Does attendance to a four-year academic college versus vocational college affect future wages?

Abstract

Taiwan is one of the few countries in which bachelor degrees can be earned by attending either 4-year academic colleges or vocational colleges. This paper offers new evidence on whether returns to B.A. degrees are significantly different between academic and vocational 4-year colleges using the 1998–1999 Taiwanese College Graduate Survey. The multinomial logit model is applied to correct self-selection for employment status, and a wage equation is then estimated. The results suggest that the returns to 4-year academic colleges are 6% higher than those to 4-year vocational colleges. We also find a significant effect of college quality on wages. Moreover, public academic college graduates have the highest returns whereas those who attend private vocational colleges have the lowest returns.

Appendix

We have the following system of equations accordingly:

$$ Y_{1i}^{*} = \alpha_{11} + \alpha_{21} {\text{VOCATION}}_{i} + \alpha_{31} {\text{PUBLIC}}_{i} + \alpha_{X1}^{\prime } X_{i} + e_{1i} $$

(3)

$$ Y_{2i}^{*} = \alpha_{12} + \alpha_{22} {\text{VOCATION}}_{i} + \alpha_{32} {\text{PUBLIC}}_{i} + \alpha_{X2}^{\prime } X_{i} + e_{2i} $$

(4)

$$ Y_{3i}^{*} = \alpha_{13} + \alpha_{23} {\text{VOCATION}_i} + \alpha_{33} {\text{PUBLIC}_i} + \alpha_{X3}^{\prime } X_{i} + e_{3i} , $$

(5)

where $Y_{ji}^{*} , \, j = 1,2,3$ represents the utility level derived from employment, pursuit of an advance degree, and unemployment; X refers to a vector of exogenous variables that determines the probability of choosing the jth option including college quality; e _ji is the error term. Let Y _i be a discrete variable with values 1, 2, or 3 indicating an individual’s choice of employment, pursuit of an advanced degree, and unemployment, respectively.Individual i will choose option j if the following condition holds:

$$ Y_{i} = j\;{\text{iff}}\;Y_{j}^{*} > \mathop {\max }\limits_{k \ne j} Y_{k}^{*} . $$

(6)

Let us define $\eta_{ji} = \mathop {\max }\limits_{k \ne j} Y_{k}^{*} - e_{ji}$. The probability of choosing option j will be

$$ \begin{gathered} P(Y_{i} = j) = P\left( {\eta_{ji} < \alpha_{1j} + \alpha_{2j} {\text{VOCATION}}_{i} + \alpha_{3j} {\text{PUBLIC}}_{i} + \alpha_{Xj}^{\prime } X_{i} } \right) \hfill \\ \, = F\left( {\alpha_{1j} + \alpha_{2i} {\text{VOCATION}}_{i} + \alpha_{3i} {\text{PUBLIC}}_{i} + \alpha_{Xj}^{\prime } X_{i} } \right), \hfill \\ \end{gathered} $$

(7)

where ${\text{F(}}\eta_{ji} )$ is the cumulative distribution function of η _ji . Equation 7 treats the choice of the jth alternative as a binary decision. Given that e _ji is assumed to be independently and identically distributed with the Weibull distribution, the probability of choosing alternative j is equal to

$$ P(Y_{i} = j) = {\frac{{\exp \left( {\alpha_{1j} + \alpha_{2j} {\text{VOCATION}}_{i} + \alpha_{3j} {\text{PUBLIC}}_{i} + \alpha_{Xj}^{\prime } X_{i} } \right)}}{{\sum\limits_{k = 1}^{3} {\exp \left( {\alpha_{1k} + \alpha_{2k} {\text{VOCATION}}_{i} + \alpha_{3k} {\text{PUBLIC}}_{i} + \alpha_{Xk}^{\prime } X_{i} } \right)} }}} $$

(8)

The coefficients in Eq. 8 can be estimated using a multinomial logit. In order to identify the coefficients in the multinomial logit, the parameters of option 3 (unemployment) are normalized to zero.

We transform the logistic random variable η _ji to a standard normal random variable $\eta_{ji}^{*} = J(\eta_{ji} )$, where J = Φ⁻¹ F and Φ⁻¹ is the inverse of the cumulative density function of the standard normal distribution (details of the transformation are available in Lee (1983) and Maddala (1983)). In other words, option j will be chosen if and only if the following condition holds:

$$ J\left( {\alpha_{1j} + \alpha_{2j} {\text{VOCATION}}_{i} + \alpha_{3j} {\text{PUBLIC}}_{i} + \alpha_{Xi}^{\prime } X_{i} } \right) > \eta_{ji}^{*} $$

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Given that both ɛ _it and $\eta_{ji}^{*}$ are jointly normally distributed, Lee (1983) shows that conditional on the first option (employment) being chosen, the wage equation can be estimated as follows:

$$ \begin{gathered} \ln W_{i} = \beta_{1} + \beta_{2} {\text{VOCATION}}_{i} + \beta_{3} {\text{PUBLIC}}_{i} + \beta_{4} {\text{EXP}}_{i} + \beta_{5} {\text{EXP}}_{it}^{2} \hfill \\ \, + \beta_{4} {\text{GRANT}}_{it} + \beta_{5} {\text{FLOOR}}_{it} + \beta_{6} {\text{RATIO}}_{it} + \beta_{6} {\text{PARTIME}}_{it} \hfill \\ \, + \beta_{Z}^{\prime } Z_{i} - \sigma \rho {\frac{{\varphi \left( {\Upphi^{ - 1} (P(Y_{i} = 1))} \right)}}{{P(Y_{i} = 1)}}} + \xi_{i} \hfill \\ \end{gathered} , $$

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where φ is a standard normal density function; ξ _i is a disturbance term; σ is the standard deviation of the disturbance ɛ _it ; and ρ is the correlation coefficient of ɛ _it and $\eta_{ji}^{*}$. The disturbance term in Eq. 11 is defined as

$$ \xi_{i} \equiv \varepsilon_{i} + \sigma \rho {\frac{{\varphi \left( {\Upphi^{ - 1} (P(Y_{i} = 1))} \right)}}{{P(Y_{i} = 1)}}} $$

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It is heteroschedastic, because the last term in Eq. 12 varies across different sample observations. The conditional variance of ξ is

$$ \begin{gathered} \text{var} (\left. {\xi_{i} } \right|Y_{i} = 1) = \sigma^{2} - (\sigma \rho )^{2} \Upphi^{ - 1} (P(Y_{i} = 1)){\frac{{\varphi \left( {\Upphi^{ - 1} (P(Y_{i} = 1))} \right)}}{{P(Y_{i} = 1)}}} \hfill \\ \, - (\sigma \rho )^{2} \left[ {{\frac{{\varphi \left( {\Upphi^{ - 1} (P(Y_{i} = 1))} \right)}}{{P(Y_{i} = 1)}}}} \right]^{2} \hfill \\ \end{gathered} $$

(12)