Vertical or horizontal: optimal integration strategy under separation of ownership and control

Figures & data

Figure 1. Vertical and horizontal integration.

Source: own research.

Table 1. PBEs of benchmark and integration case without control.

		Integration without control
	No integration ($N$)	Vertical integration ($VF$)	Horizontal integration ($HF$)
$q_1$	$\frac{-c\eta -\alpha +c}{2\eta -4}$	$\frac{[{\eta }^2\lambda -4+(\lambda -2)\eta ](c\eta +\alpha -c)(\lambda -1)}{{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16}$	$\frac{-c\eta -\alpha +c}{{\lambda \eta }^2-(\lambda -2)\eta -4}$
$q_2$	$\frac{-c\eta -\alpha +c}{2\eta -4}$	$\frac{[{\eta }^3{\lambda }^2+\lambda (\lambda -1){\eta }^2+(\lambda -2)\eta +4\lambda -4](c\eta +\alpha -c)}{{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16}$	$\frac{-c\eta -\alpha +c}{{\lambda \eta }^2-(\lambda -2)\eta -4}$
${\omega }_1$	$-\frac{-c\eta +\alpha +c}{2\eta -2}$	$\frac{\varphi (\eta )}{\left(\eta -1\right)[{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16]}$	$\frac{\tau (\eta )}{\left(\eta -1\right)[{\lambda \eta }^2-(\lambda -2)\eta -4]}$
${\omega }_2$	$-\frac{-c\eta +\alpha +c}{2\eta -2}$	$\frac{\varphi \left(\eta \right)-4\lambda [c{\eta }^3+\alpha {\eta }^2-(3c-\alpha )\eta +2(c-\alpha \left)\right]}{\left(\eta -1\right)[{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16]}$	$\frac{\left(-\alpha \lambda +c\right){\eta }^2+\left[\left(\lambda -1\right)\alpha -3c\right]\eta +2(c+\alpha )}{\left(\eta -1\right)[{\lambda \eta }^2-(\lambda -2)\eta -4]}$
${\pi }_U$	$\frac{{(c(\eta -1)+\alpha )}^2}{2(\eta -1)(\eta -2)}$	$\frac{(\eta +2){\left(c\eta +\alpha -c\right)}^2(\lambda \eta +\lambda -2)}{\left(\eta -1\right)[{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16]}$	$\frac{{\left[\right(\eta -1)c+\alpha ]}^2}{\left(\eta -1\right)[{\lambda \eta }^2-(\lambda -2)\eta -4]}$
${\pi }_{D_1}$	$\frac{{(c(\eta -1)+\alpha )}^2}{4{(\eta -2)}^2}$	$\frac{{\left(c\left(\eta -1\right)+\alpha \right)}^2}{\left(\eta -1\right){\left[{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16\right]}^2}{\psi }^{VF}(\eta )$	$\frac{{(\lambda \eta +\lambda +1)\left[\right(\eta -1)c+\alpha ]}^2}{{[{\lambda \eta }^2-(\lambda -2)\eta -4]}^2}$
${\pi }_{D_2}$	$\frac{{(c(\eta -1)+\alpha )}^2}{4{(\eta -2)}^2}$	$\frac{{\left(c\left(\eta -1\right)+\alpha \right)}^2}{{\left[{\eta }^4{\lambda }^2-{\left(\lambda -2\right)}^2{\eta }^2-16\lambda +16\right]}^2}{\chi }^{VF}(\eta )$	$\frac{{\left[\right(\eta -1)c+\alpha ]}^2}{{[{\lambda \eta }^2-(\lambda -2)\eta -4]}^2}$

*${\psi }^{VF}(\eta )$ and ${\chi }^{VF}(\eta )$ are given by (13) and (14).

$\mathrm{ }\varphi \left(\eta \right)={c\lambda }^2{\eta }^5-c\lambda \left(\lambda +1\right){\eta }^4-\left[c{\lambda }^2-\left(6c-\alpha \right)\lambda +2c\right]{\eta }^3+\left[c{\lambda }^2+\left(c+\alpha \right)\lambda +2\left(c+\alpha \right)\right]{\eta }^2-\left[\left(22c-6\alpha \right)\lambda -8c\right]\eta +16c\lambda -8(c+\alpha ).$

$\mathrm{ }\tau \left(\eta \right)=c\lambda {\eta }^3-\left(2\lambda -1\right)c{\eta }^2+\left[c\left(\lambda -3\right)-\alpha \right]\eta +2(c+\alpha ).$

Source: own research.

Figure 2. Profits of integrated firms without control.

Source: own research.

Table 2. PBEs of benchmark and integration case with control.

		Integration with control
	No integration ($N$)	Vertical integration ($VC$)	Horizontal integration ($HC$)
$q_1$	$\frac{-c\eta -\alpha +c}{2\eta -4}$	$\frac{\left(1+\eta \right)\lambda {\rm Y}(\eta )}{({\lambda }^2+6\lambda +1){\eta }^2-8\lambda }$	$\frac{(\eta +1)(c\eta +\alpha -c)\lambda }{{(\lambda +1)}^2\eta +4\lambda }$
$q_2$	$\frac{-c\eta -\alpha +c}{2\eta -4}$	$\frac{\left(1+\eta \right)\left[c\eta \right(\eta -1){\lambda }^2+(\eta -2\left)\right(c\eta +\alpha -c)\lambda +\alpha \eta ]}{{\eta }^2{\lambda }^2+6{\eta }^2\lambda +{\eta }^2-8\lambda }$	$\frac{(\eta +1)(c\eta +\alpha -c)\lambda }{{(\lambda +1)}^2\eta +4\lambda }$
${\omega }_1$	$-\frac{-c\eta +\alpha +c}{2\eta -2}$	$0$	$\frac{c\eta \left(\eta -1\right){\lambda }^2+\left(\eta +2\right)\left(c\eta -\alpha -c\right)\lambda -\alpha \eta }{\left(\eta -1\right)[\eta {\lambda }^2+2(\eta +2)\lambda +\eta ]}$
${\omega }_2$	$-\frac{-c\eta +\alpha +c}{2\eta -2}$	$\frac{c\eta \left(\eta -1\right)\left(\eta +2\right){\lambda }^2-\left({\eta }^2-2\eta -4\right)\left(c\eta +\alpha -c\right)\lambda -\alpha \eta (\eta +2)}{{\eta }^2{\lambda }^2+6{\eta }^2\lambda +{\eta }^2-8\lambda }$	$\frac{c\left(\lambda +1\right){\eta }^2-\left[\alpha {\lambda }^2-\left(c-\alpha \right)\lambda +c\right]\eta -2\lambda (c+\alpha )}{\left(\eta -1\right)[{\left(\lambda +1\right)}^2\eta +4\lambda ]}$
${\pi }_i$		$\frac{-\lambda \left(1+\eta \right)\xi \left(\eta \right)}{{\eta }^2{\lambda }^2+6{\eta }^2\lambda +{\eta }^2-8\lambda }$	$\frac{(1+\lambda ){{\lambda }^2(1+\eta )}^2{(c\eta +\alpha -c)}^2}{{\left(1-\eta \right)[{\left(1+\lambda \right)}^2\eta +4\lambda ]}^2}$
${\pi }_i^{\prime }$		$\frac{{\left(1+\eta \right)}^2{\left[c\eta \right(\eta -1){\lambda }^2+(\eta -2\left)\right(c\eta +\alpha -c)\lambda +\alpha \eta ]}^2}{{\eta }^2{\lambda }^2+6{\eta }^2\lambda +{\eta }^2-8\lambda }$	$\frac{(1+\eta )\lambda {(c\eta +\alpha -c)}^2}{\left(1-\eta \right)[{\left(1+\lambda \right)}^2\eta +4\lambda ]}$

$\mathrm{{\rm Y}}\left(\eta \right)=2c\lambda {\eta }^3+\left(c+2\alpha -\lambda c\right){\eta }^2+\left(\alpha -c+\lambda \alpha -5c\lambda \right)\eta +4\lambda c-4\alpha .$

$\mathrm{ }\xi \left(\eta \right)$ is given by (26).

$i\in \{{UD}_1,D_1{D}_2\}.$

${\pi }_i^{\mathrm{\text{'}}}$ represents the profit rival of firm ${\pi }_i.$

Source: own research.

Figure 3. Profits of integrated firms with control.

Source: own research.

Figure 4. Profits of integrated firms in consistent circumstance between ownership and control.

Source: own research.

Figure 5. Impacts of market environment without control.

Source: own research.

Figure 6. Impacts of market environment with control.

Source: own research.

Figure 7. Profits of vertical and horizontal integrated firms.

Source: own research.

Figure 8. Profits of integrated firms and market structure.

Source: own research.

Figure 9. Profits of integrated firms in case of independent market.

Source: own research.

Table 3. Regression results of firm’s short-term (long-term) performance.

	Full sample						Integration sample
	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7
NHM	0.071*	0.051*	0.066*	0.037	0.027	0.054	−0.107**
	(0.084**)	(0.032**)	(0.051**)	(0.029*)	(0.21*)	(0.060**)	(−0.099*)
VER	0.183***	0.167***	0.173**	0.109***	0.127**	0.109**
	(0.161***)	(0.140*)	(0.150**)	(0.134**)	(0.114*)	(0.132*)
HOR	0.129***	0.095***	0.110***	0.066**	0.062**	0.084*
	(0.081*)	(0.066*)	(0.072*)	(0.012*)	(0.102*)	(0.093**)
MS		0.035**			0.026**
		(0.044*)			(0.032**)
MC			0.010*			0.007*
			(0.007**)			(0.013**)
VER$\times$MS		0.022**
		(0.010*)
HOR$\times$MS		0.017*
		(0.011*)
VER$\times$MC			−0.037
			(−0.014)
HOR$\times$MC			0.011
			(0.008**)
COD				−0.028**	−0.031**	−0.028*
				(−0.017*)	(−0.017*)	(−0.019**)
VER$\times$COD				−0.021*	−0.018*	−0.026*
				(−0.024**)	(−0.023*)	(−0.014**)
HOR$\times$COD				−0.029**	−0.038*	−0.027**
				(−0.014*)	(−0.029**)	(−0.019*)
VER$\times$COD$\times$MS					0.017*
					(0.026**)
HOR$\times$COD$\times$MS					0.009
					(0.011)
VER$\times$COD$\times$MC						−0.026
						(−0.035)
HOR$\times$COD$\times$MC						0.007**
						(0.014*)
HNM^2							0.129**
							(0.106*)
Control variables	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Obs.	1764	1764	1764	1764	1764	1764	406
Adj. R-squared	0.3028 (0.3119)	0.3274 (0.3283)	0.3169 (0.3198)	0.3449 (0.3691)	0.3601 (0.3789)	0.3582 (0.3621)	0.0977 (0.1014)

This table presents the results of ordinary least-square (OLS) regressions. The dependent variable is CAR. The t-values are in the parentheses. All control variables are defined in Sec. 5.1.

*, **, *** are significant at 10%, 5%, and 1%, respectively.

Source: own research.

Table 4. Robustness check for different levels of control-ownership disparity.

	Low level of disparity		High level of disparity
	Model 8	Model 9	Model 10	Model 11
NHM	0.049*	0.074**	0.040*	0.055*
	(1.92)	(2.53)	(1.84)	(1.95)
VER	0.149***	0.144***	0.166**	0.158*
	(4.87)	(7.32)	(2.12)	(1.90)
HOR	0.089***	0.111***	0.095*	0.087**
	(3.99)	(3.79)	(1.90)	(2.11)
MS	0.041*		0.039***
	(1.81)		(3.33)
MC		0.013*		0.015*
		(1.87)		(1.76)
VER$\times$MS	0.037		0.027**
	(0.58)		(2.28)
HOR$\times$MS	0.009*		0.021
	(1.69)		(1.05)
VER$\times$MC		−0.035		−0.024
		(−0.59)		(−0.44)
HOR$\times$MC		0.007*		0.008***
		(1.77)		(6.06)
Control variables	Yes	Yes	Yes	Yes
Obs.	660	660	1104	1104
Adj. R-squared	0.3247	0.2973	0.3001	0.2612

*, **, *** are significant at 10%, 5%, and 1%, respectively.

Source: own research.

Table 5. Robustness check based on DID approach.

	Substitute market		Complementary market
	Model 12	Model 13	Model 14	Model 15
$Du{m}_{\mathit{COD}}$	−0.060**	−0.047*	−0.051**	−0.064*
	(−2.15)	(−1.60)	(−2.55)	(−1.73)
$Du{m}_{\mathit{VER}}$	0.180***		0.117**
	(3.61)		(2.10)
$Du{m}_{\mathit{HOR}}$		0.120*		0.105**
		（1.69）		(1.97)
$Du{m}_{\mathit{COD}}\times Du{m}_{\mathit{VER}}$	−0.031		−0.017**
	(−0.67)		(−2.13)
$Du{m}_{\mathit{COD}}\times Du{m}_{\mathit{HOR}}$		−0.025*		−0.011
		(−1.70)		(−0.82)
Control variables	Yes	Yes	Yes	Yes
Obs.	1935	1935	1161	1161
Adj. R-squared	0.2017	0.1980	0.2491	0.1631

*, **, *** are significant at 10%, 5%, and 1%, respectively.

Source: own research.