Computes H values (cross-sectional variance) according to the clustering
algorithm by Phillips and Sul (2007, 2009)
Usage
computeH(X, quantity = "H", id)
Arguments
X
matrix or dataframe containing data (preferably filtered, in order to remove business cycles)
quantity
string indicating the quantity that should be returned. The options are
"H", the default, only the vector of cross-sectional variance is returned; "h",
only the matrix of transition path h is return; "both", a list containing
both h and H is returned.s
id
optional; row index of regions for which H values are to be computed;
if missing, all regions are used
Value
A numeric vector, a matrix or a list, depending on the value of quantity
Details
The cross sectional variation \(H_{it}\) is computed as the quadratic
distance measure for the panel from the common limit and under the
hypothesis of the model should converge to zero as t tends towards infinity:
$$H_t = N^{-1} \sum_{i=1}^N (h_{it}-1)^2 \rightarrow 0 , \quad t\rightarrow \infty$$
where
$$h_{it} = \frac{\log y_{it}}{( N^{-1} \sum_{i=1}^N log \, y_{it} )} $$
References
Phillips, P. C.; Sul, D., 2007. Transition modeling and econometric convergence tests. Econometrica 75 (6), 1771-1855.
Phillips, P. C.; Sul, D., 2009. Economic transition and growth. Journal of Applied Econometrics 24 (7), 1153-1185.
# NOT RUN {data("countryGDP")
h <- computeH(countryGDP[,-1], quantity="h")
H <- computeH(countryGDP[,-1], quantity="H")
b <- computeH(countryGDP[,-1], quantity="both")
# }