down to the portion of EuEg to illustrate how government higher education policy will affect the unemployment rate and re-examination/reapplication rate of higher educated labors. 3.2. Unemployment and re-examination of higher educated labors Fig. 2 shows a modified Harris–Todaro higher education investment model which consists of undergraduate-level and graduate-level labors. Given the wage rate wg, the demand for graduate-level labor Lg is determined by the demand curve GG. According to Eqs. (9) and (10), we can find an undergraduate-level wage rate wu that equalizes the expected graduate-level and undergraduate-level wage rates (wge = wue). The demand for undergraduate-level labor Lu can be derived from the demand curve UU. The qq curve represents the indifference curve of expected wage rates. After solving the values of wu and Lu, we can derive the corresponding Dg and ϕg for graduate-level labors and Du and ϕu for undergraduate-level labors. If the undergraduate-level wage rate remains at a relatively lower level compared to graduate-level wage rate, which means graduate education investment becomes more valuable, the total number of graduate-level labor will increase. This will lead to the increase of the unemployment rate for graduate-level labor. Meanwhile, as the supply of graduate-level labors increases, Option,Wage
Option,Wage
ð11Þ
G’ U
In Eq. (11), θ can be viewed as a higher education policy instrument which is mainly controlled by the government. As the government allocates more resources into graduate school education, more people will be able to enroll in graduate programs, and hence the supply of graduate-level labors will increase. Assume that the increase in labor demand for graduate-level labors (dLg) is not enough to absorb the increase in labor supply (dDg) due to graduate programs expansion, the wage rate wg will decrease and the unemployment rate ϕg will increase. According to Eqs. (7) and (10), the wage rate wu will decrease and the unemployment rate ϕu will increase. This means that the expected wage rates for higher educated labors (wge,wue) will both be decreased due to the oversupply of graduate-level labors, ∂we ∂ϕ ∂we ∂ϕ that is, ∂ϕ g ∂θg b0 and ∂ϕ u ∂θg b0. g g The consequences of the oversupply of graduate-level labors can be illustrated with a modified Harris–Todaro real option model as
G
U’ Eg Eu
G G’
U’
U 0g
0u
OG OU
the pool of higher educated labors
Fig. 1. Modified Harris–Todaro model with real options of human capital investment.
W.-Y. Hwang et al. / Economic Modelling 31 (2013) 447–452 graduate-level wage
Undergraduate-level wage
u hand, given ∂w ∂φ e
g
U
G
U’
q
G’ wg
wu
wue
wge G
G’
0u
U’
Lu
Ng
Dg
U
Lg
0g
Fig. 2. Unemployment and re-examination of higher educated labors.
those who cannot get a graduate-level job will be willing to accept job offers lower than their education level. This will further lower the expected wage rate for labors with an undergraduate degree as their employment opportunities decrease. The total number of individuals who decided to invest in graduate school education (Ng) can be found at the interaction point of G′G′ and U′U′ curves. For simplicity, we assume that there will be no re-examination/reapplication demand when Ng is less than Dg, that is, the total number of undergraduate-level and graduate-level labors equals Du plus Dg. The number of re-examination/reapplication becomes positive when Dg is less than Ng. In this case, the unemployment number of undergraduate-level labors (Uu) will increase as Du becomes larger due to the decrease of Dg. In this case, Uu will include undergraduate-level labors that are either unemployed or failed to get accepted into a graduate school. As the gap between Ng and Dg increases, the expected wage rate of graduate-level labor wge will increase, and hence graduate education investment becomes more valuable. 4. Implications for higher education policy As shown in Fig. 3, suppose that the number of graduate-level labors increases from Dg to Dg′ when the government decide to expand graduate school programs. This implies that θ will increase and thus lead to the change in expected wage rates. Then the expected wage rate curve for graduate-level labor will shift downward from G′G′ to ∂weg ∂φg ∂φg ∂θ
G″G″, given
b0 derived above. The number of unemployed
∂φg ∂θ
451
b0, the expected wage rate curve for undergraduate-
level labor will also shift downward from U′U′ to U″U″ due to the increase of θ. If the job opportunities for higher educated labors remain unchanged then the decrease of wge will be greater than the decrease of wue. In this case, the total number of individuals who decided to invest in graduate school education will decrease from Ng to Ng′. This will cause the number of unemployed undergraduate-level labor to increase from LuNg to LuNg′. Furthermore, as the supply of labors with a graduate degree increases, those who cannot get a graduate-level job will be willing to accept job offers lower than their education level. This will further lower the expected wage rate for labors with an undergraduate degree as their employment opportunities decrease. As illustrated in Fig. 3, the number of re-examination/reapplication will be reduced by the graduate school expansion policy. However, it is very likely to cause negative impacts on the higher educated labor market when the increase in graduate-level job opportunities fails to keep up with the increase in graduate-level labor supply. There are two major negative effects under this unfavorable situation including: (1) the increase in the unemployment rates for both graduate-level and undergraduate-level labors; (2) the decrease in the expected wage rates for both graduate-level and undergraduate-level labors. Both negative effects will raise the issues of inefficient or overinvestment of higher education and increase the need for higher education policy reform. In general, it will be difficult to reduce the number of graduate programs once it has been established by the public higher education expansion policy. Especially when the economic growth rate is lower than expected, the increase in the job opportunities is very likely to be less than the increase in higher educated labor supply. Under this circumstance, the real option value of waiting to invest in higher education will decrease due to the decrease in expected wage rate. Therefore, individuals will either decide to invest in higher education immediately after graduation or never consider enrolling in higher education. It is widely recognized that there are spillover effects from the labor market to the education market. In other words, individuals will tend to stay in school when the expected wage rate decreases. This explains why the unemployment rates for higher educated labor are relatively high in some developed countries. Because the public higher education policy is mainly determined by political reasons, it requires the integration of other social welfare maximization criteria to increase the economic efficiency of higher education investment and reduce the risk for individual's education investment. 5. Conclusion
graduate-level labors will increase from DgLg to Dg′Lg. On the other undergraduate-level wage
graduate-level wage
U
G
U’
G’
G”
U”
q
q G” w ue w u e’
0u
w ge
U” G
G’
Lu
U’
N g N ’g D ’g D g
U
Lg
Fig. 3. Higher education policy and expected wage rate.
w ge’
0g
The expansion of higher education has been considered as a key element to facilitate a country's economic growth and international competiveness. Many wealthy developed countries and poor developing countries have allocated a great amount of resources into undergraduate and graduate school programs. In addition to regular higher education programs, many countries also have on-job education programs that provide individuals the opportunity to invest in higher education even if they have entered the labor market for a long time. Therefore, individuals can reenter education at a later age which suggests that the option to go to work is not really irreversible. However, it is irreversible once the individual decided to invest in higher education. Because the higher education program is somewhat difficult to be shut down once it has been established, it raises the issue of overinvestment in higher education in some developed countries when the unemployment rate for higher educated labor started to increase. By incorporating the concept of real option into a modified Harris–Todaro model, this paper demonstrates why the unemployment rates for higher educated labor are relatively high in some developed countries.
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It is well-known that the wage rate for graduate-level labor is relatively higher than that for undergraduate-level labor, and hence the value of the option to postpone higher education investment is relatively low. As the wage rate for undergraduate-level labor remains relatively low and the government devotes more resources into graduate school programs, individuals will be less reluctant to invest in higher education immediately after graduation. However, it is generally difficult for a country to create sufficient job opportunities to absorb the increase of graduate-level labor supply especially when the economic growth is lower than expected. Due to the illiquidity and irreversibility of education investment, unemployed graduate-level labors will be willing to accept job offers lower than their education level. This will crowd out the job opportunities for undergraduatelevel labors and increase the unemployment rate for the entire higher educated labors. These adverse phenomena can be explained by our modified Harris–Todaro model as the number of graduate-level labors increases under the government education expansion plan. Based on our analysis, the unemployment rate of higher educated labors will increase and the wage rates will decrease due to inadequate higher education expansions. Therefore, an integrated higher education policy based on both political factors and economic efficient criteria is needed to mitigate the adverse impacts of higher education expansions on labor markets. References Ashenfelter, O., Harmon, C., Oosterbeek, H., 1999. A review of estimates of the schooling/earnings relationship, with tests for publication bias. Labour Economics, Elsevier 6 (4), 453–470 (November).
Card, D., 1999. The causal effect of education on earnings. In: Ashenfelter, O., Card, D. (Eds.), Handbook of Labor Economics, vol. 3. Elsevier Science, Amsterdam, pp. 1801–1863. Denny, K., Harmon, C., 2001. Testing for sheepskin effects in earning equations: evidence for five countries. Applied Economic Letters 8, 635–637. Dixit, A.K., Pindyck, R.S., 1994. Investment Under Uncertainty. Princeton University Press, New Jersey. Friedman, M., 1962. Capitalism and Freedom. University of Chicago Press, pp. 85–96. Groot, W., Oosterbeek, H., 1992. Optimal investment in human capital under uncertainty. Economics of Education Review 11, 41–49. Groot, W., van den Brink, H., 2000. Overeducation in the labor market: a meta-analysis. Economics of Education Review 19, 149–158. Harmon, C., Oosterbeek, H., Walker, I., 2003. The returns to education: microeconomics. Journal of Economics Surveys 17, 115–156. Harris, J.R., Todaro, M., 1970. Migration, unemployment and development: a twosector analysis. American Economic Review 126–142 (May). Hogan, V., Walker, I., 2007. Education choice under uncertainty: implications for public policy. Labour Economics 14, 894–912. Hungerford, T., Solon, G., 1987. Sheepskin effects in the returns to education. Review of Economics and Statistics 69, 175–177. Jacobs, B., 2007. Real options and human capital investment. Labour Economics 14, 913–925. Mincer, J., 1974. Schooling, Experience and Earnings. National Bureau of Economic Research, New York. Palacios-Huerta, I., 2004. An empirical analysis of the risk properties of human capital returns. American Economic Review 93, 948–964. Palacios-Huerta, I., Serrano, R., 2006. Rejecting small gambles under expected utility. Economics Letters 91 (2), 250–259. Park, J.H., 1999. Estimation of sheepskin effects using the old and the new measures of educational attainment in the Current Population Survey. Economic Letters 62, 237–240. Silles, M., 2008. Sheepskin effects in return to education. Applied Economic Letters 15, 217–219.
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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod
Real option, human capital investment returns and higher educational policy Wei-Yei Hwang a, 1, Shu-Yi Liao b, 2, Mao-Lung Huang c,⁎ a b c
Department of Marketing and Logistics Management, Chung Chou Institute of Technology, Changhua 51003, Taiwan Department of Applied Economics, National Chung Hsing University, Taichung 40227, Taiwan Bachelor's Degree Program of Hotel Management, Tainan University of Technology, Tainan 71002, Taiwan
a r t i c l e
i n f o
Article history: Accepted 30 November 2012 JEL classification: D81 J24 I21 Keywords: Real option Human capital investment Higher education Unemployment rate
a b s t r a c t This paper incorporates the concept of real option into a modified Harris–Todaro model to investigate the relationship between higher education and unemployment rates. We found that the real option value of waiting to invest in graduate school education will decrease when the expected wage rate of labors with an undergraduate degree becomes relatively lower than that with a graduate degree. As a result, more undergraduate students will decide to go to graduate schools immediately after graduation. As the supply of labors with a graduate degree increases and the job creations fail to meet the increasing demand, those who cannot get a graduate-level job will be willing to accept job offers lower than their education level. Our modified Harris–Todaro model shows that it will lead to an increase in the number of unemployed and underemployed higher educated labors. This explains why the unemployment rates for higher educated labor are relatively high in some developed countries. © 2012 Elsevier B.V. All rights reserved.
1. Introduction It is widely recognized in the economics of human capital that educational returns are positively correlated with schooling years (e.g., Denny and Harmon, 2001; Hungerford and Solon, 1987; Mincer, 1974; Park, 1999; Silles, 2008). There are basically two schools of thought about the returns to education. One considers wages as educational returns in order to identify sheepskin effects based on various step-function specifications. The other treats education as a signal for employers to recognize individual ability in the labor market. According to the screening theory, diplomas are important for primary matching labor choices in work, however, diploma effects will decline as working experience increases. That is, education demand is negatively correlated with working experience. In contrast to the screening theory, the human capital hypothesis asserts that investments in education can improve labor skills. Therefore, employers are willing to pay more for employees with a higher education diploma than those with a primary or secondary education diploma. The real options method has attracted significant interests in the fields of individual decision making for the purchase of durable goods, employee hiring, career choices, and human capital investment (see e.g., Ashenfelter et al., 1999; Card, 1999; Harmon et al.,
⁎ Corresponding author. Tel.: +886 6 2421046; fax: +886 6 2433836. E-mail addresses: [email protected] (W.-Y. Hwang), [email protected] (S.-Y. Liao), [email protected] (M.-L. Huang). 1 Tel.: +886 4 8359000x3114; fax: +886 4 8314515. 2 Tel.: +886 4 22840350x208; fax: +886 4 22840255. 0264-9993/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econmod.2012.11.061
2003; Jacobs, 2007). In comparison with the net present value (NPV) method, the real options method is more capable of incorporating return and cost uncertainties into the individual human capital investment decision-making process (Groot and Oosterbeek, 1992; Hogan and Walker, 2007). Friedman (1962) claims that human capital should be considered as non-liquid assets. That is, individuals can recover their foregone wages and schooling expenditures only after they start working. Therefore, the educational investment is considered an irreversible sunk cost. During the human capital investment decision-making process, individuals can decide when to invest in order to reduce risks in the labor market. The real options value of educational investment is mainly determined by the current average wage rates, estimated direct and indirect educational expenditures, and expected future wage rates after graduation (Jacobs, 2007; Palacios-Huerta, 2004; Palacios-Huerta and Serrano, 2006). For example, the real options value of higher education investment for an individual with a Bachelor's diploma is the educational risk premium subtracted by sheepskin effects. Because the future wage rate and the probability of obtaining a job after graduation are both uncertain, it is important to take both factors into account in an individual's human capital investment decision-making process. The issue of relatively high unemployment rate for higher educated labor in some developed countries has been widely studied since the 1990s (see e.g., Groot and van den Brink, 2000). Most previous literatures conclude that overinvestment in higher education could lead to the supply surplus of higher educated labor based on either qualitative analysis or simple quantitative models. There is still lack of a
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theoretical model to investigate the positive relationship between higher education and unemployment rates in some developed countries. In this paper, we try to resolve this important issue by incorporating the concept of real options value into a modified Harris–Todaro model. According to the Harris–Todaro migration model (Harris and Todaro, 1970), the expected wage rate in the urban modern sector plays the key role in the migration decision making process for rural labors. A similar analytical framework is developed in this paper by replacing rural and urban wage rates with undergraduate-level and graduate-level wage rates. However, in addition to expected wage rate, we further incorporate real options value in the decision making process for an undergraduate student choosing between job markets and graduate schools. This implies that the real options value of higher education investment and the re-examination rate (or reapplication rate) will affect the choice between job markets and graduate schools for an undergraduate student. While the Harris–Todaro migration model assumes that the rural labor market will be cleared with urban labor migrations, we assume that unemployment exists for labors with an undergraduate degree. Labors with a graduate degree that accept a job below their educational level are considered as underemployment. In this paper, we attempt to identify how government's higher education expansion policy affects the relationship between the unemployment rate of labors with an undergraduate degree (undergraduate-level labor), the re-examination/reapplication rate of people who have decided to go to graduate schools but failed to get accepted, and the unemployment rate of labors with a graduate degree (graduate-level labor). According to our analysis, overinvestment in higher education is very likely to cause the increase in the unemployment rate of higher educated labors and the decrease of higher educated labor wage rates. The magnitude of these negative impacts will depend upon the demand of higher educational labor markets. Therefore, our model can be used to explain why there are relatively high unemployment rates for higher educated labor in some developed countries. The remainders of this paper are organized as follows. Section 2 demonstrates how to incorporate the real options concept into the decision-making process of human capital investment. In Section 3, we develop a modified Harris–Todaro higher education investment model to explain the relationship between unemployment rate, re-examination/reapplication, and unemployment rate of higher educated labor. In Section 4, a graphical analysis is used to explain the impacts of overinvestment in higher education on the unemployment, re-examination/reapplication, and wage rate of higher educated labor. In the last section, we summarize the main conclusions and implications for higher education policy. 2. Education investment and real options Dixit and Pindyck (1994) point out that there are two strong unrealistic assumptions implicit in the traditional NPV criterion of human capital investment models: reversibility and non-postpone decision making. The former assumes that investment activities would create feedback costs or drawbacks for the individual's original investments if the market condition worsens. The latter assumes that there are only two choices for an individual. That is whether to invest right now or abandon investment forever. Several recent studies have also concluded that the above assumptions are in conflict with the investment decision making process in reality because individual higher education investment decision is deferrable but irreversible (see e.g., Hogan and Walker, 2007; Jacobs, 2007). Therefore, higher educational investment is irreversible and the schooling expenditure and forgone labor earnings should be considered as sunk costs. In general, an individual can decide to invest in higher education immediately (or at later date) or enter the labor market after completing the compulsory levels of education. The decision is highly affected by the direct and indirect costs of education and uncertainties in the labor market. More importantly, real options are present in the
irreversible and risky higher education investment because the individual can influence the timing of the investment. As a result, the higher education investment decision making process is more consistent with the concept of real options than traditional NPV method. The real options of higher education investment can be considered as a put option without a predetermined expiration date. Individuals can influence the timing of the decision and wait for more information about the costs and returns of higher education investment. Therefore, the real options value is derived from the fact that individuals can invest in higher education immediately after graduation or enter the labor market and wait until the expected return is sufficiently large to give up the valuable option. Once individuals decide to invest in higher education, they cannot recover forgone labor earnings and school tuition expenses by selling their human capital asset. As a result, the risk and illiquidity of higher education investment explain why the real option emerges. If individuals decide to give up this valuable real option to wait and decide to invest in higher education, they must be compensated with higher returns. This explains why the wage rate for labors with a graduate degree is in general significantly higher than that for labors with an undergraduate degree. To calculate the real option value of higher education investment, we assume that the annual forgone labor earnings (indirect costs) is w, the annual school expenses (direct costs) is k, and it takes T years to graduate. For simplicity, we assume that w, k, and T are known to the individual during the investment decision process. The present value of total costs I for higher education investment at the date of graduation (t = 0) can be calculated as 0 X wþk ¼ωþκ ð 1 þ r Þt t¼−T r : real interest rate w t¼0 ω≡∑t¼−T : present value of gross wages ð1 þ r Þt k t¼0 : present value of direct expenditures: κ≡∑t¼−T ð1 þ r Þt
I≡
ð1Þ
For simplicity, we assume that the retiring date after graduation is farther enough and thus the time-horizon for future labor earnings can be viewed as infinite. Assume that the expected return right after graduation (t = 0) is R0 and it will increase by v with probability q and decrease by δ with probability (1 − q) at t = 1 after all uncertainty is revealed. That is the future expected return from t = 1 to t = ∞ equals (1 + v)R0 with probability q and equals (1 − δ)R0 with probability (1 − q). The present value of total labor earnings V0 for higher education investment at t = 0 can be calculated as ∞ X V 0 ¼ R0 þ ðqð1 þ vÞR0 þ ð1−qÞð1−δÞR0 Þ
¼
R0 ð1 þ r þ qðv þ δÞ−δÞ : r
1 ð 1 þ r Þt t¼1 ð2Þ
If the individual has to decide whether to invest in higher education or not immediately after graduation, that is, without the option to postpone the decision, then the decision will be made depending on the net present value (NPV) of the investment. Let Ω0 represent the NPV of higher education investment without the option to wait, Ω0 can be defined as Ω0 ≡ maxfV 0 −I; 0g ¼
R0 ð1 þ r þ qðv þ δÞ−δÞ −ω−κ; 0 : r
ð3Þ
For simplicity, we assume that the individual will consider to invest in higher education only if Ω0 is greater than zero. The individual will never consider to enroll in higher education if Ω0 is equal to zero.
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On the other hand, the real options value emerges if the individual can postpone his/her higher education investment decision and gain more information about future expected returns. Assume that the information about the magnitudes and probabilities of the upswing (v) or the downswing (δ) will be revealed one year after graduation (t = 1). Let F0 represent the NPV of higher education investment with the real option and V 1 and V 1 denote the NPV3 of the upswing (v) with probability q and the NPV4 of the downswing (δ) with probability of (1− q) at t = 1,5 respectively. F0 can be defined as Ω0 ; qF 1 þ ð1−qÞ F 1 1þr ( ) max V 1 −I; 0 max V 1 −I; 0 ¼ max maxfV 0 −I; 0g; q þ ð1−qÞ : 1þr 1þr
F 0 ≡ max
ð4Þ The real option value of higher education investment (O) can be defined as the difference of NPV with and without the option to wait (O ≡ F0 − Ω0). 6 According to Eqs. (3) and (4), the value of the real option O will decrease as the expected return to higher education R0 increases. That is the option to delay investment becomes less valuable as the individual's loss to invest in higher education immediately increases. On the contrary, the value of the real option O will increase as the costs of higher education investment I increase. In other words, the opportunity costs of waiting decrease as the costs of investment increase, and thus the value of the option to wait increases. Therefore, the criteria for the individual to decide whether to invest in higher education immediately after graduation or wait for one year can be stated as 1 −I a. If V 0 −I > q V1þr and Ω0 > 0, the value of the option to wait equals 0 (O = 0). It is optimal for the individual to invest in higher educationimmediately. 1 −I , the value of the option to wait becomes positive b. If V 0 −Ibq V1þr (O > 0). The individual will be more reluctant to invest immediately and will wait for one year to see if the expected returns turn out to be high V 1 or low ð V 1 Þ. It is optimal for the individual to invest in higher only when the expected returns turn out education to be high V 1 . 3. Real option and modified Harris–Todaro model 3.1. Real option and modified Harris–Todaro model In this paper, we assume the higher educated labor market consists of undergraduate-level labors (u) and graduate-level labors (g). Assume capital input is fixed, a CES production function (X ρ) with higher educated labor input can be defined as ¼ α K ρ þ ∑β Lρ ; X ¼ F Li ; K i i ρ
i ¼ u; g;
α þ βu þ βg ¼ 1;
ρb1 ð5Þ
is second-order differentiable with decreasing marginwhere F Li ; K al productivity of labor. Assume that the factor markets for capital and labor are competitive, the marginal productivity of capital (MPk),
3
4
5
6
ð1−δÞR0 ð1 þ r Þ −ω−κ; 0 . F 1 ≡ maxf V 1 −I; 0g ¼ r ð1 þ r Þð1 þ vÞR0 −ω−κ; 0 . F 1 ≡ max V 1 −I; 0 ¼ r V 1 −I ð1−δÞR0 ω þ κ V 1 −I ¼ ð1 þ vÞR0 − ω þ κ ; ¼ . − 1þr 1þr 1þr 1þr r r n o 8 9 < max V 1 −I; 0 maxf V 1 −I; 0g= þ ð1−qÞ O≡F 0 −Ω0 ¼ max maxfV 0 −I; 0g; q :. ; 1þr 1þr − maxfV 0 −I; 0g
449
undergraduate labor (MPu), and graduate labor (MPg) will equal to capital price (V), undergraduate-level wage rate (wu), and graduatelevel wage rate (wg), respectively. ρX ρ−1 MP k ¼ ραK ρ−1 ¼ V ρX ρ−1 MP u ¼ ρβu Luρ−1 ¼ wu ρX ρ−1 MP g ¼ ρβg Lgρ−1 ¼ wg : 1 Let σ ¼ 1−ρ , the above three equations can be rewritten as
MP σk ¼ α σ AP k ; MP σu ¼ βσu AP u σ σ MP g ¼ βg AP g
σ¼
1 1−ρ
ð6Þ
Assume that the price of the output is P, the cost share for undergraduate-level labor input (Su) and graduate-level labor input (Sg) can be derived as wu Lu wu Lu 1 ¼ ¼ wg Lg PX V K þ wu Lu þ wg Lg VK þ1þ wu Lu wu Lu wg Lg wg Lg 1 ¼ sg ¼ ¼ : wu Lu PX V K þ wu Lu þ wg Lg V K þ 1 þ wg Lg wg Lg
su ¼
ð7Þ
For simplicity, we assume that the elasticities of the substitution between various factor inputs are the same: σ ¼ σ uk ¼ σ gk ¼ σ ug ¼ u −d log LLug =d log w wg . The output elasticity of labor can be derived as τi = − d log X/d log wi and the cross elasticity of demand for capital and labor can be derived as μK = − d log(K)/d log(wi). According to Eq. (6), the logarithmic difference between the labor wage rate log(w) and the output price log(P) can be derived as σ[log(w) − log(P)]= σ log βi + log X − log Li. Differentiating it with respect to log wi, we have σ 1− τηi ¼ λi −τ i . Therefore, the output elasticity of labor i can h i be calculated as τ i ¼ η =ðη−σ Þ ðλi −σ Þ, in which η is the elasticity of product demand and λi represents the elasticity of labor demand. The relationship between the capital–labor ratio and the factor price ratio in the above CES production function can be derived as log(K) − log(Li) = σ log(α/βi) − σ log V + σ log wi. By differentiating this equation with respect to log wi, we have λi −μ k ¼ σ μek þ σ, in which μk represents the cross elasticity of demand for capital with respect to wage rates. Let e represents the elasticity of demand for caph i ital, given μ k ¼ e =ðσþeÞ ðλi −σ Þ we have λi −μ k ¼ σσþe ðλi þ eÞ and σ ðηþeÞ τi −μ k ¼ ðλi −σ Þ ðσþe Þðη−σ Þ . After the derivations of various elasticities above, the total differentiation of output X with respect to undergraduate-level labor wage rate wu can be calculated as dLg dX dK dL dK ¼ MP k þ MP u u þ MP g ¼ 1−su −sg AP k dwu dwu dwu dwu dwu w dK dLg dL w dX u þsu AP u u þ sg AP g ⇒ u⋅ ¼ 1−su −sg dwu dwu X dwu K dwu þsu
wu dLu w dL þ sg u u : Lu dwu Lg dwu
Therefore, the output elasticity of undergraduate-level labor can be redefined as τu = (1− su − sg)μk + suλuu + sgλug where λii represents the own elasticity of labor demand and λug denotes the cross elasticity of demand for two different educational levels of labor. By combin σ ing equations τu −μ k ¼ su ðλuu −μ k Þ þ sg λug −μ k ¼ σþe ½su ðλuu þ eÞþ σ ðηþeÞ sg λug þ e and τ u −μ k ¼ ðλuu −σ Þ ðσþeÞðη−σ Þ , we can calculate the
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σ own and cross elasticity of labor demand: λuu ¼ η−σ þ ηþe1 1− ηþe su η−σ −su σ esu þ sg λug þ e , λgg ¼ η−σ þ ηþe1 esg þ su λug þ e , and 1− ηþe sg η−σ −sg n h i ηþe o ηþe 1 λug ¼ sg λuu η−σ −su þ e sg −su − η−σ σ .
For simplicity, we assume that the labor market for each individual higher educated labor is competitive. In equilibrium, marginal productivity of labor i (FiL) equals its wage rate (wi). L
L
F u ¼ wu and F g ¼ wg :
ð8Þ
Following the fundamental assumption about the expected wage rate in the Harris–Todaro migration model, the expected wage rate for graduate-level labors (wge) and for undergraduate-level labors (wue) can be defined as e
Lg Lg 1 Lu e ¼ wg ¼ wg and wu ¼ wu 1 þ ϕg Lg þ U g Dg Lu þ U u L 1 ¼ wu u ¼ wu 1 þ ϕu Du
wg ¼ wg
ð9Þ
where Lg and Lu represent the number of employed graduate-level and undergraduate-level labors; Ug and Uu represent the number of unemployed graduate-level and undergraduate-level labors; Dg and Du represent the total number of graduate-level and undergraduate-level labors that obtain their diploma from regular graduate programs and on-job graduate programs; ϕg = (Ug/Lg) and ϕu = (Uu/Lu) represent the unemployment rate of graduate-level and undergraduate-level labors. Therefore, the equilibrium condition in the Harris–Todaro migration model can be modified as e
e
wu ¼ wg ⇔wg ¼
1 þ ϕg L Dg w ¼ wu u ⋅ : 1 þ ϕu u Lg Du
ð10Þ
To account for the individuals who decided to invest in higher education but were unable to get the acceptance of a graduate school, we define the total number of individuals who decided to invest in graduate school education as Ng. In general, the gap between Ng and Dg (i.e., the number of re-examination/reapplication) will be affected by the government policy of graduate school education. More people who decide to invest in higher education will be accepted as the supply of graduate program increases. Therefore, the re-examination/reapplication rate for graduate school will be smaller. Similar to the Harris–Todaro model, we assume that higher educated labor wage rates are exogenously determined by various economic factors and government higher education policy. Suppose θ represents the total number of people who can go to graduate schools, the expected wage rate for higher educated labors (wge and wue) will be a function of θ. e wg
g ; ϕg ðθÞ; ϕu ¼f w
and
e wu
u ; ϕg ðθÞ; ϕu ¼f w
shown in Fig. 1. In Fig. 1, GG and UU curves, which are functions of market wage rates wg and wu, represent the derived demands for graduate-level and undergraduate-level labors, respectively. G′G′ and U′U′ curves represent the expected wage rate for graduate-level and undergraduate-level labors, respectively. If the magnitude of upswing (v) and its corresponding probability (q) are sufficiently large, the expected wage rate can be greater than the market wage rate. This explains why G′G′ (U′U′) curve interacts with GG (UU) curve at a relatively high wage rate level in Fig. 1. The difference between G′ G′ (U′U′) curve and GG (UU) curve can be defined as the real option value of higher education investment, that is, Oi = wie − wi. As the value of Oi decreases to less than zero (i.e., wi ≥ wie), the optimal decision for the individual is to invest immediately in higher education without waiting. Only when Oi becomes positive, it is optimal for the individual to wait and enroll in higher education at a later date. Therefore, having the option to wait will reduce the required expected return to consider the investment in higher education. As shown in Fig. 1, the segment between the intersection of G′G′ and GG curves (point Eg) and the intersection of U′U′ and UU curves (point Eu) represent the individuals who have decided to invest in higher education. The segment EuEg can be viewed as the total number of undergraduate-level and graduate-level labors when the option to postpone higher education investment is taken into account. Therefore, the modified Harris–Todaro real option model in Fig. 1 can be scaled down to the portion of EuEg to illustrate how government higher education policy will affect the unemployment rate and re-examination/reapplication rate of higher educated labors. 3.2. Unemployment and re-examination of higher educated labors Fig. 2 shows a modified Harris–Todaro higher education investment model which consists of undergraduate-level and graduate-level labors. Given the wage rate wg, the demand for graduate-level labor Lg is determined by the demand curve GG. According to Eqs. (9) and (10), we can find an undergraduate-level wage rate wu that equalizes the expected graduate-level and undergraduate-level wage rates (wge = wue). The demand for undergraduate-level labor Lu can be derived from the demand curve UU. The qq curve represents the indifference curve of expected wage rates. After solving the values of wu and Lu, we can derive the corresponding Dg and ϕg for graduate-level labors and Du and ϕu for undergraduate-level labors. If the undergraduate-level wage rate remains at a relatively lower level compared to graduate-level wage rate, which means graduate education investment becomes more valuable, the total number of graduate-level labor will increase. This will lead to the increase of the unemployment rate for graduate-level labor. Meanwhile, as the supply of graduate-level labors increases, Option,Wage
Option,Wage
ð11Þ
G’ U
In Eq. (11), θ can be viewed as a higher education policy instrument which is mainly controlled by the government. As the government allocates more resources into graduate school education, more people will be able to enroll in graduate programs, and hence the supply of graduate-level labors will increase. Assume that the increase in labor demand for graduate-level labors (dLg) is not enough to absorb the increase in labor supply (dDg) due to graduate programs expansion, the wage rate wg will decrease and the unemployment rate ϕg will increase. According to Eqs. (7) and (10), the wage rate wu will decrease and the unemployment rate ϕu will increase. This means that the expected wage rates for higher educated labors (wge,wue) will both be decreased due to the oversupply of graduate-level labors, ∂we ∂ϕ ∂we ∂ϕ that is, ∂ϕ g ∂θg b0 and ∂ϕ u ∂θg b0. g g The consequences of the oversupply of graduate-level labors can be illustrated with a modified Harris–Todaro real option model as
G
U’ Eg Eu
G G’
U’
U 0g
0u
OG OU
the pool of higher educated labors
Fig. 1. Modified Harris–Todaro model with real options of human capital investment.
W.-Y. Hwang et al. / Economic Modelling 31 (2013) 447–452 graduate-level wage
Undergraduate-level wage
u hand, given ∂w ∂φ e
g
U
G
U’
q
G’ wg
wu
wue
wge G
G’
0u
U’
Lu
Ng
Dg
U
Lg
0g
Fig. 2. Unemployment and re-examination of higher educated labors.
those who cannot get a graduate-level job will be willing to accept job offers lower than their education level. This will further lower the expected wage rate for labors with an undergraduate degree as their employment opportunities decrease. The total number of individuals who decided to invest in graduate school education (Ng) can be found at the interaction point of G′G′ and U′U′ curves. For simplicity, we assume that there will be no re-examination/reapplication demand when Ng is less than Dg, that is, the total number of undergraduate-level and graduate-level labors equals Du plus Dg. The number of re-examination/reapplication becomes positive when Dg is less than Ng. In this case, the unemployment number of undergraduate-level labors (Uu) will increase as Du becomes larger due to the decrease of Dg. In this case, Uu will include undergraduate-level labors that are either unemployed or failed to get accepted into a graduate school. As the gap between Ng and Dg increases, the expected wage rate of graduate-level labor wge will increase, and hence graduate education investment becomes more valuable. 4. Implications for higher education policy As shown in Fig. 3, suppose that the number of graduate-level labors increases from Dg to Dg′ when the government decide to expand graduate school programs. This implies that θ will increase and thus lead to the change in expected wage rates. Then the expected wage rate curve for graduate-level labor will shift downward from G′G′ to ∂weg ∂φg ∂φg ∂θ
G″G″, given
b0 derived above. The number of unemployed
∂φg ∂θ
451
b0, the expected wage rate curve for undergraduate-
level labor will also shift downward from U′U′ to U″U″ due to the increase of θ. If the job opportunities for higher educated labors remain unchanged then the decrease of wge will be greater than the decrease of wue. In this case, the total number of individuals who decided to invest in graduate school education will decrease from Ng to Ng′. This will cause the number of unemployed undergraduate-level labor to increase from LuNg to LuNg′. Furthermore, as the supply of labors with a graduate degree increases, those who cannot get a graduate-level job will be willing to accept job offers lower than their education level. This will further lower the expected wage rate for labors with an undergraduate degree as their employment opportunities decrease. As illustrated in Fig. 3, the number of re-examination/reapplication will be reduced by the graduate school expansion policy. However, it is very likely to cause negative impacts on the higher educated labor market when the increase in graduate-level job opportunities fails to keep up with the increase in graduate-level labor supply. There are two major negative effects under this unfavorable situation including: (1) the increase in the unemployment rates for both graduate-level and undergraduate-level labors; (2) the decrease in the expected wage rates for both graduate-level and undergraduate-level labors. Both negative effects will raise the issues of inefficient or overinvestment of higher education and increase the need for higher education policy reform. In general, it will be difficult to reduce the number of graduate programs once it has been established by the public higher education expansion policy. Especially when the economic growth rate is lower than expected, the increase in the job opportunities is very likely to be less than the increase in higher educated labor supply. Under this circumstance, the real option value of waiting to invest in higher education will decrease due to the decrease in expected wage rate. Therefore, individuals will either decide to invest in higher education immediately after graduation or never consider enrolling in higher education. It is widely recognized that there are spillover effects from the labor market to the education market. In other words, individuals will tend to stay in school when the expected wage rate decreases. This explains why the unemployment rates for higher educated labor are relatively high in some developed countries. Because the public higher education policy is mainly determined by political reasons, it requires the integration of other social welfare maximization criteria to increase the economic efficiency of higher education investment and reduce the risk for individual's education investment. 5. Conclusion
graduate-level labors will increase from DgLg to Dg′Lg. On the other undergraduate-level wage
graduate-level wage
U
G
U’
G’
G”
U”
q
q G” w ue w u e’
0u
w ge
U” G
G’
Lu
U’
N g N ’g D ’g D g
U
Lg
Fig. 3. Higher education policy and expected wage rate.
w ge’
0g
The expansion of higher education has been considered as a key element to facilitate a country's economic growth and international competiveness. Many wealthy developed countries and poor developing countries have allocated a great amount of resources into undergraduate and graduate school programs. In addition to regular higher education programs, many countries also have on-job education programs that provide individuals the opportunity to invest in higher education even if they have entered the labor market for a long time. Therefore, individuals can reenter education at a later age which suggests that the option to go to work is not really irreversible. However, it is irreversible once the individual decided to invest in higher education. Because the higher education program is somewhat difficult to be shut down once it has been established, it raises the issue of overinvestment in higher education in some developed countries when the unemployment rate for higher educated labor started to increase. By incorporating the concept of real option into a modified Harris–Todaro model, this paper demonstrates why the unemployment rates for higher educated labor are relatively high in some developed countries.
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It is well-known that the wage rate for graduate-level labor is relatively higher than that for undergraduate-level labor, and hence the value of the option to postpone higher education investment is relatively low. As the wage rate for undergraduate-level labor remains relatively low and the government devotes more resources into graduate school programs, individuals will be less reluctant to invest in higher education immediately after graduation. However, it is generally difficult for a country to create sufficient job opportunities to absorb the increase of graduate-level labor supply especially when the economic growth is lower than expected. Due to the illiquidity and irreversibility of education investment, unemployed graduate-level labors will be willing to accept job offers lower than their education level. This will crowd out the job opportunities for undergraduatelevel labors and increase the unemployment rate for the entire higher educated labors. These adverse phenomena can be explained by our modified Harris–Todaro model as the number of graduate-level labors increases under the government education expansion plan. Based on our analysis, the unemployment rate of higher educated labors will increase and the wage rates will decrease due to inadequate higher education expansions. Therefore, an integrated higher education policy based on both political factors and economic efficient criteria is needed to mitigate the adverse impacts of higher education expansions on labor markets. References Ashenfelter, O., Harmon, C., Oosterbeek, H., 1999. A review of estimates of the schooling/earnings relationship, with tests for publication bias. Labour Economics, Elsevier 6 (4), 453–470 (November).
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