Hello everyone,
I am using system GMM for my study. My panel covers 1990–2023 for about 190 countries, although some variables have missing observations for some years. I averaged the annual data into 5-year periods, so my final panel has approximately N = 190 and T = 7.
My main model is:
GDP_it = ρ₁GDP_i,t−1 + ρ₂GDP_i,t−2 + β₁Health_it + β₂Schooling_it + β₃Trade_it + β₄Investment_it + β₅Inflation_it + β₆OldAgeDependency_i,t−1 + country fixed effects + time fixed effects + ε_it.
In this model, the dependent variable is GDP per worker. My main explanatory variable is health. OldAgeDependency_i,t−1 is entered as lag to avoid simultaneity between health and old age dependency ratio. I treat the lagged dependent variables, health, trade openness, investment, and inflation as endogenous. I treat schooling, capital, and the lagged old-age dependency ratio as predetermined.
I have three questions:
I am using system GMM for my study. My panel covers 1990–2023 for about 190 countries, although some variables have missing observations for some years. I averaged the annual data into 5-year periods, so my final panel has approximately N = 190 and T = 7.
My main model is:
GDP_it = ρ₁GDP_i,t−1 + ρ₂GDP_i,t−2 + β₁Health_it + β₂Schooling_it + β₃Trade_it + β₄Investment_it + β₅Inflation_it + β₆OldAgeDependency_i,t−1 + country fixed effects + time fixed effects + ε_it.
In this model, the dependent variable is GDP per worker. My main explanatory variable is health. OldAgeDependency_i,t−1 is entered as lag to avoid simultaneity between health and old age dependency ratio. I treat the lagged dependent variables, health, trade openness, investment, and inflation as endogenous. I treat schooling, capital, and the lagged old-age dependency ratio as predetermined.
I have three questions:
- Panel unit root tests
Which panel unit root test would be appropriate in this context, given that (T=7) after averaging and the panel has missing observations? I tried Fisher-type and Pesaran/CIPS tests, but some variables do not work properly because of missing observations. - Instrument relevance in system GMM
System GMM reports Hansen and difference-in-Hansen tests, which help assess instrument validity/exogeneity. However, I also want to assess instrument relevance. Is it meaningful to check first-stage regressions using ivreg2, or is this not directly comparable to the internal-instrument structure of system GMM? - Lagged predetermined variable as regressor
According to Arellano-Bond, Blundell-Bond, and Roodman, for a predetermined variable, valid instruments in the differenced equation can start from (t-1) and earlier. In my model, old-age dependency ratio enters as a lagged regressor, (oldage_{i,t-1}). After differencing, this becomes (\Delta oldage_{i,t-1}).
My confusion is about the correct starting lag for GMM instruments. Since the underlying variable is predetermined, and it is uncorrelated with differenced error term, should the valid instruments for the differenced equation be (oldage_{i,t-1}), (oldage_{i,t-2}), and earlier? Or, because the regressor itself is already lagged, should the instruments start from (oldage_{i,t-2}). instead? - My understanding is that, in the level equation of system GMM, the instruments are first differences. For endogenous variables, we use the nearest valid lagged difference (e.g., ΔGDP_{it-1} for GDP_{it-1}, and ΔHealth_{it-1} for Health_{it}). For predetermined variables, the first difference dated the same as the regressor in the level equation (e.g., if the regressor is OldAgeDependency_{it-1}, then the instrument is ΔOldAgeDependency_{it-1}). Is this understanding correct?
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