Hofstra University From the SelectedWorks of Lonnie K. Stevans

June, 2012

Income Inequality and Economic Incentives: Is There an Equity-Efficiency Tradeoff? Lonnie K. Stevans, Hofstra University

Available at: http://works.bepress.com/lonniekstevans/10/

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright

Author's personal copy Research in Economics 66 (2012) 149–160

Contents lists available at SciVerse ScienceDirect

Research in Economics journal homepage: www.elsevier.com/locate/rie

Income inequality and economic incentives: Is there an equity–efficiency tradeoff? Lonnie K. Stevans ∗ Hofstra University, Zarb School of Business, Department of IT/QM, 134 Hofstra University, Hempstead, NY 11549-1270, United States

article

info

Article history: Received 18 January 2011 Accepted 24 October 2011 Keywords: Cointegration Vector Error Correction (VEC) Income inequality Equity Efficiency Unit root Hysteresis Incomplete markets Political outcomes

abstract What is the basis and direction of relationship between income inequality and economic growth? The equity versus efficiency dictum which predicts a positive relationship between inequality, capital formation, and real GDP growth—emphasizes the importance of economic incentives. Subsequently, this was challenged by the incomplete markets and political outcomes theories, because of increasing empirical evidence of an inverse relationship between income inequality and economic growth. In this paper, we offer a further explanation of the basis and nature of the inequality–capital–growth relationship which emphasizes the divergence between savings and investment. For the United States over the period 1970–2006, we have found no empirical evidence for the support of the equity versus efficiency hypothesis—that economic incentives are necessary for capital accumulation and growth. In fact, it was discovered that in most cases, inequality has had little or no impact on movements in the US capital stock, net investment, and consequently, economic growth. Another interesting finding of this study was that inequality exhibits hysteresis—implying that any positive shock, such as the dot-com boom, can lead to persistent and enduring increases in inequality. © 2011 University of Venice. Published by Elsevier Ltd. All rights reserved.

1. Introduction Can we have less inequality without reducing prosperity in the United States? In the US, 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%) 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

∗

Tel.: +1 516 463 5375 (Office), +1 631 598 8518 (Home). E-mail addresses: [email protected], [email protected].

1090-9443/$ – see front matter © 2011 University of Venice. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.rie.2011.10.003

Author's personal copy 150

L.K. Stevans / Research in Economics 66 (2012) 149–160

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 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 Keynesian raison d’etre will be offered as an alternative explanation of the relationship between inequality and a country’s capital stock. Following this, the association between inequality and capital 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 here.3 2. 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 – resulting in a positive relationship between inequality and economic growth. 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; 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. The political process also can explain the relationship among inequality, government policy, and economic growth. 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 Rodrik, 1994; Persson and Tabellini, 1992, 1994). This approach also predicts a negative relationship between inequality and economic growth. There is another way 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, the argument is that this should create incentives for the rich to save and invest more, increasing the demand for capital goods, and thus expanding economic growth. Of course, this ‘‘trickle-down’’ depends in large part upon the linkage between inequality, savings, investment, the capital stock, and GDP. But 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 both) 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 additional savings will generate the requisite amount of investment spending in the economy, due to liquidity concerns5 ; and (2) even if the savings and investment of the rich increased, the investment schedule may be interest inelastic—responding more to changes in income 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.

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. 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 John Maynard Keynes, The General Theory of Employment, Interest, and Money, First Harvard, Harcourt, Inc.: 1936.

Author's personal copy L.K. Stevans / Research in Economics 66 (2012) 149–160

151

Thus, inequality could have little or no effect on net investment in the short-run, little or no influence on capital formation in the long-run, and therefore no discernible effect on 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 along with 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 25–30 years across countries (Persson and Tabellini, 1994; Alesina and Rodrik, 1994; Perotti, 1993; 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 formation because of incentives;

• the incomplete markets and political outcomes theories would predict an inverse relationship between inequality and capital formation due to incomplete information, and;

• the Keynesian approach presented in this study would predict no perceptible relationship between inequality and capital formation 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 US from 1970 to 2006—the relationship amongst the US 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 purpose will be to determine and test the direction of cointegrating relationships of income inequality measures with the US capital stock in the long-run. 3. Empirical model Following Beare (1978), the structural form of the demand for capital at time t , Kt , is specified as a function of the rental price/user cost of capital, c, the price level, P, and output, Q , Kt = f (ct , Pt , Qt , εt ), ct = PKt (δt + it − P˙ Kt ),

(1)

Kt —demand for capital goods, ct —rental price/user cost of capital services, PKt —price of capital goods, P˙ Kt —dPKt /dt, δt —capital goods depreciation rate, it —nominal interest rate, εt —random error. Ignoring the question of what measure to use for the moment, the structural form of inequality may be expressed as, INt = g (Pt , Qt , ηt ),

(2)

where INt is income inequality. This specification involving prices and output on the right-hand side of Eq. (2) has empirical support dating back to Kuznets (1955). Considering a linear reduced form, Eqs. (1) and (2) may be expressed as,6 Kt =

p 

a11i Kt −i +

p 

i=1 p

INt =

 i=1

a12i INt −i +

p 

i=1 p

a21i Kt −i +

 i =1

a13i ct −i +

p 

i=1 p

a22i INt −i +

 i=1

a14i Pt −i +

p 

i=1 p

a23i ct −i +

 i =1

a15i Qt −i + εt

i =1 p

a24i Pt −i +



(3) a25i Qt −i + ηt .

i=1

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, 6 It is important to note that this is a VAR model and the equations for c , P , and Q are omitted for reasons of brevity. t t t

Author's personal copy 152

L.K. Stevans / Research in Economics 66 (2012) 149–160

⇀

⇀

1 X t = π X t −1 +

p−1 

⇀

π i 1 X t −i + ν t ,

(4)

i =1

where, ⇀′

′ X t = (Kt INt ct Pt Qt )

π =− I−

p 

Ai

= αβ ′

i =1

πi = −

p 

Aj

j=i+1

Ai —5 × 5 matrix of the parameters as,k,i s, k = 1, 2, 3, 4, 5 i = 1, 2, 3, . . . , p. ⇀

If the matrix π has full rank (r = 5), then all components of X t 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 βi′ X it is stationary and unique if r = 1. β is the matrix of cointegrating parameters and α is the matrix of adjustment weights with which each cointegrating vector enters the five equations of the VEC. The α can also be considered as the matrix of the speed of adjustment parameters. Our interest lies with the unique case when r = 1. ⇀

β ′ X it may be written as, νt = β1 Kt + β2 INt + β3 ct + β4 Pt + β5 Qt ,

(5) ⇀

which is nothing more than a linear combination of the variables. One motivation for the VEC form is to consider β ′ X it as defining the underlying economic relations and assume that the agents react to a ‘‘shock’’ through the adjustment coefficient α to restore equilibrium, that is, they satisfy the economic relationship (5) when νt = 0. The econometric use of the term ‘‘equilibrium’’ is any long-run relationship among nonstationary variables.7 The cointegrating vector, β , is sometimes referred to as the vector of long-run parameters. We can also normalize Eq. (5) with respect to Kt , Kt = θ1 + θ2 INt + θ3 ct + θ4 Pt + θ5 Qt + ηt

θi = −

βi β1

ηt = −

ηt ∼ white noise.

νt β1

(6)

Eq. (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 θi 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. It is important to note that while Eq. (6) characterizes movement in the long-run capital stock, the first equation of the system represented by the VEC (Eq. (4)) represents the period-to-period adjustment of changes in the capital stock, or net investment. The πj 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. 4. Estimation results A complete description of the data used for the above variables, Kt , INt , ct , Pt , and Qt is in Appendix, and the time plots of Kt , Pt , ct , and Qt (from left to right) over from 1970 to 2006 may be found in Fig. 1.8 All are expressed in natural logarithm units. Four measures of inequality are used in this analysis,

• • • • •

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.

7 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 (1987) use of the term, the equilibrium relationship may be causal, behavioral, or simply a reduced form relationship among similarly trending variables (Enders, 2004). 8 Although all of the analyses used quarterly data from 1970 to 2006, the figures (graphs) are expressed in annual averages.

Author's personal copy L.K. Stevans / Research in Economics 66 (2012) 149–160

153

Fig. 1. Real net investment, implicit price deflator, rental value of capital, and real gdp (annual and in natural log units).

The chained quantity index of the capital stock, Kt , is graphed along with each of the above inequality measures in Fig. 2.9 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.10 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. 4.1. Unit root tests Since each of the time series in a VEC/cointegration analysis must be integrated of order one, (I (1)), 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.11 Perron (1989) has developed a formal procedure to test the null hypothesis of a unit root with a one-time impulse change, H0 : Yt = ϕ0 + ϕ1 DP92 + Yt −1 + εt ,

(7)

9 Ibid. 10 http://www.ncpa.org/sub/dpd/index.php?Article_ID=12523. It has also been said that the increase in 1992–1993 was partially due to a change in the Census Bureau data collection methods. 11 See Enders, Walter, Applied Econometric Time Series, Second Edition, John Wiley and Sons, Inc.: New York, NY, 2004, page 201.

Author's personal copy 154

L.K. Stevans / Research in Economics 66 (2012) 149–160

Fig. 2. Capital stock vs. inequality measures (annual, 1970 = 100).

versus the alternative of a step level change in the intercept of a trend stationary process, HA : Yt = ϕ0 + ϕ1 D92 + ϕ2 t + εt ,

(8)

where DP92 = 1 when t = Q 4 : 1991 + 1 = Q 1 : 1992 and zero (0) otherwise, and D92 = 1 when t > Q 1 : 1992 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, INit , INit = ϕi0 + ϕi1 DP92 + ϕi2 D92 + ϕi3 t + γi INit −1 +

4 

ϕij 1INit −j + εit i = 1, 2, 3, 4, 5.

(9)

j =1

Under the null hypothesis of a one-time impulse change in the level of the unit root process, γi = 1, ϕi1 ̸= 0, ϕi3 = 0. The results of this estimation and unit root tests are presented in Table 1. According to Perron (1989), the distribution of γˆ depends upon λ, (found in Table 1), which is the proportion of observations occurring before the break. It should be noted that the null 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.12 Efficient unit root tests developed by Elliott et al. (1996) were run for the remaining variables, Kt (capital stock), ct (rental price/user cost of capital), Pt (price level), and Qt (real GDP). In each case, the null hypothesis of a unit root could not be rejected.13 4.2. 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.14 Suppose an

12 It is important to note that the Perron (1989) test allows for a known and exogenous structural break in the time series. Lee and Strazicich (2003) (LS) have proposed a Lagrange Multiplier (LM) unit root test with endogenous breaks in which the alternative hypothesis implies that the series is trend stationary. The findings from applying the LS test confirmed the Perron (1989) results—the inequality series all had a unit root with an endogenous break in the second quarter of 1992. Results will be made available from the author upon request. 13 The results are omitted for brevity, but will be made available from the author upon request. 14 Because of these adjustments, there are no other cointegration tests available that have superior local power and size properties (Lutkepohl et al., 2003).

Author's personal copy L.K. Stevans / Research in Economics 66 (2012) 149–160

155

Table 1 Structural change unit root test. H0 : inequality measure has a unit root Dependent variable: LOG_GINI Sample (adjusted): 1971 2006 Included observations: 116 after adjustments Variable

Coefficient

Std. error

t-statistic

Prob.

C DP92 D92 @TREND LOG_GINI(−1) D(LOG_GINI(−1)) D(LOG_GINI(−2)) D(LOG_GINI(−3)) D(LOG_GINI(−4))

−0.617835

0.224467 0.005583 0.007483 0.000881 0.195190 0.126437 0.112583 0.101407 0.092698

−2.752459 5.574280 1.454566 2.958171 −2.709765 1.884834 −0.724271 2.011069 1.687300

0.0113 0.0000 0.1593 0.0070 0.0722 0.4762 0.0562 0.1051

∗

0.031120 0.010884 0.002607 0.471081 0.238313 −0.081541 0.203936 0.156409

Perron’s t-statistic∗

λ

−3.76

0.57

Perron’s t-statistic∗

λ

−3.76

0.57

Perron’s t-statistic∗

λ

−3.76

0.57

Perron’s t-statistic∗

λ

−3.76

0.57

α = 0.05

Dependent variable: LOG_U05_L20 Sample (adjusted): 1971 2006 Included observations: 116 after adjustments Variable

Coefficient

Std. error

t-statistic

Prob.

C DP92 D92 @TREND LOG_U05_L20(−1) D(LOG_U05_L20(−1)) D(LOG_U05_L20(−2)) D(LOG_U05_L20(−3)) D(LOG_U05_L20(−4))

0.243914 0.120555 0.034696 0.005599 0.616914 0.171179 −0.179293 0.205737 −0.008166

0.117148 0.017947 0.020996 0.001824 0.142795 0.108568 0.084555 0.103652 0.104379

2.082089 6.717354 1.652524 3.070513 −2.682769 1.576699 −2.120445 1.984872 −0.078235

0.0477 0.0000 0.1109 0.0051 0.1274 0.0441 0.0582 0.9383

∗

α = 0.05

Dependent variable: LOG_U05_L40 Sample (adjusted): 1971 2006 Included observations: 116 after adjustments Variable

Coefficient

Std. error

t-statistic

Prob.

C DP92 D92 @TREND LOG_U05_L40(−1) D(LOG_U05_L40(−1)) D(LOG_U05_L40(−2)) D(LOG_U05_L40(−3)) D(LOG_U05_L40(−4))

−0.065558

0.051027 0.026963 0.035996 0.002366 0.212230 0.081272 0.123667 0.092445 0.133617

−1.284770 3.319969 1.645806 2.478462 −2.272600 3.357367 −1.598362 2.073797 0.114280

0.2106 0.0028 0.1123 0.0203

∗

0.089517 0.059242 0.005864 0.517686 0.272861 −0.197665 0.191712 0.015270

0.0025 0.1225 0.0486 0.9099

α = 0.05

H0 : inequality measure has a unit root Dependent variable: LOG_U05_L60 Sample (adjusted): 1971 2006 Included observations: 116 after adjustments Variable

Coefficient

Std. error

t-statistic

Prob.

C DP92 D92 @TREND LOG_U05_L60(−1) D(LOG_U05_L60(−1)) D(LOG_U05_L60(−2)) D(LOG_U05_L60(−3)) D(LOG_U05_L60(−4))

−0.198711

0.094462 0.025624 0.033957 0.001729 0.188057 0.080190 0.116001 0.059699 0.118587

−2.103601

0.0456 0.0003 0.2133 0.0344

∗

0.108690 0.043363 0.003868 0.649258 0.246053 −0.238751 0.198791 −0.010180

4.241681 1.276976 2.237269 −1.865083 3.068388 −2.058179 3.329891 −0.085841

0.0051 0.0501 0.0027 0.9323

α = 0.05 (continued on next page)

⇀

n-dimensional time series, X t , is generated by the following mechanism, ⇀

⇀

X t = µ0 + µ1 t + µ2 DP + µ3 D + Y t ,

(10)

Author's personal copy 156

L.K. Stevans / Research in Economics 66 (2012) 149–160

Table 1 (continued) Dependent variable: LOG_U05_L80 Sample (adjusted): 1971 2006 Included observations: 116 after adjustments Variable

Coefficient

Std. error

t-statistic

Prob.

C DP92 D92 @TREND LOG_U05_L80(−1) D(LOG_U05_L80(−1)) D(LOG_U05_L80(−2)) D(LOG_U05_L80(−3)) D(LOG_U05_L80(−4))

−0.273517

0.107251 0.021232 0.027834 0.001026 0.149826 0.100602 0.139080 0.092232 0.107734

−2.550250

0.0173 0.0002 0.1288 0.0127

∗

0.092729 0.043727 0.002756 0.656488 0.252079 −0.205751 0.213103 0.035729

4.367401 1.570997 2.685132 −2.292739 2.505706 −1.479373 2.310514 0.331636

Perron’s t-statistic∗

λ

−3.76

0.57

0.0191 0.1515 0.0294 0.7429

α = 0.05 ⇀

where DP is an impulse dummy and D is a step level dummy variable. Y t is a stochastic error which is assumed to have a VAR process with the VEC representation, ⇀

⇀

1 Y t = π Y t −1 +

p−1 

⇀

π i 1 Y t −i + ϖ t .

(11)

i =1

Saikkonen and Lutkepohl (2000) recommend forming the series, ⇀

Y˜t = X t − µ0 − µ1 t − µ2 DP − µ3 D,

(12)

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

1Y˜t = π Y˜t −1 +

p−1 

πi 1Y˜t −i + ϖt .

(13)

i =1

This adjustment was only made for the five inequality measures, since stability tests indicated that there were no discernible breakpoints from 1970 to 2006 for each of the remaining series.15 The results of the cointegration tests are in Table 2.16 It is important to note that in each case involving the maximum eigenvalue tests for the null hypothesis of H0 : Cointegrating Rank = 0 versus the alternative HA : Cointegrating Rank = 1, the null hypothesis was rejected in favor of the unique alternative. Thus, these single, cointegrating relationships may be represented by the normalized linear models (Eq. (6)), Kt = θ1j + θ2j INtj + θ3j ct + θ4j Pt + θ5j Qt + ηtj

j = 1, 2, 3, 4, 5,

(14)

where the j represents each of the five inequality measures.17 4.3. Vector error correction estimation The estimation results of the single cointegrating equations (Eq. (14)) are presented in Table 3. In each of the equations, the variables ct , Pt , and Qt all have the expected sign (negative, positive, and positive, respectively) and are statistically significant at α = 0.01 in every equation. The only two inequality measures that have a statistically significant influence on the US 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 3). 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).18 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

15 Using EViews 6, the Quandt–Andrews breakpoint test over the period 1970–2006 was performed on K , c , P , and Q and the null hypothesis of no t t t t breakpoints within the trimmed data could not be rejected in each case. Results will be made available from author upon request. 16 The lag length for each model, p, was determined by using the sequential modified likelihood ratio test in EViews 7.1. 17 Remember that the inequality measures, IN , are essentially residuals—the effect of the deterministic variables have been removed. tj 18 The effect of inequality on net investment will be presented shortly.

Author's personal copy L.K. Stevans / Research in Economics 66 (2012) 149–160

157

Table 2 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 no. of CE(s) ∗

None At most 1 At most 2 At most 3 At most 4

Eigenvalue

Max-eigen statistic

0.05 critical value

Prob.∗∗

0.780867 0.522302 0.516642 0.392361 0.331507

51.61459 25.11841 24.71790 16.93792 13.69281

38.33101 32.11832 25.82321 19.38704 19.41798

0.0009 0.2795 0.0694 0.1095 0.1095

Eigenvalue

Max-eigen statistic

0.05 critical value

Prob.∗∗

0.756527 0.591848 0.480530 0.409836 0.371872

46.62078 29.57180 21.61322 17.40268 15.34535

38.33101 32.11832 25.82321 19.38704 19.42312

0.0045 0.0992 0.1634 0.0949 0.0951

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) Hypothesized no. of CE(s) ∗

None At most 1 At most 2 At most 3 At most 4

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) Hypothesized no. of CE(s)

Eigenvalue

Max-eigen statistic

0.05 critical value

Prob.∗∗

None∗ At most 1 At most 2 At most 3 At most 4

0.787474 0.576534 0.463000 0.357559 0.308806

51.10687 28.35631 20.51797 14.60186 12.18804

38.33101 32.11832 25.82321 19.38704 19.51798

0.0011 0.1346 0.2148 0.2162 0.2255

Eigenvalue

Max-eigen statistic

0.05 critical value

Prob.∗∗

0.800354 0.572472 0.457606 0.373281 0.343586

53.16999 28.04123 20.18820 15.41949 13.89181

38.33101 32.11832 25.82321 19.38704 19.56799

0.0005 0.1453 0.2325 0.1719 0.1822

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 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) Hypothesized no. of CE(s) ∗

None At most 1 At most 2 At most 3 At most 4

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. (continued on next page)

theories outlined above. The rest of the inequality measures are found to have no statistically significant influence on the US capital stock—indicating corroboration of the aforementioned Keynesian approach. 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 estimates of the short-run πi parameters in the VEC of Eq. (14) are

Author's personal copy 158

L.K. Stevans / Research in Economics 66 (2012) 149–160

Table 2 (continued) 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) Hypothesized no. of CE(s)

Eigenvalue

Max-eigen statistic

0.05 critical value

Prob.∗∗

None∗ At most 1 At most 2 At most 3 At most 4

0.791162 0.541585 0.478971 0.405936 0.373482

51.68455 25.73935 21.51437 17.18536 15.43008

38.33101 32.11832 25.82321 19.38704 19.62798

0.0009 0.2454 0.1676 0.1015 0.1108

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.

Table 3 Estimation results. Capital stock cointegration equations (t statistics in parentheses). Dependent variable: US 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 Trend

−0.943 0.014 (3.80)** −0.180 (−1.37) 0.257 (4.37)** 0.362 (3.69)** −0.164 (−4.01)**

0.876 0.014 (3.49)** −0.027 (0.711) 0.253 (3.80)** 0.356 (3.41)** −0.158 (−3.59)**

1.410 0.012 (3.76)** −0.067 (−2.54)* 0.250 (4.97)** 0.434 (5.35)** −0.159 (−4.71)**

1.680 0.010 (3.26)** −0.059 (−2.06)* 0.277 (5.16)** 0.459 (5.46)** −0.180 (−5.04)**

1.601 0.011 (3.28)** −0.049 (−1.61) 0.275 (4.79)** 0.449 (5.32)** −0.176 (−4.70)**

Inequality Price Real GDP User Capital Cost * **

Statistically significant at 0.05 level. Statistically significant at 0.01 level.

Table 4 Estimation results. Net investment VEC (t statistics in parentheses). Dependent variable: net investment (1Kt -change in capital stock) Inequality explanatory variables

πˆ i

Change in Gini at Lag 1

0.004 (0.051) −0.015 (−0.204) −0.011 (−0.562) 0.009 (0.463) −0.004 (−1.98)** −0.002 (−0.173) −0.003 (−1.89)* −0.001 (−1.78)* 0.004 (0.184) 0.002 (0.096)

Change in Gini at Lag 2 Change in upper five to lower twenty at lag 1 Change in upper five to lower twenty at lag 2 Change in upper five to lower forty at lag 1 Change in upper five to lower forty at lag 2 Change in upper five to lower sixty at lag 1 Change in upper five to lower sixty at lag 2 Change in upper five to lower eighty at lag 1 Change in upper five to lower eighty at lag 2 * **

Statistically significant at 0.10 level. Statistically significant at 0.05 level.

presented in Table 4. For reasons of brevity, only the first and second lags of the net investment (1Kt ) 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

Author's personal copy L.K. Stevans / Research in Economics 66 (2012) 149–160

159

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. 5. 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 net investment, the capital stock, and consequently economic growth. The three remaining inequality measures have had an inverse effect on capital formation — positing the existence of market failure in the capital markets due to credit rationing. 5.1. Study limitations There are some statistical/estimation issues regarding the model used for this study which could tend to temper the results. It is well known that although the Johansen (1988) estimators have less bias than other estimators, they exhibit more variation. However, this does not appear to be a considerable problem in this analysis, given the degree of statistical significance of the parameter estimators in Table 4. In addition, the following issues may be problematic and arise from Monte Carlo studies on the Johansen (1988) cointegration tests,19 1. 2. 3. 4.

the tabulated critical values based on asymptotic distributions may be inappropriate if sample sizes are small; all tests can be misleading if too few variables are included; insufficient lag length can lead to substantial size distortions, over-specification leads to loss of power; and if a low-order VAR model is used, both the trace and λmax statistics are biased toward finding cointegration.

This study could be criticized based upon any or all of these issues, but the use of detrending methods, as was done in this analysis, has been shown to improve the power of the Johansen tests.20 Appendix. Variable descriptions (all data downloaded from http://www.haverselect.com) Variable Capital stock (Kt ) Inequality measures: Gini (GINIt ) Upper five/lower twenty (L20t ) Upper five/lower forty (L40t ) Upper five/lower sixty (L60t ) Upper five/lower eighty (L80t ) Price of capital (PKt )

Depreciation rate (t)

Interest rate (it ) Price level (Pt ) Output (Qt )

Description Net stock of fixed assets and consumer durables: Chained quantity index (2000 = 100) 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 Ratio of income share of top five percent relative to income share of lower eighty percent Geometric average of: private fixed investment: chained price index (2000 = 100) and personal consumption expenditures durable goods: chained price index (2000 = 100) 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) Long-term treasury composite, over 10 years (%) Implicit price deflator: gross national product (2000 = 100) Real gross domestic product (billions of chained 000$)

19 G.S. Maddala and In-Moo Kim, Unit Roots, Cointegration, and Structural Change, Cambridge University Press, Cambridge, UK: 2004, pp. 219–220. 20 Ibid.

Author's personal copy 160

L.K. Stevans / Research in Economics 66 (2012) 149–160

References Alesina, A., Rodrik, D., 1994. Distributive politics and economic growth. Quarterly Journal of Economics 109 (2), 465–490. Barro, Robert J., 1999. Inequality, growth, and investment. NBER Working Paper 7038. Barro, Robert J., Xavier, Sala-i-Martin, 1995. Economic Growth. McGraw-Hill, New York. Beare, John B., 1978. Macroeconomics: Cycles, Growth, and Policy in a Monetary Economy. MacMillan, New York. Bertola, G., 1991. Market structure and income distribution in endogenous growth models. NBER Working Paper No. 3851. Cambridge, MA. National Bureau of Economic Research. Deininger, K., Squire, L., 1996. A new data set measuring income inequality. World Bank Economic Review 10 (3), 565–591. Deininger, K., Squire, L., 1998. New ways of looking at old issues: inequality and growth. Journal of Development Economics 57 (2), 259–287. Elliott, G., Rothenberg, T.J., Stock, J.H., 1996. Efficient tests for an autoregressive unit root. Econometrica 64, 813–836. Enders, Walter, 2004. Applied Econometric Time Series, second ed. John Wiley and Sons, Inc., New York, NY. Engle, Robert F., Granger, Clive W.J., 1987. Co-integration and error correction: representation, estimation, and testing. Econometrica 55 (2), 251–276. Forbes, Kristin J., 2000. A reassessment of the relationship between inequality and growth. American Economic Review 90 (4), 869–887. Johansen, Soren, 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254. Kopcke, Richard W., 1993. The determinants of business investment: has capital spending been surprisingly low? New England Economic Review 3–31. Kuznets, Simon, 1955. Economic growth and income inequality. American Economic Review 1–28. Lee, J., Strazicich, M.C., 2003. Minimum LM unit root test with two structural breaks. Review of Economics and Statistics 63, 1082–1089. Lutkepohl, H., Saikkonen, P., Trenkler, C., 2003. Comparison of tests for the cointegrating rank of a VAR process with a structural shift. Journal of Econometrics 113 (2), 201–229. MacKinnon, James G., Haug, Alfred A., Michelis, Leo, 1999. Numerical distribution functions of likelihood ratio tests for cointegration. Journal of Applied Econometrics 14, 563–577. Maddala, G.S., Kim, In-Moo, 2004. Units Roots, Cointegration, and Structural Change. Cambridge University Press, Cambridge, UK. Okun, A.M., 1975. Equality and Efficiency: The Big Tradeoff. The Brookings Institution, Washington, DC. Perotti, R., 1993. Political equilibrium, income distribution and growth. Review of Economic Studies 60, 755–776. Perron, Pierre, 1989. The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57 (6), 1361–1401. Persson, T., Tabellini, G., 1992. Growth, distribution and politics. European Economic Review 36, 593–602. Persson, T., Tabellini, G., 1994. Is inequality harmful for growth. American Economic Review 84, 593–602. Saikkonen, P., Lutkepohl, H., 2000. Testing for the cointegration rank of a VAR process with structural shifts. Journal of Business and Economic Statistics 18 (4), 451–464. Stiglitz, J.E., 1969. The distribution of income and wealth among individuals. Econometrica 37 (3), 382–397.