MarkGanzersInsanityBlog: Revised Estimates of Intergenerational Income Mobility in the United States by Bhashkar Mazumder

Abstract: Solon’s (1992) landmark study estimated the intergenerational elasticity (IGE) in income

between fathers and sons to be 0.4 or higher. This dramatically changed the consensus view of the U.S.

as a highly mobile society. In this comment, I show both analytically and empirically how Solon and

others have actually underestimated this parameter by about 30 percent, suggesting that the IGE is

actually close to 0.6 and that the U.S. appears to be among the least mobile countries. There are two key

measurement issues that lead researchers to underestimate the IGE. First, the use of short-term averages

of fathers’ earnings is a poor proxy for lifetime economic status due to highly persistent transitory shocks.

Second, the variance of transitory fluctuations to earnings varies considerably by age causing a

“lifecycle” bias when samples include measures of fathers’ earnings when they are especially young or

old. In this comment Solon’s results are replicated and then re-estimated using a new technique that is

able to address these issues using the same PSID sample. The results confirm that the intergenerational

elasticity is likely to be around 0.6.

In a highly influential study in the American Economic Review, Gary Solon presents compelling

evidence that the U.S. exhibits substantially less income mobility than had been previously thought

(Solon 1992). Before Solon’s article, researchers typically estimated the intergenerational correlation in

income between fathers and sons in the U.S. to be 0.2 or less. These studies appeared to confirm the

widely held view that the U.S. is an exceptionally mobile society and prompted Gary Becker to conclude

that “…low earnings as well as high earnings are not strongly transmitted from fathers to sons…”.1

Solon demonstrates how these previous estimates were sharply biased downwards by using only a

single year of income as a proxy for permanent economic status, and by using non-representative

samples. Solon then constructs an intergenerational sample containing as many as five years of income

for fathers using the Panel Study of Income Dynamics (PSID) and estimates the intergenerational

elasticity (IGE) in income to be “at least 0.4 and possibly higher”. In a separate analysis published in the

same issue, David Zimmerman finds a similar result using panel data from the National Longitudinal

Surveys (NLS). 2

As a result of their careful analyses of the measurement issues and the use of superior data, these

studies led to a rethinking of the degree of intergenerational mobility in the U.S. In particular, it called

into question the ideal of America as a highly mobile society. For example, Solon shows that an IGE of

0.4 implies that a son whose father is at the fifth percentile, has only a 0.17 chance of rising above the

median.3 On the other hand, an IGE of 0.4 also implies that on average, 60 percent of earnings

differences between two families are eliminated in a generation. So observers might still disagree as to

whether we should view the glass as “half-full” or “half-empty”.

In this paper, I argue that despite the dramatic improvement over previous work, Solon still

underestimates the IGE in the U.S. by about 30 percent or more suggesting that the true value of the

parameter is about 0.6. As a point of comparison, recent studies using a similar methodology to Solon

1have estimated the IGE to be only about 0.2 in Canada and Finland and 0.3 in Germany.4 Clearly, an IGE

of 0.6 suggests that the U.S. may be exceptional for its relative lack of mobility.

Still, how much difference does it make if the IGE is 0.4 or 0.6? To illustrate the implications in

practical terms, consider a family whose earnings are half the mean. If the true IGE is 0.6, then it would

require, on average, 5 generations instead of just 3, before the family substantially closed the gap with the

mean.5 Obviously a difference of 2 generations, or about 50 years, is quite significant and strongly

suggests that the glass is more than half-empty.

If the IGE represents a causal relationship, then it also has powerful implications on the

intergenerational impact of government policies.6 For example, Chay (1995) estimates that the Civil

Rights Act of 1964 reduced the earnings gap between blacks and whites born in the 1920s by about 30

percent.7 An IGE of 0.6 suggests that the black-white gap for children of these families might have been

reduced by as much as 18 percent simply due to the elimination of racially based employment

discrimination for the previous generation.8

There are two reasons why Solon’s study leads to estimates that are too low, and both reasons

reflect problems inherent in using the PSID or the NLS for this type of analysis. First, owing to small

samples and high rates of attrition in panel data, Solon and other researchers are forced to measure

fathers’ permanent income using just a few years of data. Solon’s sample is reduced to just 290 fatherson

pairs when he averages five-years of income for fathers to obtain his highest estimate of 0.41.9

However, studies of earnings dynamics suggest that the transitory component to earnings is highly

persistent so that even a five-year average might still provide a rather poor measure of “permanent” or

lifetime economic status. Second, several studies have also shown that there may be substantial differences in the variance of transitory fluctuations in earnings by age causing a “lifecycle bias”. In

particular, the income of fathers who are especially young or especially old, even if averaged over several

years, is not likely to produce an accurate proxy for lifetime economic status.

Solon was certainly aware that transitory shocks might be highly correlated but given the state of

the literature on earnings dynamics at the time, he preferred not to make any strong assumptions and

instead provided bounds for the results. As Solon put it “If the process governing earnings dynamics

were known, that knowledge could be exploited to achieve consistent estimation of the intergenerational

correlation in long-run earnings…because considerable uncertainty still clouds the current understanding

of earnings dynamics and because the data set used in the present study could not possibly resolve the

issues, the present study settles for inconsistent estimators and discussing the likely direction of the

inconsistency.”10 Recent studies on earnings dynamics using much richer models and significantly better

data (e.g. Baker and Solon, 2003; Mazumder 2001a), have made great strides in resolving some of the

issues that were unsettled at the time of Solon’s study. Given these methodological advances it makes

sense to reexamine previous studies on intergenerational mobility.

In this comment I first explore analytically how incorporating serially correlated transitory shocks

into Solon’s measurement framework affects the analysis. Using a simple model of earnings and

incorporating parameter estimates from previous studies on earnings dynamics, I run simulations on the

expected bias from using time averages of various lengths as a proxy for lifetime earnings. The results

suggest that Solon’s estimate of 0.4 based on a five-year average is biased down by just under 30 percent

due solely to the persistence of transitory shocks.

I also replicate the results from Solon’s article and then re-estimate the IGE on the same sample

using a new econometric method, the Heteroskedastic Errors in Variables (HEIV) estimator developed by

Sullivan (2001). With this procedure I am able to take into account measurement problems due to both

persistent transitory fluctuations to earnings and lifecycle bias using data. The HEIV estimator is a two step process. First estimates of the reliability ratio of each data point are needed. I do this by estimating a

highly structured earnings dynamics model using a different dataset containing lifetime earnings histories

drawn from social security earnings records.11 The parameter estimates from this model are then used to

construct reliability ratios for each observation in Solon’s PSID sample. In the second step, the HEIV

estimator directly incorporates these estimated reliability ratios to produce an unbiased estimate of the

IGE. The HEIV estimate is actually larger than 0.6.

These results are also consistent with the empirical findings in Mazumder (2001b) which uses a

much larger intergenerational sample containing the social security earnings records of fathers and their

children. In that study the IGE between fathers and sons is estimated to be around 0.4 when using just

four-year averages of fathers’ earnings, tracking the findings from earlier studies. However, the estimates

rise to more than 0.6, when 16-year averages of father’s earnings are used.

...

II. Re-estimation using the HEIV estimator

I now empirically attempt to quantify the effects of both measurement problems on estimates of

the IGE using a new econometric method. The basic idea is that rather than simply applying a single correction factor for the entire sample an attempt is made to directly address the fact that each observation

has a different degree of measurement error due to the differences in the fathers’ age range. A very large

dataset containing the social security earnings histories of over 20,000 men is used to infer the reliability

ratio for each of the fathers in Solon’s PSID sample. This information is then incorporated in the most

efficient manner possible to derive a new estimate of the IGE. As part of the analysis, Solon’s results are

almost exactly replicated.

The HEIV estimator

In many economic studies it is known that a right hand side variable is measured with error. If

the reliability ratio can be determined, then a simple solution is to divide the regression coefficient by the

reliability ratio to scale up the estimate. This “errors in variables” or EIV estimator is commonly

estimated by statistical packages such as STATA. However, in many situations there is reason to think

that the reliability ratios might vary within the sample. A common situation where this occurs is when

using individual-level data and an explanatory variable is an average of some characteristic of the

population taken at a particular geographic level (e.g. state or county). In this case, the sampling variance

for the right hand side variable and the degree of measurement error will vary across individuals

depending on the size of the sample for each geographic area.

One approach to address this problem is to average the reliability ratios across the observations,

use this as an estimate for an overall reliability ratio and then implement the EIV estimator. While such

an approach is consistent, Sullivan (2001) shows that the most efficient estimator will utilize the

reliability ratio for each observation. He presents an alternative estimator, the Heteroskedastic Errors-In-

Variables (HEIV) estimator that does exactly this. The HEIV estimator is the OLS regression of the

dependent variable on the best linear predictor of the right hand side variable. In a case of a single

mismeasured variable the best linear predictor is simply the regression of the dependent variable on the

right hand side variable multiplied by the observation-specific reliability ratio. The HEIV estimator is

correction factor for the entire sample an attempt is made to directly address the fact that each observation