As the interest in Economics on inequality has exploded, intergenerational mobility is one of the fundamental areas concerning inequality since it is related to many normative questions such as equal opportunity and fairness. Despite its importance, research on measuring intergenerational mobility has received relatively little attention. The dominant approach is still the scalar-based regression approach, which employs a regression of some statistics of offspring on some statistics of parents. In connection with this issue, this dissertation introduces a novel measure for intergenerational mobility based on modern economic theory and empirically analyzes intergenerational mobility in the U.S. and Korea.The first chapter analyzes the empirical aspect of the relationship between parental income trajectory and a child's success in the U.S. using a novel approach, functional approach.In particular, we find that parental income when their children are in their late teens is more correlated with children's income in their early 30s. In addition, children whose parental income tends to increase in their late teens are more likely to have a higher economic position than their parents. This implies that upward income mobility is positively associated with the steadily increasing economic status of the family over the first 20 years of children's life. Investigated further are the effects on explaining a child's success of the role of other trajectories, such as the family structure of unemployment and job type of household head, and the impact of parental education level. We also investigate the association between parental income profile and their children's college attendance and derive a similar finding that late teens are crucial periods when parents' income has a more significant impact on children's educational success.While the first chapter addresses issues in intergenerational mobility in the U.S., the second chapter focuses on intergenerational mobility in Korea. In the second chapter, using a similar approach to Chapter 1, we analyze the intergenerational mobility in all three dimensions - income, education, and occupation. In addition, reflecting Korea's unique historical and social characteristics, we study the association between investment in private tutoring and a child's economic and educational success. Our findings highlight the importance of parental intervention in teens on a child's educational success. The pattern of parental income profile of the upward mobility group shows a stronger upward trend than that of the downward mobility group, similar to what we observe in the U.S. data in Chapter 1. In Korea, both upward and downward mobility groups show steadily increasing parental income trajectories, reflecting the rapid economic growth Korea has experienced over the last six decades. This interesting and unique finding of mobility patterns in Korea reveals various social and economic structural changes Korea has gone through.The third chapter studies the various methodological issues. In this chapter, we consider how our functional estimate can be varied by the fluctuation of measurement error in parental income. Using Beveridge-Nelson decomposition, we decompose parental income into permanent and transitory components and consider the transitory component as a measurement error. We also compare our estimation method with the methods based on the fixed basis approach. Using too many bases in this approach yields nonsensical estimates, while the estimates using too few bases strongly depend on the shape of the basis. We also find that the fixed basis approach is not robust to measurement error. A possible endogeneity issue is also studied in this chapter. Parental income can affect their children's success through two channels, transmission of human capital and providing financial resources. To focus on the effect of financial resources, we measure intergenerational income mobility using instrumental variables to control the effect of human capital.