The development version of the package can be installed via
if (!require(remotes)) install.packages("remotes")
remotes::install_github("cadam00/poobly")The Hsiao poolability/homogeneity test (Hsiao 1986; 2022) for panel data is used to determine the homogeneity of coefficients across individuals in panel data. The test is composed of three consecutive hypotheses. The hypothesis that slope and intercept (constant) coefficients are the same across the panel is initially tested. If this hypothesis is not rejected, then the total homogeneity (pool) of both slopes and intercepts is concluded. If the first hypothesis is rejected, the second hypothesis tests the homogeneity of the slope coefficients. If this second hypothesis is rejected, different slope coefficients for all individuals are indicated, suggesting total heterogeneity. If this hypothesis is not rejected, then homogeneity of slope coefficients is implied. If this second hypothesis is not rejected, then the the third hypothesis tests the homogeneity of the intercept coefficients across individuals is performed. If this last hypothesis is not rejected, then total homogeneity is resulted. If this last hypothesis is rejected, equal slopes but different intercepts across individuals are indicated. The current implementation is derived from Hsiao (2022). This procedure is capitulated in Figure 1 and Table 1.
Fig. 1: Hsiao homogeneity hypothesis testing flow chart.
| Hypothesis | Null | Alternative |
| H1 | Pooled | H2 |
| H2 | H3 | Heterogeneous intercepts & slopes |
| H3 | Pooled | Heterogeneous intercepts & Homogeneous slopes |
Table 1: Hsiao homogeneity hypothesis testing table.
For this example, the data Gasoline from plm R package will be
used.
# Import poobly and plm packages to workspace
library(poobly)
library(plm)
# Import "Gasoline" dataset
data("Gasoline", package = "plm")
# Print first 6 rows
head(Gasoline)## country year lgaspcar lincomep lrpmg lcarpcap
## 1 AUSTRIA 1960 4.173244 -6.474277 -0.3345476 -9.766840
## 2 AUSTRIA 1961 4.100989 -6.426006 -0.3513276 -9.608622
## 3 AUSTRIA 1962 4.073177 -6.407308 -0.3795177 -9.457257
## 4 AUSTRIA 1963 4.059509 -6.370679 -0.4142514 -9.343155
## 5 AUSTRIA 1964 4.037689 -6.322247 -0.4453354 -9.237739
## 6 AUSTRIA 1965 4.033983 -6.294668 -0.4970607 -9.123903
A pdata.frame or a data.frame object is expected as and a formula are
required as minimum essential input for the hsiao function. Note that
data.frame object input should be able to be transformed as pdata.frame
object and index input can be used as well. For more about pdata.frame see
at plm::pdata.frame.
# Hsiao hypothesis testing
x <- hsiao(lgaspcar ~ lincomep + lrpmg + lcarpcap, Gasoline)
print(x)##
## Hsiao Homogeneity Test
##
## Hypothesis| Null | Alternative
## ----------+------+---------------------------------------------
## H1 |Pooled| H2
## H2 | H3 | Heterogeneous intercepts & slopes
## H3 |Pooled|Heterogeneous intercepts & homogeneous slopes
## ===============================================================
##
## formula: lgaspcar ~ lincomep + lrpmg + lcarpcap
##
## Hypothesis F-statistic df1 df2 p-value
## 1 H1 129.3166 68 270 < 0.001
## 2 H2 27.3352 51 270 < 0.001
## 3 H3 83.9608 17 321 < 0.001
According to this result, the coefficients of the given countries have both
heterogeneous intercept & slope. In detail, the first hypothesis,
Hsiao, C. (2022) Analysis of Panel Data. 4th edn. Cambridge: Cambridge University Press (Econometric Society Monographs), pp. 43-49. doi:10.1017/9781009057745