Income Inequality, Tax Policy, and Economic Growth∗
Siddhartha Biswas
Indraneel Chakraborty
Rong Hai†
July 1, 2015
Abstract
We investigate how reduction of income inequality through tax policy affects economic
growth. Taxation at different points of the income distribution has heterogeneous impacts on
households’ incentives to invest, work, and consume. Using U.S. state-level data and microlevel household tax returns over the last three decades, we find that reduction of income inequality between low and median income households improves economic growth. However,
reduction of income inequality through taxation between median and high income households
reduces economic growth. These economic growth effects are attributable both to supply-side
factors (changes in small business activity and labor supply) and to consumption demand.
JEL Codes: E2, H2, H3.
∗ We
thank Scott Ashworth, Christopher Berry, Dan Black, Stéphane Bonhomme, Naijia Guo, James J. Heckman,
Dirk Krueger, Alok Kumar, Ethan Bueno de Mesquita, Anthony Fowler, João Gomes, Tong Li, B. Pablo Montagnes,
José-Vı́ctor Rı́os-Rull, James Smith, Rex Thompson, Xi Weng, Harald Uhlig, Motohiro Yogo, Li-An Zhou and seminar participants at University of Chicago, Peking University, Fourth Society of Labor Economists/EALE World Conference 2015, and Chinese University of Hong Kong for helpful comments and suggestions. We thank Daniel Feenberg
at NBER for access to TAXSIM individual tax return data.
† Siddhartha Biswas: Department of Economics CB 3305, University of North Carolina, Chapel Hill, NC 27599.
Email: sbsw89@gmail.com. Indraneel Chakraborty: Department of Finance, School of Business Admin., University
of Miami, Coral Gables, FL 33124. Email: indranil@alum.mit.edu. Tel: (312) 208-1283. Rong Hai: Center for the
Economics of Human Development and Becker Friedman Institute for Research in Economics, University of Chicago.
1155 E. 60th Street, Room 223, Chicago, IL 60637. Email: ronghai@uchicago.edu. Tel: (267) 254-8866.
Modern governments have utilized tax policy to not only raise capital for government operations, but also to reduce income inequality among citizens. Progressive taxation with negative net
tax rates for the lowest income households aims to achieve two distinct objectives: (i) to provide a
minimum level of consumption for the low income population, and (ii) to reduce income inequality between different groups of population.1 The underlying economic justification for this tax
policy is that income inequality creates lower economic growth. Researchers using cross-country
regressions of GDP growth on income inequality, find mixed evidence regarding the relationship
between income inequality and economic growth.2
Our paper investigates how tax policies that reduce income inequality have affected economic
growth in U.S. states in the last three decades.3 We distinguish between the impact of tax policy on households below median income level and on those above median income level. We find
that poverty alleviation i.e. reduction of income inequality between low income and median income households improves economic growth. At the same time, we find that reduction of income
inequality through taxation between median income households and high income households reduces economic growth. We explore three major economic components of economic growth as
well. We find that reduction of income inequality between below median and median households
encourages growth in labor supply on both the extensive and intensive margin, while reduction in
income inequality between above median households and median households reduces labor supply.
Further, reduction in income inequality through taxation between above median and median households reduces job creation by small businesses. In contrast again, below median income inequality
reduction through tax policy encourages small businesses to employ more workers. Finally, we
also find that reduction in income inequality between lower income households and median in1 See
Figure I, which shows how income inequality is reduced in U.S. through tax policy which effectively compresses the income distribution around the median household.
2 Alesina and Rodrik (1994), Persson and Tabellini (1994), Perotti (1996) among others find that there is a negative
correlation between average growth and inequality since 1960s. Persson and Tabellini (1994) document that a similar
negative relationship existed in nine developed economies since 1830s. However, Forbes (2000) finds a positive
relationship between income inequality and economic growth in high and mid-income countries, and Barro (2000)
finds a positive relationship between income inequality and growth in rich and negative relationship in poor countries.
See Bénabou (1996), Ostry et al. (2014), and Cingano (2014) for detailed surveys of the literature.
3 Literature on endogenous growth of countries includes seminal work by Romer (1986), Lucas (1988), Barro
(1990), and Barro (1991) among others. Our paper focuses on the impact of U.S. tax policy to reduce income inequality
on economic growth of U.S. states.
1
come households increases per capita consumption expenditure growth rate.
Our empirical strategy relies on within-state variation in tax policies that reduce income inequality to explain within-state variation in growth rates of U.S. states over time. We utilize a
simple measure that calculates the changes in income distribution induced by income tax policy
for each state using actual tax return data. In other words, the measure calculates the additional
average income tax paid for each additional dollar earned by a person at the higher/lower income
level, compared to the reference point of median income level household. Since this is analogous
to a contraction function on income distribution, we refer to it as the contraction factor. As we
show, this cross-sectional differential tax rate measure is able to explain economic growth even
after controlling for marginal tax rate for a given individual over time (See, for example, Barro
and Redlick (2011) who consider the impact of marginal tax rate). This is because we argue that
an individual considers the impact of tax policy on her personal income in two dimensions. She
considers the tax-induced change in her income with respect to the reference point of median income household. This is in addition to the impact of tax policy on her marginal dollar, where her
reference point is herself. We calculate this contraction factor between the median income and
bottom income group, and the median income and top income group for each U.S. state and year
from 1979 to 2008.
To address potential endogeneity of tax policy to economic conditions in the state, we use a set
of exogenous instrumental variables (IV). We estimate our model using a generalized method of
moments (GMM) approach developed by Blundell and Bond (1998) which refines the approach of
Arellano and Bond (1991) for panel data that is persistent. The instrumental variables are the exogenous tax shocks identified by Romer and Romer (2009, 2010) and later refined by Mertens and
Ravn (2013) at the national level, and their interactions with state-specific initial income inequality and initial propensity towards charity. The intuition is that state level conditions, specifically
initial income inequality and initial propensity towards charity, affect tax policies to reduce inequality, and different states respond differently to tax shocks based on these initial conditions.
Since we include state fixed effects to control for any time-invariant state level heterogeneity, only
the exogenous tax shocks and interaction of the shocks with initial state conditions are exogenous
2
instruments.
The main dataset of the project is a large sample of income tax returns, TAXSIM micro data,
provided by the Internal Revenue Service (IRS) and made available to researchers by the National
Bureau of Economic Research (NBER). Combining both TAXSIM micro data and simulation program, we calculate the tax rates and contraction factors for each state and each year. The state level
per capita real GDP growth is created from the U.S. Bureau of Economic Analysis (BEA) data.
We calculate labor market figures using data from the March Current Population Survey (CPS)
Supplement. We collect data on small business activity from Business Dynamics Statistics (BDS),
as made available by U.S. Census Bureau. BEA also provides us with state level consumption data.
Additional datasets include state minimum wage data from Autor et al. (2014), state level expenditure data from U.S. Census Bureau’s State Government Finances, state level schooling from CPS,
state level population growth from BEA, and unionization rates in each state from the State Union
Coverage Density database provided by Hirsch et al. (2001). Our results are robust to a large set
of controls that literature has suggested in prior work.4 The exhaustive specification, the instrumental variables approach that addresses potential concerns regarding endogeneity of tax policy
to economic conditions, data on U.S. states which are relatively more homogenous than countries,
and the relatively long length of the sample period, provide us confidence in our results – that
tax policy’s effects of inequality reduction at different income percentiles relative to the median
household have a heterogenous impact on economic growth.
We find that one percentage point (pp) reduction in income gap between the median household
and the 10th percentile household through taxation increases the GDP growth rate by 0.38 pp.5
The reduction of income gap between the above median households and the median household,
however, has a negative effect on GDP growth. We find that if the income gap between the median
household and the 90th percentile household is reduced by one pp, then GDP growth decreases by
0.47 pp. As discussed later, these results are obtained using an instrumental variables approach,
4 See
Barro (1991), Levine and Renelt (1992), Alesina and Rodrik (1994), Persson and Tabellini (1994), Perotti
(1996), Bénabou (1996) and Sala-I-Martin (1997) among others.
5 The mean contraction factor in the sample is 9.1 pp and the mean state level GDP growth rate is 1.46 pp; a one pp
increase at the mean to 10.1 pp leads the state level GDP growth rate to increase to 1.84 pp.
3
that controls for marginal tax rates, state fixed effects, and other important economic characteristics.
Regarding components that drive this difference in state GDP growth rate, we find that one pp
reduction in income inequality through tax policy between below median and median household
increases the average employment rate by 0.29 pp.6 In contrast, employment rate is reduced by
0.32 pp for each pp increase in contraction factor between above median households and median
households. On the intensive margin, the growth rate of average annual hours worked reduces by
0.18 pp for each pp reduction in income inequality through tax policy between above median and
median household. The contraction factor between below median and median household does not
have a statistically significant effect on the growth rate of hours worked.
The second GDP component we investigate is business activity. We find that one pp increase
in income inequality between above median households compared to median households reduces
growth of the number of small businesses by 0.28 pp.7 Reduction of income inequality between
below median households and median households encourages business activity as one pp reduction
in below median household income inequality with respect to median households increases growth
rate of the number of small business by 0.25 pp.
Finally, one pp increase in contraction factor between below median income households and
median income households increases per capita consumption growth by 0.43 pp. This result shows
that tax policy to reduce inequality has a demand side effect as well.8 We also find that the sen6 Our
paper does not study the impact of specific programs on particular population groups. Meyer and Rosenbaum
(2000) document the magnitude and timing of various social and tax policy changes in recent years that have encouraged work by single mothers, and provide causal evidence of tax effects on employment. Meyer and Rosenbaum
(2001) show that a large share of the increase in work by single mothers during 1984–1996 can be attributed to the
Earned Income Tax Credit (EITC) and other tax changes, with smaller shares for welfare benefit cuts, welfare waivers,
training programs and child care programs. Eissa and Hoynes (2004) study the impact of EITC on labor market participation of married couples, and finds that EITC is reducing labor supply of married women, while increasing that
of married men. Michalopoulos et al. (2005) shows that, in a social experiment setting, financial incentives increased
full-time employment, earnings, and income. Eissa and Hoynes (2006) and Eissa et al. (2008) find that labor supply
responds to EITC, specially on the extensive margin.
7 Aghion et al. (2015) find causality from innovation to top income inequality in the U.S. over the past decades. We
focus only on small business establishments in this paper because we study the impact of personal income taxes, and
many such businesses file taxes at the personal income tax rates using the S corporation structure. See http://www.
irs.gov/Businesses/Small-Businesses-&-Self-Employed/S-Corporations for more details regarding S
corporation status.
8 Meyer and Sullivan (2004) examine the consumption patterns of single mothers and their families from 1984–
2000, and find that material conditions of single mothers have improved slightly due to tax and welfare programs. We
4
sitivity of consumption of durable goods to tax policy is higher (almost three times) than that of
non-durable goods and services, which is intuitive.
Our results show that reduction of income inequality between low income households and
median income households through tax policy supports economic growth. However, we also document that reduction in income gap for above median households with respect to median households
through taxation hurts economic growth. These results support the incentives based argument as
formalized by Mirrlees (1971), Okun (1975) and Becker (2011) and also support the arguments
that taxation can have positive effects if it is used to provide social insurance for the low income
households (see Bénabou (2000), Saint-Paul and Verdier (1993, 1997)). Becker (2011) has argued
that “good inequality” motivates individuals to exert much effort, including creative effort, whereas
“bad inequality” reduces efficiency, productivity, and utility. As far as we know, this asymmetric
effect of redistributive tax policy along the income distribution has not been shown empirically
before this paper.
Our results contribute to the literature on tax policy and economic growth. Theoretical predictions regarding impact of taxes on economic growth are mixed.9 Thus, the question is primarily
an empirical one. Empirical literature has investigated the effects of taxation on economic growth
within U.S., across U.S. states, and across countries. Using U.S. post-WWII data, recent studies
find that a positive change in taxes has a negative impact on GDP growth.10 Several studies focus
on state level taxes and economic growth. Based on annual data from 1965 to 1979 for 48 states,
Helms (1985) shows that state and local tax increase is bad for economic growth when the revenue
is used to fund transfer payments and is good for economic growth when the revenue is used to fido not study consumption responses of specific policies for individual population groups.
9 Mirrlees (1971), Okun (1975) and Becker (2011) argue that taxes reduce economic growth by dampening incentives to work and invest. Barro (1990) shows that taxes can be beneficial for economic growth in presence of public
goods, but as government size increases, the benefits are outweighed by the costs of taxation. Bénabou (2000) shows
that taxation can help growth if they finance public investment. Saint-Paul and Verdier (1993, 1997) shows that higher
health and education spending benefits the poor, helping to offset labor and capital market imperfections.
10 Blanchard and Perotti (2002) finds positive tax shocks have negative effects on output in the U.S. from 1947 to
1997. Romer and Romer (2010) find that a tax increase of 1 percent of GDP implies a 3 percent fall in output in the
U.S. economy from 1947 to 2007. Mertens and Ravn (2013) find that a large short run output effects of tax shock and
personal income tax cuts being more effective in creating jobs and stimulating consumption in the short run than cuts
to corporate profit taxes from 1950 to 2006. Barro and Redlick (2011) find a large and significantly negative impact of
an increase in marginal tax rates on U.S. annual economic growth over the time period 1950 to 2006.
5
nance improved public services (such as education, highways, and public health and safety). Reed
(2008) finds that taxes used to fund general expenditure are associated with significant, negative
effects on income growth from 1970 to 1999 over U.S. states. There are also a large number of
studies using cross-country data, which generally find negative effects of tax increase on output.11
Building upon this literature, we show that redistributive policies have heterogenous effects on
households.
Our empirical analysis relies on a large sample of administrative record of actual tax return
data in the U.S. states over three decades. Thus, our analysis suffers less from measurement error
issues that can exist in cross-country data comparisons.12 Furthermore, compared to cross-country
differences, the economic development and institutions are more homogenous across U.S. states.
This allows us to assume that the same underlying economic relationship between GDP growth,
tax policy, and inequality exists across states, which is more defensible than a similar assumption
regarding countries.13
A large literature has also studied the relationship between inequality and economic growth,
and has also provided mixed predictions. Inequality can reduce economic growth through the following three channels. First, political economy theory suggests that greater inequality is conducive
to the adoption of distortionary redistributive tools and growth-retarding policies, which hurt economic growth (See, for example, Alesina and Rodrik (1994), Persson and Tabellini (1994), and
Benhabib and Rustichini (1996)). Second, in presence of financial market imperfections, higher
inequality exaggerates the adverse effects of credit constraints on human capital accumulation, reducing growth (See, for example, Galor and Zeira (1993) and Galor and Moav (2004)). A similar
argument can also be applied to business growth. Third, Murphy et al. (1989) show that a more
equal society with homogenous tastes helps to create large market for domestic manufactures.
11 See
Koester and Kormendi (1989), Easterly and Rebelo (1993), Mendoza et al. (1997), Miller and Russek (1997),
Kneller et al. (1999), Lee and Gordon (2005), Alesina and Ardagna (2010), Gemmell et al. (2011), Arnold et al.
(2011), Ferede and Dahlby (2012), Padovano and Galli (2001), among others.
12 Measurement error can cause estimation bias. For example, if more unequal society underreport their inequality
statistics and also grow slower, cross-country estimates of the impact of inequality on growth may suffer from a
negative bias.
13 This is because the relationship between inequality, tax policies and economic growth may depend on time-varying
developmental stage or political environment of countries.
6
On the other hand, greater inequality might increase growth. Higher inequality provides the
incentives to work harder, invest more and undertake risks to take advantage of high rates of return (See, for example, Mirrlees (1971), Lazear and Rosen (1981), Rebelo (1991), Heckman et al.
(1998) and Guvenen et al. (2013)). Higher inequality can also foster aggregate savings and therefore capital accumulation, because the rich have a lower propensity to consume (See Kaldor (1956)
and Bourguignon (1981)). Our results show that both sets of predictions above may be at work simultaneously.
Our results have important implications for tax policy. Kuznets (1955) conjectured that inequality increases in the early stages of economic development for a country (due to industrialization and
urbanization). As industries attract a larger fraction of the labor force, inequality starts decreasing.
As observed by Aghion and Williamson (1998), up to the 1970s, the prediction of Kuznets (1955)
was corroborated by data. However, in recent times, wage inequality between and within groups
of workers has been increasing.14 These evidence provide support for action by policy makers to
reduce income inequality.15 Our results demonstrate that reduction of income inequality between
all groups of income may not have similar effects. When income inequality is reduced between
above median households and median households, economic growth may decrease. Our results do
not say what the optimal tax rate at various levels should be.16 We just document the asymmetric
nature of redistributive tax policies on economic growth, and argue that policymakers should not
assume that reduction of income inequality would translate into economic growth, as the opposite
occurs in some cases.
The rest of the paper is structured as follows: Section I introduces a measure that captures
the reduction in income distribution through tax policy. Section II discusses the framework of the
analysis. Section III describes the data. Section IV describes the results. Section V discusses
14 Katz and Murphy (1992) document increasing wage inequality in recent years,
and show that rapid secular growth
in the demand for more-educated workers, “more-skilled” workers, and females appears to be the driving force behind
observed changes in the wage structure. Juhn et al. (1993) find that the trend towards increased wage inequality is
apparent within narrowly defined education and labor market experience groups as well. Piketty and Saez (2003) show
that top shares of income and wages in the United States display a U-shaped pattern over the 20th century.
15 Blundell et al. (2008) show that such redistributive tax policies in U.S. have helped reduce consumption inequality,
even in presence of income inequality.
16 See Diamond and Saez (2011) for a survey of the literature on optimal taxation. Recent papers include Conesa
et al. (2009) and Holter et al. (2014) among others.
7
robustness tests, and Section VI concludes.
I
Taxes, Incentives and Contraction Factor
A
Progressive Taxation and Tax Credits
Income inequality reduction through tax policy is obtained through two main mechanisms: progressive taxation, which leads to higher marginal taxes for higher income households, and tax
credits which provide negative tax rates for the lower income households. The source of variation
in taxation between states and within states comes from multiple sources. While federal taxes are
the same for households in nominal terms, irrespective of where they reside in United States, state
income tax schedules vary (i) by state and (ii) within each state over time.17 Further, the actual net
taxes paid by a household depends on (iii) the demographics of the households which also varies
within and between states, and over time. These differences in demographics affect income tax
rates at federal and state level and also affect the tax credits available to each household.
Our data on tax returns is the NBER’s TAXSIM micro data, prepared by the Statistics of Income
Division of the Internal Revenue Service (IRS) for public use. TAXSIM data is a large stratified
random sample of total 3, 544, 410 actual tax returns from the IRS administrative records for each
states and for each years from 1979 to 2008 (except 1982, where total tax liability is not available).
It contains detailed information on Form 1040, such as adjusted gross income, total federal and
state tax liability, and tax credits.18 We use adjusted gross income (AGI) as our measure of pretax income (hereafter referred to as “income”), which is defined by the IRS as total income (line
22, Form 1040) minus statutory adjustments (lines 23 through 36, Form 1040).19 The total tax
17 For state income tax rates over time, please follow the link by The Tax Foundation: http://taxfoundation.
org/article/state-individual-income-tax-rates.
18 The IRS does not identify the state for the returns with above $200, 000 adjusted gross income. NBER reassigns
these records to states, such that the number of those returns by state matched figures provided by the Joint Committee
on Taxation. However, since our top income bracket is the 90th percentile, which does not cross $200, 000 of income
in the sample, this issue is not a concern.
19 Total income is all positive sources of income less negative amounts, including wages and salary, taxable interest
and dividends, net income from a business, etc. Statutory adjustments include educator expenses, certain business
expenses, health savings account deduction, moving expenses, IRA deductions, etc.
8
liability (hereafter “tax”) includes all income tax after credits, self employment tax, and any tax
adjustments from previous years. A detailed description of all the components of tax according to
the IRS is in Section A of the Appendix.
The tax data help show that progressive taxation and tax credits “compress” the income distribution. To illustrate the “compression” effect, we compare the national before-tax income distribution and after-tax income distribution in Figure I. The figure utilizes the full sample of TAXSIM
tax return data for all U.S. states for the years 1979 to 2008, in 2009 U.S. Dollars.20 The mean
pre-tax income (AGI) in 2009 U.S. Dollars is $49, 548, with inequality measured by the standard
deviation of log income of 1.188. The darker region shows that the after tax distribution is shifted
to the left and contracted – it has a lower mean ($42, 508) and smaller standard deviation of log
income (1.139). Measured in terms of reduction of variance of log income, the income inequality
on average is reduced by about 8% through taxation.
The progressive taxation and tax-credit policies, in effect, are moving the after-tax income of
both the lower and upper income households towards the median to reduce inequality. Thus, the
median income household is a natural reference point to measure the impact on inequality reduction through tax policy. In Section B, we measure the extra tax liability for each additional dollar
earned by the lower income and upper income households compared to the reference household
(the median income household) respectively.
B
Contraction Factor
Before we can estimate the impact of reduction in income inequality through tax policy on economic growth, we need to estimate the impact of tax policy on income distribution. In this section,
we propose a simple measure that evaluates the changes in income inequality induced by the progressive tax policy.
Let Incomet (i) denote the average pre-tax income for households in the i percentile in the
national income distribution in year t, and Taxs,t (i) denote the associated total income tax liability
20 Throughout
this paper, all monetary figures are deflated to 2009 USD using the GDP deflator from BEA.
9
in year t and state s. The before-tax income inequality is then measured by the difference between
pre-tax income percentile i and j in a given year t, Incomet (i) − Incomet ( j). Similarly, the aftertax income inequality in year t and state s is given by (Incomet (i) − Taxs,t (i)) − (Incomet ( j) −
Taxs,t ( j)). Using the median income household as the reference point, we define the reduction in
the after-tax income inequality as a fraction of the before-tax income inequality, referred to as the
“contraction factor” Cs,t (i), as follows:
(Incomet (i) − Taxs,t (i)) − (Incomet (50) − Taxs,t (50))
Incomet (i) − Incomet (50)
Taxs,t (i) − Taxs,t (50)
=
Incomet (i) − Incomet (50)
Cs,t (i) ≡ 1 −
(1)
where i denotes national income percentile. In a progressive tax system, Taxs,t (i) − Taxs,t (50) and
Incomet (i) − Incomet (50) share the same sign. Further, as long as taxes are used to reduce income
inequality, Cs,t ∈ [0, 1). In the future section, we suppress the subscript s,t of Cs,t (i) for simplicity.
The contraction factor measures the taxation induced reduction in the income gap between the
income percentile of interest and the median income households. In particular, one percentage
point increase in the contraction factor C(i) is the same as one percentage point reduction in the
after-tax income gap relative to before-tax income gap between the ith and median percentiles.
The contraction factor can also be interpreted as the additional average income tax paid for each
additional dollar earned by a person at the ith income percentile, compared to the median income.
Our variable is different from the average marginal tax rate (See Barro and Redlick (2011)) that
affects an individual’s decision to earn an additional dollar given her present income and income
tax rate. Barro (1990) and Barro and Redlick (2011) among others, have discussed the importance
of marginal tax rates for economic growth. In contrast, contraction factor aims to capture the
impact of tax policy induced reduction in income inequality, with respect to the median household
as the reference household, on economic growth. Our framework for analysis considers the impact
of contraction factor for above median households and below median households separately, and
also controls for changes in marginal tax rate over time for the reference household. Additional
discussion of the framework of the analysis, including the empirical specification, instrumental
10
variables and system GMM approach, is in Section II.
Our main analysis will rely on two contraction factors: C(90), that measures the effects of taxation on after-tax income gap reduction between 90th percentile household (high income household) and the median household; and C(10) which evaluates the reduction of after-tax income gap
through taxation between the median household and the 10th percentile household (low income
household). The top and bottom panels of Figure C.I graphically demonstrate an increase in contraction factors C(90) and C(10) respectively. In our robustness check section (Section V), we also
show that our analysis yields similar results if we use different thresholds for above median and
below median contraction factors such as C(80) and C(20).
We use the TAXSIM tax return data to construct contraction factors at different income percentiles for each state and for each year from 1979 to 2008.21 In a given year, using national
income distribution, we create a 10 percentile income bracket centered around the national pre-tax
income percentile i. For each state, we then calculate the state-level average tax liabilities associated with the national income percentile i by averaging all tax liabilities associated with incomes
that fall within the specified 10 percentile national income band.22 Similarly, for each state we also
calculate the average income that are within the 10 percentile national income bracket. Finally, we
calculate contraction factors using Equation 1.
The thought experiment here is to take a group of households that are representative at the
national income distribution level, and assign them to different states, imposing the state specific
tax burden. Therefore the measured contraction factor in a given year captures the effects of statelevel variation in tax policy to reduce income inequality. By fixing the income distribution across
states in a given year, we also reduce the concern of geographic mobility of labor force where, for
example, a 90th percentile person from a relatively poorer state moves to a neighboring relatively
21 Data
from 1982 is not included as tax liability is not available in the microdata. We exclude Washington D.C.
because it is not a state. We also impose a sample size restriction, dropping any state-year point if that state does not
have at least 500 observations in that year. Lastly, due to small sample size and large differences between moments of
TAXSIM data and IRS full SOI sample, we also exclude Alaska from our analysis. Table B.I reports the availability
of data in our selected sample from TAXSIM.
22 For example, let us consider creating the median income for each state in a given year. We first calculate the 45th
percentile and 55th percentile of the national income distribution as the lower and upper bound of the 10 percentile
band around the median. Then, within each state, we average the adjusted gross income and total tax liability of all
returns that fall between the 45th and 55th percentile of the national income distribution.
11
richer state, moving into a lower income percentile in the process. Using a national pre-tax income
distribution allows us to isolate the impact of the variation in tax burden attributed to the changes
in the tax policies and demographic distribution in each state over time, from confounding effects
such as labor movement and state income distribution differences. As shown in our robustness
check section (Section V), the alternative approach of using state level income distribution as the
starting point for contraction factor calculation also yields similar results.
Our identification strategy requires variation in contraction factors over time and across states.
Figure II shows the distribution of contraction factors in our analysis across states for the sample
period. Figure III plots the standard deviations of contraction factors for each state.23 Table B.II in
the Appendix summarizes the average one period lagged contraction factors as well as average per
capita annual GDP per capita growth rates for the 49 states in our analysis for the sample period
of 1980–2009. The figures and table suggest significant variation in contraction factors over time
and across states.
Table B.III in the Appendix reports correlation between state level Gini coefficient in a given
year with the contraction factors C(10) and C(90) in the state in that year. As expected, a higher
level of income inequality measured by Gini correlates with less contraction. We also note that
the Gini coefficient correlates more strongly with the ratio of income of 90th and 50th percentile
households, than with the ratio of 50th and 10th percentile households. This is intuitive because
of the positively skewed income distribution. This observation provides additional motivation
for using contraction factors which allow distinguishing the impact of above and below median
households on the economy.
II
Framework of Analysis
This section discusses our empirical specification and estimation strategy.
23 Figure
C.II in the Appendix plots the levels of contraction factors for each state averaged over the same time
period.
12
A
Empirical Specification
In our paper, we focus on the impact of reduction in inequality induced by tax policy on economic growth. As discussed before, this effect where households compare themselves with other
households is different from the marginal tax rate that affects an individual’s decision to earn an additional dollar given her present income and income tax rate (See, for example, Barro and Redlick
(2011)). Furthermore, we distinguish the inequality reduction through taxation between the upper and lower ends of the income distribution, and allow their impact on economic growth to be
different. In particular, the reduction of income inequality through taxation in lower and upper
income distribution are measured by the below median and above median contraction factors measures respectively. This is because households who benefit from income distribution compression
(lower than median income households) may respond differently than households that are adverse
impacted by income distribution compression (upper income households).
We estimate the effects of below median and above median contraction factors on state-level
annual per capita economic growth, using the following specification:
log GDPs,t − log GDPs,t−1 =κ1 · logCs,t−1 (10) + κ2 · logCs,t−1 (90)
+ γ1 · (MT Rs,t−1 (50) − MT Rs,t−2 (50)) + γ2 · MT Rs,t−1 (50)
+ h1 · log
Income(90)
Income(50)
+ h2 · log
Income(10)
Income(50)
+ α · log GDPs,t−1 + Xs,t−1 β + δs + εs,t−1
(2)
where Cs,t−1 (90) is previous years’ contraction factor between the 90th percentile household and
the median household; we use it as a measure of income inequality reduction between high income households and median income households. Cs,t−1 (10) is previous year’s contraction factor
between the 10th income percentile household and the median household; it represents the income
inequality reduction between median income households and low income households. Xs,t−1 is a
vector of additional controls and δs denotes state fixed effects.
Banerjee and Duflo (2003) show that an empirical specification that includes both the level
13
and change of the inequality measure is consistent with both the endogenous political economy argument and imperfect financial market mechanisms. Hence, we include log Income(90)
Income(50) and
log Income(50)
Income(10) to capture the level of income inequality between the 90th percentile income household and median household, and median household and 10th percentile household respectively.
The change in income inequality is captured by the contraction factors themselves.
As discussed before, previous literature has also shown that changes in marginal tax rates have
important implications on economic growth because they affect households’ current choices on
employment and consumption compared to the previous period.24 As marginal tax rates increase,
incentives to work decline for the same household irrespective of the tax rate of other households.
Therefore, following Barro and Redlick (2011), we include both levels and changes in median
Marginal Tax Rates (MT R(50)) in our estimation equation. Specifically, for each state s we control for changes in marginal tax rate at the median income level between year t − 1 and t − 2
(MT Rs,t−1 (50) − MT Rs,t−2 (50)), and marginal tax rate at the median income level in year t − 1.
Lastly, Mankiw et al. (1992) show that a neoclassical growth model (see Solow (1956)) augmented with accumulation of human capital as well as physical capital yields an empirical specification where GDP growth rate log GDPs,t − log GDPs,t−1 depends on level of GDP in the previous
period (i.e. log GDPs,t−1 ), accumulated human capital level measured by average schooling level
(log Schools,t−1 ), and population growth (ns,t−1 ). Within the framework of neoclassical growth
model, (1 + α) in Equation 2 measures the rate of convergence in economic growth. When the
economic growth is around the steady state, we expect α to be a small negative number (which is
what we find). Following Mankiw et al. (1992), we include state specific human capital level measured by average schooling level (log Schools,t−1 ) and state population growth (ns,t−1 ) into Xs,t−1
which represents the set of controls. We also control the state government per capita expenditure
gI
s,t−1
on goods and services (log GDP
), because Helms (1985) finds that state expenditure on public
s,t−1
services and investment (such as highways and education) is good for economic growth. Finally,
Card and DiNardo (2002) argue that the changes in non-market factors such as changes in min24 Literature
includes, but is not limited to Mirrlees (1971), Barro (1990), Barro (1991), Alesina and Rodrik (1994)
and Barro and Redlick (2011).
14
imum wage and declining unionization can explain the changes in inequality of wages. Hence,
we also include both these factors in the growth regression to account for their effects on income
inequality.
In sum, Xs,t−1 includes a constant term, state level human capital measured by average schooling levels (log Schools,t−1 ), state population growth (ns,t−1 ), changes in effective state level minimin ), and changes in the fraction of labor force covered by unions (∆Union
mum wage (∆Ws,t−1
s,t−1 )
(see Table I, Panel B for details).
B
Estimation Strategy
Our key parameters of interest are the coefficients of contraction factors, κ1 and κ2 , in Equation 2.
We first report the estimation results using Ordinary Least Squares (OLS) with state fixed effects
to address unobserved heterogeneity among states.
A potential concern with OLS is that tax policy may be an endogenous response to the economic conditions. To address this potential endogeneity concern, we use a set of exogenous instrument variables and estimate our model using a generalized method of moments approach developed
by Blundell and Bond (1998). The exogenous instrument variables are the tax shocks at the national level, and their interactions with state-specific initial income inequality and initial propensity
towards charity.
We use the exogenous tax liability shocks narratively identified by Romer and Romer (2009,
2010) and later refined by Mertens and Ravn (2013) to form exogenous instruments for changes
in our contraction factors and marginal tax rates (see the appendix in Mertens and Ravn (2013)
for more details). Romer and Romer (2009) identified a series of tax liability changes that are exogenous to economic growth in the U.S. from 1945 to 2007. Using a narrative approach based on
congressional reports and other government administrative data, Romer and Romer (2009) classify
the tax liability changes as exogenous if the motivation for the legislative action is either arising
from inherited deficit or from ideological concerns.25 Mertens and Ravn (2013) further extend the
25 Romer and Romer (2009) classify every significant tax bills into one of the four categories based on the underlying
motivation for the tax change: responding to a current or planned change in government spending, offsetting other
15
analysis by distinguishing between changes in personal and corporate income tax liability, and by
distinguishing between unanticipated and anticipated tax changes on the basis of the implementation lag.
These tax shocks, identified by Romer and Romer (2009) and refined by Mertens and Ravn
(2013), are exogenous to the current state of the economy, because they relate to unanticipated tax
liability changes that are not a response to the growth prospects of the economy.26 Figure C.III
in the Appendix depicts personal income tax shocks given by Mertens and Ravn (2013) together
with contraction factors averaged across states from 1979 to 2007.27 During this time period,
the largest exogenous change in personal income taxes relates to the Jobs and Growth Tax Relief
Reconciliation Act of 2003, which includes across-the-board reductions in marginal tax rates as
well as increases in child credit. The largest exogenous increase in personal income taxes relates
to Omnibus Budget Reconciliation Act of 1993, which increased income taxes, mostly for higher
earners.
The impact of the exogenous tax shocks at the national level varies based on conditions present
at the state level. We focus on two initial conditions which are relevant to contraction factors: initial state level inequality measures (as measured by 90th percentile/50th percentile and 50th/10th
percentile log income ratio in 1979), and initial attitude towards charity (measured by the share of
charity to income ratio in 1979).28 The intuition is that initial inequality in a state affects tax policy, and that if households in a state are interested in charity, then that affects their attitude towards
using tax policy to reduce inequality. The interaction of the tax shocks with these state specific
influences on economic activity, reducing an inherited budget deficit, and attempting to increase long-run growth.
Romer and Romer (2009) classify the last two types of tax changes as exogenous to the current state of the economy
in the sense that they are not a response to the growth prospects of the economy.
26 Furthermore, in practice, these tax liabilities changes are often related to the changes in progressivity of the tax
schedule and thus correlate with changes in contraction factors as well as marginal tax rates. In particular, Barro
and Redlick (2011) use the changes in exogenous tax liabilities identified by Romer and Romer (2009) to form an
instrument for changes in the marginal tax rate in the GDP growth regression analysis.
27 In particular, Mertens and Ravn (2013) create the personal income tax shock as the narratively identified exogenous personal income liability change divided by previous personal taxable income, z pi ; the corporate income tax
shock is defined as narratively identified exogenous corporate income tax liability changes scaled by previous period
corporate profits, zci . Mertens and Ravn (2013) provide both quarterly and annual data; we choose the annual level
data for our analysis.
28 To develop a measure of attitude towards redistribution, we collect total charitable contributions, cash and assets,
as recorded on tax returns from the TAXSIM data. We scale the total charitable contributions by the total income in
the state.
16
initial conditions satisfies the exclusion restriction because in presence of state-fixed effects, only
the time varying effect of the exogenous tax shocks interacted with initial state conditions (which
are time invariant) is the instrument. Detailed discussion regarding the relevance of these exogenous instruments to our contraction factors is in Section IV.A.2 where we discuss empirical results.
Table B.VI in the Appendix reports the results.
In addition to endogeneity of tax policy to state level economic growth, one may be concerned
about the possibility of Nickell bias in Equation 2 given a small T = 30 years and large N = 49
states. Hence, we implement our estimation using the system GMM method developed by Blundell
and Bond (1998). The system GMM approach is an improvement upon the difference GMM
proposed by Arellano and Bond (1991). Such IV GMM methods have become increasingly popular
in the empirical literature on inequality and economic growth (See, for example, Forbes (2000),
Ostry et al. (2014), Cingano (2014)).
Besides exogenous instrument variables, system GMM also utilizes lagged values of control
variables as internal instrumental variables in the estimation. Specifically, for our internal instruments, we use lagged dependent variable and predetermined control variables at t − 3 and t − 4.29
Our estimation results are robust to using more lags as internal instruments. In our estimation table,
we also report the Arellano-Bond test for autocorrelation, as well as the test for over-identification
and validity of instrument variables, all of which provide confidence in our results.
III
A
Data
Data Description
We utilize multiple data sources to construct our state-year level panel dataset. Data include information on GDP growth, income distribution, taxes, and other economic control variables. The state
29 As
shown in our specification, the controls for our primary estimation are lagged one period: inequality levels
relating the 50th and 10th percentile incomes and 90th and 50th percentile incomes, log of GDP per capita, log of the
average years of schooling, the change in state government expenditure, and labor market conditions, such as change
in effective minimum wage and unionization rates. We do not use second order lags, i.e. Xs,t−2 , as internal instruments
because we are concerned about the possible first order correlation of the error terms. However, our results are robust
if we use Xs,t−2 as internal instruments.
17
level GDP per capita growth rate is constructed from the U.S. Department of Commerce Bureau of
Economic Analysis (BEA). As discussed in Section I, we use TAXSIM data to obtain information
on contraction factors, income percentiles, and the corresponding tax liability and marginal tax
rates in each state and each year. We also utilize the TAXSIM data to gather data on initial income
inequality and charitable contributions in 1979 to create variables on attitudes towards inequality
and redistribution.
Additional datasets include (i) U.S. Census Bureau for state government finances, (ii) Mertens
and Ravn (2013) for narratively identified personal and corporate income tax shocks exogenous to
economic growth, (iii) Current Population Survey (CPS) data for state level schooling and labor
market variables, (iv) unionization rates from the State Union Coverage Density database (Hirsch
et al. (2001)), (v) minimum wage information from Autor et al. (2014), (vi) the Business Dynamics
Statistics (BDS) database for information on small businesses, and (vii) the BEA for personal
consumption expenditures and population growth by state. Table I Panel A, summarizes all the
dependent variables in our analysis and their data sources. Panel B of Table I lists our explanatory
variables and their sources.
The exogenous instruments have already been discussed in Section II along with the estimation
strategy, below we discuss dependent and explanatory variables.
A.1
Dependent Variables
GDP Growth
The primary dependent variable in our analysis is the state level log change in real GDP per capita
(log GDPs,t − log GDPs,t−1 ). The state level real GDP is the state level real chained GDP in 2009
dollars from BEA.30 BEA also provides the state level population estimates for each year, which
we use to create GDP per capita, and consequently the annual log change in GDP per capita.
30 We collect real chained GDP in 2009 dollars for 1997 to 2009, and real chained GDP in 1997 dollars from 1987
to 1997 from BEA. We use available changes in quantity indices (from BEA) to extend our state GDP series in 1997
dollars backwards for the period of 1977 to 1986. We then convert the pre-1997 real chained GDP series from 1997
dollars to 2009 chained dollars by using the ratio of 2009 dollar GDP to 1997 dollar GDP in 1997, where both series
are available.
18
Labor Supply
We also investigate how contraction factors impact components of GDP. In particular, we look into
both the extensive and intensive margins of the labor supply. Our data on labor supply comes from
March CPS for individuals aged 18 to 64. For the extensive margin, we consider an individual to
be employed in year t if she works at least 26 weeks in a year and at least 20 hours per week. The
employment rate (Ẽs,t ) in each state is calculated as the fraction of employed individuals among
the population aged 18 to 64. Furthermore, to analyze the intensive margin, we also calculate the
average annual hours worked among those who are employed in each state (Hrss,t ). For each of
these two variables we construct state specific change variables from the previous year (∆Ẽs,t =
Ẽs,t − Ẽs,t−1 , ∆ log Hrss,t = log Hrss,t − log Hrss,t−1 ).
Small Business Activity
The second component of GDP that we consider is small business activity. We use the Business
Dynamics Statistics (BDS) database to collect state level data on small businesses, which are referred to as establishments. An establishment is a fixed physical location where economic activity
occurs. We focus our attention on the number of establishments (BDS variable: estabs) of size
5 to 19 and of size 5 to 49. We then investigate the state level growth rate of the number of
establishments in each of the two size buckets (∆ log estabss,t = log estabss,t − log estabss,t−1 ).
Consumption
The last GDP component we consider is personal consumption expenditures per capita (PCE).
BEA provides data on nominal consumption for several categories for each state from 1997 to
2009. We deflate the nominal consumption by the GDP deflator and use the same population
denominator from real GDP per capita (both available from BEA) to calculate real PCE per capita
for total consumption, consumption of durable goods, and consumption of nondurable goods and
services. Consumption growth rates are measured by the changes of log consumption.
19
A.2
Explanatory Variables
Our main explanatory variables in are two specifications are one period lagged log contraction factors. We focus on the effect of reducing income inequality between the 10th percentile household
and the median household (logCs,t−1 (10)) and the effect of reducing income inequality between
the 90th percentile household and the median household (logCs,t−1 (90)) on our various dependent
variables. In addition, we add several control variables based on previous literature.
Marginal Tax Rates
Using the TAXSIM micro tax return data as an input, we utilize NBER’s TAXSIM simulation program to compute overall marginal tax rates (including federal, state, and FICA tax) for each return,
and then calculate the median household’s marginal tax rate MT Rs,t−1 (50).31 Furthermore, when
calculating the changes in marginal tax rate, ∆MT Rs,t−1 (50), we use the t − 2 national income
distribution to calculate marginal tax rates for both t − 1 and t − 2 following Barro and Redlick
(2011). This strategy eliminates any shifts in income distribution that might move a household
into a different tax bracket, and helps ensure that the changes in marginal tax rates are specifically
due to changes in tax policies.
State Government Spending
Data on state and local government spending is available from U.S. Census Bureau’s State Government Finances. Following Barro and Redlick (2011), we consider only the government spending
on goods and services, excluding transfers or interest payments. Specifically, government spending on goods and services includes expenditures on education, highways, police protection, and
correction. We deflate the state government spending on goods and services by the GDP deflator
and create state government spending per capita (gIs,t ).32 Government spending per capita enters
gI
s,t−1
).
the control variables in our estimation as a log fraction of state GDP per capita (log GDP
s,t−1
31 We
utilize the TAXSIM model’s “wages” option to calculate marginal tax rates.
government expenditure include the following detailed categories: higher education, elementary and secondary education, educational administrative services, libraries, highways, police protection, traffic safety, and correction.
32 The
20
State Inequality Measures
To control for the previous year’s level of inequality within each state, we use the TAXSIM state
income distribution in calculating two ratios measuring the 50th percentile income in comparison
(50)
Income
to the 10th percentile income ( Incomes,t−1 (10) ), and the 90th percentile income in comparison to
s,t−1
Income
(90)
the 50th percentile income ( Incomes,t−1 (50) ). In our specification we use the logs of these ratios
s,t−1
Income
(50)
Income
(90)
(log Incomes,t−1 (10) , log Incomes,t−1 (50) ). Table B.IV summarizes the state fiscal and inequality controls
s,t−1
s,t−1
for the 49 states in our analysis.
State Human Capital
We also control for the level of schooling in each state as a measure of the human capital stock.
Specifically, we use CPS data to calculate the average years of schooling (with the maximum value
being 17, signifying more than 4 years of college) among the 18 to 64 year old population in each
state. Schooling then enters our specification as a one year lagged log value (log Schools,t−1 ).
State Population Growth
Using the population information from BEA used to calculate per capita GDP, we create a population growth variable, ns,t = log Pops,t − log Pops,t−1 . Specifically, it enters our estimation as a one
year lag.
State Labor Market Institutions
Changes in labor market institutions such as minimum wages and unionization rate are also immin , is obtained from
portant factors in impacting GDP growth. The state minimum wage data, Ws,t
Autor et al. (2014). If the state specified minimum wage is lower than federal minimum wage, we
use the federal minimum wage as the effective state minimum wage. The effective state minimum
wage is then deflated using GDP deflator, and it enters our controls as the annual lagged growth
min =
rate of the effective state minimum wage, from year t − 2 to t − 1 (∆Ws,t−1
21
min −W min
Ws,t−1
s,t−2
).
min
Ws,t−2
The unionization rates (Unions,t ) are the fractions of nonagricultural wage and salary workers
covered by a collective bargaining agreement and are available from the State Union Coverage
Density database (Hirsch et al. (2001)). Unionization enters our controls as the lagged change in
unionization rates (∆Unions,t−1 = Unions,t−1 −Unions,t−2 ). Table B.V summarizes the remaining
controls for the 49 states that enter our IV model.
B
Summary Statistics
Table II provides summary statistics for all of the variables used in this paper. All statistics shown
are pooled across all states and years from 1980 to 2009 for dependent variables and 1979 to 2008
for independent variables, as we measure the effect of our lagged regressors on our variables of
interest. All the nominal figures are deflated to 2009 dollars using GDP deflator.
Panel A reports summary statistics for all the dependent variables in our analysis. The equal
weighted average real GDP growth from 1980 to 2009 in U.S. states is 1.5% with a median growth
rate of 1.7%. The equal weighted pooled standard deviation of growth rate is significant at 2.8%.
Regarding small business activity variables, the number of establishments of size 5 to 19 grow at
a 1.47% rate and establishments of size 5 to 49 grow at a 1.54% rate. Our calculations on labor
supply show that, on average, 70.1% of the working age population are employed, with an average
annual change in employment rate of −0.06%. We also note that the employed population works
on average 2, 073 hours per year, with an average annual change of −0.06%. Lastly, BEA data
shows that the average real total personal consumption expenditure (PCE) per capita is $30, 217
in 2009 U.S. Dollars. The growth rate of real PCE per capita from 1998 to 2009 was 1.5%. The
average real PCE per capita on durable goods is $3, 871 and the annual growth rate is −0.31%. On
average, real PCE on nondurable goods and services per capita is $26, 346 in 2009 U.S. Dollars,
and the average annual growth rate is 1.7%.
Panel B reports summary statistics pooled across all states and years from 1980 to 2009 for
explanatory variables, controls, and instruments. These variables enter our estimation as lagged
measures, and the subscript denotes the applied lag. The contraction factor between median and
22
10th percentile household is 9%, and that between 90th and median household is almost double
of that at 17%. Thus, the marginal tax rate almost doubles on the additional income between the
two groups. The other key explanatory variable we utilize is the lagged annual change in median
marginal tax rate, which has an average of 0.11%, and ranges from a minimum of −5% to a
maximum of 4.9% across states.
We also include a large number of controls identified in the literature as possible determinants
of GDP growth rate. This is in addition to state fixed effects, which are included in our OLS and
instrumental variables specification. Along with the change in median marginal tax rates, we also
control for the lagged median marginal tax rate, which is an average of 35.4%. On average, the
90th percentile income is 3.2 times the median income, and the median income is on average 5.9
times the 10th percentile income. We note that states on average spend $1, 723 per capita on goods
and services such as education, highways, police protection, and correction, and the average state
spending as a portion of GDP is −3.1 in logs. The average population growth is 1%. On average,
the effective state minimum wage is $6.18 and grows at a 0.1% annual rate.33 Lastly the average
unionization rate is 16.8%, and the annual change in unionization is on average −0.4%.
Our system GMM analysis with IV will employ exogenous tax shocks to personal and corporate income as identified by Mertens and Ravn (2013), as well as interaction terms with charitable
contributions and inequality levels in 1979. The average personal income tax liability shock is 0.06% of the previous period personal taxable income, with a minimum of −1.1% and a maximum
of 0.44%. The average corporate income tax liability shock is −0.04% of the previous period corporate profits, with a minimum of −3.28% and a maximum of 7.38%. We interact these tax shocks
with the charitable donations in 1979, which were on average 1.54% of income. Furthermore, we
interact tax shocks with the inequality levels of 1979, where the 90th percentile income was 2.7
times the median income, and the median income was 5.5 times the 10th percentile income.
33 For
the states where the minimum wage is lower than federal minimum wage, the federal minimum wage applies,
thus the effective state minimum wage has a minimum of the federal minimum wage.
23
IV
Empirical Results
This section first conducts an estimation of the relationship between reduction of income inequality
through tax policy and economic growth. For this, we use ordinary least squares (OLS) estimation
with state fixed effects, and instrumental variables approach with the system GMM estimator (IV
GMM) to gain additional confidence in our results. Then, we explore three important channels
through which reduction of income inequality through tax policy affects economic growth: (i)
Employment, (ii) Business activity, and (iii) Consumption.
A
Income inequality, tax policy and economic growth
Table III reports the results of the impact of contraction factor on economic growth using both OLS
and IV GMM approaches.
A.1
Ordinary Least Squares Approach
We first discuss OLS results, and then the IV GMM results. Column (1) does not include any
controls other than the below median contraction factor, and Column (2) adds the above median
contraction factor. Column (3) includes median marginal tax rate variables and initial condition
controls from 1979. Column (4) removes the initial condition controls, but adds state fixed effects.
Column (5) is our most exhaustive OLS specification adding dynamic controls denoted by Xs,t−1
above in Equation 2 along with state fixed effects.
Column (1) shows that for one percent decrease in income inequality at the mean, between the
10th percentile household and the median household, GDP per capita increases by 0.013 pp. If
we scale up the numbers to 1 pp decrease in income inequality at the mean, i.e. increase C(10) to
10.14 pp, then according to Column (1), there is a corresponding change of 0.14 pp in the growth
rate of GDP per capita.34 This is a statistically and economically significant result given that the
average real GDP per capita growth rate in our sample is 1.5 pp, and hence a 1 pp change in C(10)
34 Since the mean value of contraction factor C(10) is 9.14 pp, one percent at the mean is 0.0914 pp. We can
calculate the GDP per capita increase in growth rate as approximately 0.013 × 1/0.0914 = 0.14.
24
increases the GDP per capita growth rate to 1.64 pp.
When we add the above median contraction factor in Column (2) this effect strengthens, as a
one percent decrease in income inequality between the 10th percentile household and the median
household results in a 0.026 pp increase in GDP growth. At the same time, by noting the coefficient
of the contraction factor C(90), we find that if we reduce income inequality between the 90th
percentile household and the median household, by increasing taxes by one percent on the 90th
percentile household, GDP growth rate declines by 0.034 pp. These results become stronger as
we add marginal tax rate variables and either initial condition controls in Column (3) or state fixed
effects in Column (4). We note that one pp increase in median marginal tax rate from year t − 2 to
t − 1 (as measured on t − 2 income distribution) correlates with a 0.68 pp decrease in average real
GDP per capita growth rate in the presence of state fixed effects. State fixed effects help control
for heterogeneity between states, both observed and unobserved.
Following literature, Column (5) includes additional lagged inequality, human capital, fiscal,
and labor institution variables that may also affect GDP growth rates in addition to state fixed effects. In this exhaustive specification, our results remain statistically and economically significant
and similar to previous columns. Specifically, a one percent higher C(90) is related to a 0.082 pp
lower GDP growth rate, while a higher C(10) is associated with a 0.022 pp higher GDP growth
rate. As before, in pp terms, Column (5) implies an increase of 1 pp C(10) is associated with 0.24
pp increase in the GDP growth rate. Column (5) also suggests that 1 pp change in C(90) at the
mean of 17.21 pp in the sample to 18.21 pp is associated with 0.48 pp decrease in the GDP growth
rate.35
We find that one percent above the mean GDP in the last year predicts an 0.064 pp below the
mean real GDP per capita growth rate in this year. We also note that one pp increase in minimum
wage correlates with 0.069 pp decline in per capita GDP growth rate. Higher population growth is
also associated with a higher GDP growth rate. Higher state government spending on goods and
services in the previous year, and change in unionization from year t − 2 to t − 1 are insignificantly
related to GDP growth rate after controlling for state fixed effects.
35 As before, we can calculate the GDP per capita decrease in growth rate as approximately 0.082×1/0.1721 = 0.48.
25
A.2
Instrumental Variables Approach With System GMM Estimation
The results above regarding the relationship between contraction factor and GDP growth rates,
though suggestive, do not lend themselves to causal interpretation. Even though we have included
an exhaustive set of controls, one may be concerned that an unobservable or omitted variable
which is correlated with the contraction factor and GDP growth rate is driving their correlation.
This concern should be partially assuaged by the presence of lagged GDP growth rate and state
fixed effects, which control for any observed/unobserved heterogeneity between states and years.
However, the concern may be that the omitted or unobserved variable is dynamic and varies by
state in a way not captured by lagged GDP growth rate. Specifically, an important concern maybe
that tax policy driving the contraction factors could be itself endogenously chosen by policymakers
in response to economic conditions that also affect GDP growth rate in the state.
To address these concerns, Column (6) utilizes an IV approach with system GMM with our
most exhaustive specification. In Section II, we have already discussed the estimation strategy and
the instruments. The coefficients on the contraction factors in Column (6) of Table III again show
that contraction factors have a significant impact on per capita economic growth. The economic
magnitudes are comparable to the OLS estimates. In particular, one percent decrease in income
inequality between the 10th percentile household and the median household increases the GDP per
capita growth rate by 0.035 pp (0.38 pp increase in GDP growth rate for 1 pp increase in C(90)). At
the same time, one percent reduction in income inequality between the 90th percentile household
and the median household, by increasing taxes by one percent on the 90th percentile household,
reduces GDP growth rate by 0.081 pp (0.47 pp decrease in GDP growth rate for 1 pp increase in
C(90)).
In all tables including Table III, we conduct two important diagnostic tests for the System
GMM estimator. First, to test for overidentifying restrictions, we report the Hansen J statistic and
the corresponding p-value. The p-value fails to reject the null (the p-value is in fact almost 1),
providing confidence in our choice of instruments.36 Another important diagnostic is the test for
36 Given
the large degree of freedom (approximately 550) because of large number of internal instruments, the Jstatistic is also relatively quite small in all cases, compared to the critical value of χ 2 . J-statistic is approximately 44
26
autocorrelation of the residuals. If a significant autocorrelation is present, the lags of endogenous
variables will not be appropriate instruments for their current values (in this case Xs,t−1 ) in the
System GMM estimator. The results of the test are reported against M3 where 3 represents the
third lag. The p-values of M3 are always above 0.10, comfortably rejecting the null that there is
significant autocorrelation. This provides us confidence that Xs,t−3 and Xs,t−4 are valid internal
instrument variables in the System GMM estimator.37
Table B.VI in the Appendix reports the relevance of our exogenous instruments with respect to
contraction factors (see the discussion in Section II.B). The first three columns report the relation
between below median contraction factor and our instruments, and the last three columns repeat
the exercise for the above median contraction factor. Columns (1) and (4) do not include state fixed
effects, to analyze the effect of cross sectional variations between states on the contraction factors.
All other columns include state fixed effects.
Columns (1) and (4) show that positive shocks to personal income tax rates are positively
associated with contraction factors. This is because higher tax rates lead to decrease in post-tax
income inequality relative to pre-tax income inequality. We also note from Columns (1) and (4) that
higher corporate income tax rates correlate with higher C(10), although this result does not survive
when state fixed effects are included in Column (3). Between states, higher levels of inequality as
measured by ratio of income of median household to 10th percentile households (in the year 1979)
are associated with higher C(10). However, care must be taken to interpret such associations given
that Columns (1) and (4) do not have state fixed effects. We also note that states with higher charity
have lower contraction factors, possibly suggesting a substitution between the public support vs
private charity. Lack of state fixed effects remain a caveat.
In the System GMM approach with IV, we include state fixed effects to eliminate the impact of
initial conditions. Hence, all remaining columns report results with state fixed effects. We include
interaction between exogenous tax shocks and inequality levels in 1979 and aggregate fraction of
income in a state donated to charity in year 1979 as additional instruments. The argument is that
in Table III, where the critical value of χ 2 even at p = 0.995 is close to 468.
37 We do not use second order lags, i.e. X
s,t−2 , as internal instruments because we are concerned about the possible
first order correlation of the error terms. However, our results are robust if we use Xs,t−2 as internal instruments.
27
tax rate shocks affect states differently based on level of initial inequality and charity level.
After including state fixed effects, we find that variation in below median contraction factor
is explained by personal income taxes and interactions; and variation in C(90) is explained by
corporate income tax shocks and interactions. Column (2) shows that in presence of state fixed
effects, personal income tax shocks remain positively associated with C(10). Interaction between
initial below median inequality and personal tax shocks are negatively related to C(10). This
suggests that states with higher initial income inequality may be partially undoing the redistributive
effects of federal tax shocks through state level policies. Similarly, Column (6) suggests that the
corporate income taxes and interaction with initial income inequality remain relevant for above
median income households i.e. C(90). This is intuitive given that above median households own
equity in firms more often.
However, Column (3) shows that in presence of state fixed effects, corporate tax shocks and
related interactions are unable to explain variation in C(10). This is also reasonable given less
ownership of equity in firms by below median income households. Similarly, Column (5) shows
that personal tax shocks and interactions are unable to explain variation in C(90). The reported
test statistics also confirm that the instruments are jointly relevant to contraction factors, and satisfy
instrument validity concerns regarding under-identification and weak instruments problem.
B
Components of GDP
Next, we focus on three main components through which reduction of income inequality through
tax policy affect economic growth: (i) Labor supply by households, (ii) Activities of small businesses, and (iii) Consumption.
The intuition is as follows: (i) If the below median contraction factor is higher, it is generally
achieved by providing tax credits to the lower income households. Earned income tax credit, and
other such programs should encourage households at the lower income levels to supply more labor
relative to similar income levels in other states. This should support economic growth. At the same
time, households at higher income level note that their taxes are higher compared to the reference of
28
median households, and this reduces their incentives to supply labor. (ii) Regarding small business
activity, if the tax rate at the higher percentiles of income in a state is higher compared to other
states, then small businesses who file as households in that state will be less encouraged to invest
and grow than in other states, hampering economic growth.38 (iii) Finally, the changes in tax rate
also affect households’ consumption through both the substitution effects and wealth effects.
B.1
Labor Supply
Table IV reports the impact of above and below median contraction factors on our first component, i.e. labor supply. Columns (1) through (3) investigate the extensive margin, and Columns
(4) through (6) investigate the intensive margin of labor supply. Columns (1) and (4) include the
contraction factors, the lagged change in median marginal tax rates, and state fixed effects, while
Columns (2) and (5) show the full OLS specification, and Columns (3) and (6) show the most exhaustive IV GMM specification. The extensive margins (Columns (1) through (3)) look at change
in annual employment rate for all workers aged 18 to 64 in a state, considering an individual employed if she has worked at least 26 weeks and at least 20 hours per week in a year in CPS data.
The intensive margins (Columns (4) through (6)) consider the growth rate of average annual hours
worked by the employed population in each state (See Panel A of Table I for more details).
Column (1) shows that the number of individuals providing labor supply increases by 0.03
pp for each percent reduction in below median income inequality through tax policy C(10). On
the other hand, an equal increase in above median income inequality reduction through tax policy
C(90), reduces labor supply by 0.034 pp. Column (2), under the full OLS specification, shows
that these results remain robust to introduction of full set of controls. One percent reduction in
below median income inequality increases labor supply by 0.021 pp, while an equal reduction in
above median income inequality reduces labor supply by 0.041 pp. Column (3), where we conduct
an instrumental variables approach with system GMM estimator as in Section A, shows similar
economic magnitudes to that obtained from OLS approach. Column (3) shows that 1 pp reduction
38 We
focus on small businesses because identification of impact of tax policy on larger businesses can be complex,
due to multiple locations, transfer pricing and additional concerns.
29
in income inequality between 90th percentile household and median income household achieved
through taxes reduces GDP growth rate by 0.32 pp. Reducing income inequality between the 10th
percentile household and median household, however, causes GDP growth rate to increase by 0.30
pp.
The next three columns of Table IV reports the results for the intensive margin of labor supply,
i.e. the growth rate of average annual hours worked for the employed individuals. Column (4)
shows that annual hours worked growth rate for all workers are reduced by 0.023 pp for each
percent increase in above median contraction factor. The column also shows that if C(10) increases
by one percent, then average hours worked growth rate for all employed workers increases by
0.014 pp. Column (5) adds the full set of controls and shows that annual hours worked growth
rate decrease by 0.033 pp for one percent reduction in above median income inequality through
taxation, and annual hours worked growth rate increases by 0.006 pp for an equal reduction in
below median income inequality. Column (6) conducts the IV GMM analysis, and finds effects of
reducing above and below median inequality factors that are similar in magnitude to effects found
in Columns (4) and (5), providing more confidence in the results.
B.2
Small Business Activity
Table V reports the impact of above and below median contraction factors on our second mechanism – small business activity. We focus on small businesses which are affected by personal
income taxes due to many small businesses filing as S Corporations.39
All columns focus on the growth rate of the number of establishments as the dependent variable.
Columns (1) through (3) focus on businesses of size 5 to 19, and Columns (4) through (6) consider
businesses of size 5 to 49. Columns (1) and (4) include the contraction factors, marginal tax rate
variables, and state fixed effects, Columns (2) and (5) have the full OLS specification with state
fixed effects, and Columns (3) and (6) report the most exhaustive IV specification with system
GMM estimator.
39 Through
the Technical Amendments Act of 1958, small businesses were allowed to file as Subchapter S corporations. The benefit of such a tax structure is that firms can operate as limited liability corporations, without suffering
double taxation on business earnings.
30
We note in Column (1), for establishments with 5 to 19 employees, the above median contraction factor has a negative impact on establishment growth, while the below median contraction
factor has a positive impact on establishment growth. Column (2) reports similar results, which
are corroborated by the system GMM estimator in Column (3). One percent reduction in above
median income inequality results in a 0.049 pp decrease in establishment growth, and an equal reduction in below median income inequality results in a 0.023 pp increase in establishment growth.
In other words, when income inequality between 90th and 50th percentile is reduced through taxes
by 1 pp, growth rate of small businesses declines by 0.28 pp. At the same time, reducing inequality
between 10th and 50th percentile by 1 pp causes growth rate of small businesses to increase by
0.25 pp.
When we consider establishments with 5 to 49 employees, the growth rates remain similar in
sign and magnitude: the above median contraction factor has a negative impact on establishment
growth, while the below median contraction factor has a positive effect of establishment growth.
These results suggest that the incentives of small businesses to grow upto median income increase,
and beyond median income decrease due to tax policy that seeks to bring everyone towards the
median.
B.3
Consumption
Table VI reports the impact of above and below median contraction factors on our final mechanism
– personal consumption growth rates in states. The first two columns consider the impact of inequality reduction through tax policy on total personal consumption. The next two columns focus
on durable goods, and the final two columns focus on personal consumption growth rates of nondurable goods and services. All columns include the full set of controls as before with Columns
(1), (3), and (5) showing OLS results and Columns (2), (4), and (6) showing IV results with system
GMM estimator.
Although Column (1) does not show a significant relationship between the contraction factors
and consumption growth, the system GMM estimator in Column (2) shows a stronger relationship.
We see that decreasing inequality between 10th percentile and median household by one percent
31
through tax policy results in consumption growth rate increasing by 0.04 pp (or 1 pp increase
in C(10) results in 0.44 pp increase). We do not find that consumption is increased by reducing
inequality between above median households and median households. This may be because budget
constraints bind more often on households below median income, and reduction in inequality in
that income band improves the ability of households to consume more.
Columns (3) and (4) focus on durable goods, and find higher sensitivity to changes in contraction factor compared to overall consumption discussed earlier. This is also logical, because durable
goods may relatively be more discretionary than non-durable goods and services. Finally, Column
(6) with an IV approach and system GMM estimator highlights, that consumption growth rate of
non-durable goods and services increase by 0.032 pp for each percent reduction in income inequality through tax policy for below median income households. Again, we do not see a statistically
significant impact of reducing above median inequality.
In sum, this section shows that inequality reduction through tax policy for below median
households encourages labor supply, business activity, and consumption, and ultimately economic
growth. At the same time, inequality reduction between above median and median households
through tax policy deters labor supply and business activity, hampering economic growth. Additional mechanisms may also be at work, but in this section, we only focused on labor supply,
business activity and personal consumption.
V
Robustness
We have tested that our results are robust to many reasonable alternative specifications. We report
our main results (as shown in Table III) with three alternative specifications next. The first alternative specification utilizes contraction factors calculated for the 20th and 80th percentile households
(i.e. C(20) and C(80)) in place of C(10) and C(90). This helps address possible concerns that our
results are extremely sensitive to the chosen points on the income distribution. The second alternative specification substitutes the log income ratio controls with the Gini coefficient of the given
state in the previous year, as an alternative measure of state level inequality. The third specification
32
removes the charitable contributions exogenous instrument from our IV GMM model, to test the
robustness of our approach.
Table VII reports the consolidated results from these robustness checks. Columns (1) and (2)
report the first robustness check, while Columns (3) and (4) report the second test. Columns (1)
and (3) report OLS results with the full specification, and Columns (2) and (4) show IV results with
system GMM estimator under the most exhaustive specification. Columns (5) and (6) utilize our
last robustness check and show IV GMM results with log income ratios and the Gini coefficient,
respectively, as controls for income inequality.
The table shows that our main findings hold under each robustness check: a reduction in income inequality between median income households and low income households improves economic growth, and a reduction in income inequality between median income households and high
income households decreases economic growth. In particular, changing the contraction factors
to different income percentiles under the exhaustive IV GMM model in Column (2) shows that
one percent decrease in income inequality between the 20th income percentile and the median
household increases the state level economic growth rate by 0.026 pp, while an equal decrease
in income inequality between the 80th income percentile and the median household reduces state
level growth by 0.064 pp. In Column (4), where we switch our income inequality control to the
Gini coefficient, we find that a one percent reduction in below median income inequality results
in a 0.028 pp increase in economic growth, while a similar reduction in above median income inequality through taxation results in a 0.084 pp reduction in economic growth. Our results are also
robust to removing the charitable contributions from our instrumental variables set, as the resulting
coefficients remain similar in sign and magnitude.
To further test the robustness of our results, we conduct our analysis on two different income
distributions. As shown in Table VIII, we consider using the state income distribution and the
national market income distribution from TAXSIM. Columns (1) through (3) use the state income
distribution; specifically, we use the 10th, 50th, and 90th income percentiles within each state
to calculate contraction factors, rather than at the national level as previously conducted. We
find similar results, and as seen in Column (3), a one percent reduction in below median income
33
inequality results in a 0.032 pp increase in economic growth, while a similar reduction in above
median inequality results in a 0.07 pp decrease in economic growth. Columns (4) to (6) utilize
the national level market income. Market income is our original income measure, less the taxable
portions of social security and unemployment insurance. We find, in Column (6), that a one percent
reduction in above median income inequality results in a 0.071 pp decrease in economic growth,
while a similar reduction in below median income inequality results in positive economic growth,
albeit not significant. Obtaining similar results using different income distributions gives us further
confidence in our main findings.
VI
Conclusion
Modern democracies have accepted the role of income taxation in addressing income inequality.
This paper distinguishes the economic growth effect of income taxation in reducing inequality between below median and median income households, from the economic growth effect of taxation
in reducing inequality between median household and above median households.
We find that the tax policy that provides poverty alleviation improves economic growth. At
the same time, we find that reduction of incentives that is caused by lower after-tax income gap
between median and rich households, reduces economic growth. This paper does not address
optimal taxation and general equilibrium effects of tax policy. We also do not investigate the impact
of specific tax policies and welfare programs on economic growth. Literature has been addressing
these questions. More research needs to be done on the impact of tax policy on economic growth.
Hopefully, our research will help policymakers make more informed decisions regarding tax
policy by carefully balancing social insurance with incentive preservation.
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38
Table I: Variables List
Panel A provides descriptions and sources for the dependent variables in our ordinary least squares and instrumental variables approaches. Panel B
provides descriptions and sources for all of the independent variables and instruments.
Panel A: Dependent Variables
Variable
Description
Source
Annual state level log change in chained real GDP per capita
BEA
Annual log change in number of establishments of size i to j
BDS
Annual change in state employed population (worked at least 26 weeks AND 20 hours per week) as
fraction of 18-64 aged population
Annual log change in state average annual hours worked if employed
CPS
Total personal consumption expenditures per capita annual log change
Durable goods personal consumption expenditures per capita annual log change
Nondurable goods and services personal consumption expenditures per capita annual log change
BEA
BEA
BEA
Economic Growth
∆ log GDPs,t
Small Business Activity
∆ log Estabs(i)to( j),s,t
Labor Supply
∆Ẽs,t
∆ log Hrss,t
CPS
Consumption*
∆ log PCEs,t
∆ log PCEDG,s,t
∆ log PCENDGS,s,t
All changes in monetary figures are deflated to 2009 US Dollars using GDP deflator.
*Consumption change variables are available from 1998 to 2008.
39
Panel B: Independent and Instrumental Variables
Independent Variables
Contraction factor, i.e. reduction of income inequality, between ith percentile household
and median household
Log of the contraction factor, i.e. reduction of income inequality, between ith percentile
household and median household
Change in overall marginal tax rate at ith percentile from previous year
Overall marginal tax rate at ith percentile
Income ratio of the ith percentile to the jth percentile, where i > j
Cs,t (i)
logCs,t (i)
∆MT Rs,t (i)
MT Rs,t (i)
Income(i)
Income( j)
Income(i)
log Income(
j)
log GDPs,t
gIs,t
log GDP
s,t
Log of the income ratio of the ith percentile to the jth percentile, where i > j
Log chained real GDP per capita
Log of per capita state government spending on goods and services (education, highways,
police protection, and correction) as a fraction of state GDP per capita
Log change in total population
Log of average years of schooling for population of age 18 to 64
Change in real state level effective minimum wage from previous year
Change in fraction of state labor force covered by unions from previous year
ns,t
log Schools,t
min
∆Ws,t
∆Unions,t
NBER Taxsim
NBER Taxsim
NBER Taxsim
NBER Taxsim
NBER Taxsim
NBER Taxsim
BEA
US Census State
Finances, BEA
BEA
CPS
Autor et al. (2014)
Hirsch et al. (2001)
Exogenous Instruments (Zs,t )
z pi,t
zci,t
Income
(i)
z pi,t × Income s,1979( j)
s,1979
Incomes,1979 (i)
zci,t × Income
s,1979 ( j)
z pi,t ×CCs,79
zci,t ×CCs,79
Narratively identified personal income tax shock
Narratively identified corporate income tax shock
Narratively identified personal income tax shock interacted with state inequality ratio in
1979
Narratively identified corporate income tax shock interacted with state inequality ratio in
1979
Narratively identified personal income tax shock interacted with state share of total
income contributed to charity in 1979
Narratively identified corporate income tax shock interacted with state share of total
income contributed to charity in 1979
Fixed Effects
δs
State fixed effects
All changes in monetary figures deflated to 2009 US Dollars using GDP deflator.
*Mertens and Ravn (2013)
40
MR*
MR*
NBER Taxsim, MR*
NBER Taxsim, MR*
NBER Taxsim, MR*
NBER Taxsim, MR*
Table II: Summary Statistics
Panel A shows summary statistics (number of observations, mean, standard deviation, minimum, maximum, and median) for all the dependent
variables that enter our specification, as well as the corresponding levels to each growth and change variable. Panel B shows the summary statistics
for the main explanatory variables, controls, and instruments that enter our model, and the corresponding levels to each growth and change variable.
All characteristics are at the state level, and all summary statistics shown are pooled across states from 1980 to 2009. Panel C shows average
adjusted gross income and tax rates for select income percentiles, pooled across states from 1980 to 2009. Observations are state (s) by year (t).
Panel A: Summary Statistics for Dependent Variables in Model
Variable
Observations
Mean
SD
Min
Max
Median
1076
1076
37703.91
.0146
9019.30
.0282
18624.96
-.1090
69946.16
.1323
37450.88
.0167
1076
1076
1076
1076
53015.30
66369.73
.0147
.0154
45412.78
57450.33
.0204
.0206
4044
4904
-.0948
-.0873
275491
353980
.1310
.1314
38313.5
47674.5
.0142
.0148
1076
1076
1076
1076
.7009
-.0006
2073.22
-.0006
.0468
.0189
42.48
.0129
.5142
-.0606
1937.42
-.0408
.8226
.0679
2204.47
.0380
.7030
-.0002
2075.49
-.0007
484
448
484
448
484
448
30216.51
.0150
3870.95
-.0031
26345.57
.0174
4378.86
.0243
448.66
.0535
4121.36
.0222
19320.49
-.0769
2674.85
-.1721
15981.81
-.0649
43628.41
.0770
5081.66
.1663
39472.44
.0915
29433.85
.0161
3855.95
.0045
25641.63
.0186
Economic Growth
GDPs,t
∆ log GDPs,t
Small Business Activity
Estabs5to19,s,t
Estabs5to49,s,t
∆ log Estabs5to19,s,t
∆ log Estabs5to49,s,t
Labor Supply
Ẽs,t
∆Ẽs,t
Hrss,t
∆ log Hrss,t
Consumption*
PCEs,t
∆ log PCEs,t
PCEDG,s,t
∆ log PCEDG,s,t
PCENDGS,s,t
∆ log PCENDGS,s,t
All monetary figures deflated to 2009 US Dollars using GDP deflator.
* The consumption series is available from BEA for 1997 to 2009; the growth variables are from 1998 to 2009.
The unit of observation is state-year. For more information on sample selection, see Section I.
41
Panel B: Summary Statistics for Key Explanatory Variables, Controls, and Instruments in Model
Variable
Observations
Mean
SD
Min
Max
Median
1076
1076
1076
1076
1076
1076
1076
1076
983
.0914
.1721
.1058
.1457
-2.4192
-1.7679
-2.2733
-1.9386
.0011
.0205
.0221
.0236
.0231
.2387
.1269
.2363
.1596
.0109
.0362
.1134
.0433
.0819
-3.3197
-2.1767
-3.1392
-2.5029
-.0498
.1466
.2514
.1700
.2179
-1.9199
-1.3807
-1.7719
-1.5239
.0487
.0918
.1713
.1062
.1444
-2.3886
-1.7646
-2.2425
-1.9350
.0014
1076
5.4836
.5057
4.1431
7.7806
5.4630
1076
2.7051
.1349
2.4368
3.1011
2.7096
1076
1.6974
.0936
1.4214
2.0516
1.6980
1076
.9939
.0502
.8907
1.1318
.9968
1076
1076
1076
10.2282
2.4933
.0154
.1626
.0389
.0039
9.8687
2.4038
.0076
10.5983
2.5716
.0397
10.2106
2.5004
.0150
Key Explanatory Variables
Cs,t−1 (10)
Cs,t−1 (90)
Cs,t−1 (20)
Cs,t−1 (80)
logCs,t−1 (10)
logCs,t−1 (90)
logCs,t−1 (20)
logCs,t−1 (80)
∆MT Rs,t−1 (50)
Initial Condition Control Variables
Incomes,1979 (50)
Incomes,1979 (10)
Incomes,1979 (90)
Incomes,1979 (50)
Income
(50)
log Incomes,1979 (10)
s,1979
Incomes,1979 (90)
log Income
s,1979 (50)
log GDPs,1979
log Schools,1979
CCs,1979
Dynamic Control Variables
MT Rs,t−1 (50)
1076
.3537
.0322
.2633
.4481
.3557
1076
5.9233
.9033
3.2776
10.2265
5.8610
1076
3.1711
.4402
2.3927
8.8194
3.1239
1076
1.7674
.1519
1.1871
2.3250
1.7683
1076
1.1459
.1236
.8724
2.1770
1.1391
log GDPs,t−1
log Schools,t−1
gIs,t−1
1076
1076
1076
10.4938
2.5464
1722.78
.2448
.0391
460.71
9.843
2.4008
787.81
11.1555
2.6348
2965.33
10.5112
2.5500
1667.41
s,t−1
log GDP
s,t−1
ns,t−1
min
Ws,t
min
∆Ws,t−1
Unions,t
∆Unions,t−1
1076
-3.0787
.2329
-3.7269
-2.4055
-3.0926
1027
1076
1027
1076
1027
.0104
6.18
.0010
.1681
-.0038
.0101
.63
.0528
.0744
.0136
-.0617
5.20
-.0380
.0330
-.0650
.0707
8.15
.3334
.3990
.0480
.0082
6.06
-.0204
.1625
-.0030
1000
1000
1000
1000
-.0642
-.0389
-.0010
-.0006
.2920
1.6763
.0047
.0263
-1.0796
-3.2839
-.0428
-.1302
.4350
7.3821
.0100
.1693
0
0
0
0
1000
-.0637
.2900
-1.1534
.4621
0
1000
-.0366
1.6730
-3.5081
8.0508
0
1000
-.1099
.4977
-1.9774
.7888
0
1000
-.0701
2.8565
-6.0146
14.0119
0
Incomes,t−1 (50)
Incomes,t−1 (10)
Incomes,t−1 (90)
Incomes,t−1 (50)
Income
(50)
log Incomes,t−1 (10)
s,t−1
Income
(90)
log Incomes,t−1 (50)
s,t−1
gI
Exogenous Instruments
z pi,t−1
zci,t−1
z pi,t−1 ×CCs,1979
zci,t−1 ×CCs,1979
Income
(90)
z pi,t−1 × log Incomes,1979 (50)
s,1979
Income
(90)
zci,t−1 × log Incomes,1979 (50)
s,1979
Incomes,1979 (50)
z pi,t−1 × log Income
s,1979 (10)
Income
(50)
zci,t−1 × log Incomes,1979 (10)
s,1979
Panel C: Mean Income and Tax by Income Percentile
Incomes,t−1 (i)
Taxs,t−1 (i)
Incomes,t−1 (i) − Taxs,t−1 (i)
Taxs,t−1 (i)
Incomes,t−1 (i)
i = 10th Pct.
i = 20th Pct.
i = 50th Pct.
i = 80th Pct.
i = 90th Pct.
Mean
5192.76
76.19
5116.57
10838.74
306.81
10531.93
30645.82
2375.68
28270.14
69065.13
7880.4
61184.73
98179.19
13816.57
84362.62
48068.45
6865.26
41203.19
.0147
.0283
.0775
.1141
.1407
.1428
All monetary figures in 2009 US Dollars (using GDP deflator).
The unit of observation is state-year. For more information on sample selection, see Section I.
42
Table III: The Effects of Log Contraction Factors on State Level GDP Growth (∆ log GDPs,t )
This table shows our regression results for our main specification with state level real GDP per capita growth as our dependent variable. We look at
the log change in GDP per capita, ∆ log GDPs,t = log GDPs,t − log GDPs,t−1 , where GDP is the GDP per capita. Column (1) shows OLS estimates
with logC(10) as the only regressor, while Column (2) adds logC(90) as a regressor. Column (3) includes ∆MT Rs,t−1 (50), MT Rs,t−1 (50), and
several initial condition controls at t = 1979. Column (4) shows OLS estimates for the log contraction factors, marginal tax rate variables, and
state fixed effects. To this specification, Column (5) adds dynamic controls from the previous year, Xs,t−1 . Lastly, Column (6) shows the IV GMM
estimation results with log contraction factors, marginal tax rate variables, and dynamic controls. The lower panel of the table shows regressions
statistics: the use of state fixed effects, R2 , number of observations and states, the mean of the dependent variable and log contraction factors, and
IV GMM statistics such as autocorrelation tests, Hansen statistic, and number of instruments.
Specification:
Income
(90)
Income
(50)
∆ log GDPs,t = α0 + α1 logCs,t−1 (10) + α2 logCs,t−1 (90) + α3 ∆MT Rs,t−1 (50) + h1 log Incomes,t−1 (10) + h2 log Incomes,t−1 (50) + Xs,t−1 β + δs + εs,t
s,t−1
Model
Regressors
logCs,t−1 (10)
OLS
OLS
OLS + X1979
OLS + δs
OLS + Xt−1 + δs
IV GMM
(1)
(2)
(3)
(4)
(5)
(6)
0.013***
(0.004)
0.026***
(0.005)
-0.034***
(0.010)
0.034***
(0.005)
-0.033***
(0.011)
-0.640***
(0.060)
0.044*
(0.024)
0.048***
(0.009)
-0.056***
(0.017)
-0.678***
(0.063)
0.138***
(0.048)
0.022*
(0.011)
-0.082***
(0.020)
-0.697***
(0.051)
0.191***
(0.056)
0.035**
(0.015)
-0.081**
(0.032)
-0.681***
(0.076)
0.143
(0.101)
logCs,t−1 (90)
∆MT Rs,t−1 (50)
MT Rs,t−1 (50)
(50)
Income
s,t−1
log Incomes,1979 (10)
s,1979
-0.006
(0.011)
(90)
Income
log Incomes,1979 (50)
s,1979
0.019
(0.015)
-0.010
(0.008)
-0.008
(0.026)
-0.121
(0.166)
log GDPs,1979
log Schools,1979
CCs,1979
Income
(50)
log Incomes,t−1 (10)
s,t−1
log
Incomes,t−1 (90)
Incomes,t−1 (50)
log GDPs,t−1
log Schools,t−1
gI
s,t−1
log GDP
s,t−1
ns,t−1
min
∆Ws,t−1
∆Unions,t−1
δs
N
N
N
Y
-0.021**
-0.005
(0.009)
(0.020)
0.048**
0.036
(0.021)
-0.064***
(0.014)
0.001
(0.088)
(0.048)
-0.037
(0.027)
0.048
(0.244)
-0.018
-0.029
(0.012)
0.663***
(0.173)
-0.069***
(0.015)
0.033
(0.084)
(0.023)
0.156
(0.508)
-0.087***
(0.026)
-0.091
(0.160)
Y
M3 (p-val)
Hansen J statistic
Hansen (p-val)
R2
# Observations
# States
Means:
Dep. Variable
logC(10)
logC(90)
C(10)
C(90)
Y
0.150
44.610
1.000
0.013
1076
49
0.025
1076
49
0.108
983
49
0.092
983
49
0.080
983
49
983
49
0.0146
-2.4192
0.0146
-2.4192
-1.7679
0.0914
0.1721
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0914
Significance Levels: * 10% ** 5% *** 1%
The exogenous instruments for the IV GMM estimation are the narratively identified exogenous tax shocks to personal and corporate income from Mertens and Ravn (2013), as well as these
shocks interacted with initial conditions on state level charitable donations and inequality levels. Internal instruments include the predetermined control variables, such as inequality level,
GDP per capita, schooling, state investment, population growth, and labor market institutions at t − 3 and t − 4.
OLS standard errors are clustered at the state level. IV GMM model uses robust, two step System GMM estimator with Windmeijer-corrected standard errors.
43
Table IV: The Effects of Log Contraction Factors on Changes in Employment Outcomes
This table shows our regression results for the change in annual employment outcomes for each state: employment rate (∆Ẽs,t ) and the log change
in average annual hours worked if employed (∆ log Hrss,t ). We define employed as having worked at least 26 weeks and at least 20 hours per week
in a year and our base population is individuals aged 18 through 64. Columns (1) through (3) report regression results using ∆Ẽs,t as the outcome
variable, and Columns (4) through (6) report estimates using ∆ log Hrss,t as the outcome variable. Column (1) and Column (4) show OLS estimates
for regressing the outcome variable for all workers on the log contraction factors, marginal tax rate variables, and state fixed effects. Column (2)
and Column (5) show OLS estimates for the complete specification, that is using log contraction factors, marginal tax rate variables, all dynamic
controls, and state fixed effects as regressors. Column (3) and Column (6) show IV GMM estimation results with log contraction factors, marginal
tax rate variables, and dynamic controls. The lower panel of the table shows regressions statistics: the use of state fixed effects, R2 , number of
observations and states, the mean of the dependent variable and log contraction factors, and IV GMM statistics such as autocorrelation tests, Hansen
statistic, and number of instruments.
Specification:
Income
(90)
Income
(50)
∆Ys,t = α0 + α1 logCs,t−1 (10) + α2 logCs,t−1 (90) + α3 ∆MT Rs,t−1 (50) + h1 log Incomes,t−1 (10) + h2 log Incomes,t−1 (50) + Xs,t−1 β + δs + εs,t
s,t−1
s,t−1
Employment Outcomes for All Workers (employed if work ≥ 26 weeks/year and ≥ 20 hours/week)
Ys,t
∆Employment Rate
Model
Regressors
logCs,t−1 (10)
logCs,t−1 (90)
∆MT Rs,t−1 (50)
MT Rs,t−1 (50)
Income
OLS + δs
OLS + Xt−1 + δs
IV GMM
OLS + δs
OLS + Xt−1 + δs
IV GMM
(1)
(2)
(3)
(4)
(5)
(6)
0.030***
(0.004)
-0.034***
(0.009)
-0.121*
(0.064)
-0.006
(0.025)
0.021***
(0.005)
-0.041***
(0.009)
-0.125*
(0.063)
0.035
(0.027)
0.027**
(0.011)
-0.055***
(0.016)
-0.127
(0.100)
0.047
(0.068)
0.014***
(0.003)
-0.023***
(0.006)
-0.037
(0.044)
0.004
(0.018)
0.006*
(0.003)
-0.033***
(0.006)
-0.038
(0.043)
0.038*
(0.020)
0.006
(0.005)
-0.031***
(0.010)
-0.049
(0.052)
0.039
(0.043)
(50)
log Incomes,t−1 (10)
s,t−1
log
Incomes,t−1 (90)
Incomes,t−1 (50)
log GDPs,t−1
log Schools,t−1
gI
s,t−1
log GDP
s,t−1
ns,t−1
min
∆Ws,t−1
∆Unions,t−1
δs
Log Change in Average Annual Hours Worked (if employed)
Y
0.003
0.003
-0.003
-0.004
(0.005)
(0.021)
(0.003)
(0.009)
0.022**
0.031
0.008
-0.016
(0.008)
-0.022***
(0.006)
0.014
(0.040)
(0.028)
-0.018
(0.022)
-0.040
(0.169)
(0.006)
-0.013***
(0.005)
-0.035
(0.031)
(0.015)
-0.006
(0.005)
0.000
(.)
-0.024***
-0.023
-0.005
-0.012
(0.006)
-0.085
(0.135)
-0.050***
(0.010)
0.016
(0.053)
(0.022)
-0.400
(0.304)
-0.052***
(0.016)
0.064
(0.096)
(0.004)
0.042
(0.076)
-0.021**
(0.009)
-0.021
(0.034)
(0.009)
0.074
(0.150)
-0.012
(0.010)
0.030
(0.102)
Y
M3 (p-val)
Hansen J statistic
Hansen (p-val)
Y
Y
Y
0.214
36.305
1.000
Y
0.125
46.951
1.000
R2
# Observations
# States
0.042
983
49
0.067
983
49
983
49
0.015
983
49
0.022
983
49
983
49
Means:
Dep. Variable
logC(10)
logC(90)
C(10)
C(90)
-0.0003
-2.4338
-1.7757
0.0902
0.1707
-0.0003
-2.4338
-1.7757
0.0902
0.1707
-0.0003
-2.4338
-1.7757
0.0902
0.1707
-0.0004
-2.4338
-1.7757
0.0902
0.1707
-0.0004
-2.4338
-1.7757
0.0902
0.1707
-0.0004
-2.4338
-1.7757
0.0902
0.1707
Significance Levels: * 10% ** 5% *** 1%
In this regression change in employment rate is Es,t − Es,t−1 , and log change in hours worked is log Hrss,t − log Hrss,t−1 .
The exogenous instruments for the IV GMM estimation are the narratively identified exogenous tax shocks to personal and corporate income from Mertens and Ravn (2013), as well as these
shocks interacted with initial conditions on state level charitable donations and inequality levels. Internal instruments include the predetermined control variables, such as inequality level,
GDP per capita, schooling, state investment, population growth, and labor market institutions at t − 3 and t − 4.
OLS standard errors are clustered at the state level. IV GMM model uses robust, two step System GMM estimator with Windmeijer-corrected standard errors.
44
Table V: The Effects of Log Contraction Factors on Small Business Growth
This table summarizes our regression results for small business growth. Our dependent variable is the growth in the number of establishments
of size 5 to 19, and size 5 to 49. Specifically, we look at the log change in number of establishments for each size bucket, ∆ log Estabss,t =
log Estabss,t − log Estabss,t−1 . Columns (1) through (3) report regression results using growth of establishments of size 5 to 19 as the dependent
variable, and Columns (4) through (6) report estimates using growth of establishments of size 5 to 49 as the dependent variable. Column (1) and
Column (4) show OLS estimates for regressing the outcome variable for all workers on the log contraction factors, marginal tax rate variables, and
state fixed effects. Column (2) and Column (5) show OLS estimates for the complete specification, that is using log contraction factors, marginal
tax rate variables, all dynamic controls, and state fixed effects as regressors. Column (3) and Column (6) show IV GMM estimation results with
log contraction factors, marginal tax rate variables, and dynamic controls. The lower panel of the table shows regressions statistics: the use of state
fixed effects, R2 , number of observations and states, the mean of the dependent variable and log contraction factors, and IV GMM statistics such as
autocorrelation tests, Hansen statistic, and number of instruments.
Specification:
Income
(90)
Income
(50)
∆Ys,t = α0 + α1 logCs,t−1 (10) + α2 logCs,t−1 (90) + α3 ∆MT Rs,t−1 (50) + h1 log Incomes,t−1 (10) + h2 log Incomes,t−1 (50) + Xs,t−1 β + δs + εs,t
s,t−1
s,t−1
Establishment Growth
Ys,t
Establishment Size: 5 to 19
Model
Regressors
logCs,t−1 (10)
logCs,t−1 (90)
∆MT Rs,t−1 (50)
MT Rs,t−1 (50)
Income
OLS + δs
OLS + Xt−1 + δs
IV GMM
OLS + δs
OLS + Xt−1 + δs
IV GMM
(1)
(2)
(3)
(4)
(5)
(6)
0.034***
(0.005)
-0.024***
(0.009)
-0.182**
(0.069)
-0.060
(0.039)
0.020***
(0.005)
-0.023**
(0.009)
-0.169**
(0.067)
-0.081*
(0.045)
0.023*
(0.012)
-0.049***
(0.017)
-0.163**
(0.077)
-0.028
(0.047)
0.035***
(0.005)
-0.025***
(0.009)
-0.163**
(0.070)
-0.036
(0.040)
0.022***
(0.005)
-0.020**
(0.009)
-0.148**
(0.067)
-0.074
(0.046)
0.026***
(0.009)
-0.051***
(0.012)
-0.145*
(0.083)
0.000
(0.052)
(50)
log Incomes,t−1 (10)
s,t−1
log
Incomes,t−1 (90)
Incomes,t−1 (50)
log GDPs,t−1
log Schools,t−1
gI
s,t−1
log GDP
s,t−1
ns,t−1
min
∆Ws,t−1
∆Unions,t−1
δs
Establishment Size: 5 to 49
Y
-0.005
-0.016
-0.005
-0.015
(0.006)
(0.012)
(0.007)
(0.010)
0.016
0.009
0.021*
0.016
(0.011)
-0.005
(0.010)
0.020
(0.065)
(0.021)
-0.019
(0.018)
-0.013
(0.127)
(0.011)
-0.002
(0.010)
0.043
(0.067)
(0.022)
-0.022
(0.016)
0.014
(0.119)
-0.060***
-0.021*
-0.065***
-0.022*
(0.010)
0.492***
(0.178)
-0.033***
(0.011)
-0.040
(0.052)
(0.011)
0.422
(0.326)
-0.042**
(0.018)
-0.157
(0.119)
(0.010)
0.520***
(0.175)
-0.035***
(0.012)
-0.047
(0.054)
(0.012)
0.444
(0.272)
-0.050**
(0.019)
-0.174
(0.111)
Y
M3 (p-val)
Hansen J statistic
Hansen (p-val)
Y
Y
Y
0.691
46.909
1.000
Y
0.344
47.007
1.000
R2
# Observations
# States
0.083
983
49
0.098
983
49
983
49
0.070
983
49
0.086
983
49
983
49
Means:
Dep. Variable
logC(10)
logC(90)
C(10)
C(90)
0.0146
-2.4338
-1.7757
0.0902
0.1707
0.0146
-2.4338
-1.7757
0.0902
0.1707
0.0146
-2.4338
-1.7757
0.0902
0.1707
0.0153
-2.4338
-1.7757
0.0902
0.1707
0.0153
-2.4338
-1.7757
0.0902
0.1707
0.0153
-2.4338
-1.7757
0.0902
0.1707
Significance Levels: * 10% ** 5% *** 1%
In this regression, establishment growth is ∆ log Estabss,t = log Estabss,t − log Estabss,t−1 , where Estabs is the number of establishments in the specific size bucket.
The exogenous instruments for the IV GMM estimation are the narratively identified exogenous tax shocks to personal and corporate income from Mertens and Ravn (2013), as well as these
shocks interacted with initial conditions on state level charitable donations and inequality levels. Internal instruments include the predetermined control variables, such as inequality level,
GDP per capita, schooling, state investment, population growth, and labor market institutions at t − 3 and t − 4.
OLS standard errors are clustered at the state level. IV GMM model uses robust, two step System GMM estimator with Windmeijer-corrected standard errors.
45
Table VI: The Effects of Log Contraction Factors on Personal Consumption Growth
This table shows our regression results for the log change in per capita personal consumption expenditure in each state, ∆ log PCEs,t = log PCEs,t −
log PCEs,t−1 . We use three separate categories of these consumption log change variables: total, durable goods, and nondurable goods and services.
Column (1) and Column (2) show results for total consumption growth; Column (3) and Column (4) show results for durable goods consumption
growth; and Column (5) and Column (6) show results for nondurable goods and services consumption growth. Column (1), Column (3), and Column
(5) show OLS estimates for the complete specification, that is using log contraction factors, marginal tax rate variables, all dynamic controls, and
state fixed effects as regressors. Column (2), Column (4), and Column (6) show IV GMM estimation results with log contraction factors, marginal
tax rate variables, and dynamic controls. The lower panel of the table shows regressions statistics: the use of state fixed effects, R2 , number of
observations and states, the mean of the dependent variable and log contraction factors, and IV GMM statistics such as autocorrelation tests, Hansen
statistic, and number of instruments.
Specification:
Income
(90)
Income
(50)
∆Ys,t = α0 + α1 logCs,t−1 (10) + α2 logCs,t−1 (90) + α3 ∆MT Rs,t−1 (50) + h1 log Incomes,t−1 (10) + h2 log Incomes,t−1 (50) + Xs,t−1 β + δs + εs,t
s,t−1
s,t−1
∆Per Capita Personal Consumption
Ys,t
∆Personal Consumption
Model
Regressors
logCs,t−1 (10)
logCs,t−1 (90)
∆MT Rs,t−1 (50)
MT Rs,t−1 (50)
Income
(50)
log Incomes,t−1 (10)
s,t−1
Income
(90)
log Incomes,t−1 (50)
s,t−1
log GDPs,t−1
log Schools,t−1
gI
s,t−1
log GDP
s,t−1
ns,t−1
min
∆Ws,t−1
∆Unions,t−1
δs
∆Durable Goods
∆Nondurable Goods & Services
OLS + Xt−1 + δs
IV GMM
OLS + Xt−1 + δs
IV GMM
OLS + Xt−1 + δs
IV GMM
(1)
(2)
(3)
(4)
(5)
(6)
0.006
(0.010)
-0.021
(0.017)
-0.260***
(0.092)
-0.080
(0.094)
0.040**
(0.016)
-0.023
(0.028)
-0.290***
(0.100)
0.154
(0.147)
-0.007
(0.020)
-0.031
(0.034)
-0.698***
(0.177)
-0.274
(0.180)
0.090**
(0.042)
-0.000
(0.065)
-1.056***
(0.225)
-0.037
(0.397)
0.008
(0.010)
-0.020
(0.016)
-0.193**
(0.091)
-0.058
(0.091)
0.032*
(0.016)
-0.026
(0.028)
-0.177
(0.115)
0.215
(0.150)
-0.019
-0.004
-0.031
0.009
-0.018
-0.008
(0.013)
(0.016)
(0.019)
(0.040)
(0.013)
(0.015)
-0.054**
-0.048
-0.146***
-0.118
-0.041**
-0.024
(0.020)
-0.123***
(0.035)
-0.481***
(0.139)
(0.033)
-0.053
(0.050)
-0.083
(0.218)
(0.036)
-0.487***
(0.075)
-0.894***
(0.269)
(0.094)
-0.154*
(0.078)
-0.259
(0.580)
(0.019)
-0.072**
(0.031)
-0.435***
(0.134)
(0.029)
-0.066
(0.064)
0.161
(0.342)
-0.076***
-0.049*
-0.183***
-0.095
-0.062**
-0.041*
(0.024)
0.466
(0.414)
-0.038
(0.024)
-0.210*
(0.120)
(0.028)
0.459
(0.715)
-0.078*
(0.041)
-0.047
(0.214)
(0.042)
0.735
(0.705)
-0.119***
(0.040)
-0.279
(0.200)
(0.075)
1.138
(1.130)
-0.111
(0.075)
-0.227
(0.382)
(0.024)
0.428
(0.382)
-0.030
(0.024)
-0.202*
(0.113)
(0.021)
0.591
(0.767)
-0.084**
(0.039)
-0.141
(0.165)
Y
Y
Y
Y
Y
Y
M3 (p-val)
Hansen J statistic
Hansen (p-val)
0.167
33.238
1.000
0.485
33.624
1.000
0.475
33.358
1.000
R2
# Observations
# States
0.092
434
39
434
39
0.139
434
39
434
39
0.070
434
39
434
39
Means:
Dep. Variable
logC(10)
logC(90)
C(10)
C(90)
0.0144
-2.6213
-1.8442
0.0742
0.1591
0.0144
-2.6213
-1.8442
0.0742
0.1591
-0.0045
-2.6213
-1.8442
0.0742
0.1591
-0.0045
-2.6213
-1.8442
0.0742
0.1591
0.0170
-2.6213
-1.8442
0.0742
0.1591
0.0170
-2.6213
-1.8442
0.0742
0.1591
Significance Levels: * 10% ** 5% *** 1%
The consumption growth rate data series is available from 1998 to 2008.
Change in consumption variables are log changes of the form log PCEs,t − log PCEs,t−1 , where PCE is the personal consumption expenditures per capita.
The exogenous instruments for the IV GMM estimation are the narratively identified exogenous tax shocks to personal and corporate income from Mertens and Ravn (2013), as well as these
shocks interacted with initial conditions on state level charitable donations and inequality levels. Internal instruments include the predetermined control variables, such as inequality level,
GDP per capita, schooling, state investment, population growth, and labor market institutions at t − 3 and t − 4.
OLS standard errors are clustered at the state level. IV GMM model uses robust, two step System GMM estimator with Windmeijer-corrected standard errors.
46
Table VII: Robustness 1 - The Effects of Log Contraction Factors on State Level GDP Growth
This table presents three robustness checks for our estimation with the state level real GDP per capita growth (∆ log GDPs,t ) as the dependent
variable. The first robustness check uses our main specification, keeps the change in median marginal tax rates, and replaces our main contraction
factors with Cs,t−1 (80) and Cs,t−1 (20). Column (1) shows OLS results using the full specification and Column (2) shows IV GMM estimates for the
full specification. The second robustness check uses our original specification and substitutes the log income ratio controls with the Gini coefficient.
Column (3) shows OLS results using the full specification and Column (4) shows IV GMM estimates for the full specification. The last robustness
check removes charitable contributions from our exogenous instrument list. Column (5) shows IV GMM estimates for the original specification
with log income ratios as a control for income inequality, while Column (6) shows IV GMM estimates for the version using the Gini coefficient as
a control for income inequality. The lower panel of the table shows regressions statistics: the use of state fixed effects, R2 , number of observations
and states, the mean of the dependent variable and log contraction factors, and IV GMM statistics such as autocorrelation tests, Hansen statistic,
and number of instruments.
Specification:
∆ log GDPs,t = α0 + α1 logCs,t−1 (i) + α2 logCs,t−1 ( j) + α3 ∆MT Rs,t−1 (50) + h Income Inequality + Xs,t−1 β + δs + εs,t
Using logC(20) & logC(80)
Model
Regressors
IV GMM
OLS + Xt−1 + δs
IV GMM
IV GMM
IV GMM
(1)
(2)
(3)
(4)
(5)
(6)
0.019
(0.012)
-0.078***
(0.021)
0.028**
(0.014)
-0.084***
(0.025)
0.035**
(0.015)
-0.080**
(0.032)
0.028**
(0.014)
-0.083***
(0.025)
-0.719***
(0.055)
0.226***
(0.056)
-0.726***
(0.076)
0.194**
(0.095)
-0.682***
(0.076)
0.144
(0.101)
-0.726***
(0.076)
0.195**
(0.095)
logCs,t−1 (90)
logCs,t−1 (80)
∆MT Rs,t−1 (50)
MT Rs,t−1 (50)
Income
(50)
log Incomes,t−1 (10)
s,t−1
Income
(90)
log Incomes,t−1 (50)
s,t−1
0.007
(0.009)
-0.066***
(0.013)
-0.682***
(0.050)
0.176***
(0.048)
0.026*
(0.014)
-0.064**
(0.030)
-0.688***
(0.073)
0.146
(0.110)
-0.020**
-0.006
-0.005
(0.009)
(0.020)
(0.020)
0.045**
0.022
0.036
(0.022)
(0.049)
(0.048)
-0.079***
(0.016)
0.001
(0.089)
-0.052*
(0.028)
0.131
(0.191)
0.054*
(0.031)
-0.061***
(0.014)
0.022
(0.089)
-0.024**
-0.039**
-0.023**
-0.030
-0.029
-0.030
(0.011)
0.734***
(0.192)
-0.065***
(0.015)
0.037
(0.085)
(0.017)
0.129
(0.454)
-0.087***
(0.024)
-0.054
(0.140)
(0.011)
0.651***
(0.169)
-0.069***
(0.014)
0.029
(0.086)
(0.027)
0.219
(0.397)
-0.088***
(0.025)
-0.053
(0.158)
(0.023)
0.156
(0.508)
-0.086***
(0.026)
-0.094
(0.160)
(0.027)
0.219
(0.397)
-0.088***
(0.025)
-0.055
(0.158)
Y
Y
Y
Y
Y
Y
0.123
44.142
1.000
0.149
44.621
1.000
0.123
44.147
1.000
Ginis,t−1
log GDPs,t−1
log Schools,t−1
gI
s,t−1
log GDP
s,t−1
ns,t−1
min
∆Ws,t−1
∆Unions,t−1
δs
M3 (p-val)
Hansen J statistic
Hansen (p-val)
R2
# Observations
# States
Means:
Dep. Variable
logC(10), logC(20)
logC(90), logC(80)
C(10),C(20)
C(90),C(80)
No Charitable Contributions Instrument
OLS + Xt−1 + δs
logCs,t−1 (10)
logCs,t−1 (20)
Gini as Income Inequality Control
0.170
43.977
1.000
0.034
(0.065)
-0.037*
(0.022)
0.034
(0.165)
-0.037
(0.027)
0.048
(0.244)
0.034
(0.065)
-0.037
(0.022)
0.033
(0.165)
0.065
983
49
983
49
0.099
983
49
983
49
983
49
983
49
0.0154
-2.2880
-1.9467
0.1042
0.1445
0.0154
-2.2880
-1.9467
0.1042
0.1445
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0154
-2.4338
-1.7757
0.0902
0.1707
0.0154
-2.4338
-1.7757
0.0902
0.1707
Significance Levels: * 10% ** 5% *** 1%
The exogenous instruments for the IV GMM estimation are the narratively identified exogenous tax shocks to personal and corporate income from Mertens and Ravn (2013), as well as these
shocks interacted with initial conditions on state level charitable donations and inequality levels. Internal instruments include the predetermined control variables, such as inequality level,
GDP per capita, schooling, state investment, population growth, and labor market institutions at t − 3 and t − 4.
OLS standard errors are clustered at the state level. IV GMM model uses robust, two step System GMM estimator with Windmeijer-corrected standard errors.
47
Table VIII: Robustness 2 - The Effects of Log Contraction Factors on State Level GDP Growth
This table shows our regression results for our main specification with state level real GDP per capita growth as our dependent variable. As a further
robustness check, we consider two different income distributions to calculate our income percentiles of interest: 10th, 50th, and 90th. Columns (1)
through (3) use the state level income distribution instead of the national distribution to calculate contraction factors and inequality ratio controls.
Columns (4) through (6) use the national level market income distribution to calculate analogous contraction factors and inequality ratios. Market
income is created by subtracting the taxable portions of transfer income, such as social security benefits and unemployment compensation, from our
original income distribution. Columns (1) and (3) show the basic OLS model with log contraction factors, marginal tax rate variables, and state fixed
effects. Columns (2) and (4) use the complete OLS model by adding the full set of dynamic controls from the previous year. Lastly, Columns (3)
and (6) show the complete IV GMM estimation results. The lower panel of the table shows regressions statistics: the use of state fixed effects, R2 ,
number of observations and states, the mean of the dependent variable and log contraction factors, and IV GMM statistics such as autocorrelation
tests, Hansen statistic, and number of instruments.
Specification:
Income
(90)
Income
(50)
∆ log GDPs,t = α0 + α1 logCs,t−1 (10) + α2 logCs,t−1 (90) + α3 ∆MT Rs,t−1 (50) + h1 log Incomes,t−1 (10) + h2 log Incomes,t−1 (50) + Xs,t−1 β + δs + εs,t
s,t−1
State Income Distribution
Model
Regressors
logCs,t−1 (10)
logCs,t−1 (90)
∆MT Rs,t−1 (50)
MT Rs,t−1 (50)
Income
OLS + Xt−1 + δs
IV GMM
OLS + δs
OLS + Xt−1 + δs
IV GMM
(1)
(2)
(3)
(4)
(5)
(6)
0.023***
(0.008)
-0.012
(0.019)
-0.560***
(0.057)
0.084*
(0.042)
0.005
(0.010)
-0.050**
(0.019)
-0.565***
(0.052)
0.156***
(0.045)
0.032*
(0.019)
-0.070**
(0.032)
-0.709***
(0.083)
0.244**
(0.118)
0.040***
(0.010)
-0.038**
(0.017)
-0.656***
(0.062)
0.101**
(0.048)
0.009
(0.012)
-0.067***
(0.021)
-0.671***
(0.050)
0.179***
(0.054)
0.024
(0.018)
-0.071**
(0.032)
-0.679***
(0.077)
0.144
(0.109)
(50)
(90)
log Incomes,t−1 (50)
s,t−1
log GDPs,t−1
log Schools,t−1
gI
s,t−1
log GDP
s,t−1
ns,t−1
min
∆Ws,t−1
∆Unions,t−1
δs
National Market Income Distribution
OLS + δs
log Incomes,t−1 (10)
s,t−1
Income
s,t−1
Y
-0.022**
-0.009
-0.020**
0.001
(0.008)
(0.019)
(0.009)
(0.022)
0.058***
0.047
0.038*
0.020
(0.016)
-0.065***
(0.014)
-0.017
(0.097)
(0.043)
-0.063***
(0.023)
0.211
(0.219)
(0.021)
-0.068***
(0.015)
0.017
(0.090)
(0.042)
-0.045
(0.033)
0.100
(0.212)
-0.019
-0.034
-0.022*
-0.035*
(0.012)
0.638***
(0.175)
-0.076***
(0.014)
0.019
(0.086)
(0.025)
-0.043
(0.506)
-0.104***
(0.025)
-0.100
(0.153)
(0.012)
0.692***
(0.173)
-0.069***
(0.015)
0.028
(0.084)
(0.019)
0.171
(0.475)
-0.088***
(0.027)
-0.078
(0.163)
Y
M3 (p-val)
Hansen J statistic
Hansen (p-val)
Y
Y
Y
0.243
43.452
1.000
Y
0.160
43.868
1.000
R2
# Observations
# States
0.062
983
49
0.051
983
49
983
49
0.086
983
49
0.074
983
49
983
49
Means:
Dep. Variable
logC(10)
logC(90)
C(10)
C(90)
0.0154
-2.4546
-1.7915
0.0893
0.1684
0.0154
-2.4546
-1.7915
0.0893
0.1684
0.0154
-2.4546
-1.7915
0.0893
0.1684
0.0154
-2.4173
-1.7698
0.0914
0.1717
0.0154
-2.4173
-1.7698
0.0914
0.1717
0.0154
-2.4173
-1.7698
0.0914
0.1717
Significance Levels: * 10% ** 5% *** 1%
Contraction factors and income inequality ratios are calculated using the state income distribution instead of the national income distribution in Columns (1) through (3). Columns (4) through
(6) use the national level market income distribution, which is the national level income distribution less any taxable portions of social security benefits and unemployment compensation.
The instruments used in the IV GMM estimation are the same as in previous tables.
OLS standard errors are clustered at the state level. IV GMM model uses robust, two step System GMM estimator with Windmeijer-corrected standard errors.
48
Figure I: Pre-Tax and Post-Tax Income Distribution
Before-Tax
After-Tax
Mean(Income)
49,548
Mean(LogIncome) 10.198
SD(Income)
298,123
SD(LogIncome)
1.188
42,508
10.115
236,306
1.139
0
.1
Density
.2
.3
.4
This figure shows the distribution, mean, and standard deviations of the logs of pre-tax and post-tax income across income groups in all states
from 1979 to 2008. The figure is shown from the 5th to 95th percentile of the pre-tax log income distribution to better see the compression in the
distribution caused by progressive taxation. The means and standard deviations shown are for the entire national income distribution.
8.5
9
9.5
10
Log(Income)
10.5
11
11.5
Before-Tax Income
After-Tax Income
Before-Tax Normal Density
After-Tax Normal Density
Figure II: Contraction Factor Distribution
This figure shows the distribution of contraction factors that cover all states from 1979 to 2008.
15
0
0
5
10
10
Density
Density
20
20
25
90th Percentile Contraction Factor
30
10th Percentile Contraction Factor
.04
.06
.08
.1
.12
.14
.12
Cs,t-1(10)
.14
.16
.18
.2
Cs,t-1(90)
49
.22
.24
Figure III: Contraction Factors across States: Standard Deviation
This figure illustrates the state standard deviations for both contraction factors, C(90) and C(10). The darker states represent a higher variation in
contraction factor.
(a) Contraction factor C(90)
(b) Contraction factor C(10)
50
Appendix: For Review and Online Publication Only
A
Tax Definitions
The IRS provides detailed definitions for total tax liability for every year it publishes a report.
Below are the definitions from 1979 and 2008, the first and last years in our current panel of data.
In 1979, total tax liability was the sum of income tax after credits, additional tax for tax preferences, self-employment tax, social security tax on tips, tax from recomputing prior-year investment
credit, taxes from individual retirement arrangements, and other taxes, reduced by the earned income credit used to offset all other taxes.
In 2008, total tax liability was the sum of income tax after credits, self-employment tax, social
security and Medicare tax on tips, additional tax on HSA and MSA distributions, tax from recapturing prior-year investment credits, low income housing credit, qualified electric vehicle credit,
Indian employment credit, new market credit, employer-provided child care facilities credit, alternative motor vehicle credit, alternative fuel vehicle refueling property credit, tax from recapture
of federal mortgage subsidy, taxes from qualified plans (including individual retirement accounts)
and other tax favored accounts, Section 72 penalty taxes, household employment taxes, tax on
golden parachute payments, Form 4970 tax, excise tax on insider stock compensation from an
expatriated corporation, and interest on tax due on installment income from sale of residential lot
and timeshares. These taxes were then reduced by the earned income credit used to offset all other
taxes, first-time homebuyer credit, recovery rebate credit and the refundable prior year minimum
tax credit, limited to zero. For the statistics, unlike the Form 1040, total tax liability does not
include any advance earned income credit payments.
B
Additional Tables
The following tables contain further statistics such as data availability, averages by states for instruments and controls, cross correlation tables, and first stage regressions.
51
Table B.I: Data Availability in Sample
This table shows the availability of data in our sample constructed from Taxsim. We drop any state that has less than 500 observations in any given
year. Furthermore, Alaska is excluded in all years from our specification due to sample size. The table shows which years for each state are dropped
due to low sample size. The table also shows the minimum, maximum, and average observations for each states in a year. Data is not available for
any state in 1982.
State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
Total
Years of Data
29
3
29
25
29
29
29
4
29
29
8
5
29
29
28
29
28
29
6
29
29
29
29
22
29
4
17
21
14
29
8
29
29
3
29
29
28
29
4
29
3
29
29
13
3
29
29
17
29
3
Years Available
79-81, 83-08
79-81
79-81, 83-08
79-81, 83, 85, 87, 89, 91-08
79-81, 83-08
79-81, 83-08
79-81, 83-08
79-81, 98
79-81, 83-08
79-81, 83-08
79-81, 83, 85, 92, 98, 00
79-81, 96-97
79-81, 83-08
79-81, 83-08
79-81, 83-85, 87-08
79-81, 83-08
79-81, 83-85, 87-08
79-81, 83-08
79-81, 83, 85, 98
79-81, 83-08
79-81, 83-08
79-81, 83-08
79-81, 83-08
79-81, 83-85, 87, 89, 91, 95-01, 03-08
79-81, 83-08
79-81, 00
79-81, 87, 93, 96-99, 01-08
79-81, 86-91, 96, 98-08
79-81, 92, 94-95, 97, 00, 03-08
79-81, 83-08
79-81, 86-90
79-81, 83-08
79-81, 83-08
79-81
79-81, 83-08
79-81, 83-08
79-81, 83-86, 87-08
79-81, 83-08
79-81, 91
79-81, 83-08
79-81
79-81, 83-08
79-81, 83-08
79-81, 90, 98, 01-08
79-81
79-81, 83-08
79-81, 83-08
79-81, 83, 85, 87-90, 01-08
79-81, 83-08
79-81
1079
52
Annual Observations in State Sample
Mean
Minimum
Maximum
2194
921
875
511
10291
914
1123
739
4238
1214
620
962
3680
1142
629
587
727
823
565
1172
1965
2481
1236
501
1115
942
503
642
506
2806
1134
6121
1480
744
2480
651
643
3265
831
730
729
1247
4650
522
1030
1424
1299
538
776
706
4590
3238
3382
2096
20758
3261
2991
1655
9138
4197
3185
2981
8382
3241
3235
2288
2744
2467
3009
3356
4248
5894
3470
2293
3050
2783
2113
2943
2462
6462
3339
13237
3169
2033
6903
2868
2604
7218
2062
2028
2304
2810
11515
4162
1711
4033
3096
1888
2555
2672
3336.069
2299.333
1665.793
790.24
15513.14
2130.172
2003.724
1167.5
6746.414
2741.793
1498.875
1763
5641.483
2037.483
1159.893
1040.276
1417.786
1413.483
1507.667
2426.103
3066
4469.414
2086.655
943.091
1833.034
1902.25
833.353
1524.095
996.714
4462.483
1725.375
8978
2508.069
1508
4626.655
1361.379
1241.429
4862
1401
1165.793
1647.333
1980.793
8011.793
1242.923
1453.667
2818.069
2195.69
930.353
1503.207
1930.333
501
20758
3061.833
Table B.II: Average State GDP Growth Rates and Contraction Factors
We pool the state level GDP, GDP growth rate, both contraction factors, and the annual change in overall marginal tax rate at the 50th percentile
across 49 states from 1979 to 2008 (GDP growth rate is from 1980 to 2009). This table shows the pooled averages for each of the economic growth
variables, contraction factors, and change in marginal tax rate at the median income.
Real Chained GDP
per Capita (2009 $)
Real Chained GDP
Growth Rate (%)
Contraction Factor
(90th Percentile)
Contraction Factor
(10th Percentile)
Change in Median
Marginal Tax Rate
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
29,999
33,583
29,658
42,569
42,028
52,587
44,958
35,195
37,799
40,828
23,762
42,493
35,171
35,086
36,275
32,164
39,354
26,264
42,580
46,276
37,077
40,695
26,366
36,431
28,603
40,144
45,699
38,494
47,774
25,066
47,619
36,974
25,777
36,318
31,990
32,359
37,053
28,041
31,640
20,096
34,294
39,233
36,708
24,457
41,815
44,809
27,915
36,520
38,914
1.53
1.27
1.86
1.54
1.59
2.18
1.54
1.23
1.61
0.16
-0.57
1.50
1.39
1.99
1.33
1.29
1.26
2.68
1.70
2.26
0.32
1.82
0.97
1.32
-0.13
1.91
-0.29
1.55
1.74
0.99
1.77
1.63
1.22
1.30
1.62
2.37
1.59
0.78
1.45
-0.64
1.54
1.46
0.53
2.60
1.79
1.22
1.12
1.56
-2.02
0.1769
0.1676
0.1841
0.1596
0.1631
0.1751
0.2066
0.1816
0.1685
0.1672
0.1901
0.1764
0.1776
0.1707
0.1743
0.1727
0.1812
0.2106
0.1559
0.1657
0.1716
0.1548
0.1757
0.1774
0.2024
0.1717
0.1722
0.1651
0.1707
0.1870
0.1642
0.1662
0.2212
0.1727
0.1716
0.1598
0.1779
0.1917
0.1617
0.2180
0.1816
0.1859
0.1458
0.1932
0.1687
0.1741
0.1873
0.1601
0.2121
0.0805
0.0838
0.0818
0.0883
0.0932
0.0985
0.1088
0.0900
0.0863
0.1089
0.0938
0.0918
0.0941
0.0931
0.0885
0.0873
0.0866
0.1080
0.0943
0.1041
0.0914
0.0967
0.0780
0.0902
0.1125
0.0863
0.0882
0.0991
0.0931
0.0967
0.0918
0.0874
0.1123
0.0988
0.0867
0.0923
0.0963
0.1263
0.0890
0.1167
0.0881
0.0865
0.0759
0.1061
0.0903
0.0948
0.0889
0.0996
0.1250
0.00118
0.00068
-0.00001
-0.00170
0.00087
0.00029
0.00187
0.00076
0.00182
0.00256
0.01173
0.00109
0.00293
0.00212
0.00124
0.00151
0.00340
0.00330
0.00187
-0.00015
0.00034
-0.00131
-0.00078
0.00100
0.00207
0.00173
0.00165
0.00499
0.00055
0.00366
-0.00016
0.00169
-0.00390
0.00027
0.00047
0.00131
0.00095
0.00354
0.00019
0.00305
0.00138
0.00200
0.00086
-0.00006
0.00158
0.00049
0.00436
0.00341
0.00405
Total
37,704
1.46
0.1721
0.0914
0.00114
State
53
Table B.III: Contraction Factors and Inequality Cross-correlation
This table shows the cross-correlations between our contraction factors, income inequality ratios, and the Gini coefficient. Panel A presents the
standard correlations, while Panel B uses demeaned variables to show correlations with state fixed effects.
Panel A: Standard Cross-Correlation
Variables
Cs,t (90)
Incomes,t (90)
Incomes,t (50)
Cs,t (10)
Incomes,t (50)
Incomes,t (10)
Ginis,t
Cs,t (90)
1.000
Cs,t (10)
0.706
1.000
Incomes,t (90)
Incomes,t (50)
-0.360
-0.586
1.000
Incomes,t (50)
Incomes,t (10)
-0.202
-0.102
-0.030
1.000
Ginis,t
-0.387
-0.524
0.758
0.153
1.000
Incomes,t (50)
Incomes,t (10)
Ginis,t
Panel B: State Fixed Effects Cross-Correlation
Variables
Cs,t (90)
Incomes,t (90)
Incomes,t (50)
Cs,t (10)
Cs,t (90)
1.000
Cs,t (10)
0.819
1.000
Incomes,t (90)
Incomes,t (50)
-0.538
-0.638
1.000
Incomes,t (50)
Incomes,t (10)
-0.266
-0.277
0.166
1.000
Ginis,t
-0.584
-0.626
0.753
0.297
54
1.000
Table B.IV: Averages for State Inequality and Fiscal Controls
We pool our income ratios between 50th and 10th, and 90th and 50th percentiles, log state level spending on goods and services as a ratio of GDP,
and median marginal tax rates across 49 states from 1979 to 2008. This table shows the pooled averages for each of our state inequality and fiscal
controls.
Income Ratio: 50th to
10th Percentile
Income Ratio: 90th to
50th Percentile
Log of State Expenditure
as Fraction of GDP
Median Marginal Tax
Rate (%)
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
5.519
5.018
5.485
5.470
6.288
6.712
5.318
4.910
5.400
5.793
5.468
6.589
6.703
6.302
6.222
5.581
5.615
5.106
6.299
6.297
6.854
6.599
5.257
5.831
5.443
6.509
4.500
7.052
6.538
6.357
5.806
5.366
7.062
6.130
5.610
5.768
6.613
5.202
5.062
6.720
5.806
5.798
5.607
5.476
6.073
6.043
5.772
6.219
6.632
4.002
3.200
3.111
3.343
3.058
3.257
3.133
3.383
3.280
3.317
3.807
3.190
2.893
2.895
3.199
3.144
3.407
2.695
3.070
3.072
3.175
3.006
3.366
3.176
4.254
3.102
3.547
2.940
3.213
3.332
3.271
3.177
2.763
2.952
3.184
2.954
3.092
2.729
3.135
2.898
3.124
3.421
2.916
3.043
3.145
2.781
3.106
2.983
2.436
-2.806
-2.969
-2.760
-3.127
-3.208
-3.509
-3.111
-3.250
-3.114
-3.141
-2.747
-3.408
-3.039
-2.829
-2.967
-2.814
-3.118
-3.068
-3.216
-3.448
-2.998
-2.977
-2.722
-3.230
-2.899
-3.128
-3.295
-3.321
-3.381
-2.521
-3.368
-2.978
-2.787
-3.125
-2.857
-2.883
-3.216
-3.194
-2.916
-2.856
-3.185
-3.232
-2.764
-2.752
-3.123
-3.016
-2.624
-3.029
-3.065
36.28
34.87
35.54
33.95
35.23
33.25
38.61
30.28
37.90
39.16
37.20
34.21
34.73
36.12
37.19
36.21
35.41
35.53
37.39
35.86
36.96
38.84
37.44
35.78
33.79
35.86
32.11
31.48
32.94
31.59
37.61
38.00
32.64
34.81
35.88
37.28
33.83
34.53
38.11
29.09
32.53
32.20
35.89
34.72
36.27
29.85
34.49
40.18
31.62
Total
5.923
3.171
-3.079
35.37
State
55
Table B.V: Averages for Other Controls
We pool our levels of schooling, population growth, change in effective state minimum wage, and change in percent of labor force covered by
unions across 49 states from 1979 to 2008. This table shows the pooled averages for each of our other controls.
Log Years of Schooling
Population Growth (%)
Change in Effective
Minimum Wage (%)
Change in Labor Force
Union Coverage (%)
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
2.510
2.541
2.507
2.535
2.590
2.584
2.537
2.540
2.534
2.547
2.533
2.556
2.532
2.561
2.578
2.508
2.516
2.506
2.574
2.581
2.550
2.582
2.512
2.552
2.543
2.569
2.539
2.588
2.568
2.508
2.554
2.526
2.511
2.548
2.544
2.565
2.548
2.503
2.516
2.495
2.505
2.513
2.577
2.532
2.559
2.580
2.486
2.562
2.541
0.70
2.99
0.93
1.54
1.83
0.46
0.36
2.30
1.97
1.20
1.84
0.39
0.57
0.19
0.61
0.59
0.18
0.48
1.04
0.42
0.29
0.91
0.56
0.68
0.49
0.55
4.36
0.93
0.58
1.37
0.30
1.65
0.56
0.23
0.63
1.39
0.21
0.02
1.33
0.04
1.13
1.86
2.29
1.00
1.34
1.72
-0.22
0.67
4.22
-0.36
0.32
-0.13
0.85
0.39
0.58
1.38
0.18
-0.36
-0.57
1.24
0.61
-0.36
0.54
-0.36
-0.30
-0.36
0.02
-0.16
0.77
0.56
-0.18
-0.28
0.15
-1.77
0.01
0.58
-0.28
0.41
-0.75
0.37
-0.16
-1.55
0.38
-0.36
0.89
0.44
-0.59
-0.36
-1.55
-0.36
-0.36
0.65
2.44
-0.36
0.79
0.10
0.01
-1.55
-0.53
-0.29
-0.32
-0.35
-0.40
-0.32
0.73
-0.22
-0.46
0.14
0.40
-0.51
-0.62
-0.35
-0.42
-0.47
-0.43
-0.14
-0.36
-0.29
-0.68
-0.56
-0.21
-0.47
-0.63
0.16
-0.35
0.57
-0.50
-0.20
-0.48
-0.25
1.00
-0.68
-0.22
-0.53
-0.61
1.16
-0.11
1.05
-0.60
-0.35
0.05
-0.20
-0.40
-0.55
-0.13
-0.57
-1.05
Total
2.546
1.04
0.10
-0.38
State
56
Table B.VI: The Effects of Exogenous Instruments on Log Contraction Factors
This table shows results on the relationship between our log contraction factors and exogenous instruments. Columns (1) through (3) show the effects
of our exogenous instruments on the below median contraction factor, while Columns (4) through (6) show the effect of exogenous instruments
on the above median contraction factors. Columns (1) and (4) show estimates for the effect of personal and corporate income tax shock on
contraction factors, while controlling for initial conditions of inequality and charitable giving without state fixed effects. Columns (2) and (5) add
state fixed effects, while changing the initial condition variables to become interaction terms with personal income tax shocks. Columns (3) and
(6) show a similar set of estimates for corporate income tax shocks, interaction terms, and state fixed effects. The lower panel of the table shows
regressions statistics: the use of state fixed effects, R2 , F statistics, Kleibergen-Paap Lagrange-Multiplier (LM) statistic and Wald F statistic, number
of observations and states, and the mean of the dependent contraction factor.
Specification:
logCs,t−1 (i) = α0 + Zs,t−1 γ + δs + εs,t
logC(10)
Model
Regressors
Personal Income Tax Shockt−1
× log
(1)
(2)
0.170***
(0.013)
0.845*
(0.437)
Incomes,1979 (50)
Incomes,1979 (10)
Income
(90)
× log Incomes,1979 (50)
s,1979
× CCs,1979
Corporate Income Tax Shockt−1
× log
logC(90)
(3)
(4)
(5)
0.089***
(0.008)
0.343
(0.341)
-0.485***
-0.041
(0.159)
(0.102)
0.132
-0.211
(0.272)
3.331
(4.300)
(0.205)
1.502
(1.440)
0.012***
(0.002)
0.177
(0.143)
Incomes,1979 (50)
Incomes,1979 (10)
-0.002
(0.002)
(6)
0.138**
(0.065)
-0.074
-0.041*
(0.046)
(0.024)
× log Incomes,1979 (50)
s,1979
-0.040
-0.069*
× CCs,1979
(0.092)
0.805
(1.814)
(0.035)
0.377
(0.493)
Income
Income
(90)
(50)
log Incomes,1979 (10)
s,1979
Income
(90)
log Incomes,1979 (50)
s,1979
CCs,1979
0.187*
-0.052
(0.096)
(0.091)
-0.162
0.088
(0.170)
-12.439***
(2.293)
(0.163)
-5.339***
(1.968)
N
Y
Y
N
Y
Y
R2
F statistic
p value
Kleibergen-Paap LM statistic
p value
Kleibergen-Paap Wald F statistic
# Observations
# States
0.115
62.452
0.0000
30.625
0.0000
122.100
907
49
0.058
168.282
0.0000
30.115
0.0000
159.327
907
49
0.034
58.081
0.0000
22.907
0.0001
54.991
907
49
0.049
32.908
0.0000
29.831
0.0000
75.166
907
49
0.030
50.018
0.0000
28.275
0.0000
47.356
907
49
0.007
11.072
0.0000
15.231
0.0042
10.483
907
49
Means:
Log Contraction Factor
Contraction Factor
-2.4020
0.0926
-2.4020
0.0926
-2.4020
0.0926
-1.7634
0.1727
-1.7634
0.1727
-1.7634
0.1727
δs
Significance Levels: * 10% ** 5% *** 1%
Standard errors are clustered at the state level.
The F statistics for the first stage using our IV GMM estimation are as follows: 578.8270 (p = 0.000) for C(10) and 196.8728 (p = 0.000) for C(90). The IV GMM model includes
exogenous tax shock instruments at t − 1 and internal control instruments at t − 3 and t − 4.
57
C
Additional Figures
Figure C.I: Graphical Interpretation of Contraction Factors
This figure illustrates the calculation and change in the contraction factors in relation to the median household (reference point R = (Income(50),
Tax(50))). The graph plots the income distribution and taxes paid at the 10th and 90th percentile. In subfigure (a), the slope of the solid line from
R to (Income(90), Tax(90)) represents the contraction factor between the 90th percentile households and the median households, C(90). As the tax
rate at the 90th percentile increases, while the median taxation is held fixed, the dotted line illustrates an increase in C(90). In subfigure (b), the
slope of the solid line from R to (Income(10), Tax(10)) represents the contraction factor between the 10th percentile households and the median
households, C(10). As the tax rate at the 10th percentile decreases, while the median taxation is held fixed, the dotted line illustrates an increase
in C(10). An increase in the contraction factor between the ith household and the median household, C(i), signifies a further reduction in income
inequality between the ith percentile and the reference median household due to taxation.
Tax(90)
C(90)
C(90)
Income(10)
R
Income(90)
Tax(10)
(a) Contraction factor C(90)
Tax(90)
Income(10)
C(10)
Income(90)
R
C(10)
Tax(10)
(b) Contraction factor C(10)
The contraction factors are in relation to reference point R = (Income(50), Tax(50))
58
Figure C.II: Contraction Factors across States: Average
This figure illustrates the state averages for both contraction factors, C(90) and C(10). The darker states represent a higher average contraction
factor.
(a) Contraction factor C(90)
(b) Contraction factor C(10)
59
Figure C.III: Average Contraction Factors and Narrative Shocks Measures
-.25
-.5
-.75
-1
Cs,t(90)
Cs,t(10)
60
zpi,t
08
20
06
20
04
20
02
20
00
20
98
19
96
19
94
19
92
19
90
19
19
86
19
84
19
82
19
80
19
88
Year
Narratively Identified Personal Income Tax Shock
.25
0
.05
0
-.05
-.1
-.15
-.2
-.25
Contraction Factor
.1
.5
.15
.75
.2
1
.25
This figure shows the average contraction factors that cover all states from 1979 to 2008. The narrative shocks measures are shocks to personal
income liability given by Mertens and Ravn (2013)