Income Inequality, Net Investment, and the U.S. Capital Stock: Is There an Equity-Efficiency Tradeoff?

Electronic copy available at: http://ssrn.com/abstract=1322067

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Income Inequality, Net Investment, and the U.S. Capital Stock:

Is There an Equity-Efficiency Tradeoff?

Lonnie K. Stevans, Ph.D. Associate Professor Hofstra University

Zarb School of Business Department of IT/QM 134 Hofstra University

Hempstead, NY 11549-1270 Office: 516 463-5375 Home: 631 598-8518

Email: [email protected]

Electronic copy available at: http://ssrn.com/abstract=1322067

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Abstract The equity versus efficiency approach emphasizes the importance of incentives and would predict a positive relationship between inequality and economic growth. This view was challenged in the 1990s by the incomplete markets and political outcomes theories, because of increasing empirical evidence of an inverse relationship between income inequality and economic growth. We offer a macroeconomic rationale which emphasizes the divergence between savings and investment in explaining the nature of the relationship amongst inequality, net investment spending, and a country’s capital stock. For the United States over the period 1970 to 2006, we have found no empirical evidence for the support of incentives being necessary for capital accumulation. In fact, it was discovered that in most cases, inequality has had little or no impact on movements in the U.S. capital stock, net investment, and consequently no effect on economic growth. Another interesting finding of this study was that inequality exhibits hysteresis--implying that any shock, such as the dot-com boom, can lead to persistent and enduring increases in inequality. JEL Codes: C32, D31, D63, E12 Keywords: cointegration, Vector Error Correction (VEC), income inequality, equity, efficiency, unit root, hysteresis, incomplete markets, political outcomes

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Introduction

Can we have less inequality without reducing prosperity in the United States? In the

U.S., the public finance literature has primarily focused on the measurement of “efficiency

losses” associated with government programs and policies. According to Okun (1975), the

efficiency cost of income redistribution or economic regulations may be large enough to result in

less national income. Thus, the argument is that although inequality may be reduced, everyone

will be worse-off because there would be less entrepreneurial-type or rent-seeking behavior and

diminished labor/capital productivity--resulting in a lower-standard of living.

From 1990 to 2000, the United States has exhibited a high rate of economic growth (3.3

percent) as compared to other industrialized nations, and contemporaneously the greatest

increase in inequality since the late 1970s. In contrast, many East Asian Economies in the post-

World War period experienced relatively low levels of inequality (for countries of comparable

income levels), yet grew at extraordinary rates and many Latin American countries had higher

levels of inequality and grew at a fraction of the average East Asian rate. These phenomena

prompted an interest in the relationship between inequality and growth, and in particular to a

conundrum regarding the correlation between inequality and economic growth: what is the

direction of relationship between inequality and economic growth? There is ample lip service

paid to the disincentives and/or inefficiencies associated with redistribution and the resultant

adverse effect on economic growth in popular media writings.1 The notion that higher inequality

is both a necessary and sufficient condition for increasing economic growth appears to be an

uncontested truth. On the other hand, in contrast to the positive relationship posited by the

1 See Roger Lowenstein, The Inequality Conundrum, How can you promote inequality without killing off the

genie of American prosperity? The New York Times Magazine, 10 June 2007, pp. 11‐14, and

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equity-efficiency approach, a number of studies in the academic literature have found an inverse

and statistically significant relationship between inequality and economic growth (Barro and

Xavier (1995)). The theoretical construct behind these approaches is grounded in the notion that

greater inequality either stimulates or discourages “productive investment” (depending on the

policy involved) and ultimately GDP.2 In this paper, a distinctively Keynesian raison d’etre will

be offered as an alternative explanation of the relationship amongst inequality, net investment,

and a country’s capital stock. Following this, the association between inequality and productive

investment in the United States between 1970 and 2006 will be examined by using a time series

approach incorporating both the effect of inequality on net investment (short-run) and capital

formation (long-run). It is important to note that although policies changing inequality may also

affect the labor market, only the impact on capital productivity will be studied in this analysis.3

Theory

In a perfectly competitive market, there would be no impact of inequality on productivity.

The only relationship that may exist would result from policy attempts that influence inequality

and also distort incentives. For example, a more progressive tax system would reduce inequality,

but may also create a “deadweight” loss and diminish work-effort.4 Okun (1975) has discussed

the tradeoffs associated with equity and efficiency--a policy imposing more redistribution or less

inequality may generate less national income—theoretically resulting in a positive relationship

between inequality and growth.

2 “Productive investment” is defined as real net investment in physical capital goods.

3 These would be the policies pronounced by the supply‐siders in the 1980s, such as the Laffer Curve which

professed increased work‐effort (with an upward‐sloping and elastic labor supply) when tax rates were reduced.

4 Of course, this depends upon the elasticity of labor demand and supply.

5

In the 1990s, this view was challenged as a result of increasing cross-country empirical

evidence of a negative relationship between income inequality and economic growth (Persson

and Tabellini (1994), Alesina and Rodrik (1994), and Deininger and Squire (1996)). The

existence of this inverse relationship has led to the development of a number of theories to

explain the empirical evidence. One is known as incomplete markets, which affirms that an

impact (not induced) of inequality on productivity can only arise when there is market failure.

This approach emphasizes the role of borrowing constraints and externalities in generating the

observed negative relationship between inequality and growth. When there are decreasing

returns to capital and credit rationing, the aggregate level of output may be affected by its

distribution (Stiglitz (1969)). Credit rationing occurs when there exist individuals who could

profitably invest borrowed funds and repay with interest, but lenders are unwilling to lend to

them in full. When this market failure arises, it drives productive borrowers out of the loan

market leading to an inefficient allocation of resources, underinvestment, and reduced

productivity. In this approach, the poor are prevented from choosing the most productive

activity available given their skills, because imperfect information and incomplete contracts

cause a credit market failure. Loans that would have been good are not made, and applicants that

are turned down remain poorer than they would otherwise be.

Another theory depends upon relationship among inequality, the political process, and

government policy. Political outcomes determining government policy are endogenous to the

distribution of income and rational economic agents vote for or against tax policies which have

redistributive consequences. Greater inequality would result in higher tax rates since a larger

proportion of voters will favor redistributive policies. As a result, the after-tax return of capital

is reduced, thus diminishing investment and economic growth (Bertola (1991), Alesina and

https://www.researchgate.net/publication/4894380_Distribution_of_Income_and_Wealth_Among_Individuals_W?el=1_x_8&enrichId=rgreq-897877d1-94cc-4c2d-91dd-47c2dd23c469&enrichSource=Y292ZXJQYWdlOzM5NzI4NDc0O0FTOjEwMzA3MDEzMDI0NTY0OEAxNDAxNTg1MjQyODY4

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Rodrik (1994), and Persson and Tabellini (1992, 1994)). This approach also predicts a negative

relationship between inequality and economic growth.

There is also another way in which changes in inequality can have little or no impact on

economic growth through the capital markets, other than the aforementioned trivial case of a

competitive market without government intervention. The equity-efficiency approach

emphasizes the importance of incentives. For example, according to this argument, if tax rates

for the rich are reduced (or made less progressive), the argument is that this should create an

incentive to increase net investment, the demand for capital goods, and thus economic growth for

all because the income, savings, and investment of the affluent has also increased. This “trickle-

down” depends in large part upon the linkage between inequality, savings, investment, the

capital stock, and GDP. However, a policy that augments inequality and concomitantly the

savings of the rich may indeed result in little or no increase in net investment spending. This

would result from any one (or more) of the following reasons: 1) Since the decisions of savers

and investors are essentially separate and distinct from one another—there is no reason to expect

that this additional savings will generate the requisite amount of additional investment spending

in the economy, due to liquidity concerns;5 and 2) Even if the savings of the rich increased,

investment is essentially interest inelastic—responding more to changes in profit, income and

consumption than fluctuations in the interest rate. Consider the following empirical finding by

Kopcke (1993),

Because all the models (in this study), either implicitly or explicitly, stress that investment is undertaken in anticipation of profit, the prospect of a greater demand for output is a principal spur for capital spending.

5 John Maynard Keynes, The General Theory of Employment, Interest, and Money, First Harvard, Harcourt,

Inc.: 1936.

https://www.researchgate.net/publication/5027491_The_determinants_of_business_investment_has_capital_spending_been_surprisingly_low?el=1_x_8&enrichId=rgreq-897877d1-94cc-4c2d-91dd-47c2dd23c469&enrichSource=Y292ZXJQYWdlOzM5NzI4NDc0O0FTOjEwMzA3MDEzMDI0NTY0OEAxNDAxNTg1MjQyODY4

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Thus, inequality would have little or no perceptible effect on net investment in the short-run,

little or no influence on capital formation in the long-run, and no discernible effect on economic

growth. It is possible that a policy which changes inequality, even within the framework of a

perfectly competitive market, can have little or no influence on capital productivity and

economic growth. This result runs counter to the viewpoint that relies upon a trade-off between

equity and efficiency, since, as mentioned previously, the argument put-forth is that if a society

tries “too hard” at reducing inequality, there will be fewer incentives resulting in diminished

productivity and a lower-standard of living.

Empirically, both the microeconomic and macroeconomic evidence concerning the

relationship between inequality and growth is far from conclusive. Forbes (2000) has found a

positive relationship between inequality and economic growth. Her estimates are based upon

panel data (with country fixed effects) over a five year period. However, there were earlier

studies whose authors observed a negative impact of inequality on growth using 25 to 30 years

across countries (Persson and Tabellini (1994), Alesina and Rodrick (1994), Perotti (1996), and

Deininger and Squire (1998)). When Forbes (2000) and Barro (1999) estimate their regressions

over ten year intervals, the relationship became insignificant. The empirical evidence seems to

indicate that a positive short-run relationship becomes reversed over longer periods.

In sum, it is possible to identify three predictions from the literature as to the direction of

the relationship between inequality and investment/capital formation,

the equity-efficiency view would predict a positive relationship between inequality and capital/net investment because of incentives;

the incomplete markets and political outcomes theories would predict an

inverse relationship between inequality and capital/net investment due to incomplete information, and;

https://www.researchgate.net/publication/4759015_Distributive_Politics_and_Economic_Growth?el=1_x_8&enrichId=rgreq-897877d1-94cc-4c2d-91dd-47c2dd23c469&enrichSource=Y292ZXJQYWdlOzM5NzI4NDc0O0FTOjEwMzA3MDEzMDI0NTY0OEAxNDAxNTg1MjQyODY4

https://www.researchgate.net/publication/4901252_Is_Equality_Harmful_for_Growth?el=1_x_8&enrichId=rgreq-897877d1-94cc-4c2d-91dd-47c2dd23c469&enrichSource=Y292ZXJQYWdlOzM5NzI4NDc0O0FTOjEwMzA3MDEzMDI0NTY0OEAxNDAxNTg1MjQyODY4

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the Keynesian position presented in this study would predict no perceptible relationship between inequality and capital/net investment as a consequence of the interest inelasticity of investment spending.

The question as to which prediction dominates, is an empirical one that will be tested

using quarterly time series data for the U.S. from 1970 to 2006--the relationship amongst the

U.S. capital stock, income inequality, the rental price of capital, the price level, and real GDP,

will be examined. All of these variables are treated as jointly endogenous in the context of a

reduced form VEC/cointegration model. The advantage to using this approach is twofold: first,

the statistical results are not subject to endogeneity bias, since the models used have only

predetermined or exogenous variables on the right-hand side. Second, given testing for

cointegrating relationships, there is little concern about the problem of “spurious” associations

among the variables that may exist when one simply correlates two or more random walks with

each other (Enders (2004)). The fundamental purpose will be to determine and test the direction

of cointegrating relationships of income inequality measures with U.S. net investment in the

short-run and the capital stock in the long-run.

Empirical Model

In order to ascertain the direction of cointegrating relationships amongst the

aforementioned macroeconomic variables, endogenous variables that affect net investment and

the demand for capital goods have been selected for this analysis.

Following Beare (1978), the structural form of the demand for capital at time t , tK , is

specified as a function of the rental price/user cost of capital, c , the price level, P , and output,

Q ,

( , , , ),

( ),

t t t t t

t Kt t t Kt

K f c P Q

c P i P

, (1)

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- demand for capital goods,

- rental price/user cost of capital services,

- price of capital goods,

- / ,

- capital goods depreciation rate,

- nominal interest rate,

t

t

Kt

Kt Kt

t

t

K

c

P

P dP dt

i

- random error. t

Ignoring the question of what measure to use for the moment, the structural form of inequality

may be expressed as,

( , , ),t t t tIN g P Q (2)

where tIN is income inequality. This specification involving prices and output on the right-hand

side of equation (2) has empirical support dating back to Kuznets (1955). Considering a linear

reduced form, equations (1) and (2) may be expressed as,6

11 12 13 14 15

1 1 1 1 1

21 22 23 24 251 1 1 1 1

p p p p p

t i t i i t i i t i i t i i t i ti i i i i

p p p p p

t i t i i t i i t i i t i i t i ti i i i i

K a K a IN a c a P a Q

IN a K a IN a c a P a Q

. (3)

All variables are endogenous. If the variables are random walks, (integrated of order one), the

reduced form can be appropriately restricted. Using all of the variables and creating a Vector

Error Correction (VEC) model,

1

11

p

t t i t i ti

X X X

, (4)

where,

6 It is important to note that this is a VAR model and the equations for , ,t tc P and tQ are omitted for

reasons of brevity.

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1

1

, ,

( )

- 5 x 5 matrix of the parameters

, 1,2,3,4,5 1,2,3,...,

t t t t t t

p

ii

p

i jj i

i s k i

X K IN c P Q

I A

A

A a

s k i p

.

If the matrix has full rank (r = 5), then all components of tX

are stationary or

integrated of order zero. On the other hand, if the rank of the matrix is less than five, then there

are (5 – r) common stochastic trends and r stationary relationships. In this case, the

transformation i itX

is stationary and unique if r = 1. is the matrix of cointegrating

parameters and is the matrix of adjustment weights with which each cointegrating vector

enters the five equations of the VEC. The can also be considered as the matrix of the speed of

adjustment parameters. Our interest lies with the unique case when r = 1. itX

may be written

as,

1 2 3 4 5t ttt ttINK P Qc , (5)

which is nothing more than a linear combination of the variables. One motivation for the VEC

form is to consider itX

as defining the underlying economic relations and assume that the

agents react to a “shock” through the adjustment coefficient to restore equilibrium--that is,

they satisfy the economic relationship (5) when 0t . The econometric use of the term

“equilibrium” is any long-run relationship among nonstationary variables. Cointegration does

not require that the long-run relationship be generated by market forces or by the behavioral

rules of individuals. In Engle and Granger’s (1987) use of the term, the equilibrium relationship

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may be causal, behavioral, or simply a reduced form relationship among similarly trending

variables (Enders (2004)). The cointegrating vector, , is sometimes referred to as the vector of

long-run parameters. We can also normalize equation (5) with respect to tK ,

1 2 3 4 5

1 1

white noise

t t t t t t

i ti t

t

INK c P Q

(6)

It is important to note that equation (6) is nothing more than a linear (or logarithmic) form of the

capital equation (1) with all of the endogenous variables including inequality. Since all of the

variables are in natural logarithmic units, the i and their estimates are elasticity coefficients and

may be interpreted as the percentage change in capital given a one percent change in the relevant

explanatory variable, ceteris paribus. While equation (6) characterizes movement in the long-

run capital stock, the first equation of the system represented by the VEC (equation (4))

represents the period-to-period adjustment of changes in the capital stock, or net investment.

The j parameters and their respective estimates in the VEC represent the short-term effects

(year-to-year) that changes in inequality, the user cost of capital, the price level and output have

on net investment.

Estimation Results

A complete description of the data used for the above variables, tK , tIN , tc , tP , and tQ

is in Appendix I, and the time plots of tK , tP , tc , and tQ (from left to right) over the periods

1970 to 2006 may be found in Figure 1. All are expressed in natural logarithm units.

[ Insert Figure 1 Here ]

Four measures of inequality are used in this analysis,

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Gini Coefficient, Ratio of Income Share of Top Five Percent Relative to Income Share of Lower

Twenty Percent, Ratio of Income Share of Top Five Percent Relative to Income Share of Lower

Forty Percent, Ratio of Income Share of Top Five Percent Relative to Income Share of Lower

Sixty Percent, and Ratio of Income Share of Top Five Percent Relative to Income Share of Lower

Eighty Percent. The chained quantity index of the capital stock, tK , is graphed along with each of the above

inequality measures in Figure 2. It is important to note that there is a structural increase in each

of the inequality measures beginning in 1992. Many reasons have been given for this rise in

inequality: immigration, outsourcing, rising executive compensation, but according to University

of Texas researchers James K. Galbraith and Travis Hale, much of the increase in income

inequality in the late 1990s resulted from large income changes in just a few locations around the

country--precisely those areas that were heavily involved in the information technology boom.7

In addition to the level increase in 1992, it is also notable that the share of income going to the

upper five percent relative to the lower forty and sixty percent was higher (for just about the

entire period) than the income share of the upper five percent to the lower twenty percent. This

lends support to the popular notion that the middle class has been “losing ground” relative to the

rich over the past thirty years, since these particular inequality measures are essentially

comparisons of the upper five percent “tail” relative to different size lower tails of the income

distribution. The lower forty and sixty percent tend to encompass more of the middle class than

the lower twenty or lower eighty percent of the distribution.

[ Insert Figure 2 Here ]

7 http://www.ncpa.org/sub/dpd/index.php?Article_ID=12523

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Unit Root Tests

Since each of the time series in a VEC/cointegration analysis must be integrated of order

one, ( (1)I ), each series should be tested for the presence of a unit root. However, it is well

known that the usual unit root tests are biased toward accepting the null hypothesis of a unit root

in the presence of structural change.8 Perron (1989) has developed a formal procedure to test the

null hypothesis of a unit root with a one-time impulse change,

0 0 1 92 1: t t tH Y DP Y , (7)

versus the alternative of a step level change in the intercept of a trend stationary process,

0 1 92 2:A t tH Y D t , (8)

where 92 1DP when 1992 1 1993t and zero (0) otherwise, and 92 1D when 1992t

and zero (0) otherwise. The question is whether in the presence of an exogenous shock (the dot-

com “boom”), can inequality be characterized as a process that is not mean reverting or is it trend

stationary? Using Perron’s (1989) method, we consider the following regression for each

inequality measure, itIN ,

4

0 1 92 2 92 3 11

.

1,2,3,4,5

it i i i i it ij it j itj

IN DP D t IN IN

i

(9)

Under the null hypothesis of a one-time impulse change in the level of the unit root process,

1 31, 0, 0i i i . The results of this estimation and unit root tests are presented in Table I.

According to Perron (1989), the distribution of ̂ depends upon , (found in Table I), which is

the proportion of observations occurring before the break. It should be noted that the null

8 See Enders, Walter, Applied Econometric Time Series, Second Edition, John Wiley and Sons, Inc.: New York, NY, 2004, page 201.

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hypothesis of a unit root could not be rejected for each of the five inequality measures. Thus,

inequality exhibits hysteresis--implying that any shock, such as the dot-com boom, can lead to

persistent and enduring increases in inequality. Efficient unit root tests developed by Elliot,

Rothenberg, and Stock (1996) were run for the remaining variables, tK (capital stock), tc (rental

price/user cost of capital), tP (price level), and tQ (real GDP). Once again, in each case, the null

hypothesis of a unit root could not be rejected.9

[ Insert Table I Here ]

Cointegration Tests

In addition to modifying unit root tests because of the presence of structural change,

cointegration tests have also been developed for a system of variables with level shifts.

Saikkonen and Lutkepohl (2000) propose to first adjust the time series for deterministic terms

and then apply the usual likelihood ratio tests for cointegration to the adjusted series.10 Suppose

an n-dimensional time series, tX

, is generated by the following mechanism,

0 1 2 3t tX t DP D Y

, (10)

where DP is an impulse dummy and D is a step level dummy variable. tY

is a stochastic error

which is assumed to have a VAR process with the VEC representation,

1

11

p

t t i t i ti

Y Y Y

. (11)

Saikkonen and Lutkepohl (2000) recommend forming the series,

9 The results are omitted for brevity, but will be made available from the author upon request.

10 According to Lutkepohl, Saikkonen, and Trenkler (2003), cointegration tests based upon adjusted series

have superior local power and size properties.

15

0 1 2 3t tY X t DP D , (12)

then performing the usual Johansen (1988) cointegration tests using the VEC,

1

11

p

t t i t i ti

Y Y Y

. (13)

This adjustment was only made for the five inequality measures, since stability tests indicated

that there were no discernible breakpoints from 1970-2006 for each of the remaining series.11

The results of the cointegration tests are in Table II.12 It is important to note that in each case

involving the maximum eigenvalue tests for the null hypothesis of 0 : Cointegrating Rank 0H

versus the alternative : Cointegrating Rank 1AH , the null hypothesis was rejected in favor of

the unique alternative. Thus, these single, cointegrating relationships may be represented by the

normalized linear models (equation (6)),

1 2 3 4 5

1,2,3,4,5

t j j tj j t j t j t tjIN

j

K c P Q

, (14)

where the j represents each of the five inequality measures.13

[ Insert Table II Here ]

11 Using EViews 6, the Quandt‐Andrews Breakpoint Test over the period 1970‐2006 was performed on

, , ,t t tK c P and tQ and the null hypothesis of no breakpoints within the trimmed data could not be rejected in each

case. Results will be made available from author upon request.

12 The lag length for each model, p , was determined by using the sequential modified likelihood ratio test

in EViews 7.1.

13 Remember that the inequality measures, tjIN , are essentially residuals—the effect of the deterministic

variables have been removed.

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Vector Error Correction Estimation

The estimation results of the single cointegrating equations (14) are presented in Table

III. In each of the equations, the variables , ,t tc P and tQ all have the expected sign (negative,

positive, and positive, respectively) and are statistically significant at .01 in every equation.

The only two inequality measures that have a statistically significant influence on the U.S.

capital stock are the ratio of the upper five percent to the lower forty percent and the ratio of the

upper five percent to the lower sixty percent (bolded in Table III). Moreover, the sign of both

coefficients are negative. As mentioned previously, the lower forty and sixty percent tail of the

income distribution includes more of the middle class than the lower twenty or lower eighty

percent of the distribution and the movement in these particular ratios represents the erosion in

the relative position of middle class household income. However, according to the empirical

results, more inequality, as measured by these increasing ratios, has served to reduce the nation’s

capital stock and consequently economic growth in the long-run (and decrease net investment in

the short-run).14 This outcome runs counter to the hypothesized positive effect of the equity-

efficiency tradeoff and appears to lend empirical support for the incomplete markets and political

outcomes theories outlined above. The rest of the inequality measures are found to have no

statistically significant influence on the U.S. capital stock—indicating corroboration of the

aforementioned Keynesian approach.

[ Insert Table III Here ]

As far as the short-run influence of inequality on net investment, the effects are as would

be predicted by the incomplete markets/political outcomes and Keynesian theories. The

14 The effect of inequality on net investment will be presented shortly.

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estimates of the short-run i parameters in the VEC of equation (14) are presented in Table IV.

For reasons of brevity, only the first and second lags of the net investment ( tK ) equation are

displayed. While changes in inequality as measured by the change in the ratios of the upper five

percent to the lower forty percent and lower sixty percent have an inverse effect on net

investment, in the majority of the cases changes in inequality have no perceptible influence on

net investment which is what is envisaged by the Keynesian approach.

[ Insert Table IV Here ]

Conclusion

Can equality in the United States be promoted without eliminating the “genie” of

prosperity? It is clear that for over a quarter of a century, the higher the income quantile, the

more income continued to grow and the rich-get-richer pattern has continued to prevail. Many

have asked why prosperity is not spreading more equally, but when it came to hard policy

decisions, the response has always been that there is a trade-off between equality and growth--if

a country tries too hard to redistribute income to the lower quantiles, there would be fewer

entrepreneurs, less capital investment, and therefore a lower standard of living. According to

the results of this study, there is no empirical evidence over the past 30 years in the United

States to support such a contention. In three of the five inequality measures, increases

(decreases) in inequality have had no influence on the U.S. capital stock, net investment, and

consequently economic growth. The three remaining inequality measures have had an inverse

effect on capital formation.

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References

Alesina, A. and D. Rodrik, Distributive Politics and Economic Growth. Quarterly Journal of Economics, 109(2), 1994, pp. 465-490. Barro, Robert J. and Sala-i-Martin, Xavier. Economic Growth, New York: McGraw-Hill, 1995. Beare, John B. Macroeconomics: Cycles, Growth, and Policy in a Monetary Economy, New York: MacMillan, 1978. Bertola, G., Market Structure and Income Distribution in Endogenous Growth Models. NBER Working Paper No. 3851, 1991, Cambridge, MA: National Bureau of Economic Research. Deininger, K. and L. Squire, A New Data Set Measuring Income Inequality. World Bank Economic Review, 10(3), 1996, pp. 565-591. Deininger, K. and L. Squire, New Ways of Looking at Old Issues: Inequality and Growth. Journal of Development Economics, 57(2), 1998, pp. 259-287. Elliott, G., Rothenberg, T.J. and Stock, J.H., Efficient Tests for an Autoregressive Unit Root. Econometrica, 64, 1996, pp. 813–836. Enders, Walter. Applied Econometric Time Series, Second Edition, John Wiley and Sons, Inc.: New York, NY, 2004 Johansen, Soren, Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12, June-September 1988, pp. 231-254. Kopcke, Richard W., The Determinants of Business Investment: Has Capital Spending Been Surprisingly Low? New England Economic Review, January/February 1993, pp. 3-31. Kuznets, Simon, Economic Growth and Income Inequality. American Economic Review, March 1955, pp. 1-28. Lutkepohl, H., P. Saikkonen, and C. Trenkler, Comparison of Tests for the Cointegrating Rank of a VAR Process with a Structural Shift. Journal of Econometrics, 113(2), April 2003, pp. 201-229. Maddala, G.S. and In-Moo Kim, Units Roots, Cointegration, and Structural Change, Cambridge University Press, Cambridge, UK: 2004. Okun, A.M., Equality and Efficiency: The Big Tradeoff. Washington, D.C.: The Brookings Institution, 1975. Perron, Pierre, The Great Crash, The Oil Price Shock, and The Unit Root Hypothesis. Econometrica, 57(6), November 1989, pp. 1361-1401.

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Perotti, R., Political Equilibrium, Income Distribution and Growth. Review of Economic Studies, 60, 1993, pp. 755-776. Persson, T. and G. Tabellini, Growth, Distribution and Politics. European Economic Review, 36, 1992, pp. 593-602. Persson, T. and G. Tabellini, Is Inequality Harmful for Growth. American Economic Review, 84, 1994, pp. 593-602. Saikkonen, P. and H. Lutkepohl, Testing for the Cointegration Rank of a VAR Process with Structural Shifts. Journal of Business and Economic Statistics, 18(4), October 2000, pp. 451-464. Stiglitz, J.E., The Distribution of Income and Wealth Among Individuals. Econometrica, 37(3), 1969, pp. 382-397.

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Appendix I

Variable Descriptions

(All Data Downloaded from http://www.haverselect.com) Variable Description Capital Stock ( tK ) Net Stock of Fixed Assets and Consumer Durables:

Chained Quantity Index (2000=100) Inequality Measures:

Gini ( tGINI ) Gini Coefficient

Upper Five/Lower Twenty ( 20tL ) Ratio of Income Share of Top Five Percent Relative

to Income Share of Lower Twenty Percent Upper Five/Lower Forty ( 40tL ) Ratio of Income Share of Top Five Percent Relative

to Income Share of Lower Forty Percent Upper Five/Lower Sixty ( 60tL ) Ratio of Income Share of Top Five Percent Relative

to Income Share of Lower Sixty Percent Upper Five/Lower Eighty ( 80tL ) Ratio of Income Share of Top Five Percent Relative

to Income Share of Lower Eighty Percent Price of Capital ( KtP ) Geometric Average of:

Private Fixed Investment: Chained Price Index (2000=100) and Personal Consumption Expenditures Durable Goods: Chained Price Index (2000=100)

Depreciation Rate ( t ) Ratio of Depreciation: Fixed Assets and Consumer

Durable Goods: Chained Quantity Index (2000=100) to Net Stock of Fixed Assets and Consumer Durables: Chained Quantity Index (2000=100)

Interest Rate ( ti ) Long-Term Treasury Composite, Over 10 Years

(%) Price Level ( tP ) Implicit Price Deflator: Gross National Product

(2000=100) Output ( tQ ) Real Gross Domestic Product (Billions of Chained

000$)

21

3.6

3.8

4.0

4.2

4.4

4.6

4.8

70 75 80 85 90 95 00 05

Net Stock of Fixed Assets and Consumer DurablesChained Quantity Index (2000=100)

3.2

3.6

4.0

4.4

4.8

70 75 80 85 90 95 00 05

Gross Domestic Product Implicit Price Deflator(2000=100)

-1.6

-1.2

-0.8

-0.4

0.0

0.4

70 75 80 85 90 95 00 05

Implicit Rental Value of Capital Services

8.2

8.4

8.6

8.8

9.0

9.2

9.4

70 75 80 85 90 95 00 05

Real Gross Domestic Product

Figure 1

Time Plots (all values are in natural log units)

22

80

120

160

200

240

280

320

1970 1975 1980 1985 1990 1995 2000 2005

Net Stock of Fixed Assets and Consumer Durables: Chained Quantity Index (2000=100)GiniRatio of Upper Five to Lower TwentyRatio of Upper Five to Lower FortyRatio of Upper Five to Lower SixtyRatio of Upper Five to Lower Eighty

Figure 2

Time Plot (1970=100)

Capital Stock v. Inequality Measures

23

Table I

Structural Change Unit Root Test

0 : Inequality measure has a unit rootH

Dependent Variable: LOG_GINI Sample (adjusted): 1971 2006 Included observations: 116 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. Perron's t-Statistic*

C -0.617835 0.224467 -2.752459 0.0113 DP92 0.031120 0.005583 5.574280 0.0000 D92 0.010884 0.007483 1.454566 0.1593

@TREND 0.002607 0.000881 2.958171 0.0070 LOG_GINI(-1) 0.471081 0.195190 -2.709765 -3.76 .57

D(LOG_GINI(-1)) 0.238313 0.126437 1.884834 0.0722 D(LOG_GINI(-2)) -0.081541 0.112583 -0.724271 0.4762 D(LOG_GINI(-3)) 0.203936 0.101407 2.011069 0.0562 D(LOG_GINI(-4)) 0.156409 0.092698 1.687300 0.1051

* .05 Dependent Variable: LOG_U05_L20 Sample (adjusted): 1971 2006 Included observations: 116 after adjustments


C 0.243914 0.117148 2.082089 0.0477 DP92 0.120555 0.017947 6.717354 0.0000 D92 0.034696 0.020996 1.652524 0.1109

@TREND 0.005599 0.001824 3.070513 0.0051 LOG_U05_L20(-1) 0.616914 0.142795 -2.682769 -3.76 .57

D(LOG_U05_L20(-1)) 0.171179 0.108568 1.576699 0.1274 D(LOG_U05_L20(-2)) -0.179293 0.084555 -2.120445 0.0441 D(LOG_U05_L20(-3)) 0.205737 0.103652 1.984872 0.0582 D(LOG_U05_L20(-4)) -0.008166 0.104379 -0.078235 0.9383



C -0.065558 0.051027 -1.284770 0.2106 DP92 0.089517 0.026963 3.319969 0.0028 D92 0.059242 0.035996 1.645806 0.1123

@TREND 0.005864 0.002366 2.478462 0.0203 LOG_U05_L40(-1) 0.517686 0.212230 -2.272600 -3.76 .57

D(LOG_U05_L40(-1)) 0.272861 0.081272 3.357367 0.0025 D(LOG_U05_L40(-2)) -0.197665 0.123667 -1.598362 0.1225 D(LOG_U05_L40(-3)) 0.191712 0.092445 2.073797 0.0486 D(LOG_U05_L40(-4)) 0.015270 0.133617 0.114280 0.9099

* .05

24

Table I (Continued)

Structural Change Unit Root Test

0 : Inequality measure has a unit rootH

Dependent Variable: LOG_U05_L60 Sample (adjusted): 1971 2006 Included observations: 116 after adjustments


C -0.198711 0.094462 -2.103601 0.0456 DP92 0.108690 0.025624 4.241681 0.0003 D92 0.043363 0.033957 1.276976 0.2133

@TREND 0.003868 0.001729 2.237269 0.0344 LOG_U05_L60(-1) 0.649258 0.188057 -1.865083 -3.76 0.57

D(LOG_U05_L60(-1)) 0.246053 0.080190 3.068388 0.0051 D(LOG_U05_L60(-2)) -0.238751 0.116001 -2.058179 0.0501 D(LOG_U05_L60(-3)) 0.198791 0.059699 3.329891 0.0027 D(LOG_U05_L60(-4)) -0.010180 0.118587 -0.085841 0.9323



C -0.273517 0.107251 -2.550250 0.0173 DP92 0.092729 0.021232 4.367401 0.0002 D92 0.043727 0.027834 1.570997 0.1288

@TREND 0.002756 0.001026 2.685132 0.0127 LOG_U05_L80(-1) 0.656488 0.149826 -2.292739 -3.76 0.57

D(LOG_U05_L80(-1)) 0.252079 0.100602 2.505706 0.0191 D(LOG_U05_L80(-2)) -0.205751 0.139080 -1.479373 0.1515 D(LOG_U05_L80(-3)) 0.213103 0.092232 2.310514 0.0294 D(LOG_U05_L80(-4)) 0.035729 0.107734 0.331636 0.7429

* .05

25

Table II

Cointegration Tests

Inequality Measure: Gini Coefficient Sample (adjusted): 1970 2006 Included observations: 118 after adjustments Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.780867 51.61459 38.33101 0.0009 At most 1 0.522302 25.11841 32.11832 0.2795 At most 2 0.516642 24.71790 25.82321 0.0694 At most 3 0.392361 16.93792 19.38704 0.1095 At most 4 0.331507 13.69281 19.41798 0.1095

Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Inequality Measure: Ratio of Top Five Percent to Bottom Twenty Percent Sample (adjusted): 1970 2006 Included observations: 118 after adjustments Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Maximum Eigenvalue)



Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Inequality Measure: Ratio of Top Five Percent to Bottom Forty Percent Sample (adjusted): 1970 2006 Included observations: 118 after adjustments Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Maximum Eigenvalue)



Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

26

Table II (Continued)

Cointegration Tests Inequality Measure: Ratio of Top Five Percent to Bottom Sixty Percent Sample (adjusted): 1970 2006 Included observations: 118 after adjustments Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Maximum Eigenvalue)



Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Inequality Measure: Ratio of Top Five Percent to Bottom Eighty Percent Sample (adjusted): 1970 2006 Included observations: 118 after adjustments Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Maximum Eigenvalue)



Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

27

Table III

Estimation Results

Capital Stock Cointegration Equations (t Statistics in Parentheses)

Dependent Variable: U.S. Capital Stock

Inequality Measures:

Explanatory Variables Gini Coefficient Upper Five to Lower 20 Upper Five to Lower 40 Upper Five to Lower 60 Upper Five to Lower 80 Intercept -.943 .876 1.410 1.680 1.601 Trend .014 .014 .012 .010 .011 (3.80)*** (3.49)*** (3.76)*** (3.26)*** (3.28)*** Inequality -.180 -.027 - .067 - .059 - .049 (-1.37) (.711) (-2.54)** (-2.06)** (-1.61) Price .257 .253 .250 .277 .275 (4.37)*** (3.80)*** (4.97)*** (5.16)*** (4.79)*** Real GDP .362 .356 .434 .459 .449 (3.69)*** (3.41)*** (5.35)*** (5.46)*** (5.32)*** User Capital Cost -.164 -.158 - .159 - .180 - .176 (-4.01)*** (-3.59)*** (-4.71)*** (-5.04)*** (-4.70)*** ** - Statistically Significant at .05 Level *** - Statistically Significant at .01 Level

28

Table IV

Estimation Results

Net Investment VEC (t Statistics in Parentheses)

Dependent Variable: Net Investment ( tK - Change in Capital Stock)

Inequality Explanatory Variables ˆi

Change in Gini at Lag 1 .004 (.051) Change in Gini at Lag 2 -.015 (-.204) Change in Upper Five -.011 to Lower Twenty at Lag 1 (-.562) Change in Upper Five .009 to Lower Twenty at Lag 2 (.463) Change in Upper Five -.004 to Lower Forty at Lag 1 (-1.98)** Change in Upper Five -.002 to Lower Forty at Lag 2 (-.173) Change in Upper Five -.003 to Lower Sixty at Lag 1 (-1.89)* Change in Upper Five -.001 to Lower Sixty at Lag 2 (-1.78)* Change in Upper Five .004 to Lower Eighty at Lag 1 (.184) Change in Upper Five .002 To Lower Eighty at Lag 2 (.096) * - Statistically significant at .10 level ** - Statistically significant at .05 level

Documents

Income Inequality, Net Investment, and the U.S. Capital Stock: Is There an Equity-Efficiency Tradeoff?