This study has been conducted to investigate the empirical evidence for and against ELG by using a new econometric methodology i.e. Markov Chain Method (MCM) and compared it with the existing methodology. MCM has many essential differences from those currently in use. One of them is that we do not treat data as being capable of giving us final answer to any question, but only as a way to give clues about reality. The exports and GDP data retrieved from WDI World Bank from 1960-2014 to assess Hypothesis whether the transition probabilities remained same across all the countries over time period used in the study. By using MCM based on median measure the analysis of exports has shown that among all the countries, there are two exceptional countries: Morocco and Nigeria which have 6/5 unusual H-L and 5/6 L-H transitions in the export level respectively. The clues obtained from the data are supported by the real world events that are the actual cause of unusual increase or decrease in exports of the underling exceptional countries. The MCM results for gross GDP have not shown any unusual behavior among any of the countries used in the sample studies. To re-examine the ELG hypothesis the data show some unusual behavior in low and high category of ΔX and ΔGDP for eight countries i.e. Brazil, China, Hong Kong, Korea, Mexico, Singapore, Spain and Senegal. In order to assess ELG for low and high exporting/income countries the results of Cross MCM have shown that there is no evidence for ELG in case any country and GLE for China, but a feedback mechanism for Senegal and Korea and no relationship for rest of the countries i.e. Brazil, Hong Kong, Mexico, Singapore and Spain. Findings of Singapore and China have shown exceptional behavior in the sense that a transition of high export led low growth for Singapore and data on China show some unusual fits that led the economy to transit from high growth led low exports with the lag of one period. These surprising fits obtained from the data have some real justification. On the other hand side results of Standard Granger Causality Test on the same data set, indicate that just for Singapore there is bidirectional causation among ΔX and ΔGDP. ELG, GLE or feedback mechanism is not found for any of the above countries: Brazil, China, Hong Kong, Korea, Mexico, Senegal, Singapore and Spain. The difference in the findings for each country is may be due to adoption of different large scale institutional reforms, abundance of natural resources, structure of economy and change in the system of incentives etc. Supervisor:- Dr. Asad Zaman