An alternative approach which is easily implemented is to use a random effects model to model the between States  and within States between year analysis simultaneously. This will allow you to estimate how the between variance function changes over time to assess convergence / divergence with confidence intervals around the estimate   

see

https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_Modeling_of_Time-Series_Cross-Sectional_and_Panel_Data

https://www.researchgate.net/publication/299604336_Fixed_and_Random_effects_making_an_informed_choice

The first part of this paper looks at the  convergence-divergence hypothesis for between country mortality finding that life expectancy in different countries converged on an improving global trend until the mid 1980's but subsequently saw greater inequalities and divergence after that date - the second part shows that countries can be grouped according to their diverging and converging trends

https://www.researchgate.net/publication/46541418_International_variations_in_life_expectancy_A_spatio-temporal_analysis

Article International variations in life expectancy: A spatio-tempor...

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...

Article Fixed and Random effects models: making an informed choice

Dear Kelvyn I appreciate your quickly answering, will review some of recomended papers. Mario

follow my two papers below 

 http://www.sciencedirect.com/science/article/pii/S1364032114004250

http://www.sciencedirect.com/science/article/pii/S0961953416301179 

Stata code is 

xtpmg d.y d.x, lr (l.y l.x) replace pmg 

Thank Kazy, I will apply your stata code recomended and review articles . Mario