Journal ArticleDOI

# A group-specific measure of intergenerational persistence

01 Sep 2008-Economics Letters (North-Holland)-Vol. 100, Iss: 3, pp 415-417
TL;DR: In this article, a method for comparing intergenerational mobility for different groups, taking account of both within-and between-group effects, is described, which yields results that are more informative than is the comparison of within-group estimates alone.

### Introduction

• Hertz (2005) discusses this problem and notes that stratifying and calculating within-group elasticities does not produce a meaningful answer.
• Children of the disadvantaged group may be quite mobile with respect to their parents when measured by their within-group intergenerational elasticity.
• In the remainder of the paper I outline the technique, and provide examples of its application using the dataset found in Hertz (2005) .

### 2. The Decomposition

• This product will be near zero if the group mean approximates the sample mean in either generation.
• On the other hand, if a group's mean lies above (or below) the sample mean in both generations, this contribution will be positive; and if there are just two groups this term would be positive both for the lower-income and the higher-income group.
• 2 Last, for a group whose mean differs from that of the other group(s) in both generations, the smaller the group, the larger will be its distance from the pooled sample mean, and the larger will be the contribution of this term of the equation.

### 3. Examples

• 3 In the two-group (b,w) case, the between-group estimator simplifies to In the row labeled "B", the between-group effect is split into its Black and White components, with the effect for Blacks being much the larger (1.046 versus 0.051).
• This occurs because their share of the sample is small, so their group mean lies farther from the sample mean than does the mean for Whites.
• Next, these between-group components are weighted by their group shares, and their sum is indeed 0.231.
• This confirms that equations [1] and [2] are indeed equivalent.

### [ TABLE 1 ABOUT HERE]

• This stands at 1.367 for Blacks and 0.349 for Whites, implying that once within-and between-group effects are both accounted for, generational income persistence for Blacks is roughly four times as high as for Whites.
• Another way to express this fact is to look at the group-share estimates in the final row (which sum to the pooled intergenerational elasticity), and to note that while Blacks make up just 18 per cent of the sample, they generate nearly half (0.248 / 0.534) of the parent-child covariance that underlies the intergenerational elasticity.
• This is not due to a larger within-group effect, but to the significant gap in mean incomes across groups.
• -7 - The regional decomposition involves four groups of more nearly equal size, and smaller differences in means.
• As expected, when this between-group component is allocated across regions (row B), it has a noticeable effect on estimated persistence for the Northeast and South (0.073 and 0.140), but little effect for the other regions, which lie closer to the mean.

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TL;DR: It is found that educational persistence, as measured by the regression coefficient of father's education as a predictor of son’s education, has declined over time, which implies that increases in average educational attainment are driven primarily by increases among children of less-educated fathers.
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### Cites background from "A group-specific measure of interge..."

• ...Hertz (2008) developed an alternative estimator for comparing IGM for different groups that takes into account both the within—and the between—group effects, and found that blacks have four time greater earnings persistence using this measure....

[...]

• ..., Van de Gaer, Schokkaert, and Martinez (2001), Roemer (2004), Swift (2005), Jencks and Tach (2006)). Roemer (2004), in particular, emphasized that a society with high equality of opportunity is one that lets children from varying backgrounds exerting the same effort to reach similar economic status....

[...]

• ..., Van de Gaer, Schokkaert, and Martinez (2001), Roemer (2004), Swift (2005), Jencks and Tach (2006))....

[...]

##### References
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Book
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