Q2. What future works have the authors mentioned in the paper "Testing for granger non-causality in heterogeneous panels" ?
This is precisely their objective for further researches.
Q3. What is the way to compute the critical values for the resampled data?
At each repetition keep the test statistics obtained for the resampled data, so as to compute the empirical critical values as the 95% percentile of the distribution of test-statistics (taken in absolute value) under the null hypothesis of no causality.
Q4. What is the power of the panel ZHncN statistic?
With T = 10, the power of the panel Z̃HncN statistic rises from 0.36 with five cross-section units to 0.87 with twenty cross-section units.
Q5. What is the main advantage of the standardized average Wald statistics?
One of the main advantages of their testing procedure is that it is very simple to implement: the standardized average Wald statistics are simple to compute and have a standard normal asymptotic distribution.
Q6. What is the purpose of this paper?
The aim of this paper is to propose a simple Granger (1969) non causality test in heterogeneous panel data models with fixed (as opposed to time-varying) coefficients.
Q7. What is the way to calculate the rejection rates for the test-statistics?
to account for cross-sectional dependence, the empirical power has to be computed from the rejection rates obtained with the bootstrapped critical values.
Q8. how can the F distribution be used to approximate the true distribution of the statistic Wi,T/?
in this dynamic model the F distribution can be used as an approximation of the true distribution of the statistic Wi,T/K for a small T sample.
Q9. What is the limiting distribution of the average statistic WHncN,T?
Theorem 1. Under assumption A2, the individual Wi,T statistics for i = 1, .., N are identically and independently distributed with finite second order moments as T →∞, and therefore, by Lindberg-Levy central limit theorem under the HNC null hypothesis, the average statistic WHncN,T sequentially converges in distribution.
Q10. What is the effect of the simulation on the results of the panel test statistics?
The simulation results clearly show that their panel based tests have very good properties even in samples with very small values of T and N .
Q11. What is the average Wald statistic for a fixed T?
For a fixed T , the Lyapunov central limit theorem is then sufficient to get the distribution of the standardized average Wald statistic when N tends to infinity.
Q12. What is the main advantage of the Monte Carlo simulations?
Monte Carlo simulations show that their panel statistics lead to substantial increase in the power of the Granger non-causality tests even for samples with very small T and N dimensions.
Q13. What is the lag order of the test-statistics?
if the lag-order differs from one individual to another, the distribution of the test-statistics, which depends on the number of restrictions imposed under the null, will vary across groups.
Q14. What is the condition for the existence of the moments of a quadratic form in normal?
If r ≤ T − 1, Magnus’s theorem (1986) identifies three conditions for the existence of the moments of a quadratic form in normal variables:(i) If AQ = 0, then E [(x′Ax/x′Bx)s] exists for all s ≥ 0.(ii) If AQ 6= 0 and Q′AQ = 0, then E [(x′Ax/x′Bx)s] exists for 0 ≤ s < r and does not exist for s ≥ r.(iii)
Q15. What is the distribution of the statistics when T tends to infinity?
Wi,T d−→ T→∞ χ2 (K) , ∀i = 1, .., N. (8)In other words, when T tends to infinity, the individual statistics {Wi,T}Ni=1 are identically distributed.