Income inequality and economic development: evidence from the threshold regression model

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1 Economics Letters 69 (000) locte/ econbse Income inequlity nd economic development: evidence from the threshold regression model b, * Andres Svvides, Thnsis Stengos Deprtment of Economics, Oklhom Stte University, Stillwter, OK 74078, USA b Deprtment of Economics, University of Guelph, Guelph, Ontrio N1G W1, Cnd Received 7 August 1999; ccepted 5 April 000 Abstrct Using pnel dt we investigte the reltionship between income inequlity nd economic development. We employ threshold regression model tht llows for endogenous income thresholds nd find strong evidence of two-regime split in our smple. 000 Elsevier Science S.A. All rights reserved. Keywords: Income inequlity; Kuznets hypothesis; Threshold regression JEL clssifiction: O15 1. Introduction According to the well-known Kuznets (1955) inverted-u hypothesis, income inequlity increses during the erly stges of economic development nd fter reching turning point declines. The reltionship hs been subject to extensive empiricl testing [see Bruno et l. (1998) for recent survey]. Most studies divide countries into two groups (developed nd less developed) s prerequisite to testing the Kuznets hypothesis. The implicit ssumption is tht the nture of the reltionship differs ccording to country s level of economic development. Therefore, the smple should be split into groups reflecting the level of economic development. It is importnt to note, however, tht the criterion ccording to which countries re divided into two groups depends on resercher s subjective notion of the ctegory (LDC or otherwise) to which ech country belongs or on notionl level of per cpit income tht divides the two groups. The purpose of this pper is to reexmine the inequlity development reltionship using recently *Corresponding uthor. Tel.: ; fx: E-mil ddress: thnsis@css.uoguelph.c (T. Stengos) / 00/ $ see front mtter 000 Elsevier Science S.A. All rights reserved. PII: S (00)0093-7

2 08 A. Svvides, T. Stengos / Economics Letters 69 (000) 07 1 developed econometric techniques tht test endogenously the existence of threshold level nd, thus, llow for the possibility of endogenous smple seprtion. The threshold regression (TR) model llows the level of economic development (per cpit income) to determine the existence nd significnce of threshold level in the Kuznets reltionship rther thn imposing priori n rbitrry clssifiction scheme. If indeed there exists well-defined reltionship between income inequlity nd per cpit income tht depends on the level of economic development, the TR model cn identify the threshold level nd test simultneously for such reltionship bove nd below the threshold. The following section describes the TR model s it pplies to the Kuznets hypothesis. Section 3 presents the empiricl results.. The threshold regression (TR) model nd the Kuznets hypothesis In this pper we follow Hnsen (1999) who suggests bootstrp procedure to test the null hypothesis of liner formultion ginst TR lterntive. The TR model ssumes the dt is given n by hy t, x t, q tjt51, where yt nd qt re observtions on the dependent vrible nd threshold vrible, respectively, nd xt is p 3 1 vector of independent vribles. The threshold vrible qt splits the smple into different groups nd my be prt of x t. The TR model is given by T y 5 x b 1, q # g (1) t t 1 t t T t t t t y 5 x b 1, q. g The model cn be written in single eqution form by defining dummy vrible d t(g ) 5 I(q t# g ), where I(? ) denotes the indictor function. If we write the vrible x t(g ) 5 xd(g t t ), Eqs. (1) nd () cn be expressed s T T t t t t y 5 x b 1 x (g )u 1 where b 5 b nd u 5 b1 b. Eq. (3) llows ll the regression coefficients to differ between smple groups. Hnsen (1999) provides n lgorithm tht serches over vlues of g using conditionl OLS regressions bsed on sequentil serch over ll g 5 q i, for i 5 1,... n. The procedure lso provides estimtes of b nd u. An importnt hypothesis for our test of the Kuznets hypothesis is whether the TR model is sttisticlly significnt reltive to simple liner specifiction. The null hypothesis in this cse describes the simple liner specifiction nd cn be expressed s: H :b 5 b 0 1 Devising test for the null hypothesis in (4) runs into serious obstcle, nmely the threshold prmeter g is not identified under H 0. We follow Hnsen (1999) who suggests heteroskedsticityconsistent Lgrnge Multiplier (LM) bootstrp procedure to test the null hypothesis of liner formultion ginst TR lterntive. Since g is not identified under the null hypothesis of the no-threshold effect, the p vlues re computed by fixed bootstrp method. In tht cse the xt vlues re used s regressors nd the bootstrp-dependent vrible is generted from N(0, e ˆ t), where eˆt is the OLS residul from the estimted threshold model. Hnsen (1999) shows tht this procedure yields () (3) (4)

3 A. Svvides, T. Stengos / Economics Letters 69 (000) symptoticlly correct p vlues. It is importnt to note tht if the hypothesis in (4) is rejected nd threshold level is identified, we should test gin the TR model ginst liner specifiction fter dividing the originl smple ccording to the threshold thus identified. This procedure is crried out until the null in (4) cn no longer be rejected. In testing the inverted-u hypothesis we consider two lterntive specifictions of the TR model in (3) s follows: INEQ 5 1 INC 1 s1/inc d1 (5) it 0 1 it it it INEQ 5 b 1 b ln INC 1 b ln INC it 0 1s itd s itd 1 it (6) where INEQit is the income inequlity of country i t time period t, nd INCit is the per cpit income. The specifiction in (5) is recommended by Annd nd Knbur (1993) s pproprite when testing the Kuznets hypothesis with the Gini coefficient. We consider specifiction (6) becuse it is one of the most populr specifictions for testing the Kuznets hypothesis. In both cses, the threshold vrible, q t, is the per cpit income. We use the high-qulity pnel estimtes of the Gini coefficient of Deininger nd Squire (1998) s our mesure of income inequlity. This dt set is designed to ensure intertemporl nd interntionl comprbility of income inequlity. As in ll previous tests of the Kuznets hypothesis the level of economic development is mesured by per cpit income. We use the Summers Heston estimtes of per cpit income in interntionl dollrs t 1985 prices to llow for differences in purchsing power cross countries nd thus void rbitrry conversions vi officil exchnge rtes. Our smple consists of the 618 observtions in the Deininger Squire dt set for which Summers Heston provide estimtes of per cpit income. Given tht some of the 95 countries in this smple re represented by one or very smll number of observtions, we follow previous reserchers [for exmple, Bruno et l. (1998), Deininger nd Squire (1998)] nd consider n lterntive smple tht contins only countries for which t lest four observtions re vilble. This lterntive smple contins 547 observtions from 5 countries. In wht follows we test the sensitivity of our results to the lterntive smple nd note ny differences in results between the two smples. 3. Empiricl results First we test whether the TR model is sttisticlly significnt reltive to liner specifiction, i.e. we test the null hypothesis in (4). The vlues of the Lgrnge Multiplier (LM) test re 43.3 nd 39.4, for specifictions (5) nd (6), respectively. Bsed on 1000 bootstrp replictions, the null hypothesis in (4) cn be decisively rejected regrdless of specifiction (the p vlue for this test is less thn 0.01 in both cses). Subsequently, we subdivide the smple nd test for dditionl threshold levels. For the subsmples of observtions tht exceed the threshold level, the LM tests for specifictions (5) nd (6) yield p vlues of 0.35 nd 0.43, respectively. Thus, we conclude tht no dditionl threshold levels re present. In summry, our results provide strong evidence tht the inequlity development reltionship is described by two-regime split of the smple bsed on per-cpit income. Given the presence of only one threshold level in the inequlity development reltionship, it is necessry to estimte it nd split the smple ccordingly. The estimte of the threshold is $PPP 199

4 10 A. Svvides, T. Stengos / Economics Letters 69 (000) 07 1 Tble 1 OLS nd threshold regression estimtes of Eq. (5) Explntory OLS TR model estimtes: TR model estimtes: vribles Estimtes.threshold,threshold (1) () (3) (4) (5) (6) Constnt (3.98) (7.59) (.64) INC (7.080) (0.18) (.416) (1.6) (.356) (0.731) (1/INC) (.194) (0.781) (6.515) (.055) (1.516) (0.056) R LM-heteroskedsticity [significnce level] [0.00] [0.00] [0.00] [0.00] [0.04] [0.76] No. observtions Columns (1), (3) nd (5) report estimtes without country-specific effects nd columns (), (4) nd (6) with country-specific effects. Numbers in prentheses below coefficient estimte re t-sttistics. LM-heteroskedsticity in the Breusch Pgn Lgrnge Multiplier sttistic for heteroskedsticity ( p vlues re shown in brckets). Where the hypothesis of homoskedsticity is rejected, t-sttistics re bsed on heteroskedsticity-consistent stndrd errors. for specifiction (5) nd $PPP 10 for (6). Tbles 1 nd contin the empiricl results for models (5) nd (6), respectively. For comprison purposes, the first two columns in ech tble disply estimtes from liner specifiction tht ignores threshold effects: column (1) contins the OLS results (with common intercept cross countries) nd column () the results from pnel model tht includes country-specific intercepts. The results of column (1) indicte n inverted-u reltionship between per cpit income nd inequlity. As severl uthors hve pointed out, however, once country-specific effects re llowed for in column (), there is no evident reltion between the two vribles. Tble OLS nd threshold regression estimtes of Eq. (6) Explntory OLS TR model estimtes: TR model estimtes: vribles Estimtes.threshold,threshold (1) () (3) (4) (5) (6) Constnt (.848) (6.0) (0.594) ln INC (4.51) (0.435) (5.54) (.0.63) (0.443) (0.49) (ln INC) (4.875) (0.378) (5.38) (1.994) (0.475) (0.94) R LM-heteroskedsticity [significnce level] [0.00] [0.00] [0.00] [0.00] [0.8] [0.38] No. observtions See note to Tble 1.

5 A. Svvides, T. Stengos / Economics Letters 69 (000) The remining columns of Tbles 1 nd provide estimtes of the TR model: columns (3) nd (4) correspond to observtions bove the threshold (without nd with country-specific effects) nd columns (5) nd (6) below the threshold. It is cler tht no reltion between per cpit income nd inequlity exists for observtions below the threshold. When it comes to observtions bove the threshold [columns (3) nd (4)], n uninverted- rther thn inverted-u pttern is evident. Our conclusion, however, depends on the functionl form chosen for the underlying model. It holds in the cse of the populr specifiction in (6) but does not extend to specifiction (5) recommended by Annd nd Knbur (1993): in column (4) of Tble 1, the estimted coefficient for INCit is positive but 1 insignificnt. Finlly, the estimte of the turning point (the minimum income level) for the functionl form in (6) is $PPP 9140 nd is highly significnt (t-sttistic ). Next, we dopt the strtegy of ll previous studies nd clssify countries into two groups. In contrst to previous work, however, we use the threshold level from the TR model s our clssifiction criterion. We clssify country into the higher income ctegory if ll (or in very smll number of cses ll but one) observtions for specific country exceed the previously identified threshold levels (199 nd 10). The results re in Tble 3. Columns (1) nd () report estimtes (without nd with country-specific effects) for specifiction (5) nd columns (3) nd (4) for specifiction (6). The uninverted-u pttern reported previously is no longer evident. There is no evidence of wellidentified reltion (inverted- or uninverted-u) between per cpit income nd income inequlity. This Tble 3 Estimtes of the Kuznets curve for countries clssified s higher income Explntory vribles (1) () (3) (4) Constnt (5.975) (1.060) INC (3.009) (1.110) (1/INC) (4.64) (1.365) ln INC (0.57) (0.171) (ln INC) (0.134) (0.147) R LM-heteroskedsticity [significnce level] [0.00] [0.00] [0.00] [0.00] No. countries/ observtions 46/ / 358 5/ 40 5/ 40 Columns (1) nd (3) report estimtes without country-specific effects, nd columns () nd (4) with country-specific effects. Countries re clssified s higher income if ll observtions on per cpit income exceed the threshold level identified by the TR model. See the text for dditionl detils. 1 This conclusion holds for the full smple of 618 observtions tht includes ll countries regrdless of the number of observtions per country. We lso estimted the TR model for the limited smple with t lest four observtions per country. The results re similr to those reported for the full smple: the estimtes of the threshold level re $PPP 5449 nd $PPP 849 for the two specifictions. In this cse, however, significnt uninverted-u pttern is observed for observtions bove the threshold level for both specifictions (5) nd (6).

6 1 A. Svvides, T. Stengos / Economics Letters 69 (000) 07 1 finding points to the importnce of employing n ppropritely specified model such s the TR, rther thn relying on d hoc clssifiction criteri for dividing countries into relevnt groups. As n dditionl check on our results, we exmine the possibility of liner reltion between per cpit income nd inequlity for observtions bove nd below the threshold level. This is the methodology of Eusufzi (1997) who used the Annd nd Knbur (1993) cross-section dt set nd the Qundt log-likelihood rtio test to identify brek in the dt. The study reported positive correltion between income per cpit nd inequlity for countries prior to the brek nd negtive for countries subsequent to the brek. The uthor offered this finding s evidence in fvor of the inverted-u hypothesis. We test for liner negtive (positive) reltion between per cpit income nd inequlity for observtions bove (below) the threshold. No reltionship conforming to the inverted-u pttern is found. If nything, (wekly significnt) negtive reltionship cn be observed for the low-income observtions. Finlly, we exmine the robustness of our results to lterntive inequlity mesures. The Deininger Squire dt set includes estimtes of the quintile shres of income for smller smple of observtions (558). We use these to compute four indices of inequlity: Theil s entropy index, the income shre of the lowest 40% of the popultion, the income shre of the top 0%, nd the rtio of the income shre of the top 0% to the lowest 40%. These indictors were chosen becuse of their widespred usge. We find evidence (results vilble on request) of significnt threshold effect for ll four indices (the p vlue is less thn 0.01 in ech cse). The estimte of the threshold is $PPP 10 in ech cse. No dditionl thresholds re present (the p vlue is 0.41, 0.45, 0.38 nd 0.48, respectively). Estimtes from the TR model show tht for observtions below the threshold, there is no evidence of ny reltionship between income inequlity nd per cpit income, regrdless of inequlity index. For observtions bove the threshold the evidence is mixed: n uninverted-u reltionship is evident for Theil s entropy index nd the income shre of the top 0%, but there is no evidence of ny reltionship between income inequlity nd per cpit income for the other two mesures of inequlity. Acknowledgements T. Stengos would like to thnk the SSHRC of Cnd for finncil support. References Annd, S., Knbur, S.M.R., The Kuznets process nd the inequlity development reltionship. Journl of Development Economics 40, 5 5. Bruno, M., Rvllion, M., Squire, L., Equity nd growth in developing countries: old nd new perspectives on the policy issues. In: Tnzi, V., Chu, K.-Y. (Eds.), Income Distribution nd High-Qulity Growth. MIT Press, Cmbridge, MA. Deininger, K., Squire, L., New wys of looking t old issues: inequlity nd growth. Journl of Development Economics 57, Eusufzi, Z., The Kuznets hypothesis: n indirect test. Economics Letters 54, Hnsen, B.E., Smple splitting nd threshold estimtion, Econometric, in press. Kuznets, S., Economic growth nd income inequlity. Americn Economic Review 45, 1 8.