The study investigates the impact of trade openness on pollution in China by applying wavelet-coherence analysis, phase-difference technique and Breitung and Candelon (2006) causality test. The estimated results provide some dynamic association between trade openness and pollutant variables. The results indicate that trade openness has increased pollution in China especially after 2001 when China became member of WTO. It suggests that “pollution haven hypothesis” exists in China. These results imply that trade openness has increased exports which has increased domestic production by increasing the scale of industries, which in turn has increased pollution in the country. The findings of spectral domain causality test show that trade openness causes carbon emission both in short, medium and long runs. It indicates that trade openness forecast carbon emissions in China. The results suggest that China should take suitable measures while following trade openness policy to avoid pollution.

The importance of downside risk cannot be denied. In this study, we have replaced beta in the five-factor model of using downside beta and have added a momentum factor to suggest a new six-factor downside beta capital asset pricing model (CAPM). Two models are tested—a beta- and momentum-based six-factor model and a downside-beta- (proxy of downside risk) and momentum-based six-factor model. Beta and downside beta are highly correlated; therefore, portfolios are double-sorted to disentangle the correlation. Factor loadings, i.e., size, value, momentum, profitability, and investment, are constructed. The standard methodologies are applied. Data for sample stocks from different non-financial sectors listed in the Pakistan Stock Exchange (PSX) are taken from January 2000 to December 2018. The PSX-100 index and three-month T-bills are taken as proxies for market and risk-free returns. The study uses three subsamples for robustness—period of very high volatility, period of stability, and period of stability and growth with volatility. The results show that the value factor is redundant in both models. The momentum factor is rejected in the beta-based six-factor model only. The beta-based six-factor model shows very low R² in periods of highly volatility. The R² is high for the other periods. In contrast, the downside beta six-factor model captures the downside trend of the market in an effective manner with a relatively high R². The risk–return relationship is stronger for the downside beta model. These reasons lead us to believe that, overall, the downside beta six-factor model is a better option for investors as compared to the beta-based six-factor model in the area of asset pricing models.

The paper empirically examines the validity of purchasing power parity (PPP) in Pakistan. For this purpose, unit root properties of real exchange rates (RERs) of Pakistan against its 21 major trading partners are examined using Fourier ADF (FADF) and Fourier KPSS (FKPSS) unit root tests for the period 1983Q1 to 2014Q4. Fourier unit root tests are used as they consider multiple temporary structural breaks and nonlinearity of the data. FADF test rejects the null hypothesis of unit root (non-stationary) in three RER series, while FKPSS test rejects the null hypothesis of stationary in nine RER series. Thus, FADF unit root test provide support for PPP hypothesis in three exchange rate series, while FKPSS test validates PPP theory in 12 exchange rate series. For robustness analysis, PPP equation is also estimated using regression analysis. The regression results show that PPP hypothesis is valid for nine exchange rate series. These findings suggest that PPP hypothesis partially holds in Pakistan.