Question

Consider the following equation: GINI = 12.42 + 0.341 (GDP per capita) – 0.073 (GDP per capita)2 + error where, GINI denotes the Gini coefficient and GDP per capita is in real US$. (a) Interpret the marginal effect of GDP per capita on the Gini coefficient. (b) Draw an approximate diagram depicting the estimated relationship. (C) Is there a way of testing for nonlinearity in the above relationship? (d) Provide an alternative nonlinear equation for modelling Gini coefficient on GDP per capita. Draw a rough diagram showing its shape.

Answer 1

Joy . Date GI INI 12.42+0.341/ GYDP per capita) = 0.073 [ORDP per capitaj? +evier where and GINT GDP demotes the per capita is Gini in coefficient real us & (a) Marginal the effect of GDP por capita year toefficient is girsin d (lipp pin capital - 15 0:341 – 2 (0.073) app pur capital Marginal Effect = 634–0-846 (lub As we can see that in this case marginal ethet 4 GDP per espite is a function of of GDP por capite. Therefore, at different level of GDP per capita, the marginal effect on G, INI 'coefficient will be different st:Scanned with CamScanner

GINI culationship ated estrat 72-421 2:34 GDP per capita (6.) Nonlinearity in the above rilationship can be seen by the inclusion of square tannia in the equatico Polosince of square torm. dinotes the y shaped I tilationship betnicom GDP her capita and GINI Coefficient ! Since I louificent At Squasie tusim is negative. This means that the relation is imucited v shaped for low (GDP per capita Grini inofficient will. tirst increase with increasing Gpl per capita homener, for high values Scanned with Caricarre

Gre fui capital, Gimi couffiuesit I will all with increase in GDP per capita 10) Analizzati nez? linear Equation for modelling Giani coefficient on • GDP per capita can be Gini = a + b. ln (GDP per capita) wfronte a - contincept stein 6714 eotعدم اعتماد سط Chim 1 when GDP per capita ? Scanned with CamScanner 64 PP per capita