Making Abundant Natural Resources Work for Developing Economies

types of statistics, the within-based (or panel cointegrating) statistics and the betweenbased(or the group mean panel) statistics. The first sets of statistics are based onpooling the autoregressive coefficients across different members for the unit root testson the estimated residuals. The second sets of statistics are based on estimators thattake a simple average of the individually estimated coefficients for each member.Following Pedroni (1999), the statistics are calculated as:Panel ν statistic:N Tˆ −22 −1Z ν = ( ∑∑L11 i eˆit−1)i= 1 i=1Panel ρ statisticZN TN Tˆ−22 −1( ˆ ) ˆ−2ρ = ∑∑ L11ieit−1∑∑L11i(ˆ eit−1Δeˆit ii= 1 t=1i= 1 t=1Panel PP-statistic− ˆ λ )ZtN T1−N T= ∑∑ 11iit 1 ∑∑ i it−i= 1 t=1i= 1 t=12 ˆ−222( ˆ ˆ )2−σ L e − L11(ˆ e 1Δeˆit− ˆ λ )iPanel ADF-statisticZN T1−N T* *2 ˆ−2*2 2 ˆ−2*2 *t = ( sˆ∑∑L11ieˆit−1) ∑∑L11ieˆit Δeˆiti= 1 t=1i= 1 t=1Group ρ statistic~ZρNT2 −1= ∑∑ ( eˆit−) ∑ ( eˆi= 1 t=1Group PP statisticΔeˆ− ˆ λ )1 it−1it i~ZtNT∑ ∑2 2= ( ˆ σ eˆ)2it−1( eˆit−1Δeˆit−i= 1 t=11−T∑t=11− ˆ λ )iGroup ADF-statistic~ N T1−T*2 *2*Z ( ˆ )2( ˆ ˆ*t = ∑∑sieit−1 ∑ eit−1Δeiti= 1 t=1t=1)