A comparative analysis of the outliers influence using GMM estimation based on dynamic panel data model

Figures & data

Table 1. Effect of financial development on economic growth: DIF-GMM.

	Without considering the outliers				Considering the outliers
Explanatory Variables	1	2	Instrumenting bank development 3	Instrumenting stock market development 4	1	2	Instrumenting bank development 3	Instrumenting stock market development 4
GROWTHi,t-1	0.941*** (0.000)	0.942*** (0.000)	0.954*** (0.000)	0.953*** (0.000)	0.705*** (0.000)	0.710*** (0.000)	0.780*** (0.000)	0.784*** (0.000)
LENDINGi,t-1	−0.018* (0.095)	−0.019*** (0.000)	−0.010* (0.086)	−0.023*** (0.000)	0.174*** (0.000)	0.174*** (0.000)	0.069*** (0.000)	0.097*** (0.000)
MKTCAPi,t-1	0.026*** (0.000)	0.026*** (0.000)	0.005*** (0.000)	0.010*** (0.000)	0.066*** (0.000)	0.065*** (0.000)	0.012*** (0.000)	0.017*** (0.000)
GCONSUMP	−0.370*** (0.000)	−0.406*** (0.000)	−0.333*** (0.000)	−0.334*** (0.000)	1.180*** (0.000)	1.167*** (0.000)	1.149*** (0.000)	1.005*** (0.000)
INVESTMENT	0.056* (0.074)	0.054*** (0.000)	0.065*** (0.000)	0.055*** (0.000)	0.414*** (0.000)	0.414*** (0.000)	0.394*** (0.000)	0.382*** (0.000)
WALD STATISTIC	220.58*** (0.000)	197.05*** (0.000)	153.03*** (0.000)	107.01*** (0.000)	630.40*** (0.000)	133.55*** (0.000)	395.17*** (0.000)	315.63*** (0.000)
No. of Observations	1536	1536	1536	1536	1536	1536	1536	1536
Usable Observations	1486	1486	1486	1486	1355	1355	1354	1357
No. of Outliers	—	—	—	—	131	131	132	129

Notes: 1. Our model is: $GROWT{H}_{it}={\eta }_i+\alpha GROWT{H}_{i\left(t-1\right)}+{\beta }_{1}LENDIN{G}_{i\left(t-1\right)}+{\beta }_{2}MKTCA{P}_{i\left(t-1\right)}+{\beta }_{3}GCONSUM{P}_{it}+{\beta }_{4}INVESTMEN{T}_{it}+v_{it}$.

2. p-values are in parentheses.

3. The GMM estimates reported are all two step except column (1).

4. *, **, *** denote significance at the 10%, 5%, and 1% levels, respectively.

5. DIF-GMM is the estimator which can be found in Arellano and Bond (1991).

6. We apply the LTS estimator for the residuals from the DIF-GMM estimator and define the outliers whose LTS standardized residuals exceed 2.5.

7. The basic instrument set used in columns (1), (2) is of the form $Z_i=\left[\begin{array}{cccc}GROWT{H}_{i1}& 0& 0& \begin{array}{cccc}\cdots & 0& \cdots & 0\end{array}\\ 0& GROWT{H}_{i1}& GROWT{H}_{i2}& \begin{array}{cccc}\cdots & 0& \cdots & 0\end{array}\\ ⋮& \hspace{0.17em}& \hspace{0.17em}& \begin{array}{cccc}\ddots & 0& \cdots & 0\end{array}\\ 0& 0& 0& \begin{array}{cc}\begin{array}{cc}GROWT{H}_{i1}& \cdots \end{array}& GROWT{H}_{i32}\end{array}\end{array}\begin{array}{c}⋮\\ ⋮\\ ⋮\\ ⋮\end{array}\begin{array}{c}\mathrm{\Delta }{x}_{i3}^{\prime }\\ \mathrm{\Delta }{x}_{i4}^{\prime }\\ ⋮\\ \mathrm{\Delta }{x}_{i33}^{\prime }\end{array}\right]\begin{array}{c}1990\\ 1991\\ ⋮\\ 2020\end{array}$ where $x_{it}$ is the vector of exogenous variables included in the Equation (4)(4) $GROWT{H}_{it}={\eta }_i+\alpha GROWT{H}_{i(t-1)}+{\beta }_{1}LENDIN{G}_{i(t-1)}+{\beta }_{2}MKTCA{P}_{i(t-1)}+{\beta }_3{Z}_{it}+v_{it},$(4) . For example, the equation for 1990 in first differences can be written as $\mathrm{\Delta }GROWT{H}_{i3}=\alpha \mathrm{\Delta }GROWT{H}_{i2}+{\beta }_1\mathrm{\Delta }LENDIN{G}_{i2}+{\beta }_2\mathrm{\Delta }MKTCA{P}_{i2}+{\beta }_3\mathrm{\Delta }GCONSUM{P}_{i3}+{\beta }_4\mathrm{\Delta }INVESTMEN{T}_{i3}+\mathrm{\Delta }{v}_{i3}.$ For countries on which less than 33 observations are available, the rows of $Z_i$ corresponding to the missing equations are deleted and the missing values of dependent variable in the remaining rows are replaced by zeros. In column (3), $Z_i$ is modified to take the form.

$Z_i=\left[diag\left(GROWT{H}_{i1}\cdots GROWT{H}_{is}LENDIN{G}_{i\left(s-2\right)}LENDIN{G}_{i\left(s-1\right)}\right)⋮\left(\mathrm{\Delta }{x}_{i3}^{\prime }\cdots \mathrm{\Delta }{x}_{i33}^{\prime }\right)\right]$ $\left(s=2,\dots ,32\right)$, where $x_{it}$ is now the vector of explanatory variables excluding bank development but including stock market development, government consumption and investment; In column (4), $Z_i$ is modified to take the form.

$Z_i=\left[diag\left(GROWT{H}_{i1}\cdots GROWT{H}_{is}MKTCA{P}_{i\left(s-2\right)}MKTCA{P}_{i\left(s-1\right)}\right)⋮\left(\mathrm{\Delta }{x}_{i3}^{\prime }\cdots \mathrm{\Delta }{x}_{i33}^{\prime }\right)\right]$ $\left(s=2,\dots ,32\right)$, where $x_{it}$ is now the vector of explanatory variables excluding stock market development but including bank development, government consumption, and investment.

Arellano, M., and S. Bond. 1991. “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.” The Review of Economic Studies 58 (2): 277–297.

 Web of Science ®Google Scholar