A Stata command to generate, summarize, and visualize partial sums for modeling asymmetry with panel data.
xtasysum generates, summarizes, and visualizes partial sums for modeling asymmetry with panel data. If no options are specified then positive and negative partial sums around a threshold of zero are created. The two new variables appear as var_p and var_n, respectively. The partial sums can be used to model and test for asymmetry using regression analysis as discussed in Thombs, Huang, and Fitzgerald (2022). The user may also generate frequencies and summary tables, test for cross-sectional dependence and non-stationarity, and generate graphs of the partial sums as well as their frequencies.
xtasysum varlist [if] [in] [, Threshold(#) Frequency Sum fdm GRSum GRFre grssave(string) grfsave(save) csd CSDOpt(string asis) cips(numlist integer min=2 max=2) CIPSOpt(string asis) NOgen]
Threshold specifies the threshold by which the partial sums are generated; default is Threshold(0).
Frequency creates a table containing the frequencies of the partial sums by each variable in varlist.
Sum creates a summary table of the partial sums for each variable in varlist; see xtsum. When nogen is specified, a summary table of the original variable is provided.
fdm generates a variable of the partial sums based on the first difference method (see Allison (2019) and York and Light (2017)).
GRSum generates a line graph of the partial sums by panel. No graph is drawn, but a graph for each variable is saved.
GRFre generates a bar graph of the frequencies of the partial sums by panel. No graph is drawn, but a graph for each variable is saved.
grssave(string) saves the line graph of the partial sums by panel with a specified name.
grfsave(string) saves the bar graph of the partial sums by panel with a specified name.
csd reports the Pesaran (2015) test for weak cross-sectional dependence and the exponent of cross-sectional dependence (Bailey, Kapetanios, and Pesaran 2016, 2019); This is a wrapper of Ditzen's (2021) xtcse2 program. When nogen is specified, test results correspond to the original variable.
CSDOpt(string asis) passes options to xtcse2.
cips(numlist integer min=2 max=2) reports the Pesaran (2007) panel unit-root test in the presence of cross-sectional dependence. This is a wrapper of the xtcips program (Burdisso and Sangiácomo 2016). When specified, the first integer refers to the maximum number of lags included in the test, and the second number is the autocorrelation order used in the Lagrange multiplier test (see xtcips). When nogen is specified, test results correspond to the original variable.
CIPSOpt(string asis) passes options to xtcips.
NOgen does not create partial sums for the variable. This option cannot be combined with threshold or fdm. This option is useful if the partial sums have already been created or you are interested in examining the original variable.
An example dataset consisting of annual country-level data for GDP per capita, the percentage of the population residing in urban areas, and total population from 1971 to 2015 is available here.
To generate the partial sums:
xtasysum lngdp
The default threshold is 0, which can be changed with the Threshold option:
xtasysum lngdp, threshold(.01)
To generate the frequencies and descriptive statistics of the partial sums by each variable:
xtasysum lngdp, frequency sum
To test for cross-sectional dependence and non-stationarity:
xtasysum lngdp, csd cips(3 3)
To generate variables based on the first difference method:
xtasysum lngdp, fdm
If the partial sums are already defined, then use nogen option to test for cross-sectional dependence:
xtasysum lngdp_p lngdp_n, nogen csd
To generate a graph of the frequencies and partial sums:
xtasysum lngdp, grsum grfre
This will produce the following graphs:
xtasysum can be installed by typing the following in Stata:
net install xtasysum, from("https://raw.githubusercontent.com/rthombs/xtasysum/main") replace
Allison, Paul D. 2019. "Asymmetric Fixed-Effects Models for Panel Data." Socius: 1-12.
Bailey, Natalia, George Kapetanios, and M. Hashem Pesaran. 2016. "Exponent of Cross-Sectional Dependence: Estimation and Inference." Journal of Applied Econometrics 31: 929-960.
Bailey, Natalia, George Kapetanios, and M. Hashem Pesaran. 2019. "Exponent of Cross-sectional Dependence for Residuals." Sankhya B 81: 46–102.
Burdisso, Tamara and Máximo Sangiácomo. 2016. "Panel Time Series: Review of the Methodological Evolution." The Stata Journal 16(2): 424-442.
Ditzen, Jan. 2021. "Estimating Long-Run Effects and the Exponent of Cross-Sectional Dependence: An Update to xtdcce2." The Stata Journal 21(3): 687-707.
Pesaran, M. Hashem. 2015. "Testing Weak Cross-Sectional Dependence in Large Panels." Econometric Reviews 34(6-10): 1089–1117.
Shin, Yongcheol, Byungchul Yu, and Matthew Greenwood-Nimmo. 2014. "Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework." Pp. 281–314 in Festschrift in Honor of Peter Schmidt, edited by R. Sickle C. Horrace. New York: Springer.
Thombs, Ryan. P., Xiaorui Huang, and Jared B. Fitzgerald. 2022. "What Goes Up Might Not Come Down: Modeling Directional Asymmetry with Large-N, Large-T Data." Sociological Methodology 52(1): 1-29.
York, Richard and Ryan Light. 2017. "Directional Asymmetry in Sociological Analyses." Socius 3.
Special thanks to Jared Fitzgerald and Xiaorui Huang for helpful comments and suggestions.
Ryan P. Thombs
(Boston College)
Contact Me: thombs@bc.edu