Table 9 Entropy balancing estimations...

Table 9

Entropy balancing estimations

Panel A: Proof of convergence
Without weighting (before-balanced)
	Treated			Control
Variables	Mean	Variance	Skewness	Mean	Variance	Skewness
TANG	0.375	0.069	0.924	0.381	0.069	0.845
SIZE	7.662	4.032	0.403	7.894	4.006	0.295
ROA	0.049	0.011	0.238	0.047	0.010	0.362
LEVE	0.347	0.089	1.379	0.345	0.086	1.315
CASH	0.096	0.021	2.592	0.099	0.021	2.560
SLACK	0.650	5.553	6.872	0.670	5.745	6.698
Ln_OC	5.170	0.710	0.583	5.165	0.701	0.571
ROE	0.092	0.094	−0.831	0.082	0.086	−0.969
CFO	0.061	0.064	14.340	0.052	3.756	−18.830
Ln_Age	2.773	1.621	−1.224	2.766	1.692	−1.214
TOBINSQ	0.560	1.442	3.833	0.486	1.034	4.473
GDP_GRO	7.544	0.345	−0.604	5.022	17.930	−1.652

Panel A: Proof of convergence
Without weighting (before-balanced)
	Treated			Control
Variables	Mean	Variance	Skewness	Mean	Variance	Skewness
TANG	0.375	0.069	0.924	0.381	0.069	0.845
SIZE	7.662	4.032	0.403	7.894	4.006	0.295
ROA	0.049	0.011	0.238	0.047	0.010	0.362
LEVE	0.347	0.089	1.379	0.345	0.086	1.315
CASH	0.096	0.021	2.592	0.099	0.021	2.560
SLACK	0.650	5.553	6.872	0.670	5.745	6.698
Ln_OC	5.170	0.710	0.583	5.165	0.701	0.571
ROE	0.092	0.094	−0.831	0.082	0.086	−0.969
CFO	0.061	0.064	14.340	0.052	3.756	−18.830
Ln_Age	2.773	1.621	−1.224	2.766	1.692	−1.214
TOBINSQ	0.560	1.442	3.833	0.486	1.034	4.473
GDP_GRO	7.544	0.345	−0.604	5.022	17.930	−1.652

After weighting variable
		Treated			Control
Variables	Mean	Variance	Skewness	Mean	Variance	Skewness
TANG	0.375	0.069	0.924	0.375	0.063	0.805
SIZE	7.662	4.032	0.403	7.662	3.739	0.304
ROA	0.049	0.011	0.238	0.049	0.008	0.331
LEVE	0.347	0.089	1.379	0.347	0.076	0.944
CASH	0.096	0.021	2.592	0.096	0.019	2.624
SLACK	0.650	5.553	6.872	0.650	4.950	7.015
Ln_OC	5.170	0.710	0.583	5.170	0.702	0.504
ROE	0.092	0.094	−0.831	0.092	0.053	−0.350
CFO	0.061	0.064	14.340	0.061	5.139	79.400
Ln_Age	2.773	1.621	−1.224	2.773	1.539	−1.300
TOBINSQ	0.560	1.442	3.833	0.560	1.554	4.355
GDP_GRO	7.544	0.345	−0.604	7.543	12.750	−3.477

After weighting variable
		Treated			Control
Variables	Mean	Variance	Skewness	Mean	Variance	Skewness
TANG	0.375	0.069	0.924	0.375	0.063	0.805
SIZE	7.662	4.032	0.403	7.662	3.739	0.304
ROA	0.049	0.011	0.238	0.049	0.008	0.331
LEVE	0.347	0.089	1.379	0.347	0.076	0.944
CASH	0.096	0.021	2.592	0.096	0.019	2.624
SLACK	0.650	5.553	6.872	0.650	4.950	7.015
Ln_OC	5.170	0.710	0.583	5.170	0.702	0.504
ROE	0.092	0.094	−0.831	0.092	0.053	−0.350
CFO	0.061	0.064	14.340	0.061	5.139	79.400
Ln_Age	2.773	1.621	−1.224	2.773	1.539	−1.300
TOBINSQ	0.560	1.442	3.833	0.560	1.554	4.355
GDP_GRO	7.544	0.345	−0.604	7.543	12.750	−3.477

Panel B: Estimations with entropy balanced sample
	Investment inefficiency			Overinvestment			Underinvestment
Variables	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9
GPR	0.0083***			0.0161***			0.0037**
GPR	(0.002)			(0.004)			(0.002)
GPRT		0.0136***			0.0262***			0.0065***
GPRT		(0.002)			(0.007)			(0.002)
GPRA			0.0047***			0.0092***			0.0009
GPRA			(0.001)			(0.003)			(0.002)
TANG	0.0494***	0.0494***	0.0494***	0.0837***	0.0837***	0.0837***	−0.0187***	−0.0187***	−0.0187***
TANG	(0.010)	(0.010)	(0.010)	(0.013)	(0.013)	(0.013)	(0.003)	(0.003)	(0.003)
SIZE	−0.0057***	−0.0057***	−0.0057***	−0.0157***	−0.0157***	−0.0157***	−0.0021***	−0.0021***	−0.0021***
SIZE	(0.001)	(0.001)	(0.001)	(0.002)	(0.002)	(0.002)	(0.000)	(0.000)	(0.000)
ROA	0.0774***	0.0774***	0.0774***	0.1007*	0.1007*	0.1007*	−0.0267***	−0.0267***	−0.0267***
ROA	(0.027)	(0.027)	(0.027)	(0.058)	(0.058)	(0.058)	(0.004)	(0.004)	(0.004)
LEVE	0.0327***	0.0327***	0.0327***	0.0468***	0.0468***	0.0468***	0.0129***	0.0129***	0.0129***
LEVE	(0.004)	(0.004)	(0.004)	(0.010)	(0.010)	(0.010)	(0.001)	(0.001)	(0.001)
CASH	0.0339***	0.0339***	0.0339***	0.0752***	0.0752***	0.0752***	−0.0029	−0.0029	−0.0029
CASH	(0.008)	(0.008)	(0.008)	(0.016)	(0.016)	(0.016)	(0.002)	(0.002)	(0.002)
SLACK	0.0016***	0.0016***	0.0016***	0.0071***	0.0071***	0.0071***	0.0014***	0.0014***	0.0014***
SLACK	(0.000)	(0.000)	(0.000)	(0.002)	(0.002)	(0.002)	(0.000)	(0.000)	(0.000)
Ln_OC	−0.0005	−0.0005	−0.0005	−0.0071**	−0.0071**	−0.0071**	0.0007*	0.0007*	0.0007*
Ln_OC	(0.001)	(0.001)	(0.001)	(0.003)	(0.003)	(0.003)	(0.000)	(0.000)	(0.000)
ROE	0.0007	0.0007	0.0007	0.0013	0.0013	0.0013	−0.0026***	−0.0026***	−0.0026***
ROE	(0.003)	(0.003)	(0.003)	(0.011)	(0.011)	(0.011)	(0.001)	(0.001)	(0.001)
CFO	−0.0003	−0.0003	−0.0003	−0.0294**	−0.0294**	−0.0294**	0.0003	0.0003	0.0003
CFO	(0.000)	(0.000)	(0.000)	(0.011)	(0.011)	(0.011)	(0.000)	(0.000)	(0.000)
Ln_Age	−0.0057***	−0.0057***	−0.0057***	−0.0121***	−0.0121***	−0.0121***	−0.0009***	−0.0009***	−0.0009***
Ln_Age	(0.001)	(0.001)	(0.001)	(0.002)	(0.002)	(0.002)	(0.000)	(0.000)	(0.000)
TOBINSQ	0.0012	0.0012	0.0012	0.0081	0.0081	0.0081	−0.0017***	−0.0017***	−0.0017***
TOBINSQ	(0.002)	(0.002)	(0.002)	(0.006)	(0.006)	(0.006)	(0.000)	(0.000)	(0.000)
GDP_GRO	0.0004***	0.0003***	0.0004***	0.0000	−0.0000	0.0001	0.0007***	0.0007***	0.0007***
GDP_GRO	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
Intercept	0.0606***	0.0345**	0.0784***	0.1660***	0.1154**	0.2004***	0.1231***	0.1562***	0.1006***
Intercept	(0.012)	(0.015)	(0.010)	(0.031)	(0.041)	(0.027)	(0.005)	(0.006)	(0.004)
Industry FE	YES	YES	YES	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES	YES	YES	YES
Observations	39,599	39,599	39,599	11,919	11,919	11,919	27,680	27,680	27,680
Adj. R2	0.0833	0.0833	0.0833	0.1233	0.1233	0.1233	0.1237	0.1237	0.1237

Panel B: Estimations with entropy balanced sample
	Investment inefficiency			Overinvestment			Underinvestment
Variables	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9
GPR	0.0083***			0.0161***			0.0037**
GPR	(0.002)			(0.004)			(0.002)
GPRT		0.0136***			0.0262***			0.0065***
GPRT		(0.002)			(0.007)			(0.002)
GPRA			0.0047***			0.0092***			0.0009
GPRA			(0.001)			(0.003)			(0.002)
TANG	0.0494***	0.0494***	0.0494***	0.0837***	0.0837***	0.0837***	−0.0187***	−0.0187***	−0.0187***
TANG	(0.010)	(0.010)	(0.010)	(0.013)	(0.013)	(0.013)	(0.003)	(0.003)	(0.003)
SIZE	−0.0057***	−0.0057***	−0.0057***	−0.0157***	−0.0157***	−0.0157***	−0.0021***	−0.0021***	−0.0021***
SIZE	(0.001)	(0.001)	(0.001)	(0.002)	(0.002)	(0.002)	(0.000)	(0.000)	(0.000)
ROA	0.0774***	0.0774***	0.0774***	0.1007*	0.1007*	0.1007*	−0.0267***	−0.0267***	−0.0267***
ROA	(0.027)	(0.027)	(0.027)	(0.058)	(0.058)	(0.058)	(0.004)	(0.004)	(0.004)
LEVE	0.0327***	0.0327***	0.0327***	0.0468***	0.0468***	0.0468***	0.0129***	0.0129***	0.0129***
LEVE	(0.004)	(0.004)	(0.004)	(0.010)	(0.010)	(0.010)	(0.001)	(0.001)	(0.001)
CASH	0.0339***	0.0339***	0.0339***	0.0752***	0.0752***	0.0752***	−0.0029	−0.0029	−0.0029
CASH	(0.008)	(0.008)	(0.008)	(0.016)	(0.016)	(0.016)	(0.002)	(0.002)	(0.002)
SLACK	0.0016***	0.0016***	0.0016***	0.0071***	0.0071***	0.0071***	0.0014***	0.0014***	0.0014***
SLACK	(0.000)	(0.000)	(0.000)	(0.002)	(0.002)	(0.002)	(0.000)	(0.000)	(0.000)
Ln_OC	−0.0005	−0.0005	−0.0005	−0.0071**	−0.0071**	−0.0071**	0.0007*	0.0007*	0.0007*
Ln_OC	(0.001)	(0.001)	(0.001)	(0.003)	(0.003)	(0.003)	(0.000)	(0.000)	(0.000)
ROE	0.0007	0.0007	0.0007	0.0013	0.0013	0.0013	−0.0026***	−0.0026***	−0.0026***
ROE	(0.003)	(0.003)	(0.003)	(0.011)	(0.011)	(0.011)	(0.001)	(0.001)	(0.001)
CFO	−0.0003	−0.0003	−0.0003	−0.0294**	−0.0294**	−0.0294**	0.0003	0.0003	0.0003
CFO	(0.000)	(0.000)	(0.000)	(0.011)	(0.011)	(0.011)	(0.000)	(0.000)	(0.000)
Ln_Age	−0.0057***	−0.0057***	−0.0057***	−0.0121***	−0.0121***	−0.0121***	−0.0009***	−0.0009***	−0.0009***
Ln_Age	(0.001)	(0.001)	(0.001)	(0.002)	(0.002)	(0.002)	(0.000)	(0.000)	(0.000)
TOBINSQ	0.0012	0.0012	0.0012	0.0081	0.0081	0.0081	−0.0017***	−0.0017***	−0.0017***
TOBINSQ	(0.002)	(0.002)	(0.002)	(0.006)	(0.006)	(0.006)	(0.000)	(0.000)	(0.000)
GDP_GRO	0.0004***	0.0003***	0.0004***	0.0000	−0.0000	0.0001	0.0007***	0.0007***	0.0007***
GDP_GRO	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
Intercept	0.0606***	0.0345**	0.0784***	0.1660***	0.1154**	0.2004***	0.1231***	0.1562***	0.1006***
Intercept	(0.012)	(0.015)	(0.010)	(0.031)	(0.041)	(0.027)	(0.005)	(0.006)	(0.004)
Industry FE	YES	YES	YES	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES	YES	YES	YES
Observations	39,599	39,599	39,599	11,919	11,919	11,919	27,680	27,680	27,680
Adj. R2	0.0833	0.0833	0.0833	0.1233	0.1233	0.1233	0.1237	0.1237	0.1237

Note(s): This table presents the effects of GPR, GPRT, and GPRA on investment inefficiency, overinvestment, and underinvestment using the entropy balancing method. Firm-year observations with GPR values exceeding the median are categorized into the treatment group, while those with GPR values below the median are assigned to the control group. Panel A demonstrates the proof of convergence after entropy balancing. Panel B reports the regression results post-entropy balancing. All models employ pooled panel OLS estimation. Robust standard errors in brackets are clustered by firm and year to address serial correlation and heteroskedasticity. The measurement of the variables is in Appendix Table A1. *, **, and *** indicate significance levels of 10%, 5%, and 1%, respectively

Source(s): Authors own work

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