Existence of Solutions for a Class of Nonlinear Neumann BVPs in the Presence of Upper and Lower Solutions

In this article, we explore the monotone iterative technique (MI-technique) to study the existence of solutions for a class of nonlinear Neumann 4-point, boundary value problems (BVPs) defined as, \begin{eqnarray*} \begin{split} -\z^{(2)}(\y)=\x(\y,\z,\z^{(1)}),\quad 0<\y<1,\\ \z^{(1)}(0)=\lambda \z^{(1)}(\beta_1 ),\quad \z^{(1)}(1)=\delta \z^{(1)}(\beta_2), \end{split} \end{eqnarray*} where $ 0<\beta_1 \leq \beta_2 <1$ and $\lambda$, $\delta\in (0,1)$. The nonlinear term $ \x(\y,\z,\z^{(1)}): \Omega\rightarrow \mathbb{R} $, where $\Omega =[0,1]\times \mathbb{R}^2 $, is Lipschitz in $ \z^{(1)}(\y)$ and one sided Lipschitz in $ \z(\y)$. Using lower solution $l(\y)$ and upper solutions $u(\y)$, we develop MI-technique, which is based on quasilinearization. To construct the sequences of upper and lower solutions which are monotone, we prove maximum principle as well as anti maximum principle. Then under certain assumptions, we prove that these sequence converges uniformly to the solution $ \z(\y)$ in the specific region, where $ \frac{\partial\x}{\partial\z}<0 $ or $ \frac{\partial\x}{\partial\z}>0 $. To demonstrate that the proposed technique is effective, we compute the solution of the nonlinear multi-point BVPs. We don’t require sign restriction which is very common and very strict condition.

THE IMPACT OF THE CHINESE TEXTILE IMPORTS ON EMPLOYMENT AND VALUE ADDED IN THE TEXTILE INDUSTRY OF THE SOUTH AFRICAN ECONOMY

With the increased trade linkage between China and African economies, this paper endeavours to assess the dynamic impacts of Chinese textile imports on employment and value added in the South African textile industry. This paper makes use of the structural vector autoregressive (SVAR) methodology with sign restriction. Moreover, based on this methodology, this paper conducts a counterfactual analysis to uncover what would have happened to employment and value added trends in the South African textile industry in the absence of trade with China. The results of the empirical analysis show that total employment responds negatively to shocks to import from China. Moreover, the results of the counterfactual analysis show that the South African economy could perform better without textile imports from China.

Narrative Sign Restrictions for SVARs

We identify structural vector autoregressions using narrative sign restrictions. Narrative sign restrictions constrain the structural shocks and/or the historical decomposition around key historical events, ensuring that they agree with the established narrative account of these episodes. Using models of the oil market and monetary policy, we show that narrative sign restrictions tend to be highly informative. Even a single narrative sign restriction may dramatically sharpen and even change the inference of SVARs originally identified via traditional sign restrictions. Our approach combines the appeal of narrative methods with the popularized usage of traditional sign restrictions. (JEL C32, E52, Q35, Q43)

CREDIT-RELATED SHOCKS IN VAR MODELS: THE CASE OF LITHUANIA

This article provides empirical evidence on the role played by credit-related shocks over the business cycle in Lithuania. To this end, we estimate a vector auto regression (VAR) with credit and housing variables and identify credit-related shocks. Using sign restriction, we identify credit supply shocks; while using zero restrictions, we identify credit spread shocks. We find evidence that credit-related shocks have a significant effect on housing and credit market variables, while the effect on GDP is less pronounced but still significant. While credit supply shocks weighed down on economic growth during the period from 2008 to 2014, the effect turned positive in 2014.