Revisiting the Great Gatsby Curve Andros Kourtellos Ioanna Stylianou Charalambos Tsangarides Preliminary and incomplete Abstract The main of this paper is to uncover empirically robust determinants of income inequality considering theories proposed by the literature focusing particularly on the role of innovation and intergenerational mobility. In addition, following Chetty et al. (2014) we examine if and how the same set of theories simultaneously affect intergenerational mobility and what is the role of innovation and income inequality, investigating the theory proposed by Hassler et al. (2007). We assess the above theories using within-country data and particularly data based on commuting zones which are geographical aggregations of counties originally introduced by Tolbert and Killian (1987). Following Agnion et al. (2016) we consider the role of innovation and using patents data from Lai (2013) at the zip code level we first pair them to a county, and finally, to a commuting zone. For our analysis we consider alternative measures of intergenerational mobility (Absolute Upward Mobility using income and enrollments, and Relative Mobility) and income inequality (Top 1% income share, Gross and Net Gini). Finally, our empirical methodology allows us to deal with parameter heterogeneity by employing the Threshold Regression of Hansen (2000). Keywords: innovation, social mobility, income inequality, threshold regression. JEL Classification Codes: C59, O40, Z12. Department of Economics, University of Cyprus, P.O. Box 537, CY 1678 Nicosia, Cyprus, e-mail: andros@ucy.ac.cy. Department of Economics, University of Cyprus, P.O. Box 537, CY 1678 Nicosia, Cyprus, e-mail: sioanna@ucy.ac.cy. Research Department, International Monetary Fund, 700 19th Street NW, Washington DC 20431, USA, e-mail: tsangarides@imf.org.
1 Introduction Over the past decades wage inequality has dramatically increased particularly in the United States. According to the Economic Policy Institute (2016), the documented rise in real hourly wages in 2015 is due to the sharp decrease in inflation whereas real hourly wage growth in 2015 was fastest at the top of the wage distribution. The gap between the middle and bottom has remained stable since 2000 but the gap between the top and everyone else has grown. Considering the distribution of income between men and women from 2014 to 2015, the strongest wage growth was at the top of the mens wage distribution and at the bottom of the womens wage distribution. High and sustained levels of inequality have significant social, as well as, economic costs ( Stiglitz(2012), Ostry et al.(2014) Berg and Ostry (2011), Galor and Moav(2004), Aghion et al.(1999)). The causal forces behind the dramatic increase in inequality worldwide in the past decades have led to a considerable amount of theoretical, as well as, empirical research in order to uncover the sources of income inequality (for example, Machin and Van Reenen (1998), Katz and Murphy (1992), Berman et al. (1994), Autor et al. (2008), Card and Lemieux (2001), DiNardo et al.(1996), Blau and Kahn (1996), Aghion et al.(2016)). The contribution of this paper is multifold: First, we extend the literature and we uncover empirically robust determinants of income inequality considering theories proposed by the literature (income and population growth, racial, income and geographical segregation, taxation policies and education, labor market conditions, migration, social capital and family structure) focusing particularly on the role of innovation and intergenerational mobility. Second, following Chetty et al. (2014) we examine if and how the same set of theories simultaneously affect intergenerational mobility and what is the role of innovation and income inequality. Krueger (2012) and Corak (2013) suggest that there is a negative relationship between income inequality intergenerational mobility. In this paper however, we investigate empirically the Great Gatsby Curve considering the theory proposed by Hassler et al. (2007). In particular, the theory supports that income inequality affects negatively intergenerational mobility when the economy is very unequal (distance effect), and positively, when inequality is low (incentive effect). Third, we assess the above theories using within-country data instead of cross-country which exhibits significant advantages since the analysis is based on the same data sources and methods (Solon 2002). In particular, our analysis is based on the commuting zones level which are geographical aggregations of counties originally introduced by Tolbert and Killian (1987). There are approximately 741 CZs in the US and on average, each CZ contains 4 counties. There are significant 1
advantages estimating the model at the commuting zone level since we are able to examine the effect of regional characteristics and policies. Fourth, following Agnion et al. (2016) we consider the role of innovation and using patents data from Lai (2013) at the zip code level we first pair them to a county, and finally, to a commuting zone. Fifth, for our analysis we consider alternative measures of intergenerational mobility (Absolute Upward Mobility using income and enrollments, and Relative Mobility) and income inequality (Top 1% income share, Gross and Net Gini) using pre-tax, pre-transfer and after-tax, after-transfer income, based on data from the US Census Bureau. Finally, our empirical methodology allows us to deal with parameter heterogeneity which refers to the idea that the data generating process that describes the stochastic phenomenon of intergenerational mobility or income inequality is not common for all observations (commuting zones). We address parameter heterogeneity by employing the Threshold Regression introduced by Hansen (2000). 2 The Linear Intergenerational Mobility and Income Inequality Models Following Chetty et al.(2014), for each commuting zone i we assume that the intergenerational mobility between parents and offspring is determined by the following linear regression model, Mobility i = α + x iβ + e i (2.1) where α is an intercept, x i is a p 1 vector of intergenerational mobility determinants and e i is an i.i.d. error term for i = 1, 2,..., n. Commuting zones are a spatial measure of local labor markets consisting of one or more counties or county equivalents, originally introduced by Tolbert and Killian (1987) and Tolbert and Sizer (1996) based on commuting patterns in the 1980 and 1990 Census, respectively. In 1980, 768 commuting zones were delineated for all U.S. counties and county equivalents, and 741 in 1990. As Chetty et al.(2014) point out, using the classic intergenerational elasticity of income (IGE) by regressing log child income on log parent income, exhibits significant disadvantages: First, observations with zero income are not included leading to biased mobility estimates 2
and second, the relationship between log parent income and log child income is non-linear. These obstacles are properly addressed by Chetty et al.(2014) using a rank-rank LS regression between children s percentile rank based on their position in the distribution of child income within their birth cohorts and the percentile rank of the parents based on their position in the distribution of parent income. In particular, for each commuting zone i Chetty et al.(2014) estimate the following regression: y c ji = θ 0i + θ 1i y p ji + ϵ ji (2.2) where yji c denotes the national income rank of child j among children in his birth cohort in commuting zone i, and y p ji is the corresponding rank of the parent in the income distribution of parents in the core sample. Following Chetty et al.(2014) we measure intergenerational mobility using the Absolute Upward Mobility. Absolute mobility in general, is defined as the expected child rank of children born to a parent whose national income rank is p in commuting zone i, and Absolute Upward Mobility is specifically focused on children from families with below median parent income. Chetty et al.(2014) calculate parent and child income using data from 1040 federal income tax records from the IRS Databank and their baseline analysis is focused on a core sample of 1980-1982 birth cohorts. The children s income is defined as the mean total family income in 2011 and 2012, when they are approximately 30 years old and the their parents income is defined as the mean family income between 1996 and 2000, when the children are between the ages of 15 and 20. Chetty et al.(2014) show that estimates of intergenerational mobility stabilize when children reach their late twenties and thus, the choice of the particular birth cohort tackles successfully any problems of lifecycle bias due to measuring income at early or late ages. They also support that, mobility estimates are robust to the age of parents given that parent income is measured between age 30 and 55. Following the economics and sociology literature we consider determinants of intergenerational mobility from eleven broad categories or theories: Segregation, Income and Income Inequality, Tax, Education, College, Labor Market, Migration, Social Capital, Family Structure, Innovation and Population Growth. Following Chetty et al.(2014) we start with the racial, income, and geographical 3
segregation variables. For racial segregation we use the number of individuals who are black divided by the total population within a commuting zone and a multi-group Theil Index calculated at the census-tract level over four racial groups (white, black, hispanic and other). Income segregation is captured by a two-group Theil index and reflects the degree which individuals below the p th percentile of the local household income distribution are segregated from individuals above the p th percentile in each commuting zone. For geographical segregation we use the Fraction with Commute < 15 mins, which is the number of workers that commute less than 15 minutes to work divided by the total number of workers. All variables are from the 2000 Census and according to Chetty et al.(2014) there is a significant negative relationship between Absolute Upward Mobility, racial and income segregation whereas areas with shorter commutes have higher rates of upward mobility. The connection between income inequality and upward mobility is portrayed by the Great Gatsby Curve, initially introduced by Alan Krueger in 2012. In particular, countries with greater levels of income inequality also have lower levels of intergenerational mobility. To examine therefore if this relationship is empirically supported at the commuting zone level, we consider two income inequality measures: The Gini coefficient of parent income within each commuting zone from Census Bureau calculated over the period 2006-2010 and the Top 1% Income Share, which is the fraction of income going to the top 1% defined within the commuting zone in 2010 from the Economic Policy Institute. In addition, we include the mean level of Household Income per Capita for working-age adults in a commuting zone measured in the 2000 Census and Income per Capita for the period 2006-2010 from the Bureau of Economic Analysis. Notably, both inequality variables and Income per Capita from the Bureau of Economic Analysis were initially available at the county level which we have carefully grouped into commuting zones. It is important to mention that the empirical findings of Chetty et al.(2014) show a negative relationship between the Gini coefficient and mobility, but a limited association between mean income levels, Top 1% Income Share and mobility. The significant impact of tax policies on intergenerational mobility has also been documented in the literature (Becker and Tomes (1979, 1986), Mulligan (1997)). For example, Becker and Tomes (1979) who developed a general equilibrium model of income distribution across family generations show that even a progressive tax and public expenditure system may widen the inequality of disposable income. Following this literature, we include Local Tax rates, Tax Progressivity, state Earned Income Tax Credit and Local 4
government expenditures per capita. Local Tax rates reflect total tax revenues per capita divided by mean household income per capita for working age adults in 1992. Tax Progressivity is the difference between the state income tax rate for incomes above $100,000 and incomes in the bottom tax income bracket in 2008, whereas the state Earned Income Tax Credit is the the mean state Earned Income Tax Credit top-up rate between 1980-2001, with the rate coded as zero for states with no state Earned Income Tax Credit. Furthermore, government expenditures per capita are the total local government expenditures per capita in 1992. Chetty et al.(2014) find that commuting zones that provide more public goods and with larger tax credits for low income families tend to have higher levels or intergenerational mobility. We examine further the effect of local public goods on intergenerational mobility by considering also the role of school quality (Card and Krueger (1992), Hanushek (2003)). In particular, we include the School Expenditure per Student which is the average expenditures per student in public schools, the High School Dropout Rate which is the residual from a regression of high school dropout rates on household income per capita in 2000, the Student- Teacher Ratio which is the average student-teacher ratio in public schools in 1996-1997 and the Test Score Percentile which is the residual from a regression of mean Math and English test scores (in 2004, 2005 and 2007) appropriately standardized using the household income per capita in 2000. The first three variables are from the National Center for Education Statistics, whereas the test score Percentile is from the Global Report Card. As expected, Chetty et al.(2014) show that upward mobility is positively associated with School Expenditure per Student and the Test Score Percentile, but negatively with High School Dropout Rate and the Student-Teacher Ratio. Since the quality of local schools appears significant we extend the analysis considering the role of higher education. Specifically, we include the Number of Colleges per Capita in 2000, the College Tuition level which is the mean in-state tuition and fees for first-time, fulltime undergraduates in 2000 and finally, the College Graduation Rate which is the residual from a regression of graduation rate in 2009. All variables are calculated using data from the Integrated Postsecondary Education Data System (IPEDS). Chetty et al.(2014) find that Colleges per Capita and College Graduation Rate affect positively upward mobility but the College Tuition level, negatively. However, the effect of these variables is rather small and insignificant. Following the literature we also consider the effect of the local labor market structure on 5
income distribution by including the Labor Force Participation which is the share of people at least 16 years old that are in the labor force and the Share Working in Manufacturing which is the Share of employed persons 16 and older working in manufacturing. Both variables are from 2000 Census. Furthermore, we include the Growth in Chinese Imports which is the share of growth in imports from China per worker between 1990 and 2000 from Autor et al. (2013) and the Teenage Labor Force Participation which is the share of children born between 1985-1987 who received a W2 when they were age 14-16, computed from the 2000 Census. Chetty et al.(2014) identify a rather weak association with upward mobility for all the variables apart from the Teenage Labor Force Participation which exhibits a positive relationship. A number of papers in the literature suggest also a connection between immigration rates and labor market outcomes (Altonji and Card, 1989). In our analysis migration is measured using the Migration Inflow and Outlflow Rate which is the migration in to the commuting zone and out of the commuting zone respectively, between 2004 and 2005. Both variables are based on data from the IRS Statistics of Income. In addition, we include the Fraction of Foreign Born which is the share of commuting zone residents born outside the United States based on data from the 2000 Census. Chetty et al.(2014) find a negative, yet, small and insignificant connection between all the migration variables and upward mobility. Another important factor that affects social as well as economic outcomes is the presence of social capital which reflects the level of social networks. To consider the role of the social capital we include three variables: First, we include the Social Capital Index taken from Rupasingha and Goetz (2008), which is a standardized index combining measures of voter turnout rates, the fraction of people who return their census forms, and measures of participation in community organizations in 1990. Second, we also consider the Religious Fraction which is the share of religious adherents in 2000 based on data from the Association of Religion Data Archives. Third, we include the Violent Crime Rate which reflects the number of arrests for serious violent crimes per capita in 2000 based on the FBI s Uniform Crime Reports. Notably, as Chetty et al.(2014) document, the Social Capital Index and Religiosity are strongly and positively associated with upward mobility, whereas the Violent Crime Rate negatively. Many scholars have also emphasize the importance of the family environment on children s outcomes (Becker, 1991). In order to examine this possibility we include the Fraction of Children with Single Mothers which is the number of single female households 6
with children divided by the total number of households with children, the Fraction of Adults Divorced which is the Fraction of people 15 or older who are divorced, and the Fraction of Adults Married which is the share of people 15 or older who are married and not separated. All variables are from the 2000 Census and according to Chetty et al.(2014) there is a significant negative relationship between the Fraction of Children with Single Mothers, the Fraction of Adults Divorced and upward mobility, but the effect of Fraction of Adults Married, is positive. The relationship between innovation and social mobility has never been examined in the literature until recently from Aghion et al.(2016). In particular, using data at the commuting zone level they find that innovation is positively correlated with upward social mobility driven mostly by entrant innovators and less so by incumbent innovators, and it is dampened in states with higher lobbying intensity. Following Aghion et al.(2016), we proxy innovation using the average Utility Patents per capita over the period 2006-2010. In particular, using zip code level data from Lai et al. (2013) based on the Patent Inventor Database, we assigned each inventor to a county, and finally, to a commuting zone. Finally, following Aghion et al.(2016) we include population growth over the period 2006-2010 from the Bureau of Economic Analysis (BEA) which was initially available at the county level and we grouped into commuting zones. Aghion et al.(2016) show that population growth affects positively and strongly upward mobility. One of the most important contributions of this paper is not only to uncover empirically robust determinants of upward mobility but also, to examine if the same set of theories simultaneously affect income inequality focusing particularly on the role of upward mobility. In particular, for each commuting zone i we assume that income inequality is determined by the following linear regression model, Inequality i = b + z iδ + u i (2.3) where b is an intercept, z i is a p 1 vector of income inequality determinants and u i is an i.i.d. error term for i = 1, 2,..., n. Income inequality is measured using the Gini coefficient of parent income within each commuting zone from Census Bureau calculated over the period 2010-2014, and the Top 1% Income Share, which is the fraction of income going to the top 1% defined within the 7
commuting zone in 2013, from the Economic Policy Institute. Both variables were initially available at the county level which we have grouped into commuting zones. In this model we essentially extend the work of Aghion et al.(2016) in two key directions: First, we consider a larger set of determinants (Segregation, Income, Tax, Education, College, Labor Market, Migration, Social Capital, Family Structure, Innovation and Population Growth) and second, we pay particular attention to the role of absolute upward mobility. Aghion et al.(2016) find a positive effect of innovation and income on income inequality (Top 1% Income Share and Gini coefficient) but a negative impact of labor force participation, school expenditure, college per capita and employment manufacturing. Table 1 presents summary statistics while a detailed description of the data and the related sources is given in Table A1. 3 The Threshold Intergenerational Mobility and Income Inequality Models One of the main objectives of this paper is to identify robust determinants of Absolute Upward Mobility and Income inequality taking into account the presence of parameter heterogeneity by estimating the threshold intergenerational mobility and income inequality models. The threshold intergenerational mobility and income inequality models generalize the linear models in (2.1) and (2.3) respectively, by allowing for the presence of multiple regimes. In particular, we employ the threshold regression model that sorts the data into two groups of observations based on a particular threshold variable q i. An important feature of this model is that it allows for an estimation of the threshold parameter (sample split) as well as the regression coefficients of the two regimes. The threshold intergenerational mobility model can be described by the following regression equations Mobility i = α 1 + x iβ 1 + e i, q i γ (3.4a) Mobility i = α 2 + x iβ 2 + e i, q i > γ (3.4b) 8
Similarly, the threshold income inequality model can be defined as follows Inequality i = b 1 + z iδ 1 + u i, q i γ (3.5a) Inequality i = b 2 + z iδ 2 + u i, q i > γ (3.5b) where γ is the scalar threshold parameter or sample split value and (α 1, α 2), (b 1, b 2), (β 1, β 2) and (δ 1, δ 2), are the vectors of the regression coefficients (constant and slope) for the low and high regime, respectively. The statistical theory for this problem is provided by Hansen (2000) who proposed a concentrated least squares method for the estimation of the threshold parameter. The regression coefficients for the two regimes are obtained using LS on the two subsamples, separately. Under certain assumptions the asymptotic distribution of the threshold parameter γ is nonstandard as it involves two independent Brownian motions. Finally, the confidence intervals for γ are obtained by an inverted likelihood ratio approach. Estimation of the threshold intergenerational mobility model requires decisions on the choice of the threshold variable q i. Chetty et al.(2014) show that Income Inequality and Racial Segregation exhibit a strong and robust correlation with intergenerational mobility. Therefore, we consider Income Inequality( Gini over the period 2006-2010 or Top 1% in 2010) and Racial Segregation in 2000, as candidate threshold variables. Also, based on the recent significant empirical findings of Aghion et al.(2015) regarding the impact of innovation on upward mobility, we include the Average Patents per capita over the period 2006-2010. Hassler et al. (2003) suggest that inequality creates incentives to become skilled, and consequently, has a significant positive effect on upward mobility. Therefore, to test for this particular theory we include School expenditure per student over the period 1996-97, as an additional threshold variable. We examine also the effect of income and consider Income Segregation in 2000 and Household Income per capita (2006-2010). For the estimation of the threshold income inequality model we consider the same set of threshold variables apart from the income inequality measures which are appropriately substituted by the Absolute Upward Mobility. In practise, we test the null hypothesis of a linear model against the alternative of a threshold and discard threshold variables that do not reject the null of the linear model at 9
10%. We do so by employing the heteroskedasticity-consistent Lagrange multiplier (LM) test for a threshold of Hansen (1996). It is worth noting that inference in this context is not standard since the threshold parameter, γ, is not identified under the null hypothesis of a linear model (i.e. no threshold effect), and therefore the p-values are computed by a bootstrap method. 4 Results Table 2 shows the results of the threshold test for Absolute Upward Mobility. The table includes four different model specifications: The first and the second are the baseline models where the set of the explanatory variables include Gini (2006-2010) or Top 1% in 2010, Patents (2006-2010) and Income (2006-2010). In the third and fourth model we include the full set of the explanatory variables. The first column in Table 2 shows the threshold variable under consideration, then the corresponding P-value for the null hypothesis of a linear model against the alternative of a threshold, the threshold estimate, the confidence interval for the threshold parameter,the joint sum of squares (JSSE), and the sample sizes of the two regimes. According to the results, for almost all the models (apart from one case), the linear model null hypothesis is strongly rejected. Tables 4 and 5 show the estimation results (baseline and extended) for the best model in terms of joint sum of squares (JSSE). Table 3 shows the threshold test for Income Inequality. As previously, we consider four different model specifications. In the first and the second which are the baseline models, the set of the explanatory variables includes Absolute upward mobility, Patents (2006-2010) and Income (2006-2010). The dependent variable in the first model is Gini (2010-2014) and in the second, Top 1% in 2013. In the third and fourth model we include the full set of the explanatory variables. Notably, the null hypothesis for almost all the models (apart from seven cases) is strongly rejected. Tables 6 and 7 show the estimation results (baseline and extended) for the best model in terms of joint sum of squares (JSSE). To be completed... 10
5 Robustness To test the robustness of our results we estimate four different model variations. Fist, we consider an alternative income variable. In particular, we substitute income per capita over the period 2006-2010 from BEA (Bureau of Economic Analysis) with Household Income Per Capita in 2000 from Chetty et al. (2014). Tables 2 and 4 in the Appendix present the results from the estimation of the corresponding threshold regression models for Absolute Upward Mobility and Income Inequality, respectively. As expected, the results for the baseline models, as well as, for the extended models, remain robust. Second, we extend the set of the explanatory variables by including also the Student-Teacher Ratio and High School Dropout Rate for Education, College Tuition, College Graduation Rate and Number of Colleges per Capita for College, and finally, Violent Crime Rate for Social Capital. The addition of these variables has reduced the number of the observations from 686 to 417 and as expected, we have chosen to exclude them from the initial regressors set. Notably, the threshold regression model results remain robust for both, Absolute Upward Mobility and Income Inequality (Table 3 and 5, respectively in the Appendix). Third, we consider alternative intergenerational mobility variables. In particular, we consider Relative Mobility and Absolute Upward Mobility based on college enrollments. Relative Mobility measures the difference in income between the expected ranks of children born to parents at the top and bottom of the income distribution within a commuting zone. Given that there is a strong association between higher education and subsequent earnings we include Absolute Upward Mobility based on OLS regressions of an indicator for being enrolled in college at age 19 on parent income rank in 1996-2000 from Chetty et al. (2014). Finally, for the first time, we estimate and examine the role of Net Gini at the commuting zone level, instead of the typical market (gross) Gini. Specifically, we calculate Net Gini using pre-tax, pre-transfer and after-tax, after-transfer income using data from the US Census Bureau. To be completed... 6 Conclusion To be completed. 11
Table 1: Descriptive Statistics Variable Obs Mean Std. Dev. Min Max Intergenerational Mobility Absolute Upward Mobility 686 43.9900 5.6418 26.6717 64.0192 Income Inequality and Income Gini Coefficient, 2006-2010 686 0.4328 0.0262 0.3527 0.5535 Gini Coefficient, 2010-2014 686 0.4416 0.0244 0.3727 0.5471 Top1% Income Share, 2010 686 12.8958 4.0048 7.4000 48.8000 Top1% Income Share, 2013 686 12.9011 3.5696 7.5000 41.5000 Income Per Capita 686 11.6901 0.5786 9.8947 13.6091 Household Income Per Capita 686 32728.1 5582.1 17378.6 58628.4 Innovation Patents per capita 686 0.0610 0.0946 0.0000 1.2673 Other Population Growth 686-2.9038 0.1481-3.4146-2.4522 Segregation Fraction Black 686 0.0825 0.1250 0.0002 0.6583 Racial Segregation 686 0.1358 0.0993 0.0000 0.5537 Income Segregation 686 0.0410 0.0315 0.0000 0.1379 Fraction with Commute < 15 Mins 686 0.4426 0.1300 0.1561 0.7666 Tax Local Tax Rate 686 0.0229 0.0092 0.0081 0.0823 Local Govt Expenditures Per Capita 686 2236.3 822.4 952.2 11529.1 Tax Progressivity 686 0.7791 1.4542 0.0000 6.3000 State EITC Exposure 686 1.3877 3.9137 0.0000 21.3333 Education School Expenditure per Student 686 5.9527 1.1147 3.9202 11.9063 Test Score Percentile (Income adjusted) 686 0.1823 7.9598-31.8367 20.0705 Student Teacher Ratio 417 16.4594 1.7613 10.6852 23.3418 High School Dropout Rate (Income adjusted) 417 0.0017 0.0195-0.0338 0.0993 College Number of Colleges per Capita 417 0.0239 0.0204 0.0044 0.2432 College Tuition 417 4123.9 3716.1 0.0000 24619 College Graduation Rate (Income Adjusted) 417-0.0021 0.1311-0.2770 0.4734 Labor Market Labor Force Participation 686 0.6141 0.0586 0.3641 0.7818 Share Working in Manufacturing 686 0.1474 0.0806 0.0085 0.4370 Growth in Chinese Imports 686 1.2222 1.8127-0.0027 25.4053 Teenage (14-16) Labor Force Participation 686 0.0048 0.0014 0.0017 0.0081 Migration Migration Inflow Rate 686 0.0168 0.0104 0.0000 0.0770 Migration Outlflow Rate 686 0.0168 0.0075 0.0033 0.0525 Fraction Foreign Born 686 0.0405 0.0496 0.0034 0.3968 Social Capital Social Capital Index 686 0.0980 1.2151-3.1990 5.2660 Fraction Religious 686 0.5450 0.1577 0.1715 1.0490 Violent Crime Rate 417 0.0016 0.0009 0.0000 0.0050 Family Structure Fraction of Children with Single Mothers 686 0.2048 0.0519 0.0821 0.4337 Fraction of Adults Divorced 686 0.0971 0.0170 0.0395 0.1562 Fraction of Adults Married 686 0.5739 0.0448 0.3729 0.6947 12
Table 2: Threshold Tests and Threshold Estimates-Absolute Upward Mobility Threshold variable p-value Threshold 95% CI jsse n1 n2 Model 1 Gini 0610 0.5252 0.4095 [0.409000, 0.457875] 16992 105 581 Patents per capita 2006 to 2010 0.0020 0.0182 [0.010400, 0.026700] 16238 193 493 Income pc 2006 to 2010 0.0004 122876 66028.60, 125878.00] 16584 353 333 Income segregation 0.0000 0.0177 [0.016920, 0.019647] 14132 191 495 Racial segregation 0.0000 0.0718 [0.043901, 0.098412] 14712 202 484 School expenditure per student 0.0000 6.2566 [5.912070, 6.914530] 16253 456 230 Model 2 Top 1% in 2010 0.0050 15.2000 [11.43300, 15.20000] 20811 583 103 Patents per capita 2006 to 2010 0.0242 0.0104 [0.010400, 0.048800] 20333 102 584 Income pc 2006 to 2010 0.0000 107261 [66028.60, 200433.00] 20539 283 403 Income segregation 0.0000 0.0177 [0.017511, 0.019578] 17575 191 495 Racial segregation 0.0000 0.0718 [0.048758, 0.098412] 17528 202 484 School expenditure per student 0.0000 6.2566 [5.917000, 6.291440] 19390 456 230 Model 3 Gini 0610 0.0000 0.4483 [0.448000, 0.448333] 2636 506 180 Patents per capita 2006 to 2010 0.0000 0.0246 [0.010400, 0.075100] 2740 269 417 Income pc 2006 to 2010 0.0006 110864 [97554.80, 112356.00] 2743 309 377 Income segregation 0.0000 0.0196 [0.019634, 0.019634] 2559 217 469 Racial segregation 0.0028 0.0576 [0.040798, 0.098412] 2731 153 533 School expenditure per student 0.0000 6.4154 [6.242820, 6.537840] 2730 485 201 Model 4 Top 1% in 2010 0.0004 11.5750 [11.30000, 12.43300] 2678 278 408 Patents per capita 2006 to 2010 0.0002 0.0246 [0.010400, 0.076100] 2708 269 417 Income pc 2006 to 2010 0.0010 110864 [93689.00, 112356.00] 2721 309 377 Income segregation 0.0000 0.0196 [0.019634, 0.019647] 2546 217 469 Racial segregation 0.0028 0.0424 [0.042421, 0.057609] 2690 107 579 School expenditure per student 0.0000 6.4154 [6.256320, 6.573410] 2679 485 201 13
Table 3: Threshold Tests and Threshold Estimates-Income Inequality Threshold variable p-value Threshold 95% CI jsse n1 n2 Model 1 Absolute upward mobility 0.0000 49.1870 [45.9863, 50.2682] 0.313 566 120 Patents per capita 2006 to 2010 0.0000 0.0293 [0.021200, 0.071300] 0.317 304 382 Income pc 2006 to 2010 0.1036 67968 [66028.60, 69845.80] 0.330 107 579 Income segregation 0.0182 0.0118 [0.011547, 0.012073] 0.333 117 569 Racial segregation 0.0338 0.0427 [0.040798, 0.043901] 0.331 109 577 School expenditure per student 0.0000 6.8957 [4.825330, 6.961240] 0.326 573 113 Model 2 Absolute upward mobility 0.4882 39.5395 [39.41620, 40.38380] 7789 160 526 Patents per capita 2006 to 2010 0.1308 0.0218 [0.021200, 0.021800] 8214 235 451 Income pc 2006 to 2010 0.4690 69965 [66028.60, 73729.00] 7951 119 567 Income segregation 0.0008 0.0326 [0.032628, 0.039053] 8040 343 343 Racial segregation 0.2586 0.0416 [0.040798, 0.044338] 7399 105 581 School expenditure per student 0.0116 6.8384 [4.825330, 6.961240] 8213 561 125 Model 3 Absolute upward mobility 0.0000 43.3440 [38.20230, 43.63400] 0.173 343 343 Patents per capita 2006 to 2010 0.0084 0.0397 [0.010400, 0.054800] 0.185 380 306 Income pc 2006 to 2010 0.0026 69817 [66028.60, 72868.80] 0.181 116 570 Income segregation 0.0058 0.0112 [0.011207, 0.011207] 0.186 104 582 Racial segregation 0.0084 0.0409 [0.040798, 0.040931] 0.183 103 583 School expenditure per student 0.0002 6.6602 [6.299380, 6.736560] 0.182 536 150 Model 4 Absolute upward mobility 0.0666 39.5080 [38.20230, 43.73000] 5336 159 527 Patents per capita 2006 to 2010 0.0326 0.0766 [0.076300, 0.077900] 5358 534 152 Income pc 2006 to 2010 0.4042 66106 [66028.60, 73729.00] 5507 103 583 Income segregation 0.1878 0.0200 [0.019927, 0.055541] 5468 225 461 Racial segregation 0.0150 0.0409 [0.040931, 0.040963] 4977 103 583 School expenditure per student 0.0186 6.7442 [6.291440, 6.744160] 5594 551 135 14
Table 4: Threshold Regression-Mobility Method Linear Threshold Linear Threshold Explanatory Variables Low High Low High coef se coef se coef se coef se coef se coef se Constant 110.626 5.2114 61.6280 11.3690 100.596 5.7035 60.2662 5.9291 68.1596 9.4802 59.1372 6.7069 Gini 2006-2010 -95.3878 7.4978-106.086 14.3046-78.4358 7.9619-6.4706 4.8044-6.4093 7.3467-11.0102 5.4193 Patents pc 2006-2010 -1.0243 1.9790 4.6217 4.7609 2.0540 1.3461-1.5536 1.0118 1.4156 1.8291-1.4158 0.8214 Log Income pc 2006-2010 -2.1634 0.3089 2.7648 0.8001-2.0409 0.3152 0.3448 0.2402 0.1512 0.4099 0.3921 0.2540 Pop growth 2006-2010 - - - - - - 0.6952 1.0424 2.8438 1.5997 0.6789 1.0962 Fraction Black - - - - - - 4.0843 1.8749 5.3749 2.9459 3.6460 1.9819 Racial Segregation - - - - - - -4.7702 1.4527-2.1136 1.9455-7.0292 1.5367 Income Segregation - - - - - - -3.0599 5.8379 97.6600 41.5476-5.9546 5.8675 Fraction with Commute < 15 Mins - - - - - - 8.8429 1.7209 11.8481 3.7307 8.7533 1.6705 Local Tax Rate - - - - - - -5.8994 18.0674-22.4060 29.5009 41.6731 17.8085 Local Govt Expenditures Per Capita - - - - - - 0.0003 0.0001 0.0002 0.0002 0.0001 0.0001 Tax Progressivity - - - - - - 0.4407 0.0720 0.9525 0.1730 0.2010 0.0634 State EITC Exposure - - - - - - 0.0350 0.0247 0.0389 0.0445 0.0329 0.0284 School Expenditure per Student - - - - - - 0.0343 0.1190 0.0811 0.1975-0.0315 0.1134 Test Score Percentile - - - - - - 0.0469 0.0182 0.0702 0.0349 0.0215 0.0168 Labor Force Participation - - - - - - -7.0825 3.3462 1.6515 5.9707-9.0881 3.4592 Share Working in Manufacturing - - - - - - -10.3421 1.4859-11.4605 2.8984-9.3352 1.7474 Growth in Chinese Imports - - - - - - -0.0651 0.0395-0.0603 0.0883-0.0366 0.0346 Teenage (14-16) Labor Force Participation - - - - - - 160.176 148.942-79.3435 253.526 201.191 154.830 Migration Inflow Rate - - - - - - -47.1043 15.5859-167.184 55.8257-17.4162 16.7853 Migration Outlflow Rate - - - - - - 43.1477 23.1019 136.783 62.2070 22.2681 22.7381 Fraction Foreign Born - - - - - - 4.3117 3.0329-21.5785 6.9729 12.7259 2.6777 Social Capital Index - - - - - - 0.6102 0.1689-0.0268 0.2819 0.9943 0.1908 Fraction Religious - - - - - - 5.5015 0.7998 4.0006 1.2299 6.5722 0.8645 Fraction of Children with Single Mothers - - - - - - -56.8699 6.1430-68.6856 9.0326-46.3095 6.4592 Fraction of Adults Divorced - - - - - - -27.2714 8.7532-39.7041 15.5133-15.6322 9.1734 Fraction of Adults Married - - - - - - -6.4471 3.9581-7.8915 6.6144-7.6119 4.3023 15
Table 5: Threshold Regression-Mobility Method Linear Threshold Linear Threshold Explanatory Variables Low High Low High coef se coef se coef se coef se coef se coef se Constant 61.1051 3.8542 30.1204 7.2497 51.9952 4.6401 53.9019 5.2285 62.9338 8.4509 50.4429 5.9244 Top 1% in 2010 0.0319 0.0693-0.0020 0.0679 0.0407 0.0872 0.0852 0.0290 0.0889 0.0399 0.0305 0.0234 Patents pc 2006-2010 1.3912 2.0414-9.4181 2.8440 5.4985 2.3737-2.2725 1.1200 0.0898 2.3192-1.7483 0.8579 Log Income pc 2006-2010 -1.5065 0.3193 1.5789 0.6521-0.8826 0.3824 0.3526 0.2366 0.1731 0.4087 0.4479 0.2516 Pop growth 2006-2010 - - - - - - 0.4936 1.0048 2.3207 1.6090 0.6869 1.1103 Fraction Black - - - - - - 3.6989 1.8127 5.4211 2.9455 3.2288 1.9880 Racial Segregation - - - - - - -4.5771 1.3800-2.3974 1.8268-6.6395 1.5126 Income Segregation - - - - - - -0.4931 5.6247 90.3556 41.5973-3.6162 6.1722 Fraction with Commute < 15 Mins - - - - - - 9.3562 1.6992 11.3699 3.6723 9.3606 1.6918 Local Tax Rate - - - - - - -9.9094 18.0334-24.8446 29.3026 41.7985 18.3781 Local Govt Expenditures Per Capita - - - - - - 0.0003 0.0001 0.0002 0.0001 0.0001 0.0001 Tax Progressivity - - - - - - 0.4598 0.0715 0.9650 0.1641 0.2155 0.0638 State EITC Exposure - - - - - - 0.0396 0.0246 0.0364 0.0457 0.0396 0.0282 School Expenditure per Student - - - - - - 0.0365 0.1160 0.0973 0.1956-0.0224 0.1157 Test Score Percentile - - - - - - 0.0432 0.0176 0.0623 0.0336 0.0195 0.0171 Labor Force Participation - - - - - - -4.7721 3.3125 3.2937 5.8979-7.0147 3.5345 Share Working in Manufacturing - - - - - - -9.6365 1.4650-10.9526 2.8536-8.5413 1.7081 Growth in Chinese Imports - - - - - - -0.0628 0.0406-0.0450 0.0852-0.0439 0.0361 Teenage (14-16) Labor Force Participation - - - - - - 177.788 147.793-7.8516 249.996 210.899 156.658 Migration Inflow Rate - - - - - - -49.0498 15.0470-174.312 54.6847-17.5002 16.7235 Migration Outlflow Rate - - - - - - 41.6486 22.4400 141.193 58.3505 25.2808 22.5196 Fraction Foreign Born - - - - - - 2.0066 2.9787-22.0337 6.9206 11.0019 2.7966 Social Capital Index - - - - - - 0.5380 0.1710-0.0503 0.2728 0.9795 0.1953 Fraction Religious - - - - - - 5.1345 0.7927 3.7306 1.2238 6.2644 0.8903 Fraction of Children with Single Mothers - - - - - - -58.0281 6.0207-71.1501 8.8644-46.9550 6.5387 Fraction of Adults Divorced - - - - - - -29.6506 8.6542-40.5404 15.4205-16.4598 9.1840 Fraction of Adults Married - - - - - - -5.0718 4.0183-9.3451 6.5218-5.0795 4.5130 16
Table 6: Threshold Regression-Inequality Method Linear Threshold Linear Threshold Explanatory Variables Low High Low High coef se coef se coef se coef se coef se coef se Constant 0.6113 0.0235 0.6875 0.0270 0.2713 0.0722 0.6701 0.0535 0.7511 0.0741 0.5622 0.0695 Absolute upward mobility -0.0016 0.0002-0.0026 0.0003 0.0021 0.0006-0.0001 0.0004-0.0013 0.0007 0.0011 0.0005 Patents pc 2006-2010 -0.0192 0.0113-0.0069 0.0107-0.0423 0.0222 0.0241 0.0100 0.0552 0.0194 0.0085 0.0075 Log Income pc 2006-2010 -0.0086 0.0017-0.0114 0.0018 0.0042 0.0053-0.0030 0.0017-0.0078 0.0022 0.0002 0.0025 Pop growth 2006-2010 - - - - - - 0.0022 0.0079 0.0113 0.0113-0.0142 0.0099 Fraction Black - - - - - - 0.0133 0.0164 0.0115 0.0235 0.0238 0.0415 Racial Segregation - - - - - - -0.0096 0.0109-0.0099 0.0143-0.0147 0.0138 Income Segregation - - - - - - -0.1305 0.0502-0.0452 0.0660-0.1508 0.0774 Fraction with Commute < 15 Mins - - - - - - -0.0201 0.0136-0.0027 0.0224-0.0392 0.0180 Local Tax Rate - - - - - - -0.0001 0.1077 0.0341 0.1600 0.1599 0.1399 Local Govt Expenditures Per Capita - - - - - - 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Tax Progressivity - - - - - - 0.0005 0.0005 0.0000 0.0006 0.0003 0.0008 State EITC Exposure - - - - - - -0.0004 0.0002-0.0002 0.0005-0.0001 0.0002 School Expenditure per Student - - - - - - -0.0019 0.0009 0.0012 0.0014-0.0035 0.0011 Test Score Percentile - - - - - - 0.0003 0.0002 0.0001 0.0002 0.0005 0.0002 Labor Force Participation - - - - - - -0.1144 0.0300-0.1468 0.0411-0.1166 0.0390 Share Working in Manufacturing - - - - - - -0.0546 0.0137-0.0417 0.0175-0.0903 0.0185 Growth in Chinese Imports - - - - - - 0.0005 0.0004 0.0009 0.0005-0.0003 0.0004 Teenage (14-16) Labor Force Participation - - - - - - -4.1451 1.2461-4.8029 1.8429-4.3283 1.5859 Migration Inflow Rate - - - - - - 0.0248 0.1646-0.0102 0.2134-0.0704 0.2062 Migration Outlflow Rate - - - - - - -0.2189 0.2233-0.4469 0.2724 0.3396 0.3234 Fraction Foreign Born - - - - - - 0.0752 0.0227 0.0817 0.0319 0.0929 0.0296 Social Capital Index - - - - - - 0.0011 0.0014-0.0019 0.0018 0.0039 0.0016 Fraction Religious - - - - - - 0.0217 0.0074 0.0320 0.0109 0.0065 0.0105 Fraction of Children with Single Mothers - - - - - - 0.0857 0.0535 0.0424 0.0709 0.1753 0.0757 Fraction of Adults Divorced - - - - - - -0.0889 0.0805-0.0431 0.0961-0.1572 0.1199 Fraction of Adults Married - - - - - - -0.1385 0.0374-0.0571 0.0487-0.1763 0.0470 17
Table 7: Threshold Regression-Inequality Method Linear Threshold Linear Threshold Explanatory Variables Low High Low High coef se coef se coef se coef se coef se coef se Constant 16.3200 4.2440 24.6188 6.4560 10.8462 4.6561 13.4155 8.6791 27.6294 22.2682 7.1542 8.5691 Absolute upward mobility 0.0074 0.0226 0.0115 0.0278 0.0568 0.0379 0.1312 0.0576 0.1804 0.1508 0.1268 0.0541 Patents pc 2006-2010 7.6538 3.1354 19.5183 12.1732 3.0937 1.3573 8.0730 3.5641 43.0998 4.2180 3.7692 1.4022 Log Income pc 2006-2010 -0.3604 0.3269-1.1606 0.5399-0.0248 0.3210-0.0320 0.2944-0.0904 0.8020-0.1281 0.3364 Pop growth 2006-2010 - - - - - - 2.2824 1.6658 6.0764 3.7765-0.1557 1.4721 Fraction Black - - - - - - 3.4500 2.8128-9.5692 5.9087 4.9925 3.0854 Racial Segregation - - - - - - -1.8195 1.7255-4.9614 34.6479-1.3205 1.8396 Income Segregation - - - - - - -13.3960 10.9313 14.8334 33.2060 0.2127 8.0801 Fraction with Commute < 15 Mins - - - - - - -4.6089 2.6927-10.7967 4.4698-2.9263 2.2317 Local Tax Rate - - - - - - 81.9209 24.5189 21.5393 31.6392 71.4073 32.2345 Local Govt Expenditures Per Capita - - - - - - 0.0001 0.0002 0.0003 0.0005 0.0000 0.0002 Tax Progressivity - - - - - - -0.2365 0.1122-0.8482 0.3215-0.0803 0.0812 State EITC Exposure - - - - - - -0.0694 0.0350-0.0043 0.0959-0.0541 0.0349 School Expenditure per Student - - - - - - 0.0144 0.1744 0.3956 0.3411 0.0761 0.1798 Test Score Percentile - - - - - - 0.0445 0.0561-0.0922 0.0936 0.1050 0.0317 Labor Force Participation - - - - - - -14.8224 5.5380-8.4308 8.8990-16.9481 5.8830 Share Working in Manufacturing - - - - - - -2.1426 2.2088-4.7397 4.8839-0.8186 2.1037 Growth in Chinese Imports - - - - - - -0.0779 0.0501-0.0194 0.0564-0.0482 0.0537 Teenage (14-16) Labor Force Participation - - - - - - -34.2222 190.412 330.485 371.104-53.6701 205.742 Migration Inflow Rate - - - - - - 48.0218 39.9880-29.0418 36.8995 77.9208 41.7167 Migration Outlflow Rate - - - - - - 8.3511 44.6641-45.0542 77.1523-16.0091 43.4039 Fraction Foreign Born - - - - - - 23.4226 5.6391 40.7644 21.6010 24.3300 5.8336 Social Capital Index - - - - - - 0.7165 0.3535 0.9867 0.5284 0.3347 0.2346 Fraction Religious - - - - - - 3.5180 1.3783-0.2544 2.3380 5.4962 1.4316 Fraction of Children with Single Mothers - - - - - - 15.9159 8.8515 36.8832 16.5659 10.7065 9.4613 Fraction of Adults Divorced - - - - - - 43.8581 14.6365-45.3262 30.0733 48.4406 16.8527 Fraction of Adults Married - - - - - - -1.4617 5.7350-2.4695 11.0014-1.8589 5.7339 18
References 19
Table A1: Data Appendix Variable Description Intergenerational Mobility Absolute Upward Mobility The expected child rank of children born to a parent whose national income rank is p in commuting zone i. Absolute Upward Mobility is specically focused on children from families with below median parent income. Parent and child income is calculated using data from 1040 federal income tax records from the IRS Databank and the baseline analysis is focused on the 1980-1982 birth cohorts. The children s income is defined as the mean total family income in 2011 and 2012, when they are approximately 30 years old and the their parents income is defined as the mean family income between 1996 and 2000, when the children are between the ages of 15 and 20. Source: Chetty et al.(2014). Income Inequality and Income Gini Coefficient The Gini coefficient of parent income within each commuting zone calculated over the period 2006-2010 and 2010-2014. The variable was initially available at the county level which we have carefully grouped into commuting zones. Source: Census Bureau. Top1% Income Share The Top 1% Income Share, which is the fraction of income going to the top 1% defined within the commuting zone in 2010 and in 2013. The variable was initially available at the county level which we have carefully grouped into commuting zones. Source: Economic Policy Institute. Income Per Capita Income per Capita for the period 2006-2010, initially available at the county level which we have carefully grouped into commuting zones. Source: Bureau of Economic Analysis. Household Income Per Capita Mean level of Household Income per Capita for working-age adults in a commuting zone measured in the 2000 Census. Source: Chetty et al. (2014). Innovation Patents per capita Patents per capita over the period 2006-2010, using zip code level data which we first pair them to a county, and finally, to a commuting zone. Source: Lai et al. (2013). Other Population Growth Population growth over the period 2006-2010 initially available at the county level and then grouped into commuting zones. Source: Bureau of Economic Analysis (BEA). Segregation Fraction Black The number of individuals who are black divided by the total population within a commuting zone. Source: Census 2000. Racial Segregation Multi-group Theil Index calculated at the census-tract level over four racial groups (white, black, hispanic and other). Source: Census 2000. Income Segregation A two-group Theil index and reflects the degree which individuals below the pth percentile of the local household income distribution are segregated from individuals above the pth percentile in each commuting zone. Source: Census 2000. Fraction with Commute < 15 Mins The number of workers that commute less than 15 minutes to work divided by the total number of workers. Source: Census 2000. Table continued on next page... 20
Table A1 continued Variable Description Tax Local Tax Rate Total tax revenues per capita divided by mean household income per capita for working age adults in 1992. Source: 1992 Census of Government county-level summaries. Local Govt Expenditures Per Capita The total local government expenditures per capita in 1992. Source: 1992 Census of Government county-level summaries. Tax Progressivity The difference between the state income tax rate for incomes above $100,000 and incomes in the bottom tax income bracket in 2008. Source: State income tax rates in 2008 from the Tax Foundation. State EITC Exposure The mean state Earned Income Tax Credit top-up rate between 1980-2001, with the rate coded as zero for states with no state Earned Income Tax Credit. Source: Hotz and Scholz (2003) Education School Expenditure per Student Average expenditures per student in public schools in 1996-1997. Source: National Center for Education Statistics. Test Score Percentile (Income adjusted) The residual from a regression of mean Math and English test scores (in 2004, 2005 and 2007) appropriately standardized using the household income per capita in 2000. Source: Global Report Card. Student Teacher Ratio Average student-teacher ratio in public schools in 1996-1997. Source: National Center for Education Statistics. High School Dropout Rate (Income adjusted) The residual from a regression of high school dropout rates on household income per capita in 2000. Source: National Center for Education Statistics. College Number of Colleges per Capita Number of Colleges per Capita in 2000. Source: Integrated Postsecondary Education Data System (IPEDS). College Tuition The mean in-state tuition and fees for first-time, full-time undergraduates in 2000. Source: Integrated Postsecondary Education Data System (IPEDS). College Graduation Rate (Income Adjusted) The residual from a regression of graduation rate in 2009. Source: Integrated Postsecondary Education Data System (IPEDS). Table continued on next page... 21
Table A1 continued Variable Description Labor Market Labor Force Participation The share of people at least 16 years old that are in the labor force. Source: Census 2000. Share Working in Manufacturing Share of employed persons 16 and older working in manufacturing. Source: Census 2000. Growth in Chinese Imports Share of growth in imports from China per worker between 1990 and 2000. Source: Autor et al. (2013). Teenage (14-16) Labor Force Participation Share of children born between 1985-1987 who received a W2 when they were age 14-16. Source: Census 2000. Migration Migration Inflow Rate Migration into the commuting zone from other commuting zones between 2004 and 2005. Source: IRS Statistics of Income. Migration Outlflow Rate Migration out of the commuting zone from other commuting zones between 2004 and 2005. Source: IRS Statistics of Income. Fraction Foreign Born Share of commuting zone residents born outside the United States. Source: Census 2000. Social Capital Social Capital Index A standardized index combining measures of voter turnout rates, the fraction of people who return their census forms, and measures of participation in community organizations in 1990. Source: Rupasingha and Goetz (2008). Fraction Religious Share of religious adherents in 2000. Source: Association of Religion Data Archives. Violent Crime Rate Number of arrests for serious violent crimes per capita in 2000. Source: FBI s Uniform Crime Reports. Family Structure Fraction of Children with Single Mothers The number of single female households with children divided by the total number of households with children. Source: Census 2000. Fraction of Adults Divorced Fraction of people 15 or older who are divorced. Source: Census 2000. Fraction of Adults Married Share of people 15 or older who are married and not separated. Source: Census 2000. 22