We assume that the firm’s capital stock $K_t$ evolves according to

$\text{d}{K}_t=\left(I_t-{\delta }_K{K}_t\right)\text{d}t+ϵI_t\text{d}{Z}_t^I,$(2.1)

where $I_t$ is investment, ${\delta }_K>0$ is the depreciation rate, $ϵ>0$ is a volatility parameter; $Z_t^I$ is a standard Brownian motion. Since the firm’s output comes from its capital stock, the specification of (2.1) implies that output fluctuations arise from shocks to the marginal efficiency of investment (Keynes [16] ), that is, the investment-specific technology shocks. This specification is motivated by the growing literature that emphasizes the important role of investment-specific technology shocks as a source of aggregate volatility (e.g., Greewood, Hercowitz, and Huffman [17] ; Fisher [18] , among others).

The gross output of the firm over the period $\left(t,t+\text{d}t\right)$ is given by $K_t\text{d}{A}_t$ which is proportional to its time- $t$ capital stock $K_t$. The firm’s operating profit $\text{d}{Y}_t$ over the same period is thus given by

$\text{d}{Y}_t=K_t\text{d}{A}_t-I_t\text{d}t-G\left(I_t,K_t\right)\text{d}t,$(2.2)

where $A_t$ denotes the productivity of the capital; $G\left(I,K\right)$ is the adjustment cost. Motivated by WWY [7] , we assume that the firm is subject to productivity shocks in that

$\text{d}{A}_t={\mu }_A\text{d}t+{\sigma }_A\text{d}{Z}_t^A,$(2.3)

where $Z_t^A$ is another standard Brownian motion that is independent of $Z_t^I$; ${\mu }_A>0$ is the mean of the productivity shock, and ${\sigma }_A>0$ is the volatility of the productivity shock. Consistent with Hayashi [19] , we assume that the adjustment cost $G\left(I,K\right)$ is convex in $I$ and homogeneous of degree one in $I$ and $K$. Specifically,

$G\left(I,K\right)=g\left(i\right)K=\frac{\theta i^2}{2}K,$(2.4)

where $i=I/K$ denotes the investment-capital ratio, and the parameter $\theta$ measures the degree of adjustment cost.

Following Shleifer and Vishny [20] , La Porta et al. [21] , and the literature on investor protection, we assume that the controlling agent is fully entrenched and has complete control over the firm’s investment and payout policies. More details on how control rights differ from cash flow rights (via dual-class shares, pyramid-ownership structures, cross-ownership, etc.) can be found in Bebchuk, Kraakman, and Triantis [22] , La Porta, Lopez-de-Silanes, and Shleifer [23] , among others. Throughout the paper, we will use the names “controlling agent”, “entrepreneur”, or “controlling shareholder” interchangeably.

Building on Johnson et al. [24] , La Porta et al. [21] , and AW [6] , we model private benefits via a stealing technology in that the entrepreneur may “steal” a $s$-fraction of the firm’s average output ${\mu }_{A}K$, by incurring a convex cost in the amount of

$H\left(s,AK\right)=\frac{\beta }{2}{s}^2{\mu }_{A}K,$(2.5)

where the parameter $\beta$ measures the degree of investor protection. Specifically, a higher $\beta$ implies a larger marginal cost $\beta s{\mu }_{A}K$ of diverting cash for private benefits and hence a stronger protection for outside investors. Taking into account $s$ and $H(.)$, the entrepreneur’s consumption with the firm is given by

$C_1=yD+s{\mu }_{A}K-\frac{\beta }{2}{s}^2{\mu }_{A}K,$(2.6)

where $D$ denotes the firm’s dividend payout; $y\in \left[0,1\right]$ which denotes the entrepreneur’s cash-flow right with the firm; $s{\mu }_{A}K-\frac{\beta }{2}{s}^2{\mu }_{A}K$ denotes her net benefits from stealing.

The entrepreneur has the standard CRRA utility over her consumption as follows:

$J_t=E_t\left[{\displaystyle {\int }_t^{\infty }\zeta {\text{e}}^{-\zeta \left(v-t\right)}U\left(C_{1,s}\right)\text{d}s}\right].$(2.7)

In (2.7), $\zeta$ denotes her subjective discount rate;

$U\left(C\right)=\frac{C^{1-\gamma }}{1-\gamma },$(2.8)

where $\gamma \left(>0\right)$ denotes the (constant) coefficient of relative risk aversion.

All outside investors are identical and they have the same preference as the entrepreneur and the preferences are defined on their consumption streams with the firm². Thus, an outside shareholder $i$’s utility derived from the firm can be written as:

$J_{2,t}=E_t\left[{\displaystyle {\int }_t^{\infty }\zeta {\text{e}}^{-\zeta \left(v-t\right)}\frac{{\left(C_{2,s}^i\right)}^{1-\gamma }}{1-\gamma }\text{d}s}\right],$(2.9)

where $C_{2,s}^i={\varphi }^i{D}_s$ with ${\varphi }^i$ denoting his cash-flow right with the firm. In combination, outside shareholders own a total of $1-y$ fraction of the firm.

In addition to consumption and investment, the entrepreneur can also invest in a risk-free asset which pays a constant rate of interest $r$ and the risky market portfolio (Merton [25] ). Assume that the incremental return $\text{d}{R}_t$ of the market portfolio over the time period $\text{d}t$ is i.i.d. as follows:

$\text{d}{R}_t={\mu }_R\text{d}t+{\sigma }_R\text{d}{B}_t,$(2.10)

where ${\mu }_R$ and ${\sigma }_R$ are constant mean and volatility parameters of the market portfolio return process; $B_t$ is a standard Brownian which correlates with $Z_t^I$ and $Z_t^A$ by ${\rho }_I$ and ${\rho }_A$, respectively³.

Let $W$ and $X$ denote the firm’s liquid wealth and the amount invested in the risky asset, respectively. Their difference, $W-X$, is thus invested in the risk-free asset. Out of its liquid asset, the firm pays the cost for capital investment, distribute dividend ( $y$-fraction of which is paid to the entrepreneur), and runs the stealing cost to the entrepreneur’s private benefit. Thus, the firm’s liquid wealth evolves according to

$\text{d}{W}_t=\left[r{W}_t+\eta {\sigma }_R{X}_t-D_t-s_t{\mu }_A{K}_t\right]\text{d}t+X_t{\sigma }_R\text{d}{B}_t+\text{d}{Y}_t,$(2.11)

where

$\eta \equiv \frac{{\mu }_R-r}{{\sigma }_R},$(2.12)

which denotes the market Sharpe ratio; $\text{d}{Y}_t$ is given by (2.2). Note that $W$ can be negative, under which the firm borrows against its capital stock⁴.

Accounting for her cash-flow right, we write the entrepreneur’s value function, which is introduced in (2.7), as $J\left(K,W;y\right)$. By the standard dynamic programming argument, the entrepreneur solves the following Hamilton-Jacobi-Bellman (HJB) equation:

$\zeta J\left(K_t,W_t;y\right)=\underset{D,s,X,I}{\text{max}}\zeta U\left(C_{1t}\right)+E_t\left[\text{d}J\left(K_t,W_t;y\right)\right],$(3.1)

where $E_t[.]$ the expectation conditional on information available at time $t$. In this original version of HJB, the left-hand side (LHS) $\zeta J\left(K_t,W_t;y\right)$ reflects the required rate of return for the entrepreneur to hold the firm (per unit of time); the right-hand side (RHS) is the expected gain to the entrepreneur from holding the firm which involves two components: 1) her utility derived from the firm and 2) the expected change of her value function. By Ito’s lemma and making use of (2.1), (2.2), (2.3), and (2.11), we obtain

$\begin{array}{c}0=\underset{D,s,X,I}{\text{max}}-\zeta J\left(K,W;y\right)+\zeta U\left(C_1\right)+\left(I-{\delta }_{K}K\right)J_K\\ +\left[r{W}_t+\eta {\sigma }_R{X}_t+{\mu }_A{K}_t-I_t-G\left(I_t,K_t\right)-D_t-s_t{\mu }_A{K}_t\right]J_W\\ +\frac{{ϵ}^2{I}^2}{2}{J}_{KK}+{\rho }_IϵI{\sigma }_{R}X{J}_{KW}+\frac{{\sigma }_A^2{K}^2+2\rho {\sigma }_{A}K{\sigma }_{R}X+{\sigma }_R^2{X}^2}{2}{J}_{WW},\end{array}$(3.2)

where $C_1$ is given by (2.6)⁵. The entrepreneur chooses the firm’s optimal dividend payout according to

$\zeta U^{\prime }\left(C\right)\frac{\partial C}{\partial D}=J_W\left(K,W\right),$(3.3)

which is the usual condition that marginal utility of consumption is equated with the marginal value of wealth, with the adjustment that one unit reduction of $W$ only raises the entrepreneur’s consumption by the units of $y\left(<1\right)$ which characterizes her cash-flow right with the firm. The first-order condition (FOC) for the diversion (or stealing) $s$ is given by

$\zeta U^{\prime }\left(C\right)\frac{\partial C}{\partial s}=J_W\left(K,W\right){\mu }_{A}K.$(3.4)

Combining (3.4) with (3.3) and making use of (2.6) to evaluate the $C$-derivatives, we can explicitly solve out the optimal stealing as follows:

$s^{*}=\frac{1-y}{\beta }$(3.5)

(3.5) indicates that the entrepreneur steals more when investor protection deteriorates or when there is a high degree of control friction as indicated by a lower $y$.

The entrepreneur further chooses the firm’s investment and asset allocation policies that are optimally determined according to

$\left[1+G_I\left(I,K\right)\right]J_W-{ϵ}^{2}I{J}_{KK}-{\rho }_Iϵ{\sigma }_{R}X{J}_{KW}=J_K$(3.6)

and

$X=-\frac{{\mu }_R-r}{{\sigma }_R^2}\frac{J_W}{J_{WW}}-\frac{\rho {\sigma }_A}{{\sigma }_R}K-\frac{{\rho }_Iϵ{\sigma }_{R}I}{{\sigma }_R^2}\frac{J_{KW}}{J_{WW}},$(3.7)

respectively. Du (2024) provides the financial interpretations of the above FOCs for $I$ and $X$ under the context of a special case when the control-ownership wedge is shut down.

We conjecture (and verify later) that the controlling shareholder’s value function $J\left(K,W;y\right)$ takes the following form:

$J\left(K,W;y\right)=\frac{{\left(bP\left(yK,yW\right)\right)}^{1-\gamma }}{1-\gamma },$(3.8)

where the constant $b$ is given by

$b=\zeta {\left[1+\frac{1-1/\gamma }{\zeta }\left(r-\zeta +\frac{{\eta }^2}{2\gamma }\right)\right]}^{\frac{\gamma }{\gamma -1}},$(3.9)

which is independent of $y$⁶. In (3.8), we let the arguments of $P(.)$ to be $yK$ and $yW$ which emphasizes that the entrepreneur’s cash-flow right with the firm applies to both the liquid wealth $W$ and the capital stock $K$. We interpret $P\left(yK,yW\right)$ as the certainty-equivalent (CE) valuation of the firm by the entrepreneur: It denotes the minimum dollar amount that she would demand to permanently give up her entitlement to the firm (including her privileges with the firm through the stealing technology) and retire as a Merton-style consumer.

To establish the form of $P(.)$, we exploit the model’s homogeneity property to reduce the entrepreneur’s problem to one dimension. Specifically, we treat $K_t$ as the scaling factor, and we use lower case letters to denote the following variables: firm’s liquid wealth $w_t=W_t/K_t$, the entrepreneur’s CE valuation of the firm $p_t=P_t/K_t$, consumption $c_t=c_t/K_t$, investment $i_t=I_t/K_t$, and risky ass et al. location $x_t=X_t/K_t$. Using these notations, we can express $P\left(yK,yW\right)$ from (3.8) as

$P\left(yK,yW\right)=\left(yK\right)\cdot p\left(w;y\right)=y\cdot \left[Kp\left(w;y\right)\right],$(3.10)

where $Kp\left(w;y\right)$ is interpreted as the entrepreneur’s shadow valuation of the firm with $w$ being the measure of the firm’s financial status. Due to her incomplete ownership with the firm, the entrepreneur’s CE valuation of the firm, $P\left(yK,yW\right)$, is only $y$-fraction of this shadow valuation as indicated by (3.10)⁷. In view of (3.8)-(3.10), we can write the entrepreneur’s value function more explicitly as:

$J\left(K,W;y\right)=\frac{{\left[byKp\left(w\right)\right]}^{1-\gamma }}{1-\gamma }.$(3.11)

⁶The formula of $b$ is inferred from the solution of Merton’s [25] consumption and portfolio choice problem which can be treated as a simplified version of our model when capital investment, stochastic production, and the control-ownership wedge are all shut down.

By (3.11) we have the following expressions for $J$-derivatives:

$J_W={\left(by\right)}^{1-\gamma }{\left(p\left(w\right)K\right)}^{-\gamma }{p}^{\prime }\left(w\right),$(3.12)

$J_K={\left(by\right)}^{1-\gamma }{\left(p\left(w\right)K\right)}^{-\gamma }\left(p\left(w\right)-w{p}^{\prime }\left(w\right)\right),$(3.13)

$J_{WW}={\left(by\right)}^{1-\gamma }{\left(p\left(w\right)K\right)}^{-\gamma -1}\left[p\left(w\right)p^{″}\left(w\right)-\gamma {\left(p^{\prime }\left(w\right)\right)}^2\right],$(3.14)

$J_{KW}={\left(by\right)}^{1-\gamma }{\left(p\left(w\right)K\right)}^{-\gamma -1}\left[-wp\left(w\right)p^{″}\left(w\right)-\gamma p^{\prime }\left(w\right)\left(p\left(w\right)-w{p}^{\prime }\left(w\right)\right)\right],$(3.15)

$J_{KK}={\left(by\right)}^{1-\gamma }{\left(p\left(w\right)K\right)}^{-\gamma -1}\left[w^{2}p\left(w\right)p^{″}\left(w\right)-\gamma {\left(p\left(w\right)-w{p}^{\prime }\left(w\right)\right)}^2\right].$(3.16)

By substituting $J$ from (3.8) and (3.10) into (3.3) and simplifying, we obtain the following consumption rule:

$c_1^{*}\left(w;y\right)=y{\zeta }^{\frac{1}{\gamma }}{b}^{\frac{1-\gamma }{\gamma }}{p}^{\prime }{\left(w;y\right)}^{-\psi }p\left(w;y\right).$(3.17)

where $b$ is given by (3.9). Due to the control-ownership wedge, the entrepreneur’s consumption is naturally discounted by a factor of $y\left(<1\right)$ which reflects her partial cash-flow right with the firm. By (2.6), the firm’s dividend policy at the presence of control friction is

$D^{*}\left(w;y\right)={\zeta }^{\frac{1}{\gamma }}{b}^{\frac{1-\gamma }{\gamma }}p\left(w;y\right)p^{\prime }{\left(w;y\right)}^{-\psi }K-\frac{1-y^2}{2\beta y}{\mu }_{A}K,$(3.18)

where we’ve made use of the entrepreneur’s optimal stealing policy given in (3.5). Expressed in terms of $D^{*}$, the entrepreneur’s optimal consumption can be written as

$C_1^{*}\left(w;y\right)=y{D}^{*}\left(w;y\right)+\frac{1-y^2}{2\beta }{\mu }_{A}K.$(3.19)

Relative to her cash-flow right, the entrepreneur consumes more by the amount of $\frac{1-y^2}{2\beta }{\mu }_{A}K$ which is attributed to the stealing technology⁸.

By substituting (3.12) and (3.15)-(3.14) into (3.6)-(3.7) and simplifying, we obtain

$i^{*}\left(w\right)=\frac{p-\left(w+1\right)p^{\prime }-{\rho }_Iϵp^{\prime }\frac{\gamma p-wh}{p}\left(\eta \frac{p}{h}-\rho {\sigma }_A\right)}{\theta p^{\prime }+\left(1-{\rho }_I^2\right){ϵ}^2\frac{p^{\prime }}{p}\frac{{\left(\gamma p-wh\right)}^2}{h}-\gamma {ϵ}^2\frac{p^2{p}^{″}}{h{p}^{\prime }}},$(3.20)

$x^{*}\left(w;i\right)=\frac{\eta }{{\sigma }_R}\frac{p}{h}-\frac{\rho {\sigma }_A}{{\sigma }_R}-{\rho }_I\frac{ϵi}{{\sigma }_R}\left(\frac{\gamma p}{h}-w\right),$(3.21)

where

$h\left(w;y\right)\equiv \gamma p^{\prime }\left(w;y\right)-\frac{p\left(w;y\right)p^{″}\left(w;y\right)}{p^{\prime }\left(w;y\right)}$(3.22)

By substituting optimal policies of (3.5), (3.17), (3.20), and (3.21), as well as (3.12)-(3.16) into (3.2), scaling by $K$ wherever is necessary, and simplifying, tedious algebra gives

$\begin{array}{c}0=\frac{{\zeta }^{\psi }{b}^{1-\psi }p{\left(p^{\prime }\right)}^{1-\psi }-\zeta \psi p}{\psi -1}+{\mu }_A{p}^{\prime }-\rho \eta {\sigma }_A{p}^{\prime }+\left(r+{\delta }_K\right)w{p}^{\prime }\\ -{\delta }_{K}p+\frac{1}{2}\frac{{\eta }^{2}p{p}^{\prime }}{h}{\psi }_y{p}^{\prime }{\mu }_A-\frac{1}{2}\left(1-{\rho }^2\right){\sigma }_A^2\frac{p^{\prime }h}{p}\\ +\frac{1}{2}\frac{{\left[p-\left(w+1\right)p^{\prime }-{\rho }_Iϵp^{\prime }\frac{\gamma p-wh}{h}\left(\eta \frac{p}{h}-\rho {\sigma }_A\right)\right]}^2}{\theta p^{\prime }+\left(1-{\rho }_I^2\right){ϵ}^2\frac{p^{\prime }}{p}\frac{{\left(\gamma p-wh\right)}^2}{h}-\gamma {ϵ}^2\frac{p^2{p}^{″}}{h{p}^{\prime }}},\end{array}$(3.23)

where

${\psi }_y\equiv \frac{{\left(1-y\right)}^2}{2y\beta }.$(3.24)

The firm gets liquidated when $w$ becomes sufficiently negative, upon which the firm-held capital stock yields the terminal value of $l{K}_t$ for $l\in \left(0,1\right)$. Let $\tau$ be the (stochastic) liquidation time optimally chosen by the entrepreneur so that the firm’s liquidation value can be written as $W_{\tau }+l{K}_{\tau }$. Upon liquidation, the entrepreneur collects her entitled liquidation payment and retires as a Merton consumer (Merton [21] ) where her value function takes the form of

$J^M\left(y\left[W+lK\right]\right)=\frac{{\left(by\left[W+lK\right]\right)}^{1-\gamma }}{1-\gamma },$(3.25)

where $b$ is given by (3.9); and the expression $y\left[W+lK\right]$ again reflects the entrepreneur’s partial cash-flow right with the firm. Let $W_d$ denote the firm’s liquidation boundary with $w_d\equiv W_d/K$. Since $W_d$ is optimally chosen, we have the following value matching and smooth-pasting conditions:

$J\left(K,W_d;y\right)=J^M\left(y\left[W_d+lK\right]\right),$(3.26)

${\frac{\partial J\left(K,W;y\right)}{\partial W}|}_{W=W_d}={\frac{\partial J^M\left(y\left[W+lK\right]\right)}{\partial W}|}_{W=W_d}.$(3.27)

Simplifying (3.26)-(3.27) by making use of (3.8), (3.10), and (3.25), we obtain

$p\left(w_d;y\right)=w_d+l,$(3.28)

$p^{\prime }\left(w_d;y\right)=1.$(3.29)

At the other end when $w\to \infty$, the firm is no longer concerned about the potential liquidation under which

$\underset{w\to \infty }{\text{lim}}p\left(w;y\right)=w+\hat{q}\left(y\right),$(3.30)

where $\hat{q}\left(y\right)$ denotes the constant valuation of the firm-held capital for the given $y$. To identify $\hat{q}$, we simplify (3.20) and (3.23) at $w\to \infty$ by making use of (3.30) so as to obtain⁹

$\hat{i}=\frac{\hat{q}-1-{\rho }_Iϵ\eta \hat{q}}{\theta }$(3.31)

and

$0=\left(1+{\psi }_y\right){\mu }_A-\hat{i}-\frac{1}{2}\theta i^2-\rho \eta {\sigma }_A-\left(r+{\delta }_K\right)\hat{q}+\left(1-{\rho }_Iϵ\eta \right)\hat{i}\hat{q},$(3.32)

where ${\psi }_y$ is given by (3.24). (3.31)-(3.32) imply a quadratic equation on $\hat{i}$ and we pick the root so that $\hat{i}$ as the optimal investment in the limiting case is increasing in the firm’s expected productivity ${\mu }_A$, i.e.,

$\hat{i}\left(y\right)=\frac{r+{\delta }_K}{1-{\rho }_I\epsilon \eta }-\sqrt{{\left(\frac{r+{\delta }_K}{1-{\rho }_I\epsilon \eta }\right)}^2-\frac{2}{\theta }\left[\left(1+{\psi }_y\right){\mu }_A-\frac{r+{\delta }_K}{1-{\rho }_I\epsilon \eta }-\rho \eta {\sigma }_A\right]}.$(3.33)

Substituting (3.33) back into (3.31) identifies $\hat{q}$¹⁰. (3.28)-(3.29) combined with (3.30) thus provide the three boundary conditions required to solve the second-order ODE of (3.23) on $p\left(w;y\right)$ with the free boundary $w_d$. For simplicity, in the following we generally omit the $y$-dependences unless there is a need to highlight the control-ownership wedge.

We first analyze the impact of control friction on firm’s optimal policies and the

results are plotted in Figure 2 ¹¹. As we lower the entrepreneur’s cash-flow right $y$ for the given $\beta <\infty$, the degree of control friction gets higher and Panel A of Figure 2 shows that it facilitates stealing which is quite intuitive. Since the entrepreneur’s consumption $C_1$ depends on her cash-flow right, a lower $y$ mechanically reduces the optimal consumption-capital ratio $c_1^{*}$ (see its formula by (29)) as plotted in Panel B. We further consider $C_1/y$ which is interpreted as the entrepreneur’s consumption per unit of her cash-flow right with the firm, or “PU-consumption” in short. As shown in Panel C of Figure 2 , the optimal PU consumption-capital ratio, $c_1^{*}/y$, is monotonically decreasing in $y$ which reflects the simple fact that more stealing under a higher degree of control friction enables the entrepreneur to consume more for each unit of her cash-flow right.

The optimal investment-capital ratio $i^{*}$ and optimal portfolio allocation $x^{*}$ are plotted in Panel D&E, respectively. Like $c_1^{*}/y$, they are both decreasing in $y$. In contrast, Panel F of Figure 2 shows that the optimally chosen liquidation boundary $w_d$ is monotonically increasing as $y$ rises. Taken together, the entrepreneur at a higher degree of control friction, as indicated by a lower $y$, steals more (Panel A), consumes more in the “per-unit” sense (Panel C), over-invests (Panel D), and takes a more aggressive position in the stock market (Panel E)¹². This way, she grows the firm bigger in the longer-term which delays its liquidation (Panel F) and thus allows her to retain the control for a longer time.

We next consider the valuation of the firm. This valuation is different than $P\left(W,K\right)$, the firm’s shadow valuation by the entrepreneur, which takes into account her privileges from the stealing technology. In contrast, the firm valuation we want to calculate here is viewed by outside investors so it can be treated as the valuation of the firm in the open market. To this purpose, we need to calculate the present value (PV) of dividend payouts to outside shareholders with the appropriate discounting. Since the firm involves various risks, a discounting by the risk-free rate doesn’t seem appropriate. While we can calculate the implied risk premium demanded by the firm according to its market exposure, previous researches (e.g., Moskowitz and Vissing-Jorgensen [31] ; Mueller [32] ; WWY [7] ) show that entrepreneurial firms also claim idiosyncratic risk premium. To account for both the systematic and the additional idiosyncratic risk premium for non-diversifiable firm-level risk, we follow WWY [7] to calculate the cost of capital $\xi$, which is deemed as the internal rate of return (IRR) for the firm, as follows:

$Q\left(K_0,W_0\right)=q_0{K}_0=E\left[{\displaystyle {\int }_0^{\tau }{\text{e}}^{-\xi \left(w_0\right)t}\text{d}{Y}_t}+{\text{e}}^{-\xi \left(w_0\right)\tau }l{K}_{\tau }\right],$(5.1)

where $\tau$ denotes the stochastic liquidation time. $\xi (.)$ thus defined is state-dependent and Panel A of Figure 3 plots the implied $\xi$ as the function of $w$ for two scenarios of $\beta$ where the scenario at $\beta =\infty$, by ruling out stealing, shuts down the control friction.

Consistent with WWY [7] , the implied IRR is monotonically decreasing and it rises substantially as $w$ drops towards $w_d$. In comparison, the IRRs backed out at $\beta =20$ (solid line), denoted by ${\xi }^{\beta }\left(w\right)$, stay below their perfect-protection counterparts at $\beta =\infty$ (dashed line), denoted by ${\xi }^{\infty }\left(w\right)$, for all $w$ which implies a lower cost of capital for the entrepreneur when the degree of investor protection deteriorates. Intuitively, the entrepreneur gains privileges from the firm (through stealing) when $\beta <\infty$. Consequently, she is willing to run the firm even at a relatively low level of $\xi$.

We simulate the firm’s dividend payouts $\left\{D_t\right\}$ as the averages from 10,000 simulated firms where each firm is subject to three types of shocks: the investment-specific shocks of $Z_t^I$, the productivity shock of $Z_t^A$, and the $B_t$-shock for market risks. More specifically, we obtain a sequence of independent draws from a trivariate normal distribution with correlation coefficient being ${\rho }_I$ for $\left\{Z_t^I,B_t\right\}$, $\rho$ for $\left\{Z_t^A,B_t\right\}$, and 0 for $\left\{Z_t^I,Z_t^A\right\}$. The path of $\left\{Z_t^I,Z_t^A,B_t\right\}$ are then mapped into a path of the state variables $\left(K_t,W_t\right)$ that corresponds to one particular firm, from which we calculate the firm’s optimal policies that help drive the evolution of $\left(K,W\right)$ next period. Whenever a firm’s financial slack falls below $w_d$, it gets liquidated, delivers $\left(1-y\right)\left(w_d+l\right)K_t$ to outside shareholders in next period, and then is removed from simulation¹³. We start at $w_0=0$ for all simulated firms and without the loss of generality we further normalize their initial capital $K_0$ to one.

Panel B of Figure 3 reports the simulated dividend payouts under the two $\beta$-scenarios. Compared to $\left\{D_t^{\infty }\right\}$ that are simulated under the perfect investor protection (dashed line), the simulated $\left\{D_t^{\beta }\right\}$ at $\beta =20$ (solid line) falls below initially but rises above in the longer term, i.e., roughly after the first 160 months. The initial depression of $D$ is quite intuitive: It is due to the entrepreneur’s stealing which reduces the firm’s available resources to make payouts. On the other hand, stealing in our setup also provides the empire building incentive for the entrepreneur since she can enjoy a higher privilege with the firm when it grows bigger. With the expanded opportunity set that allows her to take unconstrained positions in the stock market, the entrepreneur has a strong incentive to re-allocate resources from payouts to asset allocation which strengthens the value-creation effect leading to even more aggressive asset allocation policies in the future¹⁴. The rising $W$ (liquid wealth) and the rising $X$ (asset allocation) reinforces each other which gives rise to the higher dividend payouts in the longer term.

We now examine whether the “short-term pain for long-term gain” pattern of dividend payouts actually benefit the outside investors. To this purpose, we combine the firm’s IRR calculated from Section V.B.1 with the simulated dividends payouts from Section V.B.2, and calculate the valuation of the firm by

$PV\left(w_0\right)\equiv \frac{1}{1-y}E\left[{\displaystyle {\int }_0^{\tau }{\text{e}}^{-\xi \left(w_s\right)s}\left(1-y\right)D_s\text{d}s}+{\text{e}}^{-\xi \left(w_{\tau }\right)\tau }\left(1-y\right)\left(W_{\tau }+l{K}_{\tau }\right)\right],$(5.2)

where $1-y$ denotes the aggregated cash-flow right by outside investors; $\tau$ denotes the firm’s (stochastic) liquidation time. To implement the definition of (5.2), we introduce the trancated version of $PV$, denoted as $P{V}^T$, which is calculated as follows:

$\begin{array}{c}P{V}^T\left(w_0\right)\equiv \frac{1}{1-y}E[{\displaystyle {\int }_0^{\min \left\{\tau ,T\right\}}{\text{e}}^{-\xi \left(w_s\right)s}\left(1-y\right)D_s\text{d}s}\\ +{\text{e}}^{-\xi \left(w_{\tau }\right)\tau }{1}_{\left\{\tau >T\right\}}\left(1-y\right)D_T+{\text{e}}^{-\xi \left(w_{\tau }\right)\tau }{1}_{\left\{\tau <T\right\}}\left(1-y\right)\left(W_{\tau }+l{K}_{\tau }\right)].\end{array}$(5.3)

In (5.3), $1_{\{.\}}$ denotes the indicator function which equals 1 when what is within {.} is correct and 0 otherwise. Apparently, $PV=P{V}^T$ when $T\to \infty$. For a finite $T$, $P{V}^T$ can be treated as the valuation of a firm which “expires” at $T$. Given $T$, we calculate $P{V}^T$ through a large sample of simulated firms. Upon its “expiration” before the liquidation, a firm delivers $\left(1-y\right)D_T$ to outside shareholders. However, if the firm is liquidated before its “expiration”, it delivers $\left(1-y\right)\left(W_{\tau }+l{K}_{\tau }\right)$ and is then excluded from the rest of the simulation. As indicated by its definition, we explicitly account for the state-dependence of the discount rates, as indicated by $\xi \left(w_s\right)$, in our calculations of $P{V}^T$.

To ensure that $P{V}^T$ converges to $PV$, we simulate a long time series of dividend payouts up to 240 years so that a further increase of the time span has little impact on the implied $P{V}^T$. We thus use the value of $P{V}^T$ obtained at the end of the 240th year as the (accurate) approximation of $PV$. To study the impact of control friction on firm valuation, we plot in Panel C&D of Figure 3 the implied $P{V}^{T}s$ from $T=0$ up to the 240th year under two scenarios of $\beta$, where the initial financial slack is set at zero without loss of generality.

In Panel C, we pair $\xi (.)s$ that are backed out according to (5.1) with the simulated dividend payouts for the same $\beta$-scenario. Relative to its perfect-protection counterpart which shuts down the control friction (dashed line), $P{V}^T$ at $\beta =20$ (solid line) falls below initially but quickly rises above. It then stays above with the implied discrepancy getting wider and wider as time goes by. In unreported exercises, we confirm that this result holds as we vary $w_0$. Thus, the “short-term pain for long-term gain” pattern of dividend payouts, which is induced by the control friction at the presence of imperfect investor protection, indeed translate into a higher valuation of the firm.

To reinforce our result, we further plot in Panel D of the Figure 3 the implied $P{V}^T$ where we use the common discounting scheme of ${\xi }^{\infty }(.)$ for its calculation under both $\beta$-scenarios. Compared to plots in Panel C, the implied $P{V}^{T}s$ at $\beta =\infty$ (dashed line) remain unchanged but the implied $P{V}^T\left(\beta =20\right)$ (solid line) falls below because the underlying dividend streams are now discounted by the higher discount rates implied from ${\xi }^{\infty }(.)$ (see Panel A of Figure 3 that shows ${\xi }^{\infty }>{\xi }^{\beta }$). Naturally, this higher discounting with ${\xi }^{\infty }(.)$ keeps $P{V}^T\left(\beta =20\right)$ below $P{V}^T\left(\beta =\infty \right)$ for a longer time. Still, the strengthened value-creation effect attributed to the entrepreneur’s empire building motives at $\beta <\infty$ eventually drives $P{V}^T\left(\beta =20\right)$ above $P{V}^T\left(\beta =\infty \right)$, albeit by a smaller margin when compared to that plotted in Panel C.

In Section V.B, we show that control friction enables a higher firm valuation for outside shareholders. One caveat for the analysis is that it focuses on mean-only information. Indeed, the definition of (5.2) indicates that only information from the first moment of dividend payouts is needed for the calculation of $PV$. As shown in Panel A&B of Figure 4 , the simulated dividend payouts are more volatile at $\beta =20$ (solid line) than at $\beta =\infty$ that shuts down the control friction (dashed line), either along the dimension of time (Panel A) or along the dimension of the firm’s initial financial slack $w_0$ (Panel B). Intuitively, the entrepreneur’s empire building motives facilitated by control friction at $\beta <\infty$ leads to over-investment and a more aggressive position in the stock market relative to the case at $\beta =\infty$. Consequently, the firm is subject to more of the investment and market risks which is captured by a more volatile dividend stream. The higher volatility is disliked by a risk averse agent which could lead to a lower utility at $\beta <\infty$ despite of the higher average payouts. In this section, we examine this logic by performing the welfare analyses for the two types of firm agents.

Since all firm agents are endowed with the same CRRA utility function given by (2.8), we calculate their accumulated utilities from the firm from period 0 up to period $T$ by

$V_1^T\left(w_0\right)\equiv E\left[{\displaystyle {\int }_0^{\min \left\{\tau ,T\right\}}{\text{e}}^{-\zeta s}U\left(C_{1,s}\right)\text{d}s}+{\text{e}}^{-\zeta \tau }{1}_{\left\{\tau >T\right\}}U\left(C_T\right)\right]$(5.4)

for the entrepreneur, and by

$\begin{array}{c}{V}_2^T\left(w_0\right)\equiv E[{\displaystyle {\int }_0^{\min \left\{\tau ,T\right\}}{\text{e}}^{-\zeta s}U\left(\left(1-y\right)D_s\right)\text{d}s}+{\text{e}}^{-\zeta \tau }{1}_{\left\{\tau >T\right\}}U\left(\left(1-y\right)D_T\right)\\ +{\text{e}}^{-\zeta \tau }{1}_{\left\{\tau <T\right\}}U\left(\left(1-y\right)\left(W_{\tau }+l{K}_{\tau }\right)\right)]\end{array}$(5.5)

for outside investors. In (5.4)-(5.5), $\tau$ denotes the firm’s (stochastic) liquidation time; $1_{\{.\}}$ denotes the indicator function; $\zeta$ denotes the (constant) subjective discount; $U(.)$ is given by (2.8). In the former case with $V_1^T$, the entrepreneur derives her utility solely from her consumption stream ${\left\{C_{1,s}\right\}}_{s=0}^T$ when the firm is alive, where $C_1$ is given by (3.19). Upon the firm’s liquidation, she obtains the

lump-sum payment of $y\left(W_{\tau }+l{K}_{\tau }\right)$ which, instead of being consumed, is used as the initial wealth for her retirement as the Merton consumer. In the latter case with $V_2^T$, outside investors derive their utilities from the firm according to their cash-flow right which include 1) the dividend payouts of $\left(1-y\right)D_s$ up to $T$ conditional on that the firm is alive; and 2) the liquidation payment of $\left(1-y\right)\left(W_{\tau }+l{K}_{\tau }\right)$ conditional on a firm liquidation that occurs before $T$. Given $V_j^T$ for $j=1,2$, the welfare that the $j$th type of agents derives from the firm is its limit $V_j$ when $T\to \infty$.

To ensure that $V_j^T$ converges to $V_j$, we again simulate a large sample of firms from which we generate a long time series of ${\left\{C_{1,s}\right\}}_{s=0}^T$ and ${\left\{D_s\right\}}_{s=0}^T$ that covers a period of 2880 months. The details on simulation are described in Section V.B.2. Without the loss of generality, we set $w_0$ to 0 and calculate $V_1^T$ and $V_2^T$ according to (5.4)-(5.5) by making use of the simulated streams of consumptions and dividend payouts. Panel C&D of Figure 4 plot the implied $V_1^T$ and $V_2^T$, respectively, for the two $\beta$-scenarios. Both $V_1^T$ and $V_2^T$ converge faily quickly in that the implied curves all start to flatten out after the first 1000 months. Given that the baseline value of $\gamma$ is greater than one, (2.8) implies that $U\left(C\right)$ is negative at any positive $C$. Consequently, the implied $V_1^{T}s$ and $V_2^{T}s$ are all negative.

Different than the plots in Figure 3 on firm valuation, the implied welfare for outside investors, calculated as $V_2^T$ in its convergence region (Panel D of Figure 4 ), is lower with the control friction at $\beta =20$ (solid line) than without the friction at $\beta =\infty$ (dashed line) which restores the usual conclusion that corporate stealing is damaging to minority shareholders from outside. Despite of the higher volatility of dividend payouts at a lower degree of investor protection (Panel A&B of Figure 4 ), the implied welfare for the entrepreneur is still higher with the control friction at $\beta =20$ than without (Panel C). To understand the difference, notice that there are two offsetting effects that determine the welfare impact of control friction. Relative to its perfect-protection counterpart, control friction at a lower $\beta$ induces the empire building motive that gives rise to both the higher dividend payouts in the longer term (cash-flow effect) and a more volatile stream of payouts (volatility effect). While cash-flow effect enhances welfare, the volatility effect depresses it. In the case with outside investors, the volatility effect dominates so that a lower degree of investor protection delivers a welfare loss. In contrast, the volatility effect is dominated by a strengthened cash-flow effect in the case with the entrepreneur because the stealing technology enables a consumption stream that stays uniformly above its perfect-protection counterpart.

We further conduct welfare analyses to quantify the impact of imperfect investor protection on both the entrepreneur and outside investors. More specifically, we calculate welfare gain (or loss) for the two types of firm agents when the degree of investor protection deteriorates from $\beta =\infty$ to $\beta =20$. To this purpose, we account for the dependences of $V_1$ and $V_2$ on their respective consumption stream by explicitly writing their formulas as follows:

$V_1\left(\left\{C_{1,s}\right\};w_0\right)\equiv E\left[{\displaystyle {\int }_0^{\tau }{\text{e}}^{-\zeta s}U\left(C_{1,s}\right)\text{d}s}\right]$(5.6)

$V_2\left(\left\{C_{2,s}\right\};w_0\right)\equiv E\left[{\displaystyle {\int }_0^{\tau }{\text{e}}^{-\zeta s}U\left(C_{2,s}\right)\text{d}s}+{\text{e}}^{-\zeta \tau }U\left(C_{2,\tau }\right)\right].$(5.7)

where $C_{1,s}$ is given by (3.19); $C_{2,s}=\left(1-y\right)D_s$ and $C_{2,\tau }=\left(1-y\right)\left(W_{\tau }+l{K}_{\tau }\right)$. It is easy to see that (5.6)-(5.7) are the limiting cases of (5.4)-(5.4) when $T\to \infty$¹⁵.

To quantify the welfare effects, we calculate the percentage change in consumptions under the perfect investor protection that is required to maintain a firm agent’s welfare level when the degree of investor protection deteriorates. Consider the entrepreneur first. For the given $w_0$, define a constant number $k_1$ such that

$V_1^{\infty }\left(\left\{\left(1+k_1\right)C_{1,s}^{\infty }\right\};w_0\right)=V_1^{\beta }\left(\left\{C_{1,s}^{\beta }\right\};w_0\right)$(5.8)

In (5.8), the superscript “ $\infty$“ denotes the case when control friction is shut down at $\beta =\infty$ while the superscript “ $\beta$“ denotes the case with the control friction at a finite $\beta$. In particular, $\left\{C_{1,s}^{\infty }\right\}$ and $\left\{C_{1,s}^{\beta }\right\}$ denote the entrepreneur’s optimal consumption stream at $\beta =\infty$ and at $\beta <\infty$, respectively. The entrepreneur is likely to gain from the control friction which implies that $V_1^{\infty }\left(\left\{C_{1,s}^{\infty }\right\};w_0\right)<V_1^{\beta }\left(\left\{C_{1,s}^{\beta }\right\};w_0\right)$. $k_1$ thus measures the welfare gain for the entrepreneur, in terms the percentage increase of her consumption from its perfect-protection level, when the degree of investor protection deteriorates which introduces the control friction. Note that an increase of $1+k_1$ applies to the entire consumption stream.

Turning to outside investors, we similarly define a constant $k_2$ for the given $w_0$ such that

$V_2^{\infty }\left(\left\{\left(1-k_2\right)C_{2,s}^{\infty }\right\};w_0\right)=V_2^{\beta }\left(\left\{C_{2,s}^{\beta }\right\};w_0\right)$(5.9)

where the superscripts “ $\infty$“ and “ $\beta$“ are defined in a similar way as that for $V_1$. As shown in Panel D of Figure 4 , an outside investor achieves the higher utility when control friction is shut down at $\beta =\infty$. Therefore, to maintain the welfare level when the degree of investor protection deteriorates, we need to adjust his consumption at $\beta =\infty$ downward from the optimal level of $\left\{C_{2,s}^{\infty }\right\}$. In other words, an outside investor feels indifferent when $\beta$ falls below $\infty$ only if his consumption stream prior to the change is actually below $\left\{C_{2,s}^{\infty }\right\}$. The implied $k_2$, as defined in (5.9), thus measures his welfare loss, in terms of the percentage decrease of his consumption stream, when the degree of investor protection deteriorates.

To gauge the impact of the firm’s initial financial status on the implied welfare effects, we vary the initial $w_0$ from −0.64 to 3 when calculating $k_1$ and $k_2$. We plot the resulting $k_1\left(w_0\right)$ and $k_2\left(w_0\right)$ in Panel E&F of Figure 4 , respectively, where both $k_1$ and $k_2$ are quoted in percentage. As $w_0$ rises, the firm’s dividend payouts become more attributable to the accumulated liquid wealth $W$ and less attributable to the firm’s capital $K$ because a higher financial slack, as measured by $w$, allows a more aggressive asset allocation strategy which enables the firm to better exploit the value-creation effect from the stock market. Given that the amount of stealing is proportional to $K$, a higher $w_0$ thus implies, in a relative sense, a lower degree of damage that stealing imposes on outside investors. This decreasing stealing effect implies a lower welfare loss so that $k_2\left(w_0\right)$ plotted in Panel F of Figure 4 is monotonically decreasing. Specifically, $k_2$ can rise as high as 81.5% when $w_0$ drops to a level that is very close to $w_d$. Intuitively, a higher firm-level volatility, which is attributed the deterioration in the degree of investor protection (see Panel A&B of Figure 4 ), is quite costly to outside shareholders when it can easily trigger the firm’s liquidation at a sufficiently low $w_0$.

In comparison, the entrepreneur’s welfare gain due to the control friction is much lower (Panel E). The difference in magnitudes between $k_1$ and $k_2$ reflects the power of the control right which allows the entrepreneur to “smooth out” her welfare to $\beta$-variations. Unlike $k_2$, $k_1$ is not monotonic in $w_0$ and the dividing point is roughly at $w_0=-0.28$. When $w_0>-0.28$, the decreasing stealing effect explained in the last paragraph is dominant which also drives a decreasing $k_1\left(w_0\right)$. When $w_0$ is relatively low, on the other hand, the resource re-allocation effect, which means that the entrepreneur exploits the control friction to re-allocate resources from dividend payouts to investment and asset allocation that helps raise her consumption in the future, becomes the dominant force. A higher $w_0$ depresses the concern for liquidation and thus enhances the resource re-allocation effect which raises the entrepreneur’s welfare. Consequently, we observe an increasing $k_1\left(w_0\right)$ in the region between $w_d$ and −0.28. In summary, our model provides the first theoretical study that links the welfare effect of investor protection to the firm’s financial status. By doing so, it predicts that 1) the entrepreneur’s welfare gain following a deterioration of investor protection is hump-shaped; and 2) investor protection is more important for outside investors when the firm is in a worse financial condition.

In this subsection, we perform comparative analysis with respect to the implied welfare gains (or losses) when we vary some key model parameters. Panel A-C of Figure 5 plot the results with respect to $k_1$. Panel A shows the impact of $ϵ$ which controls the volatility of investment-specific shocks. A higher $ϵ$ means a higher firm-level volatility that comes from investment risk which drives up the volatility of the simulated dividend payouts. Consequently, it drives up the volatility of the consumption stream which is disliked by the risk-averse entrepreneur. While a deterioration of investor protection still generates the welfare gain for the entrepreneur at a higher $ϵ$, the implied consumption stream $\left\{C_{1,s}^{\beta }\right\}$ at $\beta <\infty$ becomes less desirable because of the extra volatility induced by $ϵ$. Consequently, the welfare gain from control friction as measured by $k_1$ is lower at $ϵ=1$ (dashed line) than at $ϵ=0$ (solid line).

We next allow the firm agents’ degree of risk aversion $\gamma$ to vary and plot the implications on $k_1\left(w_0\right)$ in Panel B of Figure 5 . At a higher $\gamma =4$, the higher volatility of $\left\{C_{1,s}^{\beta }\right\}$ under the control friction is more disliked by the entrepreneur which implies a lower welfare gain across all $w_0$. An interesting observation is that $k_1$ at $\gamma =4$ apparently turns negative when $w_0$ gets close to the implied liquidation boundary at $\gamma =4$, which implies welfare losses instead of gains to the entrepreneur. Intuitively, a drop of $w_0$ towards $w_d$ raises the concern about the negative effect of the higher volatility at $\beta <\infty$ because it can trigger the value-destroying liquidation more easily. When the entrepreneur is more risk

averse, the volatility effect is substantially enhanced and may even dominate the positive cash-flow effect (induced by stealing at the presence of control friction) when $w_0$ is very close to $w_d$. Consequently, she may also suffer a welfare loss following a deterioration of investor protection.

We further examine the impact of equity risk premium which is measured by the market Sharpe ratio $\eta$ holding ${\sigma }_R$ unchanged. With the market risk compensation shut down at $\eta =0$, the value-creation effect is gone so that the firm at $\beta <\infty$ no longer takes aggressive positions in the stock market. This has two effects on the entrepreneur’s welfare. First, the volatility of her consumption stream comes down since control friction facilitated by the imperfect investor protection no longer induces her to increase the firm’s market exposure. Second, without the opportunity from the stock market, the resource re-allocation effect now implies that the firm is allocating even more resources to investment. The further strengthened over-investment enables a faster growth of the firm’s capital stock $K$ which allows the entrepreneur to steal even more because the amount that she can divert is proportional to $K$. Both effects work in the same direction of driving up the welfare gain. Consequently, $k_1\left(w_0\right)$ rises uniformly when $\eta$ is reduced from its baseline level of 0.3 to 0 as plotted in Panel C of Figure 5 ¹⁶.

We now turn to Panel D-F of Figure 5 which plots the results of comparative statics for outside investors. Unlike $k_1$, $k_2$ remains positive irrespective of parametric changes which means that control friction always hurts outside shareholders. The dominant force that determines $k_2$ is apparently the firm’s initial financial slack $w_0$. In particular, when $w_0<0$ so that the firm is in debt, a drop of $w_0$ towards the firm’s liquidation boundary substantially raises $k_2$ implying a huge welfare loss to outside investors that is attributed to the control friction. The impact of all other determinants of $k_2$ are relatively minor because they’re subject to offsetting forces. For example, a higher $\gamma$ aggravates the volatility effect which tends to raise $k_2$ implying a larger welfare loss. This is indeed the case when $w_0$ is relatively small as plotted in Panel E of Figure 5 . However, a higher $\gamma$ also prompts the entrepreneur to adopt less aggressive policies on investment and asset allocation which reduces firm-level risks as indicated by a smoother dividend payout scheme. This consumption-smoothing effect is more pronounced when the firm is in a better financial status¹⁷ leading to a lower $k_2\left(w_0\right)$ at the higher $\gamma$ when $w_0$ is relatively high.

¹⁶It is worth noticing that the shape of the implied $k_1\left(w_0\right)$ in Panel C is more nuanced at $\eta =0$ (solid line) in that it also decreases a bit when $w_0$ is very close to the liquidation boundary (equaling −0.705 at $\beta =\infty$). Since $w_d^{\beta }$ at $\beta =20$ is lower than $w_d^{\infty }=-0.705$, a deterioration from perfect investor protection to $\beta =20$ enables the entrepreneur to gain the breathing room when the firm is very close to its liquidation an instant of time before the change in $\beta$. Apparently, the implied liquidation relief effect becomes stronger as $w_0$ drops towards $w_d^{\infty }.$ Still, this effect is uniformly dominated by the resource re-allocation effect in the case with $\eta =0.3$. When the market's risk compensation is shut down at $\eta =0$, however, gaining the breathing room following the deterioration of investor protection becomes more valuable because it simultaneously points to a higher percentage welfare gain as discussed in the main text. Consequently, the aforementioned liquidation relief effect is further strengthened and our numerical result indicates that it can become dominant when $w_0$ becomes sufficiently close to $w_d^{\infty }$ leading to an increased $k_1$ as $w_0$ further drops towards $w_d^{\infty }$ (leftmost of the solid line plotted in Panel C of Figure 5 ).

To summarize, welfare gains for the entrepreneur that results from stealing under imperfect investor protection is relatively small. Such gains may decrease as firm comes closer to its liquidation and they may even turn negative under certain circumstances. In contrast, outside investors suffer substantial welfare losses from a deterioration of investor protection when the firm is initially in debt (as indicated by a negative $w_0$). Variations in parameters that govern investment risk, risk preference, and risk compensation deliver clear effects on welfare changes for the entrepreneur, whereas their welfare implications are mixed for outside investors. Overall, our results deliver a clear economic message: While enhancing investor protection is indeed preferrable from the perspective of welfare analyses, it is particularly desirable when the firm is in financial distress.