Beyond education and fairness: a labor market taxation model for the Great Gatsby curve.

Lefgren, Lars ; McIntyre, Frank ; Sims, David P. 等

I. INTRODUCTION

An intergenerational income elasticity (HE) for a particular country can be thought of as the fraction of a 1% permanent income increase given to a parent that is observed, on average, in the permanent income of a child. Thus, estimates of the IIE are sometimes viewed as a summary measure of the intergenerational economic mobility in a particular country. In a 2012 speech, then chairman of the U.S. Council of Economic Advisers, Alan Krueger, emphasized the importance of the strong, positive, cross-country correlation between contemporary measures of economic inequality and economic mobility, as measured by the IIE. He further dubbed a graph of this relationship the "Great Gatsby curve." Although this witty designation is novel, the correlation it refers to has been the subject of a great deal of economic research.

Indeed, even before the availability of reliable IIE data for many countries, Seshadri and Yuki (2004), as well as Erosa and Koreshkova (2007), provided intergenerational models, calibrated to the U.S. economy, that explored potential taxation and transfer mechanisms linking contemporary inequality and mobility. However, as accurate estimates of this relationship have become available for an increasing number of countries, applied researchers investigating the cross-country divergence of IIEs (Bjorklund and Jantti 2009; Blanden 2009; Corak 2013b) have been more heavily influenced by the theoretical model proposed by Solon (1999), as later clarified and expanded in Solon (2004), which builds on the fundamental model of human capital transmission proposed by Becker and Tomes (1979).

The augmented Solon model deliberately focuses on one potential mechanism underlying differences in the IIE. More specifically, differential cross-country intergenerational mobility primarily arises, in the Solon model, from the differential government responses to the borrowing constraints faced by the parents of poor children. While all parents can choose to make human capital investments in their children, they can only finance these investments out of their own lifetime earnings, and are unable to borrow against the future earnings of the child. These borrowing constraints lead to less investment in human capital by poor parents and subsequently lower earnings for poor children. The model also allows governments to address this inequality by investing in the human capital of the future generation in a progressive manner (more investment at lower parental incomes). Thus, variations in government policy choices over educational investment combine with existing constraints created by income inequality to produce varying mobility across countries. This model is particularly attractive to applied researchers because it provides a clear, policy-relevant interpretation of the equation parameter most commonly used in the actual empirical estimation of IIEs.

Another attractive feature of the Solon model is that it makes a number of testable empirical claims about this HE parameter. Intergenerational mobility should be positively correlated with cross-sectional mobility, as well as with government educational investment in the poor. The HE should also be higher in countries where labor markets provide greater returns to schooling. Empirical work in highly developed countries has provided preliminary evidence supporting these claims. For example, Ichino, Karabarbounis, and Moretti (2011) find a negative relationship between government spending on education (particularly at the primary level) and HE across a dozen countries, while Mayer and Lopoo (2008) find the same pattern holds across U.S. states. Blanden (2009) also finds this pattern and goes further to show positive cross-country correlations between HE and both cross-sectional inequality and the returns to education. (1)

While many predictions of this class of model are borne out in the data, there is less evidence in support of the primary mechanism it articulates to produce cross-country variation in intergenerational mobility, namely a differential response to the borrowing constraints faced by some families in childhood human capital markets. While there have been efforts to directly test the magnitude of this mechanism, there is still no clear consensus on the degree to which most poor children in advanced economies are constrained in purchasing education. Some researchers find evidence of fairly sizeable credit constraints, most notably Brown, Scholz, and Seshadri (2011) in U.S. higher education. In contrast, neither Grawe (2004) nor Mazumder (2005) find consistent, statistically significant evidence of such borrowing constraints in an intergenerational setting in North American data. Mazumder does, however, find higher IIE point estimates for low net worth families in the United States, which he argues is evidence of borrowing constraints. Grawe and Mulligan (2002) review a number of older studies that also find mixed evidence about the effects of borrowing constraints.

However, while there is little consensus on the extent to which borrowing constraints determine economic mobility, it is common in both policy and academic discussions to treat this as the only important mechanism when making policy recommendations. In this view, because IIE variation is explained primarily by underinvestment in the human capital of poor children, higher IIEs are suboptimal and policy should be directed to reducing them. In other words, because observers have often come to accept the proposed mechanism as exclusive, they have been driven to use the IIE as a summary measure of fairness or opportunity in a country. For example, when discussing the policy implications of the research showing the United States has a relatively high IIEs, the Brookings Institution concluded, "A number of advanced countries provide more opportunity to their citizens than does the United States" (Sawhill and Morton 2007). Alan Krueger, in the speech referenced earlier, remarked of the cross-country IIE data, "It is hard to look at these figures and not be concerned that rising inequality is jeopardizing our tradition of equality of opportunity" (Krueger 2012).

This presumption is also implicit in many academic studies, although typically accompanied by caveats (e.g., Bjorklund and Jantti 2009; Corak 2013b; Ichino, Karabarbounis, and Moretti 2011; Mayer and Lopoo 2008). Indeed, a recent literature review (Black and Devereux 2011) typifies the very literature it sets out to summarize by duly noting, "the low [IIEs] for Nordic countries could be explained either by their compressed earnings distributions (low returns to skills) or by social and educational policies regarding childcare and education that tend to equalize educational opportunities for children," then, like most of the literature, passing over the first case to "focus here on the second type of explanations." Another important review of the issues by Corak (2013a), explains that the commonly used model, "focuses attention on the investments made in the human capital of children influencing their adult earnings and socio-economic status." Primacy is given to the educational investments mechanism, which in isolation suggests that higher IIEs are normatively bad. This study, as well as contemporary work by Holter (2013), can be seen as arguing against an acceptance of progressive government investments as the primary marginal determinant of cross-country differences in mobility. While such a mechanism may matter, especially at low levels of government investment, we suggest it is less important at the current margin than an alternative mechanism rooted in choices about tax policy.

In this article, we present a simple model that focuses on how a different mechanism can drive the observed "Great-Gatsby curve" relationship. More specifically, in this model distortionary taxation and redistribution both reduces contemporary inequality and lowers IIEs through lowering the realized returns to human capital. The insight that labor taxes change the cost-benefit calculation surrounding investment in human capital is well established (Heckman, Lochner, and Taber 1998; Trostel 1993). Indeed, the potential for taxes to affect human capital investment is commonly thought to be large enough to help resolve the disparity between large measured macroeconomic responses to labor market taxation and small measured cross-sectional labor supply elasticities (Keane and Rogerson 2012). This mechanism is also prominent in prior models of the U.S. economy that incorporate intergenerational mobility and predict that labor taxes can discourage investment in human capital and thereby compress the earnings distribution (Erosa and Koreshkova 2007; Seshadri and Yuki 2004). In contrast. Mulligan (1997) shows that in a model of endogenously determined parental altruism, a progressive income tax can actually reduce earnings mobility.

It is worth noting that these models of mobility all operate through the effect of labor taxes on the investment in human capital, the same determinant that borrowing constraints influence in the Solon model. In contrast, our model abstracts entirely from education markets to focus on the potential role of labor market choices in relating taxation and cross-generational inequality. More specifically, we treat human capital as innate and show that the distortionary effects of human capital can operate through a noninvestment mechanism, although we also show that our model can be reinterpreted to show the same effects of decreasing educational investment if desired.

Our model parallels the Solon model in its simplicity and focus on how a particular mechanism relates contemporary economic inequality and cross-country intergenerational income transmission. Notably, the model produces similar auxiliary predictions to the Solon model, but implies an opposite policy conclusion; higher IIEs are the artifact of more efficient, and therefore desirable, policies. Furthermore, this model has other distinct testable implications which we explore using cross-country data. Nevertheless, there is no need to draw an artificial dichotomy between the two models. It appears almost certain that there are multiple economic mechanisms involved in producing the cross-country variation in intergenerational mobility we see today.

Our results section provides evidence about the predictions of both models, and strongly suggests the existence of mechanisms beyond the commonly discussed underinvestments in children; the nature of the data does not allow definitive answers about magnitudes or optimal policy responses. Indeed, it is likely that a variety of mechanisms contribute to the observed crosscountry variation in IIEs, some of which suggest it is desirable for the United States to engage in policies that would lower IIEs and some which imply, contrary to the current conventional wisdom, that we should implement policies that as a side effect would keep them high. In such an environment, researchers and policymakers should be careful to avoid treating HE measures as an appropriate summary statistic for fairness or opportunity, or ignore taxation as a potential mechanism for propagating inequality.

II. THE MODEL

In this section, we introduce a model that emphasizes the role of distortionary labor taxation in generating variation in both contemporary measures of economic inequality and IIEs. Although there are income taxes on parents in the Solon (2004) model, they only influence the decisions of the child through the government's use of the tax to fund educational investment. While real-world governments do indeed invest tax revenue in education, they also levy labor taxes to fund a variety of other programs. Alternatively, they might choose to fund education programs using consumption, capital, or real estate taxes. Our model recognizes this by divorcing the labor tax from the human capital subsidy. While we describe the source of distortions in the model as taxation, this is really a convenient shorthand expression for the coupling of a labor tax with redistribution through lump-sum transfers. Indeed, one function of the payout in the model, besides adding an element of realism, is to eliminate the income effects that would need to be considered if the government were to simply burn the money.

Suppose there are two types of jobs in the economy, one that requires high human capital, 0H, and another that requires low human capital, 0L. Workers are indexed by their human capital as well. 0 < [omega] < 1 is the fraction of workers with human capital equal to [[theta].sub.H] while 1 - [omega] is the fraction of workers with human capital equal to [[theta].sub.L]. Workers with low human capital can only work at the job that requires low human capital. Workers with high human capital can work at either job. Workers are paid a wage equal to the human capital requirements of their job.

The government imposes a flat tax on wages at rate t. The government redistributes tax revenue in a lump-sum fashion. We assume that the number of workers is large so that we can ignore the idiosyncratic component of an individual's wage experience when computing the rebate, which is given by t[[alpha][[theta].sub.H] + (1 - [alpha])[[theta].sub.L]], where [alpha] is the fraction of workers that are in the high human capital sector. Note that this fraction that choose high human capital work need not equal co, which is the fraction of workers capable of working in that sector.

Only high human capital workers have a choice of jobs. These workers make their decision based on the utility in each occupation which is a function of the expected wage and a random utility component associated with the low wage occupation, [epsilon]. (2) This component can be thought of as an idiosyncratic interest in the low wage occupation or disutility of the high wage job, perhaps due to increased responsibility or hours. This implies that a high human capital worker will choose the high wage occupation if the following condition holds:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We assume that U(x) is a strictly increasing and concave utility function. The probability of a high human capital individual choosing the high human capital job is hence given by

(2) F[D(t)],

where F(x) is the cumulative distribution function of e. Note that this probability is increasing in the difference in wages between the two sectors. It is decreasing in the tax rate. The fraction of workers in the high wage industry can be written as:

(3) [alpha](t) = [omega]F[D (t)],

which is decreasing in t. That is:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Note that [I.sup.aftertax.sub.H] is the expected after-tax income, including transfers received, in the high wage occupation and there is a corresponding measure for the low wage occupation. f(x) is the density function of [epsilon].

The intuition underlying Equation (4) can be seen by considering each of its components. First, in the numerator, - ([[theta].sub.H] - [[theta].sub.L]) accounts for the difference in financial payoff between the high and low wage occupations, as it narrows with an increase in the tax rate. Next, [1 - [alpha](t)] U'([I.sup.after tax.sub.H]) + [alpha](t)U'([I.sup.after tax.sub.L]) represents the average marginal utility of income, which translates the change in financial payoff of staying in the high wage sector to a utility benefit. Finally, [omega]f[D(t)] is the fraction of all workers who have the skill to work in the high wage sector multiplied by the density of such workers who are just indifferent between working in the high and low wage sectors. Consequently, this term represents the density of workers at risk of switching sectors due to an infinitesimal reduction in the change in the utility benefit of working in the high wage sector. The denominator is greater than one and takes into account the fact that changing the tax rate has a second order effect on the size of the lump-sum transfer operating through the fraction of individuals working in the high wage sector.

More simply, the reason that the fraction of individuals in the high wage occupation is declining in the tax rate is that the after-tax income in the two occupations grows closer together with an increase in taxation. In addition, because the tax revenue is returned as a lump-sum subsidy, there is no income effect inducing individuals to select into high wage occupations in response to the tax expense. A progressive tax policy in which only high income workers were taxed would have the same effect on occupational choice, even if the tax revenues were not redistributed. However, if the revenue from a flat tax was retained by the government instead of being returned to individuals, the effect of taxation on job choice would be ambiguous due to the income effect.

For the remainder of this analysis, we will consider the effect of taxation on pre-tax income, I. This is consistent with the prior literature and aligned with our empirical tests. The implications are identical if we consider post-tax income. One consequence of this tax policy is to reduce average pretax income even as it reduces inequality. To see that this is the case, note that the expected pretax income is given by:

(5) E(I) = [alpha](t)([[theta].sub.H] - [[theta].sub.L]) + [[theta].sub.L].

Differentiating with respect to f, we obtain:

(6) ([partial derivative]E(I)/[partial derivative]t) = [alpha]'(t) ([[theta].sub.H] - [[theta].sub.L]) < 0.

This reduction in expected income is driven by the fact that as taxes increase, the fraction of high human capital individuals that choose the demanding job declines. The variance of income is given by:

(7) var (I) = [alpha](t) [1 - [alpha](t)] [([[theta].sub.H] - [[theta].sub.L]).sup.2].

Differentiating with respect to t, we find:

(8) [partial derivative]var(I)/[partial derivative]t = [[alpha]'(t) - 2[alpha]'(t) [alpha](t)] x [([[theta].sub.H] - [[theta].sub.L]).sup.2] < 0.

Equation (8) is negative if the fraction of workers who enter the high wage occupation is less than half. In this circumstance, it represents the compression in wages associated with the fact that more high human capital workers choose low human capital jobs.

It is helpful to examine the correlation between human capital and income, which is given by:

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Note that taxes affect this correlation only through the occupational choice of high ability workers. When we differentiate with respect to the tax rate, we obtain:

(10) [partial derivative]corr (I, HC)/[partial derivative]t = {[alpha]'(t)/2[alpha](t) [1 - [alpha](t)} x corr(I, HC) < 0.

Increasing the tax rate lowers the correlation between human capital and income because it increases the incentive for high human capital workers to obtain a job that is not commensurate with their skills.

We next consider the effect of taxes on intergenerational income mobility. In this simple model, skill evolves from generation to generation according to a Markov process. The probability a high human capital parent has a high human capital child is given by [[pi].sub.H] and the corresponding probability that a low human capital parent has a high human capital child is simply [[pi].sub.L], where [[pi].sub.H] > [[pi].sub.L]. To ensure a stable distribution of talent across generations, we impose that [omega][[pi].sub.H] + (1 - [omega])[[pi].sub.L] =[omega]. Under these conditions, the correlation between incomes in two generations is given simply by:

(11) corr([I.sub.child], [I.sub.parent]) = [alpha](t) (1 - [omega]) ([[pi].sub.H] - [[pi].sub.L]) / [1 - [alpha](t)] [omega].

This relationship has a couple of important implications for the possible extremes of parent-child income correlations. First, if the probability of having a high human capital child is the same for high and low human capital parents, then the correlation in income between adjacent generations is zero. Second, if there is perfect transmission of human capital ([[pi].sub.H] is one and [[pi].sub.L] is zero), and if all high human capital individuals take high human capital jobs, so that [alpha](t) = [omega], then the correlation between the incomes of parents and children will be one.

Note that the Solon model focuses on how taxation to finance educational expenditures reduces the differences in human capital investment between high and low income families. Abstracting from the endogeneity of occupational choice, this can be interpreted as reducing the difference between [[pi].sub.H] and [[pi].sub.L]. We can see the Solon result in this model that equalizing average educational outcomes between the children of high and low income workers does indeed reduce the correlation between parents' and children's incomes.

In the context of our model, when we differentiate the correlation with respect to the tax rate, we find:

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Thus, the intergenerational correlation between parents and children's income declines with the tax rate. This works through two channels. First, a higher fraction of high human capital parents choose low income jobs but still have high human capital children who are disproportionately likely to have high paying jobs. Second, the children of high income parents are likely to have high human capital themselves, but are more likely to choose low paying jobs due to the distortions in the labor market. Although this model considers the flat tax case, a progressive tax rate (higher on [[theta].sub.H]) would only increase the incentive for the high capital worker to choose the low capital job. All of the comparative statics results would remain.

While we have to this point considered a steady state scenario, in which the same tax rate applies to both generations, increasing the tax rate in any one generation (parents' or children's) will similarly reduce the correlation in incomes. (3) Suppose, for example, that taxes rise in the parents' generation. This will lead to a higher fraction of high ability parents choosing the low earnings occupation. In this case, the children of low income parents will be more likely to have high incomes because they are more likely to enjoy high skill. Conversely, if the tax rate rises in the children's generation, the children of high income parents are more likely to have low income, because even the high ability children of wealthy parents are less likely to find it personally optimal to face the utility sacrifice associated with selecting the high paying career.

This model illustrates a potential link between labor taxation, average incomes, cross-sectional inequality, and intergenerational inequality. Higher taxes reduce the incentive for high ability workers to choose jobs that are commensurate to their abilities. Our model can also be reinterpreted to illustrate the disincentive effects of taxation for efficient investments in human capital, either through on-the-job learning or college attendance by redefining epsilon in terms of these costs. Similarly, the same framework could consider effects on on-the-job effort, which increase both compensation and output.

As a consequence of the disincentive effects of taxation, aggregate output declines with the tax rate. Cross-sectional inequality declines due to the direct effect of taxation and redistribution but also because a higher fraction of high ability workers take low ability jobs. Taxes reduce the correlation between human capital and incomes. They also reduce the correlation between parents' and children's incomes. This is because there are more high ability parents among the low income workers and because a lower fraction of wealthy parents' children choose to enter demanding occupations. This model implies that in economies with high labor tax rates (even if used for pure redistribution), there will be lower returns to human capital, human capital will explain a smaller fraction of the variation in wages, and there will be lower levels of cross-sectional and intergenerational income inequality.

However, this model also has policy implications that are very different from the Solon model. In particular, it advances a different idea of economic opportunity. In the Solon model, economic opportunity is denied because equally able agents are kept from investing equivalently in human capital. In this model, economic opportunity is denied because agents with more human capital are discouraged from putting it to the most productive use. It also reaffirms that a model of human capital that only considers policy on the cost side (reducing the price of acquisition) misses out on likely policy effects on the benefits side (lowering the returns). More generally, the model reminds us that even purely distortionary policies, with no redemptive benefit of correcting market externalities, can still result in lower measured IIEs.

III. DATA

In considering prior studies of the mechanisms that generate IIE differences across countries, a couple of common points emerge. First, like most prior studies, we wish to enhance the comparability of the estimates by focusing on developed economies. Thus, we limit our data set to Organization for Economic Cooperation and Development (OECD) members for which comparable IIE estimates are available. Second, calculating accurate measures of intergenerational earnings elasticities require a large amount of linked earnings data for fathers and sons. Hence, when looking for data to test hypotheses about correlates of cross-country IIEs, the sample of candidate countries is fairly small. In fact, the survey work as recently as Solon (2002) lists IIEs for only seven countries while more recent analyses by Blanden (2009), Bjorklund and Jantti (2009), and Ichino, Karabarbounis, and Moretti (2011) each use approximately a dozen country observations.

In this study, we will be using two sources of cross-country HE estimates, Blanden (2009) which contains a dozen country observations, and Corak (2013b), which furnishes HE estimates for a wider but still limited number of countries. Both of these sources attempt some standardization of IIE estimates to enhance their comparability, but the degree and methodologies involved differ considerably. Thus, in the interests of clarity and robustness, we will present results using both sets of IIEs. In the Blanden data, we drop Brazil, as a non-OECD member, giving us a final sample of 11 country IIEs. Moving to the Corak estimates, we use the IIE estimates for all OECD countries available with the exception of Chile, which we deem to be an outlier in income level, giving us a total of 15 country IIEs. (4)

Descriptive statistics for the analysis variables, including the number of countries for which each variable is available, can be found in Table 1. The variables include a Gini-coefficient measure of contemporary (2000) cross-sectional pre-tax economic inequality and three measures of public social investments. The first two measure public investment in education, the natural logarithm of per-capita primary education spending, averaged over the 1980s, and the fraction of nominal gross domestic product (GDP) represented in public education spending during the same time period. The third measure is the fraction of GDP used for public social spending, as defined by the OECD. This broader category is meant to capture other types of transfer payments and in-kind investments in poor families.

The data also include various measures of cross-country returns to human capital. Comparable estimates of the return to schooling come from Hanushek and Zhang (2009), which is based on a common international assessment. A measure of the goodness of fit of country specific Mincer regressions and estimates of the country-specific return to experience (proxied by age), are based on our calculations from the Luxembourg Income Study database. More details of these calculations and origins of other variables can be found in the Appendix.

Because the article is about the effect of labor tax distortions on intergenerational income transmission, we require a standardized measure of tax rates. Fortunately, the OECD has produced information on tax rates at standard points in several countries' earnings distributions. We take the earliest year for which these data are available, 2000, and use the highest available point in the distributions, which is 167% of each country's average annual earnings. (5)

[FIGURE 1 OMITTED]

IV. RESULTS

We begin this section by focusing on the predictions shared by our model and the commonly employed Solon (2004) model. In particular both models suggest that IIEs should be positively correlated with observed cross-sectional income inequality. Although this pattern has been empirically confirmed in prior studies, we show the strength of that relationship in our data in Figure 1. Indeed, despite a fairly small sample of countries to work with, a bivariate regression finds a statistically significant relationship between contemporary inequality and intergenerational mobility. One standard deviation increase in the Gini coefficient predicts a rise of 0.056 in the HE, explaining 40% of the observed variation in IIEs.

Both the present model and the Solon model relate income mobility to the returns to human capital. Thus, in data terms, both predict that intergenerational mobility should be negatively correlated with the returns to schooling, as a form of human capital. Because the Solon model focuses on human capital markets, it further predicts that intergenerational mobility should be positively related to the public investment in schooling for the poor. While our model abstracts from schooling decisions, it is the case that any policy that increases human capital in the poor relative to the rich should positively correlate with intergenerational mobility. For instance, if tax revenue was used to increase the probability low human capital parents have high human capital children, [[pi].sub.L], our model would predict that this channel would increase income mobility.

Table 2 examines whether these predictions hold in the data. The first five columns consider these relationships using Blanden's measure of IIEs. All of the relationships are observed to have the predicted sign, as education spending is associated with decreases in intergenerational correlations while returns to schooling tracks them. The point estimates do suggest the possibility of substantial effects. A one standard deviation increase in the return to schooling predicts a statistically significant 0.057 increase in the IIE, which is as strong a movement as we found with the Gini coefficient. The funding measures are somewhat weaker predictors--one standard deviation increases in these predict drops of 0.022 and 0.046 in the IIE--with neither coefficient attaining conventional levels of statistical significance.

Figure 2 gives a visual representation of the results from column (4). From the graph it appears clear that any linear association would have to be negative, but it is also clear that a bivariate regression line does not fit the data particularly well. It is possible that this is due to poor measurement of education expenditure. In particular, because in the Solon model it is education spending on behalf of poor children that matters, measures of all education spending may be too noisy to pick up an effect. Alternately, there may be substantial nonlinearities in the effect of public education on the IIE, such that at low levels, public funding serves as a useful replacement for poorly functioning human capital credit markets, but the effects diminish sharply.

Of course, this narrow prediction could be seen as too literal an interpretation of the mathematics of the Solon model, which ignores its motivating idea. In particular, the device of borrowing constraints may serve as intellectually tractable shorthand for other possible mechanisms that drive underinvestment in poor children, including health, noncognitive, and parental limitations that could be ameliorated by more spending on social welfare programs. Thus, a simple measure of governmental education investments might simply be an inadequate representation of cross-country differences in investment. To address this we also regress IIEs on the OECD's measure of the fraction of GDP used for government social expenditures in column (5). Again, the results have the expected sign but fall just short of generally accepted levels of statistical significance, possibly due to the small sample size. The point estimate, though, does suggest that the underlying relationship could be important, as a one standard deviation rise in the social expenditures predicts a 0.038 decline in the IIE.

Columns (6)-(10) of the table present the same relationships using the alternative IIE measures from Corak. Once again the Gini-coefficient estimate is positive, statistically significant, and an excellent predictor of IIE. Also, the estimates of the other relationships have the correct predicted sign, though again only one of them shows statistical significance.

There is some evidence in favor of the common predictions of the present study and Solon models. Where the two models differ, however, is in the primary mechanism that produces these relationships. In the Solon model, high cross-sectional inequality and intergenerational transmission are both results of underinvestment in poor children that are only ameliorated by public investment in some countries. In our model, these relationships come from underutilization of human capital due to labor market taxation. Thus, our model makes other, testable, auxiliary predictions. Because a labor market tax is effectively a tax on human capital in any form, our model predicts that human capital from all sources, not just education, should be more tightly linked to wages in countries with lower taxes and higher intergenerational income transmission.

[FIGURE 2 OMITTED]

Figure 3 examines this relationship by plotting the observed IIEs against the [R.sup.2] from a country specific Mincer regression. Thus, it tests the proposition that the link between human capital and earnings is stronger in countries with higher IIEs. The figure shows that this is the case, as the association is positive with a moderate level of predictive power (adjusted [R.sup.2] = 0.26). Table 3 presents estimates for both our sources of IIEs. Here, using the alternative HE measures yields an even stronger, positive prediction. Depending on the HE used, a one standard deviation increase in the Mincer [R.sup.2] increases the HE by 0.04 to 0.06, which are fairly large effects.

Our model also predicts that the return to all forms of human capital, not just schooling, should be higher in countries with high IIEs. Thus, columns (2) and (6) of Table 3 present estimates of the relationship between IIEs and the country specific labor market returns to 15 years of experience (as proxied by age). This simple, linear measure attempts to capture the value of on-the-job human capital investments. As with returns to schooling, the estimates are both positive, with a one standard deviation shift in the return to age increasing the HE by 0.03 to 0.06, but are only statistically significant for one of the HE measures. (6) This may be due to the use of a noisy proxy for true on-the-job investment.

[FIGURE 3 OMITTED]

While the data provide some support for the ancillary predictions of our model, its most important prediction, inherent in its mechanism, is that IIEs should be higher in countries with lower labor tax rates, all else equal. In Figure 4, we show the bivariate relationship between marginal tax rates and measures of the IIE. Because there may be errors in the complicated business of figuring marginal tax rates, we also present the relationship of IIEs with average tax rates, in Figure 5, for robustness.

Both figures show clearly the negative significant relationships. The marginal labor tax rate is an even better predictor of Blanden IIEs than the Gini coefficient, explaining almost two-thirds of the variation. Furthermore, these estimates suggest a very large effect of labor taxation, namely a ten percentage point increase in marginal labor tax rates is associated with a decrease in IIE of 0.075-0.090. That is more than a standard deviation of observed IIE! (7) Moving to Table 3, we see by comparing columns (3)-(4) with (7)-(8) that the use of Corak IIEs only slightly attenuates the negative coefficients. (8)

[FIGURE 4 OMITTED]

While there is clearly a relationship between tax rates and IIEs, it is still possible that this is driven not by some distortion in the labor market, but by the need to raise taxes to provide revenues for public social spending. (9) Although the small number of country observations makes it difficult to compare the impact of these mechanisms in a definitive manner, we attempt some preliminary investigations in Table 4. The table also serves as a test of our model's prediction that conditional on educational spending, tax rates should be negatively correlated with IIEs.

As we see from the Table 4 estimates, tax rates remain an excellent predictor of IIE conditional on either education spending or broader social spending. Indeed, for the Blanden IIE measure, while the inclusion of both variables in the regression causes the education coefficients to attenuate by 60%, the marginal tax coefficient is almost unchanged.

Another possible test to help demonstrate the existence of multiple model mechanisms involves the absolute nature of borrowing constraints, as opposed to the distributional nature of tax rates. If borrowing constraints are the sole mechanism behind the correlation of, for example, IIEs and cross-sectional inequality, as the Solon model predicts, then controlling for the percentage of people in a country affected by those constraints should attenuate or even eliminate this relationship. In an attempt to operationalize this we have sought out estimates of comparable cross-country absolute poverty rates from the literature (Notten and Neubourg 2007). This yielded estimates for the countries in the Blanden HE sample.

[FIGURE 5 OMITTED]

In Table 5 we repeat our regression of IIEs on Gini coefficients, this time controlling for levels of absolute poverty. Column (1) restates the relationship between Gini coefficients and IIEs from Table 1. In column (2), we repeat this regression, adding a control for the fraction of residents in absolute poverty in 2000. If the driving force behind the Gini-IIE relationship is borrowing constraints for the poor, we might expect poverty to proxy for this relationship and the estimated Gini beta to attenuate substantially. Instead, the coefficient on Gini levels is almost unchanged and remains a significant predictor of HE. Meanwhile, absolute poverty level is not a significant predictor of cross-country intergenerational mobility differences, even when it is included as a sole explanatory variable in column (3). (10)

This evidence is not supportive of a sole borrowing constraints mechanism. However, the small number of countries measured and the limitations of any poverty measure mean the results are at best suggestive. Grawe and Mulligan (2002) point out that those facing borrowing constraints are not necessarily the poorest families in society, as the current structure of public investment in education may already provide them with an efficient level of human capital investment. Thus, the fraction of households below the poverty line may not be a useful measure of the fraction of households that are credit constrained.

Taken in conjunction with our model, Table 5 also offers a broader insight about the mechanisms that link IIEs and cross-sectional inequality. The model highlights a specific labor market distortion that takes the form of a labor tax with lump-sum redistribution. However, the larger implication of the model is that intergenerational income mobility will be raised by any labor market distortion that artificially compresses the earnings distribution. This intuition that the general shape rather than absolute levels of the earnings distribution is what matters can be seen in the failure of absolute poverty levels to predict HE. However, a better test would be to test the prediction that a nontax labor market distortion that also compresses wages, should also lead to lower IIEs. As a primary goal of labor unions is to compress the wage structure (Freeman and Medoff 1984), we predict that there should be a link between unionization rates and intergenerational mobility. Thus, in the final column of Table 5, we compare country-level IIEs to their levels of unionization and find that an increase of one standard deviation in union membership is associated with an HE decrease of about two-thirds of a standard deviation. This result is statistically significant and is robust to the use of the alternate Corak IIE estimates.

V. CONCLUSION

With recent reports of rising income inequality and high domestic unemployment in the United States and other OECD nations, there is a natural interest in understanding the mechanisms by which income is transmitted across generations. While there are a host of possible genetic, environmental, and institutional candidates, past research has suggested a primary role for those that effect the transmission and use of human capital (Lefgren, Lindquist, and Sims 2012). The most widely used model of cross-country differences in income transmission rates in applied and policy contexts emphasizes a mechanism through which borrowing constraints impinge on the development of human capital for children. Thus, variation in public investments in the human capital of poor children becomes the primary source of cross-country differences in mobility. Though there is little systematic, direct evidence of the mechanism, many ancillary predictions of this model are observed in the available data. Thus, it is tempting to accept its policy conclusions that higher IIEs are due to a market failure that should be corrected by government intervention.

In this article, we point out that most of these ancillary predictions also follow from a model in which there are no borrowing constraints, but rather a potential labor market distortion through taxation and redistribution or through other institutional factors that reduce the return to skill. Furthermore, we show that there is direct evidence for this potential mechanism, a clear empirical relationship between marginal tax rates and IIEs. Our model also makes other predictions which are borne out in the data. In particular, it predicts that intergenerational income transmission should be correlated with the returns to all forms of human capital.

[FIGURE 6 OMITTED]

This study can be seen as providing focused theoretical and empirical evidence that a borrowing constraints mechanism, or more generally an underinvestment mechanism may not be the primary source of the observed cross-country differences in intergenerational mobility. While the empirical case for a mechanism based on labor market distortions appears to be stronger than the underinvestment evidence, the paucity of reliable data makes any definitive conclusions impossible at this point. In practice, it is likely that observed variation in IIEs is due to multiple mechanisms, the relative importance of which remains open to further inquiry.

Though hard to answer, this deeper question is not merely an academic curiosity. Indeed, one of the most important (and to this point unmentioned) ways in which the two models compared in this article differ is in their predictions about national income. In the Solon model, because low IIEs are due to a market failure that stops the poor from realizing their human capital potential, fixing the problem should lower IIEs and raise national income. In our model, by contrast, fixing the labor market distortion will lead to higher IIEs and national income. In the end, however, as Figure 6 shows, there is no statistically discernible relationship between per-capita GDP and HE for (either of our samples of) OECD countries. While such a data exercise may seem predetermined to fail in a morass of noise, we should recall the strength of the relationships between IIEs and both tax rates and contemporary inequality. If the first-order impacts of the model are so highly correlated, why is there no apparent effect on national income? While excess noise from unrelated processes remains a possibility, it is also possible that this is evidence of the work of multiple mechanisms with different effect directions.

What is clear is that common policy conclusions about the nature of intergenerational income transmission are premature. There is no compelling evidence to support the contention that on net market distortions raise IIEs as opposed to reducing them. Given the state of the evidence, there is little scientific basis for inferring that an HE reduction is optimal from reference to the IIEs of other countries. Instead of making policy recommendations based on observed HE levels, efforts should be made to empirically document specific barriers to opportunity at all levels, and design policies to overcome them. For example, the recent work of Hoxby and Avery (2012) shows how a lack of information networks serves as a barrier to low-income students considering selective colleges.

Our model illuminates only one of a variety of ways in which cross-country differences in labor market institutions, such as group preferences, nepotism, occupational licensing, or other regulations, can create differential cross-country distortions that might affect the intergenerational transmission of income. A more detailed understanding of cross-country differences may have to consider such factors. Meanwhile, the future will also likely bring more data about the level and evolution of intergenerational income transmission that will help untangle competing explanations.

ABBREVIATIONS

GDP: Gross Domestic Product

IIE: Intergenerational Income Elasticity

OECD: Organization for Economic Cooperation and

Development

doi: 10.1111/ecin.12185

APPENDIX: DATA SOURCES AND CONSTRUCTION

As mentioned in the text of the article, several of the variables for our analysis have been obtained from outside sources. In particular, much of the data come from online data libraries. The data on pretax Gini coefficients, marginal and average tax rates at 167% of average wage earnings, government social spending, and on union membership rates, all for the year 2000, come from the online OECD Stat Extracts and iLibrary. These can be found at http://stats.oecd.org/and were accessed on May 15-20, 2013. The data on the fraction of GDP spent by governments on primary education in 2000 come from the world bank database located at http://data.worldbank.org/indicator/SE.XPD.PRIM.PC.ZS and were accessed on April 2, 2013. Where 2000 data were not available the nearest available calendar year was used.

Other external data were obtained from published and working papers, as described and cited in the text, including the data for intergenerational earnings elasticities (Blanden 2009; Corak 2013b), returns to education (Hanushek and Zhang 2009), and absolute poverty rates (Notten and Neubourg 2007).

Additionally, we utilize certain measures we computed from other source data. First, we wanted to get a public spending measure from a time closer to when the younger generation in current HE analyses was being educated. It also seemed that once we have accounted for purchasing power considerations, a log of per-capita spending measure would make more sense than a percentage of GDP measure. Thus, we average the fraction of GDP spent on schooling over the 1980s gathered from the World Development Indicators at http://data.worldbank.org/indicator/SE.XPD.TOTL. GD.ZS. We lack these data for Germany so we substitute data from the 1990s. To get the spending per capita we multiply the above averages by average GDP per capita (PPP) in the 1980s brought forward to 2005 dollars. These data also come from the World Bank, at http://data.worldbank.org/indicator/NY.GDP.PCAP.PP.KD.

Second, we require country-level measures of the labor market returns to human capital. To obtain these estimates we turn to the standardized household surveys in the Luxembourg Income Study (LIS). The surveys in the LIS are indexed by country and year and a complete list of the surveys we used can be found in Table A1. though most are from the mid-1990s. For each survey year we run a separate regression on prime-age males aged 30-45 of log earnings on age and education dummy variables. Available detail in the education level varies slightly by survey and is not typically a year-by-year breakdown. Each regression is weighted at the person level to correct for sampling design issues. We then take simple country-level averages, across years, of the [R.sup.2] to produce the Mincer [R.sup.2] value. For the age coefficient we repeat the above process but with a linear age variable instead of dummy variables. We multiply this age coefficient by 15 to get average earnings growth over 15 years.

TABLE A1
Surveys from the Luxembourg Income Study Used for the
Calculation of Returns to Human Capital

Country                     Year

Australia                   1995
Canada                      1991
Canada                      1994
Canada                      1997
Denmark                     1992
Denmark                     1995
Finland                     1991
Finland                     1995
France                      1994
Germany                     1994
Italy                       1991
Italy                       1993
Italy                       1995
Italy                       1998
Norway                      1991
Norway                      1995
Spain                       1990
Spain                       1995
Sweden                      1992
Sweden                      1995
Switzerland                 1992
United Kingdom              1999
United States               1991
United States               1994
United States               1997

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(1.) There is some contradictory evidence, however, as Grawe (2010) examines a longer time period (1940-2000) and finds a lower degree of mobility associated with a higher degree of government resources in primary and secondary education.

(2.) There can be a random utility component associated with both occupations but the occupation decision will be based on the difference of these random utility components, which is then a new error term mathematically identical to the one we use.

(3.) Mathematical derivation of these assertions is available upon request from the authors.

(4.) The 11 countries for which we have IIEs from Blanden (2009) are: Australia, Canada, Denmark, Finland, France, Germany, Italy, Norway, Sweden, the United Kingdom, and the United States. The Corak (2013b) data provide different estimates for these countries and add lapan, New Zealand, Spain, and Switzerland.

(5.) The earnings distribution in the OECD database is only computed for those with positive earnings. So while 167% of average may appear like a relatively low earnings point to look at to get high-income marginal tax rates, it actually represents individuals at a fairly high level of earnings (e.g., in the United States it would be above $70,000 if measured in 2012 dollars).

(6.) Since returns to experience also vary with education, we check to see if our results are the same when we split the sample and calculate returns to age separately for those who only complete secondary school versus those with more education. While still noisy, the same data patterns emerge in those bivariate regressions. Results are available from the authors.

(7.) A one standard deviation increase in the marginal tax rate predicts a quite large 0.07 decrease in the IIE.

(8.) Because we eliminated Chile from the estimation sample, we can further ask how well the estimated parameters predict its (out of sample) combination of IIE and tax rates. Perhaps surprisingly, despite different absolute wealth and income levels, Chile lies almost exactly on the regression prediction line suggested by Table 3, column (7).

(9.) Since governments raise money for a wide array of noneducational outcomes, and taxes can be raised in a number of ways, there is no requirement that marginal tax rates be collinear with educational spending. In the samples we use, log educational spending per capita has a correlation of 0.2 and 0.45 with marginal tax rates in the Blanden and Corak samples, respectively. Fraction of GDP spending in education has a correlation of 0.4 and 0.6, respectively.

(10.) A one standard deviation increase in the poverty rate only predicts a modest 0.02 increase in the HE. thus not only is the coefficient statistically insignificant, its magnitude is not very large, though the imprecision of the estimate makes it difficult to rule out substantive effects.

LARS LEFGREN, FRANK MCINTYRE and DAVID P. SIMS *

* The authors thank Michael Douglas for excellent research assistance.

Lefgren: Camilla Eyring Kimball Professor, Department of Economics, Brigham Young University, Provo, UT 84602, Phone 801-422-2859, Fax 801-422-0194, E-mail lars_lefgren@byu.edu

McIntyre: Assistant Professor, Department of Finance and Economics, Rutgers University, Piscataway, NJ 08654, Phone 848-445-9262, Fax 848-445-1133, E-mail frank.mcintyre@rutgers.edu

Sims: Associate Professor, Department of Economics, Brigham Young University, Provo, UT 84602, Phone 801-422-2859, Fax 801-422-0194, E-mail davesims@byu.edu

TABLE 1
Descriptive Statistics

HE Measure                                       Blanden

                                       Mean     Standard      Min
                                                Deviation

2000 GDP per capita                   $33,690    $5,527     $28,164
HE                                     0.27       0.08       0.14
Gini coefficient                       0.46       0.03       0.42
Returns to schooling                   0.05       0.02       0.03
[R.sup.2] from Mincer regression       0.09       0.04       0.05
Return to 15 years of                  0.20       0.10       0.04
  age/experience (90s)
Labor marginal tax rate in 2000        0.49       0.07       0.40
Labor average tax rate in 2000         0.37       0.08       0.29
Log(Education spending per capita)     7.11       0.22       6.89
Fraction of GDP spent on education     0.05       0.01       0.05
Fraction of GDP public social          0.22       0.05       0.15
  spending
Absolute poverty rate                  0.11       0.02       0.09
Union membership rate                  0.41       0.26       0.08

HE Measure                                Blanden

                                        Max     Obs

2000 GDP per capita                   $46,658    11
HE                                     0.41      11
Gini coefficient                       0.51      11
Returns to schooling                   0.11      7
[R.sup.2] from Mincer regression       0.17      11
Return to 15 years of                  0.35      11
  age/experience (90s)
Labor marginal tax rate in 2000        0.63      11
Labor average tax rate in 2000         0.52      11
Log(Education spending per capita)     7.43      11
Fraction of GDP spent on education     0.07      11
Fraction of GDP public social          0.29      11
  spending
Absolute poverty rate                  0.17      11
Union membership rate                  0.79      11

HE Measure                                        Corak

                                       Mean     Standard      Min
                                                Deviation

2000 GDP per capita                   $32,610    $5,640     $24,384
HE                                     0.33       0.12        0.15
Gini coefficient                       0.46       0.03        0.42
Returns to schooling                   0.05       0.02        0.03
[R.sup.2] from Mincer regression       0.10       0.05        0.05
Return to 15 years of                  0.23       0.11        0.04
  age/experience (90s)
Labor marginal tax rate in 2000        0.44       0.10        0.28
Labor average tax rate in 2000         0.34       0.09        0.21
Log(Education spending per capita)     7.03       0.29        6.34
Fraction of GDP spent on education     0.05       0.01        0.03
Fraction of GDP public social          0.21       0.05        0.15
  spending
Absolute poverty rate                  0.12       0.03        0.09
Union membership rate                  0.35       0.24        0.08

HE Measure                                 Corak

                                        Max      Obs

2000 GDP per capita                   $46,658     15
HE                                      0.50      15
Gini coefficient                        0.51      13
Returns to schooling                    0.11      8
[R.sup.2] from Mincer regression        0.23      13
Return to 15 years of                   0.37      13
  age/experience (90s)
Labor marginal tax rate in 2000         0.63      15
Labor average tax rate in 2000          0.52      15
Log(Education spending per capita)      7.43      15
Fraction of GDP spent on education      0.07      15
Fraction of GDP public social           0.29      15
  spending
Absolute poverty rate                   0.19      12
Union membership rate                   0.79      15

Note: The paper uses two regression samples consisting of non-South
American OECD countries that have IIEs available in Blanden (2009) and
Corak (2013b), respectively.

TABLE 2
Results for Common Predicted Correlates of Intergenerational
Mobility

HE Measure                                 Blanden

                       (1)       (2)      (3)       (4)       (5)

Gini coefficient     1.86 **
                     (0.67)
Returns to                     2.87 **
  schooling                    (1.03)
Ln Ed spending                           -0.10
  per capita                             (0.11)
GDP spent for                                      -4.62
  primary public                                  (2.69)
  education
Public social                                                -0.75
  expenditures as                                            (0.43)
  a fraction of
  GDP
Constant             -0.59 *    0.11      1.00    0.52 **   0.44 ***
                     (0.11)    (0.06)    (0.81)   (0.15)     (0.10)
Observations           11         7        11       11         n
Adjusted [R.sup.2]    0.40      0.53     -0.02     0.16       0.17

HE Measure                               Corak

                       (6)       (7)      (8)        (9)        (10)

Gini coefficient     2.91 **
                      (1.01)
Returns to                       3.24
  schooling                     (2.29)
Ln Ed spending                           -0.15
  per capita                             (0.11)
GDP spent for                                     -7.26 **
  primary public                                   (3.11)
  education
Public social                                                  -0.92
  expenditures as                                              (0.68)
  a fraction of
  GDP
Constant             -1.04 **    0.15    1.41 *   0.70 ***    0.52 ***
                      (0.47)    (0.13)   (0.77)    (0.16)      (0.14)
Observations            13        8        15        15          15
Adjusted [R.sup.2]     0.38      0.12     0.07      0.24        0.05

Notes: The dependent variable for all regressions is a standardized HE
taken either from Blanden (2009) or Corak (2013b). Standard errors are
provided in parentheses.

* p < .1; ** p < .05; *** p < .01.

TABLE 3
Results for Our Model's Predicted Correlates of Intergenerational
Mobility

HE Measure                                Blanden

                          (1)        (2)         (3)        (4)

[R.sup.2] from Mincer    1.07 *
  regression             (0.50)
Return to 15 years of                0.31
  age/experience                    (0.25)
Marginal tax rate                             -0.91 ***
                                               (0.22)
Average tax rate                                          -0.75 **
                                                           (0.24)
Constant                0.17 ***   0.21 ***   0.71 ***    0.55 ***
                         (0.05)     (0.06)     (0.11)      (0.09)
Observations               11         11         11          11
Adjusted [R.sup.2]        0.26       0.05       0.62        0.46

HE Measure                              Corak

                          (5)       (6)       (7)        (8)

[R.sup.2] from Mincer   1.48 **
  regression            (0.60)
Return to 15 years of             0.67 *
  age/experience                  (0.32)
Marginal tax rate                           -0.67 **
                                             (0.28)
Average tax rate                                       -0.68 *
                                                        (0.32)
Constant                0.18 **   0.18 **   0.62 ***   0.55 ***
                        (0.07)    (0.08)     (0.12)     (0.11)
Observations              13        13         15         15
Adjusted [R.sup.2]       0.30      0.23       0.25       0.20

Notes: The dependent variable for all regressions is a standardized HE
taken either from Blanden (2009) or Corak (2013b). Standard errors are
provided in parentheses. The marginal and average tax rates are
calculated for a person making 167% of the average earnings
(conditional on positive) for each country in 2000.

* p < .1, ** p < .05; *** p < .01.

TABLE 4
Tax Rates versus Education Spending as HE Predictors

IIE Measure                              Blanden

                               (1)         (2)         (3)

Marginal tax rate in 2000   -0.88 ***   -0.82 ***   -0.87 **
                             (0.23)      (0.24)      (0.28)
Log (Education spending       -0.04
  per capita)                (0.07)
Fraction of GDP spent on                  -1.87
  education                              (1.99)
Fraction of GDP public                                -0.09
  social spending                                    (0.38)
Constant                     0.96 *     0.77 ***    0.72 ***
                             (0.52)      (0.12)      (0.11)
Observations                   11          11          11
Adjusted [R.sup.2]            0.59        0.62        0.66

IIE Measure                              Corak

                               (4)        (5)         (6)

Marginal tax rate in 2000    -0.59 *     -0.43      -0.63 *
                             (0.32)      (0.35)     (0.35)
Log (Education spending       -0.06
  per capita)                (0.11)
Fraction of GDP spent on                 -4.38
  education                              (3.84)
Fraction of GDP public                               -0.14
  social spending                                   (0.76)
Constant                      1.00      0.74 ***   0.63 ***
                             (0.74)      (0.16)     (0.15)
Observations                   15          15         15
Adjusted [R.sup.2]            0.21        0.27       0.19

Notes: The dependent variable for all regressions is a standardized
IIE taken either from Blanden (2009) or Corak (2013b). Standard errors
are provided in parentheses. The marginal tax rate is calculated for a
person making 167% of the average earnings (conditional on positive)
for each country.

* p <.1; ** p < .05; *** p < .01.

TABLE 5
Alternate Predictors of Intergenerational
Mobility

                         (1)       (2)      (3)       (4)

Gini coefficient       1.86 **   1.78 **
                       (0.67)    (0.70)
Fraction in absolute              0.59      0.98
poverty in 2000                  (0.85)    (1.06)
Trade union                                         -0.21 **
membership rate                                      (0.07)
Constant                -0.59    -0.62 *    0.16    0.36 **
                       (0.31)    (0.32)    (0.12)    (0.04)
Observations             11        11        11        12
Adjusted [R.sup.2]      0.41      0.37     -0.02      0.42

Notes: The absolute poverty rate is taken from the household
survey calculations of Notten and Neubourg (2007). The
dependent variable in all regression consists of IIEs taken
from Blanden (2009). Union membership figures are from the
OECD. Standard errors are provided in parentheses.

* p < .1; ** p < .05; *** p < .01.