The article Inequality- the growth of plateau written by Daniel J. Henderson, Junhui Qian, and Le Wang, examines the potentially nonlinear relationship between inequality and growth through methods that do not require prior assumptions about the fundamental functional form. The article states that through this approach plateaus that are entirely missed by nonlinear parametric approaches expand rapidly with a large decline inequalities. It also states that the relationship between inequality and economic growth is important but controversial due to many views surrounding it. Theoretical literature shows that classical perspective states that inequality is beneficial for economic growth while the neoclassical approach states that inequality plays no role in promoting economic development. It continues to state that research shows that, inequality could have a permanent effect on economic development, but the impact is not necessarily beneficial and could be nonlinear.
The article also shows that empirical studies also show mixed results. It illustrates that while one source may show support for classical view while others show that inequality is crucial for the growth process. However such studies enforce linear structure on the equality growth relationship and ignore the potential nonlinear relationship as depicted in Theoretical literature. The inclusion of non-linearity is important because it helps in determining the relevant variables and also helps to discover key mechanisms for the growth process. Without the inclusion of non-linearity, it leads to using of assumptions that would eventually lead to nonlocal effects. However, the article provides an alternative that employs a semiparametric approach that relaxes functional form assumptions and allows the data to prove itself.
The authors of the article show various studies done by different authors like Banerjee and Duflo evaluates them and give their opinion. For example, Banerjee and Duflo adopt a nonparametric kernel estimation, but they fail to consider the panel structure of their data which in turn leads to omission of variables. As a solution to that problem, they suggest that a nonparametric panel data technique should be used on marginal incorporation to investigate the inequality-growth nexus.
The article states that the method used to reduce parametric from the relationship between inequality and growth is:
GRi,t = ai + b1Ii,t + i,t (1)
GRi,t = ai + b1Ii,t + b1I2i ,t + i,t (2)
GRi,t represents growth rate per capita GDP for country i at time t, Ii,t is the change in a measure of inequality, ai are country fixed effects, allowed to be correlated with the level of inequality and i,t is the idiosyncratic error term. The first equation assumes that the underlying relationship is linear while equation 2 assumes a quadratic relationship to capture potential non-linearity. Equation 1 and 2 can be estimated through the first different estimators. The article states that popular consistent is only obtained if the functional form is correctly specified. Assuming that the true relationship is unknown. It is at this point that they allow the data to form a relationship by using a nonparametric model:
GRi,t = ai + m(Ii,t ) + i,t , (3)
In this equation m (.) is an unknown smooth function. Fixed effects such as ai create a challenge in estimation thus resulting in a more complex equation.
GRi,t GRi,t1 = m(Ii,t ) m(Ii,t1) + i,t i,t1 (4)
1GRi,t = g(Ii,t , Ii,t1) + 1i,t .
A standard nonparametric estimation as stated in the article can help recover the function of g(.). The article states that m(.) is recovered by marginally integrating g(.). It also states that the estimator can be given by:
m(Ii,t ) =g(Ii,t , Ii,t1)f (Ii,t1)d(Ii,t1) (5)
Where f (Ii,t1) is a density function that satisfies f (Ii,t1)
The article concludes that using the nonparametric result; there is evidence that supports nonlinear relationship. However, two parametric results must emerge first. The authors also state that they found the turning point in the nonlinear relationship implicit by different approaches strikingly dissimilar. This is because while the parametric result indicated a peak around zero, the non-parametric result indicated a peak earlier. In conclusion, the article stated that there existed a negative relationship between inequality and economic growth.
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