programs, individuals with higher motivation for the training program (lower U ) are more likely to invest effort in their work (higher ε$_{0}$ and ε$_{1}$ ) than others with lower motivation (higher U ). In the example of the college premium, a lower reservation utility (lower U ) for college education ( D = 1) is more likely to go with a higher level of unobserved abilities (higher ε$_{0}$ and ε$_{1}$ ). Regarding the effect of smoking on infant birth weight, NSM suggests that controlling for observed characteristics, individuals with a lower desire (lower U ) for smoking ( D = 0) are more likely to have a healthier lifestyle (higher ε$_{1}$ and ε$_{0}$ ) than those with a higher desire (higher U ). CPQD excludes any negative dependence between ν$_{0}$ and ν$_{1}$ in the example (2). Before dis- cussing implications of CPQD, I present the concept of quadrant dependence . Quadrant dependence between two random variables is defined as follows: Definition 1 (Positive (Negative) Quadrant Dependence, ? ) Let X and Y be random variables. X and Y are positively (negatively) quadrant dependent if for any ( x, y ) ∈$_{R}$ $^{2}$, or equivalently, Intuitively, X and Y are positively quadrant dependent, if the probability that they are simul- taneously small or large is at least as high as it would be if they were independent. 10 Note that quadrant dependence is a very weak dependence measure among a variety of dependence concepts in copula theory. 11 I impose conditional positive quadrant dependence between ε$_{0}$ and ε$_{1}$ given the selection unob- servable U . In the example (2), CPQD requires that ν$_{0}$ and ν$_{1}$ be positively quadrant dependent. Note that CPQD is satisfied even when ν$_{0}$ and ν$_{1}$ are independent of each other. To intuitively understand the implications of CPQD, consider the example (2) for the three examples. For the example of job training programs, suppose that two agents A and B have the same level of motivation for the program and the identical observed characteristics. CPQD $^{10}$For details, see pp. 187-188 in ? . $^{11}$NSM is a stronger concept of dependence between two random variables than quadrant dependence. If X and Y are first order stochastically nondecreasing in Y and X , respectively, then X and Y are positively quadrant dependent. 9 P [ X ≤ x, Y ≤ x ] ≥ ( ≤ ) P [ X ≤ x ] P [ Y ≤ x ] . P [ X > x, Y > x ] ≥ ( ≤ ) P [ X > x ] P [ Y > x ] .