TY - JOUR
AU - Yufeng, Wu,
AB - Abstract I study the driving forces behind dividend smoothing by developing a dynamic agency model in which dividends signal the earnings persistence of firms. In equilibrium, managers treat dividends and earnings as informational substitutes. They smooth dividends relative to earnings to smooth negative news releases and lower their turnover risk. Empirical estimates of the model parameters imply that 39$$\%$$ of observed dividend smoothness among U.S. firms is driven by managers’ own career concerns, not shareholders’ preferences. Managers cut investments and adjust external financing policies to accommodate this career-concern-based dividend smoothing. These effects lead to a 2$$\%$$ decline in firm value. Received May 28, 2016; editorial decision September 13, 2017 by Editor David Denis. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. Introduction Dividend smoothing is one of the oldest and most puzzling phenomena in corporate finance. On the one hand, Miller and Modigliani (1961) show that in a frictionless market, managers cannot add value to a firm by changing the amount or timing of dividend payments. On the other hand, in his seminal work, Lintner (1956) provides survey evidence showing that managers put a high priority on the smoothness of dividends. Linter argues that it is “[a] mix of attitudes and sentiments, pressures and sense of responsibility, standards of fairness and good management performance” that shapes the observed dividend pattern among firms. A natural question that arises from Linter’s argument is what constitutes the “mix of attitudes and sentiment.” Is it mostly reflective of the shareholders’ preferences? In addition, do managers also have personal interests that induce them to smooth dividends? Although dividend smoothing is widely documented in the literature, little work has been done to disentangle the underlying driving forces behind this phenomenon. In this paper, I address these questions by exploring managers’ career concerns and dividend smoothing in an information-asymmetric environment. I document that in the data, changes in dividend policy are indeed a strong negative predictor of managerial turnover. Firms that lower their dividends experience, on average, a one-third higher forced executive turnover rate in the subsequent year. I also build and estimate a dynamic agency model that endogenizes this negative dividend-turnover correlation and show that managers react to it. Having career concerns induces managers to smooth dividends excessively, compared to the level of smoothness that would have been chosen to maximize shareholders’ value. This excess dividend smoothing leads to cash hoarding during good times, and it crowds out investment when earnings deteriorate, leading to a 2$$\%$$ decline in firm value in equilibrium. The model I consider features an information-asymmetric environment and a team of self-interested managers who face a turnover risk in each period. The managers choose the optimal firm policies to maximize the expected value of their lifetime utility, which is a weighted average of their expected future wage income and the value of their equity stake in the firm. Holding an equity stake aligns managers’ incentives with the shareholders’, but having career concerns diverges their personal interests. Hence, the managers’ choice of investment, financing, and payout policies will be different from those that maximize the expected cash flows to the shareholders. The shareholders cannot impose the optimal policies themselves as they lack the information necessary to determine such policies. The model yields two channels for dividend smoothing. In the first channel, the signaling channel, dividend payments convey information on earnings persistence. Current earnings are deemed to have a higher (lower) persistent component if they are accompanied by dividend increases (cuts). In equilibrium, stock prices react to this dividend informativeness, and due to the signaling costs, the magnitude of the price reaction to dividend cuts is larger than that to dividend increases. Hence, a stable dividend policy helps to protect the equity value of the firm. This signaling channel is frequently mentioned in the dividend smoothing literature (Bhattacharya, 1979, John and Williams, 1985, Miller and Rock, 1985), so the inclusion of this mechanism in the model allows me to isolate the career-concern-based explanation. The second channel operates through managers’ career concerns, which states that the information conveyed by both earnings and dividends influences decisions on managerial tenure. Therefore, managers treat dividends and earnings as informational substitutes, and this substitutability gives them a separate incentive to smooth dividends. In particular, they will typically be hesitant to increase dividends as earnings improve, because in such states, they are already far from the turnover threshold. Thus, further increasing dividends brings them very limited benefit. They will also be extremely reluctant to cut dividends when earnings decline in order to withhold the negative news and keep their turnover risk from increasing. This career-concern-based amplification channel is the focus of this paper. Quantifying the effects of the two dividend smoothing channels is difficult, in part because firms’ turnover decisions and dividend payments are both endogenous. There is no obvious instrumental variable for the managers’ career concerns ex ante at the time they set the firms’ policies. In addition, although reduced-form regressions can deliver the directional effects of proxies for managerial career concerns on dividend smoothness, they cannot, by nature, address the extent to which dividend smoothing is accounted for by each potential mechanism. In this paper, I tackle these empirical challenges by estimating the model via simulated method of moments (SMM) on a set of frequent dividend payers using data for the 1992–2011 period. The estimation results confirm that both types of dividend smoothing are present in the data and have large economic significance. In both the actual and simulated data, the average dismissal rate for top executives increases by roughly one-third following dividend cuts, after controlling for other firm- and executive-level characteristics. Managers choose smoother dividends in order to lower their potential turnover risk, and this incentive explains approximately 36$$\%$$ of the observed dividend smoothness in the data. Because turnover is only a transfer of wage income from the incumbent to future managers, this type of dividend smoothing is considered excessive from the shareholders’ point of view. Dividends would be markedly more responsive to earnings if set directly by shareholders to maximize firm value. The estimation provides three further results. First, accounting for the relation between dividend policy and executive turnover is crucial for the model to match moments in the actual data. In an alternative model, I ignore this relation, and it always fails to generate the small variance of dividends or to reproduce the low responsiveness of dividends to earnings changes. The class of dynamic investment models had been struggling with the dispersions in firm-level payouts. My results show that once I allow the managers’ career concerns to directly enter into firms’ payout decisions, the fit of the model-generated payouts significantly improves. Second, I perform subsample estimations to revisit the cross-sectional variation in dividend smoothing among heterogeneous managers. I find that managers with lower reputation, smaller equity-based compensation, and shorter tenure have higher career concerns that incentivize them to smooth dividends more aggressively. A dynamic agency model also provides a natural setting to examine the time-series trend in dividend smoothness. I find that over time, managers face increasing turnover risk, which leads to a higher degree of dividend smoothing in recent decades. Lastly, relying on a structural model, I perform counterfactual analyses and explore how career-concern-based dividend smoothing affects firm value. I find that in order to accommodate this type of dividend smoothness, managers hoard more cash in cash-rich states and they invest less at times of low cash flows, inducing both higher interest tax payments and underinvestment costs. These policy distortions decrease equilibrium firm value by 2$$\%$$. Shareholders tolerate these costs as it is even more costly for them to ignore the managers’ superior knowledge and set firm policies themselves based on their restricted information. The observation that firms tend to smooth dividend payments is first evidenced by Lintner (1956). Brav et al. (2005) document that firms may even take costly actions to avoid decreasing dividends, such as issuing new equity or even cutting positive net present value projects. Subsequent studies use different data and experimental settings to investigate why stable dividends are value-enhancing from a firm’s perspective. For example, Easterbrook (1984) argues that consistent dividend payments keep a firm in the capital market and motivate effective public monitoring. In addition, Allen, Bernardo, and Welch (2000) emphasize that ex-post stable high dividends attract more institutional investors, who typically process information more efficiently. Kaplan and Reishus (1990) are among the first to study the implications of dividend policy on managers’ personal welfare, in particular, on their ability to maintain their outside directorships. In a more recent study, Parrino, Sias, and Starks (2003) find that firms with dividend cuts or eliminations experience a greater institutional exodus, which reduces the likelihood of top executives being promoted internally. These results are all consistent with the idea that dividend instability hurts the top executives’ well-being. Given these observations, it is also interesting to examine whether managers react to such incentives by choosing an intertemporally smoother dividend profile. In this paper, I make two main contributions to the empirical corporate finance literature. First, I disentangle the managers’ versus the shareholders’ incentives to smooth dividends and analyze each of their implications on firm value. Second, I add to the literature on executive turnovers by examining the exact information content of dividends and exploring how this information helps to predict turnover decisions. Methodologically, this paper belongs to the structural estimation literature. For example, Morellec, Nikolov, and Schürhoff (2012) study how managerial resource diversion helps to explain the low leverage puzzle; Nikolov and Whited (2014) focus on the impact of agency conflicts on a firm’s cash policy. I add to this literature by devising tests to examine a new topic, the dividend smoothing puzzle, using parameters estimated from a structural model. This paper also pertains to the large theoretical literature on dynamic models of corporate payout, including Lambrecht and Myers (2012, 2017), who are the first to formally model the link between firm earnings and payout using a dynamic agency model. They derive a closed-form solution for firm-level total payout, which follows Lintner’s target adjustment equation. While Lambrecht and Myers focus on the agents’ rent extraction incentive, I examine a different form of agency friction: the managers’ turnover risk. I test the empirical relevance of this career-concern-based dividend smoothing channel to determine the quantitative and qualitative effects. In a closely related work, Fudenburg and Tirole (1995) provide a theoretical framework to assess the influence of managers’ career concerns on their choice of earnings smoothing. In their model, all reported earnings are paid to the owners period by period as dividends, and hence the smoothness of dividends arises naturally due to earnings smoothing. My paper differs from theirs in two important aspects. First, it captures the idea that dividends and earnings signal different aspects of a firm’s profitability and hence are informational substitutes. Second, I focus on how dividends vary relative to the reported earnings, instead of analyzing the smoothing of earnings and dividends against some latent profitability measures. In the robustness section, I also explore the joint determination of earnings and dividend smoothing. Consistent with Fudenburg and Tirole (1995), I find that managers smooth reported earnings relative to unobservable profitability changes. On top of that, they also smooth dividends relative to reported earnings to further delay the information release and mitigate their career concerns. This “two-tier” smoothing behavior generates interesting information dynamics that are absent in the literature. 1. Baseline Model Models on firm payouts (Miller and Rock, 1985, Allen, Bernardo, and Welch, 2000) are usually based on the implicit assumption that the dividend policy reflects shareholders’ desire to boost the stock price. However, the recent literature puts increasing emphasis on how managers’ self-interest can also shape a firm’s financial decisions (Morellec, Nikolov, and Schürhoff, 2012, Nikolov and Whited, 2014). I follow this literature and build a dynamic model of self-interested managers who set their firms’ investment, financing, and payout policies each period to maximize the expected value of their utility. Managers are subject to career concerns, which makes their policies, in general, not the same as those that maximize the shareholders’ welfare. In the baseline model, I also imbed an information asymmetry between the inside managers and outside investors. Both the managers and the investors observe the current earnings level, but only the managers know precisely how persistent earnings will be going forward. This information asymmetry gives investors an incentive to extract information out of the announced dividend policy. The dividend informativeness generates endogenous price reactions and managerial turnovers in equilibrium, which is another distinctive feature of the model. The remainder of this section provides more details on the model setup and qualitatively illustrates how managers’ utility maximization determines firm-level dividend smoothness. 1.1 The basic setup The backbone of this model is a dynamic investment model with financing frictions. The model is in discrete time and infinite horizon. The timing of events in each period is described in Figure 1. Figure 1 View largeDownload slide Time line Figure 1 summarizes the time line of the model. At the beginning of each period, the productivity shocks are realized. Managers observe their realizations and base the firm’s investment, financing, and payout decisions on this information. The investors do not directly see the underlying profitability processes. Instead, they extract information from the realized profit and the reported firm policies, and they determine the firm’s market price. The board of directors is in charge of the firm’s executive turnover decisions. Figure 1 View largeDownload slide Time line Figure 1 summarizes the time line of the model. At the beginning of each period, the productivity shocks are realized. Managers observe their realizations and base the firm’s investment, financing, and payout decisions on this information. The investors do not directly see the underlying profitability processes. Instead, they extract information from the realized profit and the reported firm policies, and they determine the firm’s market price. The board of directors is in charge of the firm’s executive turnover decisions. In the model, I focus on a representative firm that faces decreasing return-to-scale technology and uses capital, $$K_t$$, as the only input to generate per period after-tax profit, $$Y_t$$, \begin{eqnarray} \label{EQ1} Y\left(K_{t},z_{t},s_{t}\right)=(1-\tau_c)\times e^{z_{t}}e^{s_{t}}K_{t}^{\theta}, \end{eqnarray} (1) in which $$\theta < 1$$ is the curvature of a firm’s production function, and $$\tau_c$$ is the corporate tax rate. $$z_t$$ represents a shock specific to each firm-management match, which follows an AR(1) process: \begin{eqnarray} \label{EQ2} z_{t}=\rho_{z}\times z_{t-1}+\epsilon_{z,t}, \phantom{spa} \epsilon_{z,t}\overset{iid}{\sim}N\,\left(0,\sigma_{z}^{2}\right). \end{eqnarray} (2) Note that as in Mortensen and Pissarides (1994), Holmstrüm (1999), Cao and Wang (2013), $$z_t$$ should be understood as the match quality between the managers and the firm, which is time-varying and does not translate directly into some fixed properties of the firm or the person. As Cao and Wang (2013) argue, a high match quality means that the executive’s talent and experience fits well with the size of the firm, its nature of business, strategic direction, and organizational culture in this particular time frame. A manager well-matched with the firm at one point in time may not be well-matched with the same firm at another point in time, due to a change in the firm characteristics above. The time-varying match quality can also be caused by changes on the managerial side. Graham, Harvey, and Puri (2013) document that senior executives’ psychological and behavioral traits could have significant influence on corporate actions. These traits, such as optimism, patience, and risk aversion, are likely to be changing with the executive’s life cycle, causing the same executive to be better or worse matched with a firm at different points in time. $$s_t$$ is a transitory earnings shock, $$s_{t}\overset{iid}{\sim}N\,\left(0,\sigma_{s}^{2}\right)$$, which also enters exponentially into the firm’s current earnings, but it does not impact future cash flows. At the beginning of each period, the two shocks, $$z_{t}$$ and $$s_{t}$$, are realized. Managers observe them separately, and they base the firm’s investment, financing, and payout decisions on the realized values. A firm’s investment, $$I_t$$, is defined as: \begin{eqnarray} \label{EQ3} I_t = K_t-K_{t-1}\times(1-\delta), \end{eqnarray} (3) where $$\delta$$ is the depreciation rate of physical assets. A firm can either finance investment using its holdings of liquid assets, $$L_t$$, or it can go to the capital market and issue new equity. On the other hand, if a firm wants to dispose of idle cash, it can either pay dividends or make repurchases. Dividends, $$D_t$$, are subject to a personal tax rate, $$\tau_p$$, at the time of distribution. Equity issuances and repurchases are associated with a linear-quadratic financing cost. Let $$\Lambda(.)$$ denote the net cash flow from issuances and repurchases after paying the financing cost: \begin{eqnarray}\label{EQ4} \Lambda\left(E_{t}\right)=E_t-\upsilon_{1}\times |E_{t}|-\upsilon_{2}\times\frac{E_{t}^{2}}{K_{t}}. \end{eqnarray} (4) In Equation (4), $$E_t$$ denotes a firm’s net equity issuance; a positive $$E_t$$ means that the firm is receiving cash from its investors, while a negative $$E_t$$ means cash redistributes to the shareholders. $$\upsilon_{1}\times |E_{t}|$$ and $$\upsilon_{2}\times\frac{E_{t}^{2}}{K_{t}}$$ capture the linear and quadratic components of the financing costs. Empirically, firms pay sizeable fees for investment banking services when they make seasoned equity offerings (SEOs) (Gao and Ritter, 2010) or accelerated share repurchases (Dickinson, Kimmel, and Warfield, 2012). Asquith and Mullins (1986) and Corwin (2003) find that SEOs occur at discounts to market prices and that the discount increases with the size of the offering. Related to this idea, a large literature including Vermaelen (1981) documents that firms announce stock repurchases at a premium to the current share price. I summarize the effects of the fees, along with adverse selection in reduced form using Equation (4). Equation (4) implies that the cost of net issuance is monotonically increasing in size and exhibits diseconomies of scale, consistent with the evidence presented in Warusawitharana and Whited (2015). 1.2 Managers’ utility maximization In the model, managers are offered compensation contracts consisting of two components. The first component is a fixed wage income per period, contingent on the managers staying with the firm. The second captures the managers’ equity stake in the firm. I do not discuss the optimality of such a contract. Instead, I take the form of executive compensation in the data and try to infer managers’ policy choices based on the structure of their compensation packages. Managers in the model are assumed to be risk-neutral. This risk-neutrality assumption captures the idea that the top executives who can influence a firm’s policies are usually wealthy individuals, and have access to various investment and savings technologies.1 In each period, managers determine the firm’s investment, financing, and payout policies, $$\left\{I_{t}, E_{t}, L_{t}, D_{t}\right\}$$, to maximize the discounted present value of their utility: \begin{eqnarray} \label{EQ5} U_t = \max_{\left\{I_{t}, E_{t}, L_{t}, D_{t}\right\}} {\mathbb E} \Big[ \sum\limits_{s\geq t}\Big(\prod\limits_{s\geq v\geq t}\beta\left(1-\Phi_{v}\right)\Big)W +\kappa_IV_{It} +\kappa_MV_{Mt}\Big], \end{eqnarray} (5) subject to the sources and uses of funds constraint: \begin{eqnarray} \label{EQ6} Y_{t}+\tau_c\delta K_t +L_{t-1}(1+r_f-r_f\tau_c)+\Lambda(E_t) \geq I_t+D_{t}+W+L_{t}. \end{eqnarray} (6) $$U_t$$ in Equation (5) denotes the managers’ utility. $$V_I$$ and $$V_M$$ represent the intrinsic value and the market value of the firm, respectively. The two measures are usually different because investors do not directly observe firm fundamentals. Instead, they form their own forecast of firm fundamentals using available information. Managers care about the intrinsic value of the firm because they have an equity stake in it, the worth of which is tied to the firm’s long-term intrinsic value. The market value of the firm is also relevant because managers can inherit the preferences from shareholders who need to trade for liquidity reasons (John and Williams, 1985). $$\kappa_I$$ and $$\kappa_M$$ capture the weights of the firm’s intrinsic value and market value, respectively, in the managers’ utility function. $$W$$ is the managers’ per-period income, which is modeled as a constant fraction, $$\eta$$, of the firm’s steady-state asset value. In the model, I normalize the managers’ outside option to zero. With this normalization, $$W$$ should be understood as the managers’ rents instead of the nominal wages. $$\beta$$ is the managers’ discount rate and $$\Phi_{t}$$ is a dummy variable indicating forced turnover. Once a manager leaves office, he keeps his equity stake but forfeits all future rent income. 1.3 Investors’ information set and firm value One important friction embedded in the model is the information asymmetry between managers and outside investors. Unlike the managers who directly observe the underlying productivity shocks, the investors only perceive the realized profit, which is jointly determined by the persistent and transitory components. This profit is not a sufficient statistic for predicting the firm’s future performance as uncertainty exists regarding the value of each individual shock process. Any additional information that helps to disentangle $$s_t$$ from $$z_t$$ improves the investors’ knowledge of the firm’s economic standing and allows them to set more efficient stock prices. In the model, investors are allowed to extract information from all announced firm policies. To make the model solvable and estimable, I focus on the set of time-invariant linear forecasting rules,2$$ \left\{ \gamma_{0}, \gamma_{\pi}, \gamma_{{\it{\Omega}}}, \gamma_{\mathcal{F}}\right\}$$, based on which the investors predict the value of the persistent profitability component, $$z_t$$, as accurately as possible: \begin{eqnarray} \label{EQ7} &&\hat{z}_t = \gamma_{0} + \gamma_{\pi}\times\pi_t + \gamma_{{\it{\Omega}}}\times{\it{\Omega}}_t + \gamma_\mathcal{F}\times \mathcal{F}_t \\ &&\left\{ \gamma_{0}, \gamma_{\pi}, \gamma_{{\it{\Omega}}}, \gamma_{\mathcal{F}}\right\} = \arg\min{\mathbb E}|\hat{z}_t- z_t|, \nonumber \end{eqnarray} (7) where $$\pi_t = \ln Y_t-\theta\ln K_t-\ln(1-\tau_c)$$ is the log of capital- and tax- adjusted firm profit; it can be derived from Equation (1) that $$\pi_t=z_t+s_t$$. $${\it{\Omega}}_t$$ denotes the firm’s announced investment, financing, and payout policies. $$\mathcal{F}_t$$ includes investors’ previous forecast, $$\hat{z}_{t-1}$$, and a noisy signal observed in the current period, $$\varphi_t\sim z_t+N(0,\sigma_z^2)$$.3 Given the forecasted profitability processes, the firm’s intrinsic and market value, $$V_I$$ and $$V_M$$, respectively, can be written recursively as: \begin{align} V_I(K_{t-1},L_{t-1},D_{t-1},z_t,\pi_t) &= (1-\tau_p) D_t-E_t -\lambda|\triangle D_t|\notag\\\label{EQ8} &\quad+\beta {\mathbb E} V_I(K_t,L_t,D_t,z_{t+1},\pi_{t+1}) \\ \end{align} (8) \begin{align} V_M(K_{t-1},L_{t-1},D_{t-1},\hat{z}_{t-1},\pi_t) &= (1-\tau_p) D_t-E_t -\lambda|\triangle D_t|\notag\\ &\quad+\beta {\mathbb E} V_M(K_t,L_t,D_t,\hat{z}_t,\pi_{t+1}),\label{EQ9} \end{align} (9) where the law of motions for $$z$$ and $$\hat{z}$$ are specified in equations (2) and (7). The choice of $$\{I_t,E_t,L_t,D_t\}$$ that enters into equations (8) and (9) represents the optimal policies that maximize the managers’ utility defined in Equation (5). This choice is not, in general, the same choice that would be made if the managers were maximizing the expected present value of cash flows to shareholders. $$|\triangle D_t|$$ in Equation (8) denotes the unsigned dividend change from the previous period. A positive $$\lambda$$ indicates that dividends are not only associated with a higher tax rate, but also incur an adjustment cost whenever the prevailing level needs to be altered in future periods. As Brealey, Myers, and Allen (2005) argue, setting dividends at $\$$ 2 per share is a trivial decision if last year’s dividends were also $\$$2. However, it can cost substantial managerial time and effort if the choice entails decreasing last year’s dividends from $\$$2.5 to $\$$2.0. In the model, I interpret $$\lambda$$ as the firm’s real cost to change dividends. However, the model predictions will completely go through if dividend adjustments are costless at the firm level, but the executives face some personal or psychological costs to persuade the board to approve a dividend cut. In either case, no dividend changes should be made if they are likely to be reversed in the future. Firms set dividends to echo the sustainable earnings over the long term. Empirically, Grullon et al. (2005) document that current earnings increases/declines accompanied by dividend movements in the same direction are less likely to be reversed in the future.4 The announcements of dividend movements are also associated with abnormal stock returns after controlling for the changes in other forms of payout (Michaely, Thaler, and Womack, 1995), the firm’s investment needs (Ghosh and Woolridge, 1989), and the contemporaneous earnings shocks (Aharony and Swary, 1980). The empirical evidence is consistent with the idea that dividend changes can be used as an effective signal, and the market is actively screening firms based on the information revealed by dividend changes. 1.4 The state-contingent turnover risk For most dynamic investment models, the managers’ turnover rate, $$E(\Phi_t)$$, is treated as an exogenous parameter and is assumed to be constant across time and states. I deviate from this assumption by incorporating state-contingent turnover risk into the model. More specifically, the board of directors pulls the trigger whenever the perceived match quality falls below a threshold: \begin{eqnarray} \label{EQ10} \Phi_t = \left\{ \begin{array}{ll} 1, & \hat{z}_t\leq \underline{z} \\ 0, & \text{otherwise}. \end{array} \right. \end{eqnarray} (10) Equations (7) and (10) jointly determine the three factors that affect managerial turnover: The first one is the firm’s profit, which is a function of the realized shocks and is outside management’s control. The second factor is the firm’s announced policy, which could inform the investors of the latent persistence of profit, while the third factor is a noisy signal observed by investors. This signal is orthogonal to the investors’ existing information. In Figure 2, I examine how this state-contingent turnover affects managers’ decisions. The main intuition that emerges is that the managers’ optimal policy should depend on the convexity of their turnover risk. Let us assume that both $$\gamma_\pi$$ and $$\gamma_{{\it{\Omega}}}$$ in Equation (7) are positive and that the economy has a low expected turnover (region 3), which implies that the managers of an average firm would face convex turnover risk. Thus, if a firm is hit by a good profitability shock, the expected turnover moves into an even more convex region where its slope with respect to any information release becomes relatively flat. Therefore, the marginal benefit from sending out additional signals via a good policy change is very limited. On the other hand, when performance deteriorates, the turnover risk increases and it becomes increasingly sensitive to the release of additional negative information, which means if the previous policy change needs to be reversed in the future, the marginal cost could be substantial. Trading off such costs versus benefits implies that the managers have an incentive to smooth their policies relative to earnings. Figure 2 View largeDownload slide Endogenous turnover rate for managers Figure 2 depicts the expected turnover rate for the managers, holding constant a firm’s history. Regions 1, 2, and 3 correspond to economies with low, moderate, and high average turnovers, respectively. The y-axis contains the expected turnover rate, which lies between 0 and 1. The x-axis contains the investors’ assessment of the match quality between the firm and its executives. Note that $${\mathbb E}(\hat{z})$$ instead of $$\hat{z}$$ is used as the measurement because $$\hat{z}$$ contains a signal unobservable to the managers at the time when they choose the optimal policies. Figure 2 View largeDownload slide Endogenous turnover rate for managers Figure 2 depicts the expected turnover rate for the managers, holding constant a firm’s history. Regions 1, 2, and 3 correspond to economies with low, moderate, and high average turnovers, respectively. The y-axis contains the expected turnover rate, which lies between 0 and 1. The x-axis contains the investors’ assessment of the match quality between the firm and its executives. Note that $${\mathbb E}(\hat{z})$$ instead of $$\hat{z}$$ is used as the measurement because $$\hat{z}$$ contains a signal unobservable to the managers at the time when they choose the optimal policies. In an economy with moderate turnover (region 2 in Figure 2), the good and bad information have almost symmetric marginal effects. This symmetry implies that managers are neutral about how strongly earnings and other firm policies should comove. For any policy change that is quickly reversed in the future, the net effect on the managers’ expected turnover is almost zero. Lastly, when the expected turnover rate stays at a high level, the turnover profile becomes concave for a representative manager (region 1 in Figure 2). In this case, the mechanism described previously works in the opposite direction: when earnings improve, managers have a strong incentive to signal it with good policy changes. They anticipate a large marginal effect from such policy changes, which could potentially move them into a “safe” region. At the same time, they are not afraid of reversing such policies in the future when the standing of the firm declines as they expect very high turnover risk regardless of their policy choices. Which of these above predictions corresponds to the situation in reality is, of course, an empirical question that I will rely on the data to tell. If the board decides to retain the management, then the firm directly enters into the next period with its profitability $$\{z_t\}$$ and $$\{s_t\}$$ following the law of motion described in Equation (2). Otherwise, if the board decides to dismiss their management team under the criteria described in Equation (10), they reenter the labor market to search for successors at a cost $$c$$. The match-specific profitability for any new firm-management pair follows the unconditional distribution: $$z_{new} \sim N\Big(0,\frac{\sigma_z^2}{1-\rho_z^2}\Big)-c$$, which implies having executive turnover, on the one hand, allows the firm to eliminate unproductive matches. On the other hand, it also disrupts the firm’s normal operations and entails an opportunity cost, $$c$$.5 Given the turnover cost, $$c$$, the board of directors has a unique turnover threshold, $$\underline{z}$$, that maximizes the firm’s market value.6 2. Equilibrium Characterization In this section, I discuss the solution to the baseline model described in Section 1. The model can be condensed into a two-sided decision-making problem. An equilibrium is characterized by the following two incentive compatibility conditions. First, given the investors’ forecasting decision, $$\left\{\gamma_{0}, \gamma_{\pi}, \gamma_{{\it{\Omega}}}, \gamma_{\mathcal{F}}\right\}$$, managers set firm investment, financing, and payout policies in each period to maximize their expected utility. The second condition states that knowing the managers’ decision-making process, $$\left\{I_{t},E_{t},L_{t},D_{t}\right\}$$, investors choose the optimal forecasting rule in order to make the best possible predictions of the underlying profitability processes. When both conditions are satisfied, no party has an incentive to deviate from their current strategies. Hence, an equilibrium is achieved. Using the equilibrium model solution, I can examine the consequences of dividend changes on the managers’ welfare. The results illustrate why it is utility-enhancing for the managers to choose a smooth dividend path. In Table 1, I present the parameters and lists the values used for this exercise. Table 1 Parameter descriptions A: Estimated via SMM $$\rho_z$$ Autocorrelation of the persistent profitability 0.7087 $$\sigma_z$$ Standard deviation of innovations to the persistent profitability 0.3042 $$\sigma_s$$ Standard deviation of the transitory shock 0.0776 $$\theta$$ Curvature of a firm’s production function 0.5428 $$\delta$$ Capital depreciation rate 0.0988 $$\nu_1$$ Linear external financing cost 0.0544 $$\nu_2$$ Quadratic external financing cost 0.6466 $$\kappa_M$$ Weight of firm market value in executives’ utility function 0.6512 $$c$$ Cost for executive turnover 0.4822 B: Calibrated separately $$r_f$$ 1-year risk-free interest rate 2$$\%$$ $$\tau_c$$ Corporate income tax rate 35$$\%$$ $$\tau_p$$ Personal tax rate on dividends 15$$\%$$ $$\eta$$ Executive total compensation ($$\%$$ steady state asset) 0.0978 $$\kappa_I$$ Executives’ stock and option holdings ($$\%$$ shares outstanding) 1.1268 $$\lambda$$ Cost for dividend adjustment 1.21$$\%$$ C: Solved in equilibrium allocation $$\{K_t\}$$ Stock of physical capital / $$\{L_t\}$$ Holdings of liquid assets / $$\{E_t\}$$ Net equity issuance / $$\{D_t\}$$ Regular dividend distributions / $$\{\hat{z}_t\}$$ Investor’ forecasted match-specific persistent profitability / $$\{\Phi_t\}$$ Dummy variable indicating forced executive turnover / D: Shock processes $$\{\ln(z_t)\}$$ Match-specific persistent productivity shock $$\sim \rho_z\times \ln(z_{t-1}) + N(0,\sigma_z^2)$$ $$\{\ln(s_t)\}$$ Pure transitory shock to profit $$\sim N(0,\sigma_s^2)$$ $$\{\varphi_t\}$$ Additional signal observed by investors $$\sim N(\ln(z_t),\frac{\sigma_z^2}{1-\rho_z^2})$$ A: Estimated via SMM $$\rho_z$$ Autocorrelation of the persistent profitability 0.7087 $$\sigma_z$$ Standard deviation of innovations to the persistent profitability 0.3042 $$\sigma_s$$ Standard deviation of the transitory shock 0.0776 $$\theta$$ Curvature of a firm’s production function 0.5428 $$\delta$$ Capital depreciation rate 0.0988 $$\nu_1$$ Linear external financing cost 0.0544 $$\nu_2$$ Quadratic external financing cost 0.6466 $$\kappa_M$$ Weight of firm market value in executives’ utility function 0.6512 $$c$$ Cost for executive turnover 0.4822 B: Calibrated separately $$r_f$$ 1-year risk-free interest rate 2$$\%$$ $$\tau_c$$ Corporate income tax rate 35$$\%$$ $$\tau_p$$ Personal tax rate on dividends 15$$\%$$ $$\eta$$ Executive total compensation ($$\%$$ steady state asset) 0.0978 $$\kappa_I$$ Executives’ stock and option holdings ($$\%$$ shares outstanding) 1.1268 $$\lambda$$ Cost for dividend adjustment 1.21$$\%$$ C: Solved in equilibrium allocation $$\{K_t\}$$ Stock of physical capital / $$\{L_t\}$$ Holdings of liquid assets / $$\{E_t\}$$ Net equity issuance / $$\{D_t\}$$ Regular dividend distributions / $$\{\hat{z}_t\}$$ Investor’ forecasted match-specific persistent profitability / $$\{\Phi_t\}$$ Dummy variable indicating forced executive turnover / D: Shock processes $$\{\ln(z_t)\}$$ Match-specific persistent productivity shock $$\sim \rho_z\times \ln(z_{t-1}) + N(0,\sigma_z^2)$$ $$\{\ln(s_t)\}$$ Pure transitory shock to profit $$\sim N(0,\sigma_s^2)$$ $$\{\varphi_t\}$$ Additional signal observed by investors $$\sim N(\ln(z_t),\frac{\sigma_z^2}{1-\rho_z^2})$$ Table 1 presents the definitions of the parameters and the values used to calculate the baseline model solution. Table 1 Parameter descriptions A: Estimated via SMM $$\rho_z$$ Autocorrelation of the persistent profitability 0.7087 $$\sigma_z$$ Standard deviation of innovations to the persistent profitability 0.3042 $$\sigma_s$$ Standard deviation of the transitory shock 0.0776 $$\theta$$ Curvature of a firm’s production function 0.5428 $$\delta$$ Capital depreciation rate 0.0988 $$\nu_1$$ Linear external financing cost 0.0544 $$\nu_2$$ Quadratic external financing cost 0.6466 $$\kappa_M$$ Weight of firm market value in executives’ utility function 0.6512 $$c$$ Cost for executive turnover 0.4822 B: Calibrated separately $$r_f$$ 1-year risk-free interest rate 2$$\%$$ $$\tau_c$$ Corporate income tax rate 35$$\%$$ $$\tau_p$$ Personal tax rate on dividends 15$$\%$$ $$\eta$$ Executive total compensation ($$\%$$ steady state asset) 0.0978 $$\kappa_I$$ Executives’ stock and option holdings ($$\%$$ shares outstanding) 1.1268 $$\lambda$$ Cost for dividend adjustment 1.21$$\%$$ C: Solved in equilibrium allocation $$\{K_t\}$$ Stock of physical capital / $$\{L_t\}$$ Holdings of liquid assets / $$\{E_t\}$$ Net equity issuance / $$\{D_t\}$$ Regular dividend distributions / $$\{\hat{z}_t\}$$ Investor’ forecasted match-specific persistent profitability / $$\{\Phi_t\}$$ Dummy variable indicating forced executive turnover / D: Shock processes $$\{\ln(z_t)\}$$ Match-specific persistent productivity shock $$\sim \rho_z\times \ln(z_{t-1}) + N(0,\sigma_z^2)$$ $$\{\ln(s_t)\}$$ Pure transitory shock to profit $$\sim N(0,\sigma_s^2)$$ $$\{\varphi_t\}$$ Additional signal observed by investors $$\sim N(\ln(z_t),\frac{\sigma_z^2}{1-\rho_z^2})$$ A: Estimated via SMM $$\rho_z$$ Autocorrelation of the persistent profitability 0.7087 $$\sigma_z$$ Standard deviation of innovations to the persistent profitability 0.3042 $$\sigma_s$$ Standard deviation of the transitory shock 0.0776 $$\theta$$ Curvature of a firm’s production function 0.5428 $$\delta$$ Capital depreciation rate 0.0988 $$\nu_1$$ Linear external financing cost 0.0544 $$\nu_2$$ Quadratic external financing cost 0.6466 $$\kappa_M$$ Weight of firm market value in executives’ utility function 0.6512 $$c$$ Cost for executive turnover 0.4822 B: Calibrated separately $$r_f$$ 1-year risk-free interest rate 2$$\%$$ $$\tau_c$$ Corporate income tax rate 35$$\%$$ $$\tau_p$$ Personal tax rate on dividends 15$$\%$$ $$\eta$$ Executive total compensation ($$\%$$ steady state asset) 0.0978 $$\kappa_I$$ Executives’ stock and option holdings ($$\%$$ shares outstanding) 1.1268 $$\lambda$$ Cost for dividend adjustment 1.21$$\%$$ C: Solved in equilibrium allocation $$\{K_t\}$$ Stock of physical capital / $$\{L_t\}$$ Holdings of liquid assets / $$\{E_t\}$$ Net equity issuance / $$\{D_t\}$$ Regular dividend distributions / $$\{\hat{z}_t\}$$ Investor’ forecasted match-specific persistent profitability / $$\{\Phi_t\}$$ Dummy variable indicating forced executive turnover / D: Shock processes $$\{\ln(z_t)\}$$ Match-specific persistent productivity shock $$\sim \rho_z\times \ln(z_{t-1}) + N(0,\sigma_z^2)$$ $$\{\ln(s_t)\}$$ Pure transitory shock to profit $$\sim N(0,\sigma_s^2)$$ $$\{\varphi_t\}$$ Additional signal observed by investors $$\sim N(\ln(z_t),\frac{\sigma_z^2}{1-\rho_z^2})$$ Table 1 presents the definitions of the parameters and the values used to calculate the baseline model solution. To see how managers are hurt by the announcement of dividend reductions, I simulate 100,000 hypothetical firms. I create the dividend-cutting sample by sorting out the firms that cut dividends in year one. I also create a matching sample by choosing a set of non-dividend-cutting firms that have the same year-one reported earnings as in the dividend-cutting sample and use them as controls. Figure 3 shows that dividend decreases are typically associated with well below average contemporaneous earnings. When firms reduce dividends, it does not directly signal future decreases in earnings. Instead, their actions imply that large earnings shocks have already been realized and will have persistent effects on the future performance. Consequently, such firms experience slower productivity reversals, and it usually takes longer for their earnings to converge back to the steady state. These outcomes are consistent with the empirical evidence in Grullon et al. (2005). Figure 3 View largeDownload slide The information content of dividends Figure 3 reports the model-predicted firm profit and executive turnovers following dividend cuts. The dividend-cutting sample consists of simulated firms that cut dividends in year one; the matching sample is constructed from simulated firms that have the same year-one reported earnings as the dividend-cutting sample but have maintained or increased dividends. The x-axis corresponds to the number of years after dividend cuts. On the y-axis, firms’ profit and forced executive turnover rates are expressed as fractions of their corresponding steady-state levels. Figure 3 View largeDownload slide The information content of dividends Figure 3 reports the model-predicted firm profit and executive turnovers following dividend cuts. The dividend-cutting sample consists of simulated firms that cut dividends in year one; the matching sample is constructed from simulated firms that have the same year-one reported earnings as the dividend-cutting sample but have maintained or increased dividends. The x-axis corresponds to the number of years after dividend cuts. On the y-axis, firms’ profit and forced executive turnover rates are expressed as fractions of their corresponding steady-state levels. Moreover, the results in Figure 3 also suggests that dividend changes influence the managers’ turnover risk. Firms that decrease dividends experience, on average, one-third higher rates of forced managerial turnover, compared with firms in the matching sample who report similar earnings but manage to increase or maintain their dividend levels. I repeat the above exercise for the sample of dividend-increasing firms and find similar qualitative effects. However, quantitatively, the magnitudes of the effects are much weaker. This is because the parameters in Table 1 suggest an average turnover rate of approximately 2.6$$\%$$ per year (consistent with the actual data), which corresponds to the low and strongly convex turnover profile indicated by region 3 in Figure 2. This convexity implies that the benefit from raising dividends when earnings increases is very limited, while announcing a dividend cut alongside earnings deteriorations may have a larger negative impact on the expected turnover.7 In anticipation of these effects, managers will be reluctant to raise dividends when earnings improve as well as to cut dividends when earnings decline, resulting in dividends that are slow to respond to earnings. In Figure 4, I consider two model specifications: the baseline model and an alternative case in which I assume that the shareholders extract information from the dividends, but the managers ignore this effect on their tenure. Instead, they believe that their turnover probability is constant across time and states. This assumption brings me back to the first-best solution, in which the managers behave as if their personal interests are fully aligned with the best interests of the shareholders and choose the optimal policies to maximize the shareholders’ value. Figure 4 View largeDownload slide Managers’ career concerns and firm policies Figure 4 presents the firm policy functions and market-to-book ratio under two alternative model specifications. The solid line corresponds to the baseline model described in Section 1; the dashed line is a case in which the managers have constant turnover belief. On the x-axis, earnings are normalized by the steady-state level of earnings under the constant turnover model. On the y-axis, dividends, repurchases, and equity issuance are scaled by the total assets of a firm. Figure 4 View largeDownload slide Managers’ career concerns and firm policies Figure 4 presents the firm policy functions and market-to-book ratio under two alternative model specifications. The solid line corresponds to the baseline model described in Section 1; the dashed line is a case in which the managers have constant turnover belief. On the x-axis, earnings are normalized by the steady-state level of earnings under the constant turnover model. On the y-axis, dividends, repurchases, and equity issuance are scaled by the total assets of a firm. Figure 4 shows that when managers anticipate state-contingent turnover risk, they become more conservative in setting the rate of payments, which lowers the dividend level. At the same time, dividends are markedly less responsive to earnings changes, reflected by a flatter slope of the dividend policy.8 This difference in slopes captures the amount of dividend smoothing that stems from managers’ career concerns, which is not desirable from the shareholders’ point of view. Anticipating a state-contingent turnover risk also influences the managers’ other policy choices. More specifically, they will hoard cash instead of paying out dividends in cash-rich states, which is costly for the firm because interest is taxed. They will also avoid cutting dividends in an attempt to withhold bad information from investors in a low cash flow state, which may require issuing new equity or cutting investments. Figure 4 shows that these policy choices make the equilibrium firm value lower than in the alternative case in which firm policies do not reflect managers’ career concerns. 3. Data In this section, I provide a brief discussion of the data sets used to quantify the model. The data come from four sources: firm fundamentals come from Compustat; executive compensation data are from ExecuComp; dividend announcement dates and returns are from the CRSP daily file; and the top executive turnovers are from a hand-collected data set based on Businessweek, Equilar, and The Wall Street Journal. 3.1 Sample construction To construct the sample, I start with all nonfinancial and nonutility firms in the merged CRSP and Compustat database from 1992 to 2011. Analyzing firms’ dividend smoothing behavior requires that they provide sufficient dividend payment records, so that a reliable measure on the smoothness can be calculated. Therefore, I restrict the sample to the set of frequent dividend-paying firms following two steps. In the first step, I remove all observations before a firm announces its first dividend and after it makes its last dividend payment. In the second step, I divide the sample into 11 overlapping 10-year sub-periods. For any given 10-year sub-periods, I only retain the firms that have made at least six positive dividend payments. Any firm with consecutive zero payments is dropped. Those firms are likely to differ systematically from the firms with consistent positive dividends and, therefore, I do not consider zero payments as a special form of smoothed dividends. Applying these filters reduces the sample size by 68$$\%$$, from 33,590 firm-year observations in the merged CRSP-Compustat data set to 11,626 firm-year observations. However, this reduction in sample size is not due to data limitations. Instead, it is determined by the nature of the research question, because it is meaningless to examine the smoothness of dividends if the firm barely makes any payment. Although the final sample covers only 32$$\%$$ of the firm years, it accounts for 61$$\%$$ of the U.S. market capitalization as larger, more mature firms are more likely to make consistent dividend payments. Next, I calculate the magnitude of the dividend price effect by focusing on the observations where the changes in split-adjusted dividend per share are larger than 10$$\%$$. I obtain the dates for the dividend change announcements from the CRSP daily event file. I check whether these firms make any earnings disclosure in a 10-day window prior to the dividend announcements and exclude the observations where the two types of events overlap. I calculate the five-day cumulative abnormal returns (CARs) around the dividend changes and use them to quantify the price effect. The CARs are slightly below 1$$\%$$ and insignificant for dividend increases, and they average -3$$\%$$ for dividend cuts. In terms of magnitude, these results are similar in magnitude to earlier studies (Aharony and Swary, 1980, Nissim and Ziv, 2001). 3.2 Executive turnover ExecuComp tracks top executives’ compensation starting from 1992, where I retrieve data on the five highest paid managers’ total annual compensation, their percentage of stock holdings, and the percentage of nonvested versus vested stock options. I hand-collect data on executive turnovers from Businessweek, Equilar, and The Wall Street Journal. I define the year of “turnover” as the one in which the firm announces the departure of a top executive. Following Warner, Watts, and Wruck (1988), Parrino, Sias, and Starks (2003), Jenter and Kanaan (2015), I classify a turnover as “forced” if a manager leaves a firm and does not find another executive position within a year, or if a manager is reported to have retired before the age of 60. I also do a Google search to supplement the data. If any reliable source points out that the turnover is performance-based, then I interpret it as “forced.” However, if the turnover is due to health issues, I classify it as “voluntary.” The final sample consists of 10,827 distinct firm-executive pairs. Table 2 contains the variable definitions. Table 3 provides the descriptive statistics for the final sample. Table 2 Variable construction Compustat variables Investment (Capital Expenditures (CAPX) $$-$$ Sale of Property (SPPE))/Property Plant and $$\quad$$ Equipment-Total (PPEGT) Book equity Common or Ordinary Equity-Total (CEQ) + Deferred Taxes and Investment $$\quad$$ Tax Credit (TXDITC) $$-$$ Preferred or Preference Stock (Capital)-Total (PSTK) $$\quad$$ if (PSTK) missing then Preferred Stock-Redemption Value (PSTKRV) if $$\quad$$ (PSTKRV) missing then Preferred Stock-Liquidating Value (PSTKL) Market-to-book (Common Shares Outstanding (CSHO) $$\times$$ Price Close-Annual Fiscal Year $$\quad$$ (PRCC_ F) + Book Debt (BD))/Assets-Total (AT) Equity Sale of Common and Preferred Stock (SSTK)/Assets-Total (AT) Repurchase Purchase of Common and Preferred Stock (PRSTKC)/Assets-Total (AT) Dividends Dividends Common or Ordinary (DVC)/Assets-Total (AT) Managerial ownership (Shares Owned-Options Excluded (SHROWN EXCL OPTS) $$\quad$$ + Unexercised Exercisable Options (OPT UNEX EXER NUM) + Unexercised $$\quad$$ Unexercisable Options (OPT UNEX UNEXER NUM))/Common Shares $$\quad$$ Outstanding (CSHO) Managerial wage Total Compensation (TDC2)/Assets-Total (AT) Other variables Institutional ownership Institutional ownership fraction of stock owned by institutional investors (from $$\quad$$ Thompson Financial) Analyst forecast dispersion Standard deviation of analyst forecast/Absolute value of mean analyst forecast Marginal-q Errors-in-variables corrected q-proxy constructed using the Erickson and Whited $$\quad$$ high-order estimator Abnormal accruals Second-stage regression residual from the modified Jones model Compustat variables Investment (Capital Expenditures (CAPX) $$-$$ Sale of Property (SPPE))/Property Plant and $$\quad$$ Equipment-Total (PPEGT) Book equity Common or Ordinary Equity-Total (CEQ) + Deferred Taxes and Investment $$\quad$$ Tax Credit (TXDITC) $$-$$ Preferred or Preference Stock (Capital)-Total (PSTK) $$\quad$$ if (PSTK) missing then Preferred Stock-Redemption Value (PSTKRV) if $$\quad$$ (PSTKRV) missing then Preferred Stock-Liquidating Value (PSTKL) Market-to-book (Common Shares Outstanding (CSHO) $$\times$$ Price Close-Annual Fiscal Year $$\quad$$ (PRCC_ F) + Book Debt (BD))/Assets-Total (AT) Equity Sale of Common and Preferred Stock (SSTK)/Assets-Total (AT) Repurchase Purchase of Common and Preferred Stock (PRSTKC)/Assets-Total (AT) Dividends Dividends Common or Ordinary (DVC)/Assets-Total (AT) Managerial ownership (Shares Owned-Options Excluded (SHROWN EXCL OPTS) $$\quad$$ + Unexercised Exercisable Options (OPT UNEX EXER NUM) + Unexercised $$\quad$$ Unexercisable Options (OPT UNEX UNEXER NUM))/Common Shares $$\quad$$ Outstanding (CSHO) Managerial wage Total Compensation (TDC2)/Assets-Total (AT) Other variables Institutional ownership Institutional ownership fraction of stock owned by institutional investors (from $$\quad$$ Thompson Financial) Analyst forecast dispersion Standard deviation of analyst forecast/Absolute value of mean analyst forecast Marginal-q Errors-in-variables corrected q-proxy constructed using the Erickson and Whited $$\quad$$ high-order estimator Abnormal accruals Second-stage regression residual from the modified Jones model Table 2 provides the variable constructions. Table 2 Variable construction Compustat variables Investment (Capital Expenditures (CAPX) $$-$$ Sale of Property (SPPE))/Property Plant and $$\quad$$ Equipment-Total (PPEGT) Book equity Common or Ordinary Equity-Total (CEQ) + Deferred Taxes and Investment $$\quad$$ Tax Credit (TXDITC) $$-$$ Preferred or Preference Stock (Capital)-Total (PSTK) $$\quad$$ if (PSTK) missing then Preferred Stock-Redemption Value (PSTKRV) if $$\quad$$ (PSTKRV) missing then Preferred Stock-Liquidating Value (PSTKL) Market-to-book (Common Shares Outstanding (CSHO) $$\times$$ Price Close-Annual Fiscal Year $$\quad$$ (PRCC_ F) + Book Debt (BD))/Assets-Total (AT) Equity Sale of Common and Preferred Stock (SSTK)/Assets-Total (AT) Repurchase Purchase of Common and Preferred Stock (PRSTKC)/Assets-Total (AT) Dividends Dividends Common or Ordinary (DVC)/Assets-Total (AT) Managerial ownership (Shares Owned-Options Excluded (SHROWN EXCL OPTS) $$\quad$$ + Unexercised Exercisable Options (OPT UNEX EXER NUM) + Unexercised $$\quad$$ Unexercisable Options (OPT UNEX UNEXER NUM))/Common Shares $$\quad$$ Outstanding (CSHO) Managerial wage Total Compensation (TDC2)/Assets-Total (AT) Other variables Institutional ownership Institutional ownership fraction of stock owned by institutional investors (from $$\quad$$ Thompson Financial) Analyst forecast dispersion Standard deviation of analyst forecast/Absolute value of mean analyst forecast Marginal-q Errors-in-variables corrected q-proxy constructed using the Erickson and Whited $$\quad$$ high-order estimator Abnormal accruals Second-stage regression residual from the modified Jones model Compustat variables Investment (Capital Expenditures (CAPX) $$-$$ Sale of Property (SPPE))/Property Plant and $$\quad$$ Equipment-Total (PPEGT) Book equity Common or Ordinary Equity-Total (CEQ) + Deferred Taxes and Investment $$\quad$$ Tax Credit (TXDITC) $$-$$ Preferred or Preference Stock (Capital)-Total (PSTK) $$\quad$$ if (PSTK) missing then Preferred Stock-Redemption Value (PSTKRV) if $$\quad$$ (PSTKRV) missing then Preferred Stock-Liquidating Value (PSTKL) Market-to-book (Common Shares Outstanding (CSHO) $$\times$$ Price Close-Annual Fiscal Year $$\quad$$ (PRCC_ F) + Book Debt (BD))/Assets-Total (AT) Equity Sale of Common and Preferred Stock (SSTK)/Assets-Total (AT) Repurchase Purchase of Common and Preferred Stock (PRSTKC)/Assets-Total (AT) Dividends Dividends Common or Ordinary (DVC)/Assets-Total (AT) Managerial ownership (Shares Owned-Options Excluded (SHROWN EXCL OPTS) $$\quad$$ + Unexercised Exercisable Options (OPT UNEX EXER NUM) + Unexercised $$\quad$$ Unexercisable Options (OPT UNEX UNEXER NUM))/Common Shares $$\quad$$ Outstanding (CSHO) Managerial wage Total Compensation (TDC2)/Assets-Total (AT) Other variables Institutional ownership Institutional ownership fraction of stock owned by institutional investors (from $$\quad$$ Thompson Financial) Analyst forecast dispersion Standard deviation of analyst forecast/Absolute value of mean analyst forecast Marginal-q Errors-in-variables corrected q-proxy constructed using the Erickson and Whited $$\quad$$ high-order estimator Abnormal accruals Second-stage regression residual from the modified Jones model Table 2 provides the variable constructions. Table 3 Summary statistics Mean SD 25$$\%$$ 50$$\%$$ 75$$\%$$ Firm investment and financial characteristics $$\quad$$ Size 8.0269 1.6111 6.8491 7.9384 9.1646 $$\quad$$ Operating income 0.1630 0.0790 0.1091 0.1490 0.2067 $$\quad$$ Leverage 0.2542 0.1427 0.1510 0.2597 0.3546 $$\quad$$ Market-to-book 2.7443 2.4076 1.3271 2.0057 3.1630 $$\quad$$ Cash 0.0707 0.0911 0.0120 0.0339 0.0906 $$\quad$$ Equity issuance 0.0112 0.0186 0.0005 0.0041 0.0164 $$\quad$$ Investment 0.0985 0.0684 0.0591 0.0796 0.1256 $$\quad$$ Dividend 0.0240 0.0179 0.0114 0.0198 0.0311 $$\quad$$ Repurchase 0.0297 0.0331 0.0000 0.0042 0.0319 $$\quad$$ Dividend-to-earnings ratio 0.1542 0.0984 0.0813 0.1399 0.2094 $$\quad$$ Dividend per share 0.6581 0.5930 0.2141 0.4797 0.9133 $$\quad$$ Earnings per share 4.5869 3.8815 2.0428 3.5942 5.8738 $$\quad$$ Stock return 0.1226 0.4556 –0.1040 0.0820 0.2775 $$\quad$$ Asset tangibility 0.4627 0.3530 0.2220 0.4328 0.6367 $$\quad$$ Institutional holdings 0.4287 0.2420 0.2581 0.4611 0.6403 Managerial characteristics $$\quad$$ Salary 0.0251 0.0317 0.0050 0.0133 0.0318 $$\quad$$ Bonus 0.0129 0.0211 0.0010 0.0053 0.0150 $$\quad$$ Total compensation 0.0735 0.0981 0.0173 0.0399 0.0864 $$\quad$$$$\%$$ stock holdings 0.6041 1.5196 0.0318 0.0909 0.3124 $$\quad$$$$\%$$ vested options 0.1826 0.2169 0.0364 0.1067 0.2467 $$\quad$$$$\%$$ unvested options 0.1327 0.1682 0.0224 0.0762 0.1708 $$\quad$$ Tenure 8.9538 10.8480 3 9 12 Mean SD 25$$\%$$ 50$$\%$$ 75$$\%$$ Firm investment and financial characteristics $$\quad$$ Size 8.0269 1.6111 6.8491 7.9384 9.1646 $$\quad$$ Operating income 0.1630 0.0790 0.1091 0.1490 0.2067 $$\quad$$ Leverage 0.2542 0.1427 0.1510 0.2597 0.3546 $$\quad$$ Market-to-book 2.7443 2.4076 1.3271 2.0057 3.1630 $$\quad$$ Cash 0.0707 0.0911 0.0120 0.0339 0.0906 $$\quad$$ Equity issuance 0.0112 0.0186 0.0005 0.0041 0.0164 $$\quad$$ Investment 0.0985 0.0684 0.0591 0.0796 0.1256 $$\quad$$ Dividend 0.0240 0.0179 0.0114 0.0198 0.0311 $$\quad$$ Repurchase 0.0297 0.0331 0.0000 0.0042 0.0319 $$\quad$$ Dividend-to-earnings ratio 0.1542 0.0984 0.0813 0.1399 0.2094 $$\quad$$ Dividend per share 0.6581 0.5930 0.2141 0.4797 0.9133 $$\quad$$ Earnings per share 4.5869 3.8815 2.0428 3.5942 5.8738 $$\quad$$ Stock return 0.1226 0.4556 –0.1040 0.0820 0.2775 $$\quad$$ Asset tangibility 0.4627 0.3530 0.2220 0.4328 0.6367 $$\quad$$ Institutional holdings 0.4287 0.2420 0.2581 0.4611 0.6403 Managerial characteristics $$\quad$$ Salary 0.0251 0.0317 0.0050 0.0133 0.0318 $$\quad$$ Bonus 0.0129 0.0211 0.0010 0.0053 0.0150 $$\quad$$ Total compensation 0.0735 0.0981 0.0173 0.0399 0.0864 $$\quad$$$$\%$$ stock holdings 0.6041 1.5196 0.0318 0.0909 0.3124 $$\quad$$$$\%$$ vested options 0.1826 0.2169 0.0364 0.1067 0.2467 $$\quad$$$$\%$$ unvested options 0.1327 0.1682 0.0224 0.0762 0.1708 $$\quad$$ Tenure 8.9538 10.8480 3 9 12 The sample is constructed from the 2013 Compustat and CRSP files for the period 1992–2011. Nonfinancial and nonutility firms that declare at least six positive annual dividends in the surrounding 10-year window are included. This sample is merged with executive compensation data from ExecuComp, institutional ownership data from Thomson Financial, and a hand-collected data set on top executive turnovers. This process yields 10,827 distinct firm-executive pairs and 11,626 firm-year observations. Table 3 Summary statistics Mean SD 25$$\%$$ 50$$\%$$ 75$$\%$$ Firm investment and financial characteristics $$\quad$$ Size 8.0269 1.6111 6.8491 7.9384 9.1646 $$\quad$$ Operating income 0.1630 0.0790 0.1091 0.1490 0.2067 $$\quad$$ Leverage 0.2542 0.1427 0.1510 0.2597 0.3546 $$\quad$$ Market-to-book 2.7443 2.4076 1.3271 2.0057 3.1630 $$\quad$$ Cash 0.0707 0.0911 0.0120 0.0339 0.0906 $$\quad$$ Equity issuance 0.0112 0.0186 0.0005 0.0041 0.0164 $$\quad$$ Investment 0.0985 0.0684 0.0591 0.0796 0.1256 $$\quad$$ Dividend 0.0240 0.0179 0.0114 0.0198 0.0311 $$\quad$$ Repurchase 0.0297 0.0331 0.0000 0.0042 0.0319 $$\quad$$ Dividend-to-earnings ratio 0.1542 0.0984 0.0813 0.1399 0.2094 $$\quad$$ Dividend per share 0.6581 0.5930 0.2141 0.4797 0.9133 $$\quad$$ Earnings per share 4.5869 3.8815 2.0428 3.5942 5.8738 $$\quad$$ Stock return 0.1226 0.4556 –0.1040 0.0820 0.2775 $$\quad$$ Asset tangibility 0.4627 0.3530 0.2220 0.4328 0.6367 $$\quad$$ Institutional holdings 0.4287 0.2420 0.2581 0.4611 0.6403 Managerial characteristics $$\quad$$ Salary 0.0251 0.0317 0.0050 0.0133 0.0318 $$\quad$$ Bonus 0.0129 0.0211 0.0010 0.0053 0.0150 $$\quad$$ Total compensation 0.0735 0.0981 0.0173 0.0399 0.0864 $$\quad$$$$\%$$ stock holdings 0.6041 1.5196 0.0318 0.0909 0.3124 $$\quad$$$$\%$$ vested options 0.1826 0.2169 0.0364 0.1067 0.2467 $$\quad$$$$\%$$ unvested options 0.1327 0.1682 0.0224 0.0762 0.1708 $$\quad$$ Tenure 8.9538 10.8480 3 9 12 Mean SD 25$$\%$$ 50$$\%$$ 75$$\%$$ Firm investment and financial characteristics $$\quad$$ Size 8.0269 1.6111 6.8491 7.9384 9.1646 $$\quad$$ Operating income 0.1630 0.0790 0.1091 0.1490 0.2067 $$\quad$$ Leverage 0.2542 0.1427 0.1510 0.2597 0.3546 $$\quad$$ Market-to-book 2.7443 2.4076 1.3271 2.0057 3.1630 $$\quad$$ Cash 0.0707 0.0911 0.0120 0.0339 0.0906 $$\quad$$ Equity issuance 0.0112 0.0186 0.0005 0.0041 0.0164 $$\quad$$ Investment 0.0985 0.0684 0.0591 0.0796 0.1256 $$\quad$$ Dividend 0.0240 0.0179 0.0114 0.0198 0.0311 $$\quad$$ Repurchase 0.0297 0.0331 0.0000 0.0042 0.0319 $$\quad$$ Dividend-to-earnings ratio 0.1542 0.0984 0.0813 0.1399 0.2094 $$\quad$$ Dividend per share 0.6581 0.5930 0.2141 0.4797 0.9133 $$\quad$$ Earnings per share 4.5869 3.8815 2.0428 3.5942 5.8738 $$\quad$$ Stock return 0.1226 0.4556 –0.1040 0.0820 0.2775 $$\quad$$ Asset tangibility 0.4627 0.3530 0.2220 0.4328 0.6367 $$\quad$$ Institutional holdings 0.4287 0.2420 0.2581 0.4611 0.6403 Managerial characteristics $$\quad$$ Salary 0.0251 0.0317 0.0050 0.0133 0.0318 $$\quad$$ Bonus 0.0129 0.0211 0.0010 0.0053 0.0150 $$\quad$$ Total compensation 0.0735 0.0981 0.0173 0.0399 0.0864 $$\quad$$$$\%$$ stock holdings 0.6041 1.5196 0.0318 0.0909 0.3124 $$\quad$$$$\%$$ vested options 0.1826 0.2169 0.0364 0.1067 0.2467 $$\quad$$$$\%$$ unvested options 0.1327 0.1682 0.0224 0.0762 0.1708 $$\quad$$ Tenure 8.9538 10.8480 3 9 12 The sample is constructed from the 2013 Compustat and CRSP files for the period 1992–2011. Nonfinancial and nonutility firms that declare at least six positive annual dividends in the surrounding 10-year window are included. This sample is merged with executive compensation data from ExecuComp, institutional ownership data from Thomson Financial, and a hand-collected data set on top executive turnovers. This process yields 10,827 distinct firm-executive pairs and 11,626 firm-year observations. 3.3 Dividend smoothness Following Leary and Michaely (2011), I measure a firm’s dividend smoothness using the speed of adjustment (SOA), which equals the estimated coefficient $$\beta$$ in the following regression: \begin{eqnarray} \label{EQ11} D_{i,t}-D_{i,t-1}=\alpha+\beta\times(TPR_{i}\times Y_{i,t}-D_{i,t-1})+\epsilon_{i,t}, \end{eqnarray} (11) where $$D_{i,t}$$ and $$Y_{i,t}$$ refer to firm $$i$$’s dividend and earnings per share, respectively, at time $$t$$ after adjusting for stock splits. $$TPR_{i}$$ is the firm’s target dividend payout ratio, which is defined as the median dividend-to-earnings ratio for firm $$i$$ over the 10-year window. In a hypothetical case in which a firm always lets its dividends fluctuate proportionately with earnings, $$\beta$$ will have an estimated value of 1; if, on the other extreme, a firm keeps its dividend per share constant regardless of its earnings changes, then $$\beta$$ will take the value of 0. In reality, a firm’s dividend adjustment usually lies in between these two extremes, with a lower SOA implying that the dividends are smoother and less responsive to earnings changes. In Figure 5, I plot the time-series changes for dividend per share and dividend smoothness. The estimated SOA of dividends is consistently around 0.2, indicating that shocks to firms’ earnings do not translate into proportional changes in dividends. Over time, the SOA of dividends decreased slightly,9 while the level of dividend per share increased by roughly 50$$\%$$. This evidence suggests that the frequent dividend payers have been increasing their distributions over time, and they distribute in an increasingly “smoother” fashion. Figure 5 View largeDownload slide Dividend smoothing over time Figure 5 shows the time trend for dividend per share and dividend smoothness among nonfinancial and nonutility firms. Calculations are based on rolling 10-year windows from 1987 to 2011. The x-axis corresponds to the last year in each 10-year subsample. Dividend smoothness is measured by the speed of adjustment (SOA), which equals the estimated coefficient $$\beta$$ in the following regression: $$D_{i,t}-D_{i,t-1}=\alpha+\beta\times(TPR_{i}\times Y_{i,t}-D_{i,t-1})+\epsilon_{i,t} $$, where $$D_{i,t}$$ and $$Y_{i,t}$$ are the dividend and earnings per share, respectively. $$TPR_{i}$$ is a firm’s target dividend payout ratio over the surrounding 10-year period. Figure 5 View largeDownload slide Dividend smoothing over time Figure 5 shows the time trend for dividend per share and dividend smoothness among nonfinancial and nonutility firms. Calculations are based on rolling 10-year windows from 1987 to 2011. The x-axis corresponds to the last year in each 10-year subsample. Dividend smoothness is measured by the speed of adjustment (SOA), which equals the estimated coefficient $$\beta$$ in the following regression: $$D_{i,t}-D_{i,t-1}=\alpha+\beta\times(TPR_{i}\times Y_{i,t}-D_{i,t-1})+\epsilon_{i,t} $$, where $$D_{i,t}$$ and $$Y_{i,t}$$ are the dividend and earnings per share, respectively. $$TPR_{i}$$ is a firm’s target dividend payout ratio over the surrounding 10-year period. 4. Results In this section, I discuss the estimation of the model and present the quantitative results. Based on the parameter estimates, I perform two counterfactual exercises in Subsection 4.3 to quantify the amount of career-concern-based dividend smoothing and explore its effect on firm value and other policies. 4.1 Identification I estimate most parameters using the simulated method of moments (SMM), the objective of which is to pick the set of parameters that make the simulated data track the actual data as closely as possible. For the rest of the parameters, I calibrate their values separately. For example, I set the risk-free rate, $$r_f$$, equal to the average real three-month Treasury bill rate. I set the dividend income tax, $$\tau_{p}$$, equal to the average tax disadvantage of personal income relative to capital gains, which is approximately 15$$\%$$ over the sample period. I set the corporate tax rate, $$\tau_{c}$$, to 35$$\%$$. In addition, I calibrate $$\kappa_I$$ to 1.3$$\%$$ using the sum of executives’ stock holdings and stock options, and I set the per-period wage, $$\eta$$, to 0.10$$\%$$ of the steady-state firm asset value.10 This choice of $$\eta$$ matches the average levels of executive compensation reported in the ExecuComp database. I estimate the value of the dividend adjustment cost parameter, $$\lambda$$, by equating the endogenous model-predicted dividend announcement return with the five-day CARs surrounding dividend cuts in the actual data. With $$\lambda = 1.21\%$$, the model generates -3$$\%$$ and 0.41$$\%$$ abnormal returns around dividend cuts and increases, respectively, consistent with what is found in the actual data.11 Note that I do not estimate $$\lambda$$ together with the other 9 parameters (discussed below) in one big SMM system because the identification for $$\lambda$$ comes from a five-day event window, while the identifications for the other parameters come from data at annual frequencies, which makes it difficult to compute their relative weights in an optimal weighting matrix. Instead, I adopt an iterative approach to recognize the interdependence between $$\lambda$$ and other model parameters—I first pick a value for $$\lambda$$. Taking $$\lambda$$ as given, I then estimate the big SMM system with 15 moments and 9 parameters and calculate the model-implied announcement return based on the estimated parameter values. I keep iterating on these two steps until the announcement return coming from the model is equal to that in the actual data. I next estimate the remaining 9 parameters $$\{ \rho_z,\sigma_z,\sigma_s,\theta,\nu_1,\nu_2,\delta,\kappa_M,c\}$$12 by matching 15 moments. The success of this strategy depends critically on choosing the moments that are sensitive to variations in the underlying structural parameters. On the other hand, I avoid “cherry-picking” by focusing on the moments that reflect important characteristics of the data. The first two moments correspond to the two coefficients, $$\{\beta_K ,\beta_Y\}$$, in the following regression: \begin{eqnarray} \label{EQ12} \ln(Y_{i,t})=\beta_{Y}\times \ln(Y_{i,t-1})+\beta_{K}\times \ln(K_{i,t})-\beta_{Y}\times\beta_{K}\times \ln(K_{i,t-1})+\epsilon_{i,t}, \end{eqnarray} (12) where $$Y_{i,t}$$ is a firm’s operating income and $$K_{i,t}$$ denotes the stock of physical capital. As argued by Cooper and Haltiwanger (2006), Equation (12) can be derived as an auxiliary equation from the firm’s production function, Equation (2), and the profitability shock processes.13 Hence, these moments are sensitive to the underlying parameter changes, and they map monotonically into the parameters of interest. When estimating Equation (12), I focus on the first-order difference to deal with firm fixed effects. I use twice-lagged profit, as well as lagged and twice-lagged capital stock as instruments. I also impose a complete set of year dummies to absorb the time-series heterogeneity in the data. The next three moments are the mean, standard deviations, and AR(1) coefficient of a firm’s operating income. These three moments help to identify the dispersions of the shock processes. Keeping all else constant, increases in both $$\sigma_s$$ and $$\sigma_z$$ will increase the mean and variance of operating income, while only $$\sigma_s$$ has a dampening effect on the estimated AR(1) coefficients. The third set of moments includes the mean of investment, which is used to determine the depreciation rate, $$\delta$$, as well as the mean and variance of net equity issuance, which are used to pin down the fixed and quadratic equity issuance costs $$\{\nu_1, \nu_2\}$$. I then add the frequency of turnover and the correlation between turnover and earnings to help identify the opportunity cost of firing, $$c$$. I also include the mean and standard deviation of the market-to-book ratio, which are most sensitive to variations in $$\kappa_M$$; $$\kappa_M$$ measures to what extent managers care about the market value of the firm. Lastly, I add to the list the mean and standard deviation of the dividend payments, as well as the SOA of dividends. My goal with this model is to explain the degree of dividend smoothness in the data. Therefore, I need to ensure that these dividend-related moments are matched closely in the model. In Table 4, I report the Jacobian matrix of the moment conditions to each underlying parameter. The results confirm the intuition of the identification strategy discussed above.14 Table 4 Jacobian matrix of moment conditions to parameters Mean Std Auto Mean Mean Std Mean Std Mean Std Corr(profit, profit profit profit investment $$\gamma_y$$ $$\gamma_k$$ issuance issuance M/B M/B dividend dividend SOA Turnover turnover) $$\rho_z$$ –0.079 0.008 0.874 0.002 0.000 0.995 –0.037 –0.015 0.287 0.146 0.024 0.014 0.244 0.003 0.003 $$\theta$$ 0.014 0.026 0.028 0.001 0.991 0.000 0.028 0.030 0.028 0.006 –0.020 0.010 0.276 0.001 –0.025 $$\sigma_z$$ 0.199 0.436 –0.039 0.003 0.000 0.000 –0.064 0.020 0.440 0.038 0.054 –0.006 0.317 0.006 –0.009 $$\sigma_s$$ 0.049 0.398 –0.678 –0.002 0.000 0.000 –0.012 –0.024 0.072 –0.072 –0.006 0.025 –0.064 –0.002 –0.066 $$\delta$$ –0.018 0.165 –0.348 1.007 0.000 0.000 –0.012 0.026 0.071 –0.047 0.017 –0.030 –0.461 0.011 –0.058 $$\nu_1$$ –0.054 0.023 0.022 0.000 0.000 0.000 –0.278 –0.084 –0.303 0.017 0.089 0.162 0.124 –0.004 0.009 $$\nu_2$$ –0.012 0.006 0.024 0.009 0.000 0.000 0.008 –0.261 –0.018 –0.026 –0.022 0.009 0.531 0.001 –0.001 $$\kappa_M$$ 0.273 0.061 0.176 –0.061 0.000 0.000 0.180 0.120 0.532 0.216 –0.082 0.039 0.349 0.016 –0.203 $$c$$ –0.047 –0.020 –0.027 –0.001 0.000 0.000 0.031 0.025 –0.080 0.042 –0.014 0.005 0.050 –0.273 –0.192 Mean Std Auto Mean Mean Std Mean Std Mean Std Corr(profit, profit profit profit investment $$\gamma_y$$ $$\gamma_k$$ issuance issuance M/B M/B dividend dividend SOA Turnover turnover) $$\rho_z$$ –0.079 0.008 0.874 0.002 0.000 0.995 –0.037 –0.015 0.287 0.146 0.024 0.014 0.244 0.003 0.003 $$\theta$$ 0.014 0.026 0.028 0.001 0.991 0.000 0.028 0.030 0.028 0.006 –0.020 0.010 0.276 0.001 –0.025 $$\sigma_z$$ 0.199 0.436 –0.039 0.003 0.000 0.000 –0.064 0.020 0.440 0.038 0.054 –0.006 0.317 0.006 –0.009 $$\sigma_s$$ 0.049 0.398 –0.678 –0.002 0.000 0.000 –0.012 –0.024 0.072 –0.072 –0.006 0.025 –0.064 –0.002 –0.066 $$\delta$$ –0.018 0.165 –0.348 1.007 0.000 0.000 –0.012 0.026 0.071 –0.047 0.017 –0.030 –0.461 0.011 –0.058 $$\nu_1$$ –0.054 0.023 0.022 0.000 0.000 0.000 –0.278 –0.084 –0.303 0.017 0.089 0.162 0.124 –0.004 0.009 $$\nu_2$$ –0.012 0.006 0.024 0.009 0.000 0.000 0.008 –0.261 –0.018 –0.026 –0.022 0.009 0.531 0.001 –0.001 $$\kappa_M$$ 0.273 0.061 0.176 –0.061 0.000 0.000 0.180 0.120 0.532 0.216 –0.082 0.039 0.349 0.016 –0.203 $$c$$ –0.047 –0.020 –0.027 –0.001 0.000 0.000 0.031 0.025 –0.080 0.042 –0.014 0.005 0.050 –0.273 –0.192 This table reports the numerical partial derivatives of the moment conditions to the underlying model parameters. All the moment conditions are self-explanatory, except for $$\gamma_y$$ and $$\gamma_k$$, which correspond to the regression coefficients in Equation (12). $$\rho_z$$, $$\sigma_z$$, and $$\sigma_s$$ govern the persistence and standard deviation of the firms’ shock processes. $$\theta$$ is the curvature of the firms’ production function. $$\delta$$ is the rate of depreciation. $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic costs for net equity issuance. $$\kappa_M$$ measures to what extent managers care about firms’ market price, and $$c$$ captures the opportunity cost for executive turnovers. Table 4 Jacobian matrix of moment conditions to parameters Mean Std Auto Mean Mean Std Mean Std Mean Std Corr(profit, profit profit profit investment $$\gamma_y$$ $$\gamma_k$$ issuance issuance M/B M/B dividend dividend SOA Turnover turnover) $$\rho_z$$ –0.079 0.008 0.874 0.002 0.000 0.995 –0.037 –0.015 0.287 0.146 0.024 0.014 0.244 0.003 0.003 $$\theta$$ 0.014 0.026 0.028 0.001 0.991 0.000 0.028 0.030 0.028 0.006 –0.020 0.010 0.276 0.001 –0.025 $$\sigma_z$$ 0.199 0.436 –0.039 0.003 0.000 0.000 –0.064 0.020 0.440 0.038 0.054 –0.006 0.317 0.006 –0.009 $$\sigma_s$$ 0.049 0.398 –0.678 –0.002 0.000 0.000 –0.012 –0.024 0.072 –0.072 –0.006 0.025 –0.064 –0.002 –0.066 $$\delta$$ –0.018 0.165 –0.348 1.007 0.000 0.000 –0.012 0.026 0.071 –0.047 0.017 –0.030 –0.461 0.011 –0.058 $$\nu_1$$ –0.054 0.023 0.022 0.000 0.000 0.000 –0.278 –0.084 –0.303 0.017 0.089 0.162 0.124 –0.004 0.009 $$\nu_2$$ –0.012 0.006 0.024 0.009 0.000 0.000 0.008 –0.261 –0.018 –0.026 –0.022 0.009 0.531 0.001 –0.001 $$\kappa_M$$ 0.273 0.061 0.176 –0.061 0.000 0.000 0.180 0.120 0.532 0.216 –0.082 0.039 0.349 0.016 –0.203 $$c$$ –0.047 –0.020 –0.027 –0.001 0.000 0.000 0.031 0.025 –0.080 0.042 –0.014 0.005 0.050 –0.273 –0.192 Mean Std Auto Mean Mean Std Mean Std Mean Std Corr(profit, profit profit profit investment $$\gamma_y$$ $$\gamma_k$$ issuance issuance M/B M/B dividend dividend SOA Turnover turnover) $$\rho_z$$ –0.079 0.008 0.874 0.002 0.000 0.995 –0.037 –0.015 0.287 0.146 0.024 0.014 0.244 0.003 0.003 $$\theta$$ 0.014 0.026 0.028 0.001 0.991 0.000 0.028 0.030 0.028 0.006 –0.020 0.010 0.276 0.001 –0.025 $$\sigma_z$$ 0.199 0.436 –0.039 0.003 0.000 0.000 –0.064 0.020 0.440 0.038 0.054 –0.006 0.317 0.006 –0.009 $$\sigma_s$$ 0.049 0.398 –0.678 –0.002 0.000 0.000 –0.012 –0.024 0.072 –0.072 –0.006 0.025 –0.064 –0.002 –0.066 $$\delta$$ –0.018 0.165 –0.348 1.007 0.000 0.000 –0.012 0.026 0.071 –0.047 0.017 –0.030 –0.461 0.011 –0.058 $$\nu_1$$ –0.054 0.023 0.022 0.000 0.000 0.000 –0.278 –0.084 –0.303 0.017 0.089 0.162 0.124 –0.004 0.009 $$\nu_2$$ –0.012 0.006 0.024 0.009 0.000 0.000 0.008 –0.261 –0.018 –0.026 –0.022 0.009 0.531 0.001 –0.001 $$\kappa_M$$ 0.273 0.061 0.176 –0.061 0.000 0.000 0.180 0.120 0.532 0.216 –0.082 0.039 0.349 0.016 –0.203 $$c$$ –0.047 –0.020 –0.027 –0.001 0.000 0.000 0.031 0.025 –0.080 0.042 –0.014 0.005 0.050 –0.273 –0.192 This table reports the numerical partial derivatives of the moment conditions to the underlying model parameters. All the moment conditions are self-explanatory, except for $$\gamma_y$$ and $$\gamma_k$$, which correspond to the regression coefficients in Equation (12). $$\rho_z$$, $$\sigma_z$$, and $$\sigma_s$$ govern the persistence and standard deviation of the firms’ shock processes. $$\theta$$ is the curvature of the firms’ production function. $$\delta$$ is the rate of depreciation. $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic costs for net equity issuance. $$\kappa_M$$ measures to what extent managers care about firms’ market price, and $$c$$ captures the opportunity cost for executive turnovers. 4.2 Main results Panel A of Table 5 presents the moment conditions. The results show that the baseline model provides a good overall fit to the data.15 Only two simulated moments, the standard deviation of operating income and the mean market-to-book ratio, are statistically different from the corresponding actual moments at the 10$$\%$$ level. These two differences, although statistically significant, are not large in terms of their economic magnitude. An overidentification test fails to reject the model with a p-value of .2. Table 5 Simulated moments estimation: Full sample A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6997 –0.7079 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5505 –0.1497 Mean of operating income 0.1630 0.1718 –1.2552 Std of operating income 0.0738 0.0863 –1.9294 AR(1) coefficient of operating income 0.6368 0.7207 –1.3003 Mean of investment 0.0985 0.0995 –0.1517 Mean of net equity issuance –0.0185 –0.0197 0.2437 Std of net equity issuance 0.0171 0.0188 –0.1982 Mean of market-to-book 2.7443 2.4427 1.7009 Std of market-to-book 2.2892 2.3990 –0.7594 Mean of dividend 0.0240 0.0254 –1.1519 Std of dividend 0.0102 0.0107 –0.1452 SOA of dividend 0.2040 0.2001 0.0835 Mean turnover 0.0263 0.0267 –0.2977 Corr btw return and turnover –0.0674 –0.0715 0.2126 J-statistic : 8.61 p-val : .20 A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6997 –0.7079 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5505 –0.1497 Mean of operating income 0.1630 0.1718 –1.2552 Std of operating income 0.0738 0.0863 –1.9294 AR(1) coefficient of operating income 0.6368 0.7207 –1.3003 Mean of investment 0.0985 0.0995 –0.1517 Mean of net equity issuance –0.0185 –0.0197 0.2437 Std of net equity issuance 0.0171 0.0188 –0.1982 Mean of market-to-book 2.7443 2.4427 1.7009 Std of market-to-book 2.2892 2.3990 –0.7594 Mean of dividend 0.0240 0.0254 –1.1519 Std of dividend 0.0102 0.0107 –0.1452 SOA of dividend 0.2040 0.2001 0.0835 Mean turnover 0.0263 0.0267 –0.2977 Corr btw return and turnover –0.0674 –0.0715 0.2126 J-statistic : 8.61 p-val : .20 B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.7087 0.3042 0.0776 0.5428 0.0988 0.0544 0.6466 0.6512 0.4822 ( 0.0918 ) ( 0.0034 ) ( 0.0162 ) ( 0.1269 ) ( 0.0098 ) ( 0.0264 ) ( 0.1106 ) ( 0.1521 ) ( 0.0576 ) B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.7087 0.3042 0.0776 0.5428 0.0988 0.0544 0.6466 0.6512 0.4822 ( 0.0918 ) ( 0.0034 ) ( 0.0162 ) ( 0.1269 ) ( 0.0098 ) ( 0.0264 ) ( 0.1106 ) ( 0.1521 ) ( 0.0576 ) The sample consists of nonfinancial and nonutility firms in the 2013 Compustat and CRSP files for the 1992–2011 sample period. The sample contains 11,626 firm-year observations. The estimation is based on the baseline model described in Section 2, and estimation is performed with simulated method of moments (SMM). Panel A reports the simulated versus the actual moments, along with the t-statistics for the pairwise differences. The J-statistic tests the overidentification constraint for the moment conditions. Panel B reports the parameter estimates with clustered standard errors in parentheses. $$\rho_z$$, $$\sigma_z$$, and $$\sigma_s$$ govern the persistence and standard deviation of the firms’ shock processes. $$\theta$$ is the curvature of the firms’ production function. $$\delta$$ is the rate of depreciation. $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic costs for net equity issuance. $$\kappa_M$$ measures to what extent managers care about firms’ market price, and $$c$$ captures the opportunity cost for executive turnovers. Table 5 Simulated moments estimation: Full sample A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6997 –0.7079 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5505 –0.1497 Mean of operating income 0.1630 0.1718 –1.2552 Std of operating income 0.0738 0.0863 –1.9294 AR(1) coefficient of operating income 0.6368 0.7207 –1.3003 Mean of investment 0.0985 0.0995 –0.1517 Mean of net equity issuance –0.0185 –0.0197 0.2437 Std of net equity issuance 0.0171 0.0188 –0.1982 Mean of market-to-book 2.7443 2.4427 1.7009 Std of market-to-book 2.2892 2.3990 –0.7594 Mean of dividend 0.0240 0.0254 –1.1519 Std of dividend 0.0102 0.0107 –0.1452 SOA of dividend 0.2040 0.2001 0.0835 Mean turnover 0.0263 0.0267 –0.2977 Corr btw return and turnover –0.0674 –0.0715 0.2126 J-statistic : 8.61 p-val : .20 A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6997 –0.7079 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5505 –0.1497 Mean of operating income 0.1630 0.1718 –1.2552 Std of operating income 0.0738 0.0863 –1.9294 AR(1) coefficient of operating income 0.6368 0.7207 –1.3003 Mean of investment 0.0985 0.0995 –0.1517 Mean of net equity issuance –0.0185 –0.0197 0.2437 Std of net equity issuance 0.0171 0.0188 –0.1982 Mean of market-to-book 2.7443 2.4427 1.7009 Std of market-to-book 2.2892 2.3990 –0.7594 Mean of dividend 0.0240 0.0254 –1.1519 Std of dividend 0.0102 0.0107 –0.1452 SOA of dividend 0.2040 0.2001 0.0835 Mean turnover 0.0263 0.0267 –0.2977 Corr btw return and turnover –0.0674 –0.0715 0.2126 J-statistic : 8.61 p-val : .20 B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.7087 0.3042 0.0776 0.5428 0.0988 0.0544 0.6466 0.6512 0.4822 ( 0.0918 ) ( 0.0034 ) ( 0.0162 ) ( 0.1269 ) ( 0.0098 ) ( 0.0264 ) ( 0.1106 ) ( 0.1521 ) ( 0.0576 ) B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.7087 0.3042 0.0776 0.5428 0.0988 0.0544 0.6466 0.6512 0.4822 ( 0.0918 ) ( 0.0034 ) ( 0.0162 ) ( 0.1269 ) ( 0.0098 ) ( 0.0264 ) ( 0.1106 ) ( 0.1521 ) ( 0.0576 ) The sample consists of nonfinancial and nonutility firms in the 2013 Compustat and CRSP files for the 1992–2011 sample period. The sample contains 11,626 firm-year observations. The estimation is based on the baseline model described in Section 2, and estimation is performed with simulated method of moments (SMM). Panel A reports the simulated versus the actual moments, along with the t-statistics for the pairwise differences. The J-statistic tests the overidentification constraint for the moment conditions. Panel B reports the parameter estimates with clustered standard errors in parentheses. $$\rho_z$$, $$\sigma_z$$, and $$\sigma_s$$ govern the persistence and standard deviation of the firms’ shock processes. $$\theta$$ is the curvature of the firms’ production function. $$\delta$$ is the rate of depreciation. $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic costs for net equity issuance. $$\kappa_M$$ measures to what extent managers care about firms’ market price, and $$c$$ captures the opportunity cost for executive turnovers. Panel B of Table 5 reports the structural parameter estimates. On the real side, a firm’s production function has substantial curvature and the productivity shock, $$\{z_t\}$$, has a moderate degree of persistence. On the financial side, the costs for net issuance average 8$$\%$$, which is roughly the sum of gross spread and percentage discount in SEOs (Gao and Ritter, 2010). The opportunity cost from turnover, $$c$$, is positive and significant, suggesting that managerial turnover disrupts a firm’s operations and induces it to produce at below-capacity levels for subsequent periods. Having a significant turnover cost implies that the firm will retain its management team most of the times unless there is substantial bad information conveyed by earnings and dividends. I run the following logit regression on both the actual and simulated data to examine these predictions on managerial turnover, earnings, and dividends: \begin{eqnarray} \label{EQ13} {\it Prob}(\Phi_t=1)=F(\beta_0 + \beta_{Y}\times Y_t + \beta_D\times\lambda\triangle D_t + \beta_X\times X_t +\epsilon_t), \end{eqnarray} (13) where $$F$$ is the cumulative distribution function (CDF) of logistic distribution, $$\Phi_t$$ is a dummy variable indicating executive turnover, $$Y_t$$ is a measure of firm profitability, and $$\triangle D_t$$ is the change in dividends from the previous period. When the regression is run on the actual data, $$X_t$$ includes the commonly used performance and governance control variables in the turnover literature. When the regression is run on the simulated data, $$X_t$$ consists of other announced firm policies.16 Table 6 Predicting forced turnover Real data Simulated data (1) (2) (3) (4) (5) (6) Intercept –3.947$$^{***}$$ –3.858$$^{***}$$ –4.428$$^{***}$$ –3.636$$^{***}$$ –3.878$$^{***}$$ –3.425$$^{***}$$ Profit –3.540$$^{***}$$ –3.435$$^{***}$$ –3.502$$^{***}$$ –2.981$$^{***}$$ –2.341$$^{***}$$ –3.515$$^{***}$$ [–0.609] [–0.589] [–0.602] [–0.504] [–0.389] [–0.604] $$\triangle$$ DPS –0.543$$^{**}$$ –0.556$$^{***}$$ –0.650$$^{***}$$ –0.616$$^{***}$$ –0.886$$^{***}$$ –0.497$$^{**}$$ [–0.423] [–0.434] [–0.514] [–0.485] [–0.723] [–0.385] Investment 0.3836 –0.187 –0.172$$^{*}$$ [ 0.059] [–0.029] [–0.027] Net repurchase –1.3263 –0.843 –0.877$$^{***}$$ [–0.070] [–0.044] [–0.046] Size 0.013 0.009 [0.098] [0.069] Profit$$_{-1}$$ 0.304 –0.355 [0.047] [–0.056] Profit$$_{-2}$$ –1.095$$^{***}$$ –0.261 [–0.175] [–0.041] Tenure –0.007$$^{**}$$ [–0.111] $$\%$$ institution 0.817$$^{***}$$ [0.566] $$\%$$ insider 0.083$$^{*}$$ [0.032] $$\%$$ executive –0.044 [–0.364] SIC/Year FE N N N Y N N Real data Simulated data (1) (2) (3) (4) (5) (6) Intercept –3.947$$^{***}$$ –3.858$$^{***}$$ –4.428$$^{***}$$ –3.636$$^{***}$$ –3.878$$^{***}$$ –3.425$$^{***}$$ Profit –3.540$$^{***}$$ –3.435$$^{***}$$ –3.502$$^{***}$$ –2.981$$^{***}$$ –2.341$$^{***}$$ –3.515$$^{***}$$ [–0.609] [–0.589] [–0.602] [–0.504] [–0.389] [–0.604] $$\triangle$$ DPS –0.543$$^{**}$$ –0.556$$^{***}$$ –0.650$$^{***}$$ –0.616$$^{***}$$ –0.886$$^{***}$$ –0.497$$^{**}$$ [–0.423] [–0.434] [–0.514] [–0.485] [–0.723] [–0.385] Investment 0.3836 –0.187 –0.172$$^{*}$$ [ 0.059] [–0.029] [–0.027] Net repurchase –1.3263 –0.843 –0.877$$^{***}$$ [–0.070] [–0.044] [–0.046] Size 0.013 0.009 [0.098] [0.069] Profit$$_{-1}$$ 0.304 –0.355 [0.047] [–0.056] Profit$$_{-2}$$ –1.095$$^{***}$$ –0.261 [–0.175] [–0.041] Tenure –0.007$$^{**}$$ [–0.111] $$\%$$ institution 0.817$$^{***}$$ [0.566] $$\%$$ insider 0.083$$^{*}$$ [0.032] $$\%$$ executive –0.044 [–0.364] SIC/Year FE N N N Y N N The sample consists of nonfinancial and nonutility firms in the 2013 Compustat and CRSP files for the 1992–2011 period. The sample contains 47,563 executive-year observations. The regression is performed at the executive-year level. The outcome variable is an indicator of forced executive turnover. Profit$$_{-i}$$ measures the firm’s ROA in the previous $$i$$th year; $$\%$$ insider is the firm-level aggregate insider holdings; and $$\%$$ executive is the executive-level holdings of the firm’s own stocks. Net repurchase measures the firm’s stock repurchases minus new equity issuance. Both Investment and Net repurchase are scaled by the firm’s total book assets. $$^{*}$$, $$^{**}$$, and $$^{***}$$ indicate statistical significance at the 10$$\%$$, 5$$\%$$, and 1$$\%$$ levels, respectively. The significance levels in Columns (1)-(4) are calculated based on standard errors clustered by industry and year. The significance levels in Columns (5) and (6) are calculated using bootstrapped standard errors. The economic significance of the predictors are reported in brackets; the economic significance measures the probability effect on the outcome if the predictor increases from the lower to the upper 10th percentile of its distribution. Table 6 Predicting forced turnover Real data Simulated data (1) (2) (3) (4) (5) (6) Intercept –3.947$$^{***}$$ –3.858$$^{***}$$ –4.428$$^{***}$$ –3.636$$^{***}$$ –3.878$$^{***}$$ –3.425$$^{***}$$ Profit –3.540$$^{***}$$ –3.435$$^{***}$$ –3.502$$^{***}$$ –2.981$$^{***}$$ –2.341$$^{***}$$ –3.515$$^{***}$$ [–0.609] [–0.589] [–0.602] [–0.504] [–0.389] [–0.604] $$\triangle$$ DPS –0.543$$^{**}$$ –0.556$$^{***}$$ –0.650$$^{***}$$ –0.616$$^{***}$$ –0.886$$^{***}$$ –0.497$$^{**}$$ [–0.423] [–0.434] [–0.514] [–0.485] [–0.723] [–0.385] Investment 0.3836 –0.187 –0.172$$^{*}$$ [ 0.059] [–0.029] [–0.027] Net repurchase –1.3263 –0.843 –0.877$$^{***}$$ [–0.070] [–0.044] [–0.046] Size 0.013 0.009 [0.098] [0.069] Profit$$_{-1}$$ 0.304 –0.355 [0.047] [–0.056] Profit$$_{-2}$$ –1.095$$^{***}$$ –0.261 [–0.175] [–0.041] Tenure –0.007$$^{**}$$ [–0.111] $$\%$$ institution 0.817$$^{***}$$ [0.566] $$\%$$ insider 0.083$$^{*}$$ [0.032] $$\%$$ executive –0.044 [–0.364] SIC/Year FE N N N Y N N Real data Simulated data (1) (2) (3) (4) (5) (6) Intercept –3.947$$^{***}$$ –3.858$$^{***}$$ –4.428$$^{***}$$ –3.636$$^{***}$$ –3.878$$^{***}$$ –3.425$$^{***}$$ Profit –3.540$$^{***}$$ –3.435$$^{***}$$ –3.502$$^{***}$$ –2.981$$^{***}$$ –2.341$$^{***}$$ –3.515$$^{***}$$ [–0.609] [–0.589] [–0.602] [–0.504] [–0.389] [–0.604] $$\triangle$$ DPS –0.543$$^{**}$$ –0.556$$^{***}$$ –0.650$$^{***}$$ –0.616$$^{***}$$ –0.886$$^{***}$$ –0.497$$^{**}$$ [–0.423] [–0.434] [–0.514] [–0.485] [–0.723] [–0.385] Investment 0.3836 –0.187 –0.172$$^{*}$$ [ 0.059] [–0.029] [–0.027] Net repurchase –1.3263 –0.843 –0.877$$^{***}$$ [–0.070] [–0.044] [–0.046] Size 0.013 0.009 [0.098] [0.069] Profit$$_{-1}$$ 0.304 –0.355 [0.047] [–0.056] Profit$$_{-2}$$ –1.095$$^{***}$$ –0.261 [–0.175] [–0.041] Tenure –0.007$$^{**}$$ [–0.111] $$\%$$ institution 0.817$$^{***}$$ [0.566] $$\%$$ insider 0.083$$^{*}$$ [0.032] $$\%$$ executive –0.044 [–0.364] SIC/Year FE N N N Y N N The sample consists of nonfinancial and nonutility firms in the 2013 Compustat and CRSP files for the 1992–2011 period. The sample contains 47,563 executive-year observations. The regression is performed at the executive-year level. The outcome variable is an indicator of forced executive turnover. Profit$$_{-i}$$ measures the firm’s ROA in the previous $$i$$th year; $$\%$$ insider is the firm-level aggregate insider holdings; and $$\%$$ executive is the executive-level holdings of the firm’s own stocks. Net repurchase measures the firm’s stock repurchases minus new equity issuance. Both Investment and Net repurchase are scaled by the firm’s total book assets. $$^{*}$$, $$^{**}$$, and $$^{***}$$ indicate statistical significance at the 10$$\%$$, 5$$\%$$, and 1$$\%$$ levels, respectively. The significance levels in Columns (1)-(4) are calculated based on standard errors clustered by industry and year. The significance levels in Columns (5) and (6) are calculated using bootstrapped standard errors. The economic significance of the predictors are reported in brackets; the economic significance measures the probability effect on the outcome if the predictor increases from the lower to the upper 10th percentile of its distribution. The results in Table 6 suggest that the model consistently predicts a negative earnings-turnover correlation. After controlling for earnings, dividend changes still have a strong predictive power for managerial turnover. For firms whose current earnings are around the median, reducing dividend per share by a quarter will increase the expected rate of turnover by 9.43$$\%$$, while for firms whose earnings are around the lower 10th percentile, the increase in expected turnover will be 28.52$$\%$$. These results are economically large, and they remain quantitatively very similar even after I add additional controls or include higher degree polynomials of earnings. The estimated regression coefficients on the simulated data also closely track their counterparts on the actual data.17 This finding, on the one hand, serves as an external validation of the model. Although I do not directly include these coefficients in my moment matching process, the predictions arising from the model naturally parallel the marginal effects of earnings and dividends on turnover in reality. One the other hand, the results also illuminate why more frequent executive turnovers are observed among dividend-cutting firms. This observation is not mechanical due to mismeasurement in the earnings. Instead, it is because dividends reveal important information on how likely the current earnings will be repeated going forward. Therefore, the board members should base their turnover decisions on the informativeness of dividends. 4.3 Counterfactuals This subsection contains two counterfactual exercises. In the first exercise, I reestimate an alternative model specification by turning off the effect of dividends on managerial turnovers. Running a horse race between the baseline model and this nested alternative model highlights the importance of incorporating career-concern-based dividend smoothing in the model in order to explain the observed data patterns. In the second exercise, I resimulate data under different degrees of dividend price effects and managerial career concerns to quantify the sensitivity of a firm’s payout policy to such informational and agency frictions. In Table 7, I report the moment estimation results for a model in which the executive turnover rate equals 2.63$$\%$$ at all times and in all states. The results show that the overall model fit becomes significantly worse under this constant turnover specification. In particular, the model is not able to match the standard deviation of the operating income or market-to-book ratio. The model also fails to predict the level or the slow SOA of dividends. This is because setting turnover risk to a constant brings me back to a standard dynamic investment model with no agency career concerns. In this case, the price effect of dividends alone is not strong enough to induce sufficient smoothing. Note that the cost of executive turnover, $$c$$, also becomes smaller in magnitude and is now statistically insignificant. This is because the identification of this cost parameter mainly comes from the frequency of executive turnovers and the correlation between it and firm performance. Once the turnover rate is fixed exogenously, no other moments can effectively pinpoint the value of $$c$$. The J-test result shows that the simulated moments under this alternative specification are significantly different from those on the actual data, and the model is rejected at lower than the 1$$\%$$ level. Table 7 Simulated moments estimation: No agency career concerns A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6698 –0.1933 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5197 0.8325 Mean of operating income 0.1630 0.1685 –1.0752 Std of operating income 0.0738 0.0647 1.8031 AR(1) coefficient of operating income 0.6368 0.5804 0.8638 Mean of investment 0.0985 0.0966 –0.3447 Mean of net equity issuance –0.0185 –0.0196 0.2697 Std of net equity issuance 0.0171 0.0093 0.9174 Mean of market-to-book 2.7443 2.5319 1.2531 Std of market-to-book 2.2892 2.5035 –1.7006 Mean of dividend 0.0240 0.0285 –3.2027 Std of dividend 0.0102 0.0151 –1.5996 SOA of dividend 0.2040 0.3352 2.2973 Mean turnover 0.0263 0.0263 / Corr btw return and turnover –0.0674 / / J-statistic : 33.74 p-val : $$< .01$$ A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6698 –0.1933 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5197 0.8325 Mean of operating income 0.1630 0.1685 –1.0752 Std of operating income 0.0738 0.0647 1.8031 AR(1) coefficient of operating income 0.6368 0.5804 0.8638 Mean of investment 0.0985 0.0966 –0.3447 Mean of net equity issuance –0.0185 –0.0196 0.2697 Std of net equity issuance 0.0171 0.0093 0.9174 Mean of market-to-book 2.7443 2.5319 1.2531 Std of market-to-book 2.2892 2.5035 –1.7006 Mean of dividend 0.0240 0.0285 –3.2027 Std of dividend 0.0102 0.0151 –1.5996 SOA of dividend 0.2040 0.3352 2.2973 Mean turnover 0.0263 0.0263 / Corr btw return and turnover –0.0674 / / J-statistic : 33.74 p-val : $$< .01$$ B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.6702 0.2940 0.0871 0.5159 0.0968 0.0714 0.6393 0.5001 0.2952 ( 0.0466 ) ( 0.0284 ) ( 0.0123 ) ( 0.1332 ) ( 0.0133 ) ( 0.0379 ) ( 0.2734 ) ( 0.1097 ) ( 0.2276 ) B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.6702 0.2940 0.0871 0.5159 0.0968 0.0714 0.6393 0.5001 0.2952 ( 0.0466 ) ( 0.0284 ) ( 0.0123 ) ( 0.1332 ) ( 0.0133 ) ( 0.0379 ) ( 0.2734 ) ( 0.1097 ) ( 0.2276 ) The sample consists of nonfinancial and nonutility firms in the 2013 Compustat and CRSP files for the 1992–2011 period. The sample contains 11,626 firm-year observations. The estimation is based on an alternative model in which executives are assumed to face constant turnover rates across all times and states, and the estimation is performed with simulated method of moments (SMM). Panel A reports the simulated versus the actual moments, along with the t-statistics for the pairwise differences. The J-statistic tests the overidentification constraint for the moment conditions (excluding the last two moments). Panel B reports the parameter estimates with clustered standard errors in parentheses. $$\rho_z$$, $$\sigma_z$$, and $$\sigma_s$$ govern the persistence and standard deviation of the firms’ shock processes. $$\theta$$ is the curvature of the firms’ production function. $$\delta$$ is the rate of depreciation. $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic costs for net equity issuance. $$\kappa_M$$ measures to what extent managers care about firms’ market price, and $$c$$ captures the opportunity cost for executive turnovers. Table 7 Simulated moments estimation: No agency career concerns A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6698 –0.1933 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5197 0.8325 Mean of operating income 0.1630 0.1685 –1.0752 Std of operating income 0.0738 0.0647 1.8031 AR(1) coefficient of operating income 0.6368 0.5804 0.8638 Mean of investment 0.0985 0.0966 –0.3447 Mean of net equity issuance –0.0185 –0.0196 0.2697 Std of net equity issuance 0.0171 0.0093 0.9174 Mean of market-to-book 2.7443 2.5319 1.2531 Std of market-to-book 2.2892 2.5035 –1.7006 Mean of dividend 0.0240 0.0285 –3.2027 Std of dividend 0.0102 0.0151 –1.5996 SOA of dividend 0.2040 0.3352 2.2973 Mean turnover 0.0263 0.0263 / Corr btw return and turnover –0.0674 / / J-statistic : 33.74 p-val : $$< .01$$ A: Moments Actual moments Simulated moments t-test for difference Coefficient $$\gamma_y$$ in Equation (12) 0.6514 0.6698 –0.1933 Coefficient $$\gamma_k$$ in Equation (12) 0.5404 0.5197 0.8325 Mean of operating income 0.1630 0.1685 –1.0752 Std of operating income 0.0738 0.0647 1.8031 AR(1) coefficient of operating income 0.6368 0.5804 0.8638 Mean of investment 0.0985 0.0966 –0.3447 Mean of net equity issuance –0.0185 –0.0196 0.2697 Std of net equity issuance 0.0171 0.0093 0.9174 Mean of market-to-book 2.7443 2.5319 1.2531 Std of market-to-book 2.2892 2.5035 –1.7006 Mean of dividend 0.0240 0.0285 –3.2027 Std of dividend 0.0102 0.0151 –1.5996 SOA of dividend 0.2040 0.3352 2.2973 Mean turnover 0.0263 0.0263 / Corr btw return and turnover –0.0674 / / J-statistic : 33.74 p-val : $$< .01$$ B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.6702 0.2940 0.0871 0.5159 0.0968 0.0714 0.6393 0.5001 0.2952 ( 0.0466 ) ( 0.0284 ) ( 0.0123 ) ( 0.1332 ) ( 0.0133 ) ( 0.0379 ) ( 0.2734 ) ( 0.1097 ) ( 0.2276 ) B: Parameter estimates $$\rho_z$$ $$\sigma_z$$ $$\sigma_s$$ $$\theta$$ $$\delta$$ $$\nu_1$$ $$\nu_2$$ $$\kappa_M$$ $$c$$ 0.6702 0.2940 0.0871 0.5159 0.0968 0.0714 0.6393 0.5001 0.2952 ( 0.0466 ) ( 0.0284 ) ( 0.0123 ) ( 0.1332 ) ( 0.0133 ) ( 0.0379 ) ( 0.2734 ) ( 0.1097 ) ( 0.2276 ) The sample consists of nonfinancial and nonutility firms in the 2013 Compustat and CRSP files for the 1992–2011 period. The sample contains 11,626 firm-year observations. The estimation is based on an alternative model in which executives are assumed to face constant turnover rates across all times and states, and the estimation is performed with simulated method of moments (SMM). Panel A reports the simulated versus the actual moments, along with the t-statistics for the pairwise differences. The J-statistic tests the overidentification constraint for the moment conditions (excluding the last two moments). Panel B reports the parameter estimates with clustered standard errors in parentheses. $$\rho_z$$, $$\sigma_z$$, and $$\sigma_s$$ govern the persistence and standard deviation of the firms’ shock processes. $$\theta$$ is the curvature of the firms’ production function. $$\delta$$ is the rate of depreciation. $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic costs for net equity issuance. $$\kappa_M$$ measures to what extent managers care about firms’ market price, and $$c$$ captures the opportunity cost for executive turnovers. To quantify to what extent managers’ career concerns determine the firm-level dividend smoothness, I resimulate the model under several scenarios: 25$$\%$$, 50$$\%$$, and 100$$\%$$ decreases in $$\frac{W}{(\kappa_I+\kappa_M)}$$. This ratio captures the relative weight of fixed wage versus share value in the managers’ utility function (note that when $$W=0$$, an individual loses nothing upon being fired, and the career-concern-based channel is shutdown). The 25$$\%$$, 50$$\%$$, and 100$$\%$$ decreases in $$\gamma_{{\it{\Omega}}}$$ control, in equilibrium, how informative dividends are and to what extent they influence share prices. The results in Table 8 show that dividend smoothness (measured by 1$$-$$SOA) decreases gradually when either $$\frac{W}{(\kappa_I+\kappa_M)}$$ or $$\gamma_{{\it{\Omega}}}$$ decreases. The SOA of dividends reaches 0.49 when the career-concern-based channel is completely shut down, and it rises to 0.95 when the stock price effect is also eliminated. The speed of adjustment being close to unity indicates that shocks to a firm’s cash flows are almost proportionately reflected by the firm’s dividend policy. Comparing rows (1), (4), and (7) in panel A, I conclude that 61$$\%$$ of the observed dividend smoothness is related to the shareholders’ incentive to stabilize prices, whereas the remaining 39$$\%$$ is driven by managers’ career concerns. Although earnings and dividends should comove positively due to the sources and uses of funds constraint, they act as substitutes in information production. This substitutability incentivizes the managers to choose a lower dividend responsiveness. Table 8 Counterfactuals A. The consequences of career concern-based dividend smoothing SOA $$\triangle\%$$ SOA Firm value $$\triangle\%$$ value (1) Baseline 0.2001 / 2.4120 / (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.2260  3.46$$\%$$ 2.4559 0.07$$\%$$ (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4474 33.04$$\%$$ 2.4739 1.27$$\%$$ (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4913 38.89$$\%$$ 2.4938 1.99$$\%$$ (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8132 80.59$$\%$$ 2.5450 3.99$$\%$$ (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8941 92.70$$\%$$ 2.5831 4.63$$\%$$ (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.9488 100.0$$\%$$ 2.6226 4.82$$\%$$ B. Firm value under alternative policies Investment Corr(Investment, profit) Cash Corr(Cash, profit) (1) Baseline 0.1008 0.2905 0.0732 0.3513 (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1021 0.2860 0.0704 0.3409 (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1043 0.2784 0.0667 0.3341 (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1067 0.2460 0.0631 0.3279 (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1062 0.2513 0.0622 0.3269 (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1075 0.2230 0.0586 0.3277 (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1081 0.2057 0.0503 0.3060 A. The consequences of career concern-based dividend smoothing SOA $$\triangle\%$$ SOA Firm value $$\triangle\%$$ value (1) Baseline 0.2001 / 2.4120 / (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.2260  3.46$$\%$$ 2.4559 0.07$$\%$$ (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4474 33.04$$\%$$ 2.4739 1.27$$\%$$ (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4913 38.89$$\%$$ 2.4938 1.99$$\%$$ (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8132 80.59$$\%$$ 2.5450 3.99$$\%$$ (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8941 92.70$$\%$$ 2.5831 4.63$$\%$$ (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.9488 100.0$$\%$$ 2.6226 4.82$$\%$$ B. Firm value under alternative policies Investment Corr(Investment, profit) Cash Corr(Cash, profit) (1) Baseline 0.1008 0.2905 0.0732 0.3513 (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1021 0.2860 0.0704 0.3409 (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1043 0.2784 0.0667 0.3341 (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1067 0.2460 0.0631 0.3279 (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1062 0.2513 0.0622 0.3269 (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1075 0.2230 0.0586 0.3277 (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1081 0.2057 0.0503 0.3060 This table reports the model-predicted equilibrium firm value and policies under different parameterizations: 25$$\%$$, 50$$\%$$, and 100$$\%$$ decreases in $$\frac{W}{\kappa_I+\kappa_M}$$, which captures the conflict of interest between shareholders and managers, and 25$$\%$$, 50$$\%$$, and 100$$\%$$ decreases in $$\gamma_{{\it{\Omega}}}$$ (while holding $$\frac{W}{\kappa_I+\kappa_M}$$ at 0), which controls, in equilibrium, how informative dividends are and to what extent they influence the market prices of shares. Table 8 Counterfactuals A. The consequences of career concern-based dividend smoothing SOA $$\triangle\%$$ SOA Firm value $$\triangle\%$$ value (1) Baseline 0.2001 / 2.4120 / (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.2260  3.46$$\%$$ 2.4559 0.07$$\%$$ (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4474 33.04$$\%$$ 2.4739 1.27$$\%$$ (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4913 38.89$$\%$$ 2.4938 1.99$$\%$$ (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8132 80.59$$\%$$ 2.5450 3.99$$\%$$ (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8941 92.70$$\%$$ 2.5831 4.63$$\%$$ (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.9488 100.0$$\%$$ 2.6226 4.82$$\%$$ B. Firm value under alternative policies Investment Corr(Investment, profit) Cash Corr(Cash, profit) (1) Baseline 0.1008 0.2905 0.0732 0.3513 (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1021 0.2860 0.0704 0.3409 (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1043 0.2784 0.0667 0.3341 (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1067 0.2460 0.0631 0.3279 (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1062 0.2513 0.0622 0.3269 (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1075 0.2230 0.0586 0.3277 (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1081 0.2057 0.0503 0.3060 A. The consequences of career concern-based dividend smoothing SOA $$\triangle\%$$ SOA Firm value $$\triangle\%$$ value (1) Baseline 0.2001 / 2.4120 / (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.2260  3.46$$\%$$ 2.4559 0.07$$\%$$ (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4474 33.04$$\%$$ 2.4739 1.27$$\%$$ (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.4913 38.89$$\%$$ 2.4938 1.99$$\%$$ (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8132 80.59$$\%$$ 2.5450 3.99$$\%$$ (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.8941 92.70$$\%$$ 2.5831 4.63$$\%$$ (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.9488 100.0$$\%$$ 2.6226 4.82$$\%$$ B. Firm value under alternative policies Investment Corr(Investment, profit) Cash Corr(Cash, profit) (1) Baseline 0.1008 0.2905 0.0732 0.3513 (2) 25$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1021 0.2860 0.0704 0.3409 (3) 50$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1043 0.2784 0.0667 0.3341 (4) 100$$\%$$ decrease in $$\frac{W_t}{(\kappa_I+\kappa_M)}$$ 0.1067 0.2460 0.0631 0.3279 (5) 25$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1062 0.2513 0.0622 0.3269 (6) 50$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1075 0.2230 0.0586 0.3277 (7) 100$$\%$$ decrease in $$\Gamma_{\it{\Omega}}$$ 0.1081 0.2057 0.0503 0.3060 This table reports the model-predicted equilibrium firm value and policies under different parameterizations: 25$$\%$$, 50$$\%$$, and 100$$\%$$ decreases in $$\frac{W}{\kappa_I+\kappa_M}$$, which captures the conflict of interest between shareholders and managers, and 25$$\%$$, 50$$\%$$, and 100$$\%$$ decreases in $$\gamma_{{\it{\Omega}}}$$ (while holding $$\frac{W}{\kappa_I+\kappa_M}$$ at 0), which controls, in equilibrium, how informative dividends are and to what extent they influence the market prices of shares. Moreover, since shareholders are not concerned about managers’ turnover risk, they do not desire this career-concern-based dividend smoothing. The results in panel B of Table 8 confirm this concept by showing that having career-concern-based dividend smoothing reduces the equilibrium market-to-book ratio by 2$$\%$$. This value reduction comes from two sources. First, dividend smoothing allows managers to withhold private information, which implies that the realized turnover decisions will come from a more restricted information set, and they are less efficient compared with the case in which dividends are fully revealing. Second, firms need to distort their optimal investment and financing policies to accommodate this extra dividend stability—they hoard cash instead of raising dividends in cash-rich states, which leads to higher tax payments on interest. Firms also avoid dividend cuts in low cash flow states, which incurs costs of issuing new equity or cutting investments. The results in panel B suggest that having career-concern-based dividend smoothing leads to 6$$\%$$ lower investments and 16$$\%$$ higher cash balances among firms, on average. This agency conflict contributes to a larger correlation between a firm’s investment/cash and its operating cash flow.18 The counterfactual results in Table 8 allow me to determine what is behind the smooth dividends—it is a combination of shareholders’ preferences (60$$\%$$) and managers’ self-interests (40$$\%$$). The first 60$$\%$$ of the dividend smoothing benefits the shareholders by reducing the short-term price volatility. However, having extra smoothness beyond this level starts to destroy shareholders’ welfare by restricting information and distorting firm policies. Given the findings in Table 8, it is intriguing to ask: why do shareholders tolerate this career-concern-based dividend smoothing if they know it destroys firm value? If shareholders have perfect information regarding the firm’s economic state and the underlying parameter values, they could easily enforce the first-best dividend policy, which would lead to both higher SOA and larger firm value, as shown in row (3) of Table 9. However, in the current model setup, the shareholders’ information is inferior to the managers; they do not directly observe $$z_t$$ and $$s_t$$ separately, which prevents them from pinpointing the optimal dividends. Table 9 Firm value under alternative policies Policy SOA Firm value Agency career concerns (1) Baseline 0.2001 2.4120 YES (2) $$D_t=\phi(E_t)$$ 0.4913 2.3001 YES (3) First Best 0.4913 2.4938 NO Policy SOA Firm value Agency career concerns (1) Baseline 0.2001 2.4120 YES (2) $$D_t=\phi(E_t)$$ 0.4913 2.3001 YES (3) First Best 0.4913 2.4938 NO This table reports the model-predicted firm characteristics when managers employ different strategies: the baseline strategy, a strategy in which dividends are set to be a function of the realized earnings (corresponding to the dashed line in Figure 4), and the strategy that maximizes shareholders’ value. Table 9 Firm value under alternative policies Policy SOA Firm value Agency career concerns (1) Baseline 0.2001 2.4120 YES (2) $$D_t=\phi(E_t)$$ 0.4913 2.3001 YES (3) First Best 0.4913 2.4938 NO Policy SOA Firm value Agency career concerns (1) Baseline 0.2001 2.4120 YES (2) $$D_t=\phi(E_t)$$ 0.4913 2.3001 YES (3) First Best 0.4913 2.4938 NO This table reports the model-predicted firm characteristics when managers employ different strategies: the baseline strategy, a strategy in which dividends are set to be a function of the realized earnings (corresponding to the dashed line in Figure 4), and the strategy that maximizes shareholders’ value. In row (2) of Table 9, I consider an alternative strategy for the shareholders, where they force dividends to be a function of the realized earnings, $$D_t = \psi(Y_t)$$. The shareholders could choose $$\psi(\cdot)$$ so that the dividend policy corresponds to the dashed line in Figure 4.19 Note that this alternative strategy is not optimal because it assigns the same dividends to any two firms with the same realized earnings but different earnings persistence. Nevertheless, by design, this alternative strategy yields the same SOA of dividends (0.491) as the first-best policy. Next, I compare what happens when (1) a firm follows the baseline strategy where the shareholders tolerate managers’ career-concern-based dividend smoothing and (2) the firm adopts the above strategy with an SOA equal to 0.491. The results in Table 9 suggest that shareholders tolerate a suboptimal degree of dividend smoothing because it is even more costly for them to ignore the managers’ superior information on earnings persistence and force $$D_t = \psi(Y_t)$$. Setting $$D_t = \psi(Y_t)$$ implies that given any realized earnings, firms with high $$z$$ are underpaying and overaccumulating cash, whereas firms with low $$z$$ are overpaying and crowding out investments. The cost associated with the above strategy outweighs the cost arising from the baseline model, suggesting that tolerating managers’ career-concern-based dividend smoothing can actually be the best achievable equilibrium strategy for shareholders. 4.4 Subsample estimations In this subsection, I confront my model with the cross-sectional and time-series dispersions of dividend smoothing. Although dividend smoothing is prevalent among the full sample of dividend-paying firms, there is a wide heterogeneity in terms of the extent to which firms smooth. Such heterogeneity provides a natural setting to test my model and examine whether it can generate predictions consistent with the data. I first sort firms based on their executives’ reputation. An executive’s reputation is measured using the firm’s average earnings decile from $$year_{-2}$$ to the year when the executive first joins the firms (or to $$year_{-10}$$ if it is sooner). If the turnover-induced dividend smoothing story is relevant, there should be less smoothing among firms run by more reputable executives. This is because such executives have good reputations as demonstrated by their successful track records, which allows them to stay further away from the turnover threshold. Therefore, they are in better positions to “absorb” the negative impacts of earnings and dividends downgrades rather than relying on dividend smoothing. Next, I sort the firms along a different dimension: the ratio of the executives’ cash- versus stock-based compensation. If the top executives receive a higher fraction of stock-based compensation, it is more likely that over time they will accumulate a larger equity stake in the firms. Therefore, they will behave similar to the equity holders and choose a lower degree of turnover-induced dividend smoothing, which is value-destroying from the shareholders’ point of view. On the other hand, if the top executives receive more cash-based compensation, they will care more about keeping their positions so as not to forfeit their future income. Holding all else equal, this effect implies that firms who reward their executives with higher cash compensation should have smoother dividends, and a larger fraction of this smoothing should come from the turnover-related incentive. I also sort firms based on executives’ tenure. Executives with longer tenures should exhibit less career-concern-based dividend smoothing because they are more able to “capture” the board, which makes their position in the firm effectively less risky. Table 10 reports the results for the subsample estimations. First, I compare the model-generated moments with those observed in the actual data, and conclude that the model is able to fit the heterogeneous firm characteristics in each subsample. This is an important result, without which, it would be difficult to claim that the model could illuminate what drives the cross-sectional variations in dividend smoothing. Note that the fit of the model is slightly better for the Low reputation and Short tenure executives, who are associated with higher turnover risk. Next, when I focus on the actual data (Column (1) in Table 10) and compare the differences in total dividend smoothing across subsamples. I find that managers associated with greater turnover risk engage in a larger amount of dividend smoothing. Lastly, relying on the structural model, I disentangle the different incentives behind the smooth dividends (Column (2) in Table 10). I find that managers’ turnover risk accounts for 15$$\%$$ higher dividend smoothing in the Low reputation subsample, 12$$\%$$ higher dividend smoothing in the High cash subsample, and 8$$\%$$ higher dividend smoothing in the Short tenure subsample, consistent with the model’s predictions. Table 10 Subsample results (1) SOA (2) Career concern$$\%$$ (3) J-statistic (4) p-value A: Split by reputation High reputation 0.2506 28.77$$\%$$ 9.043 0.17 Low reputation 0.1748 43.14$$\%$$ 7.687 0.25 B: Split by compensation High equity 0.2248 27.61$$\%$$ 7.91 0.24 High cash 0.1499 39.94$$\%$$ 6.503 0.37 C: Split by tenure Long tenure 0.2003 30.40$$\%$$ 9.23 0.16 Short tenure 0.1708 37.96$$\%$$ 10.09 0.12 D: Split by time Early 0.2169 23.85$$\%$$ 11.44 0.09 Late 0.1682 36.46$$\%$$ 7.619 0.26 (1) SOA (2) Career concern$$\%$$ (3) J-statistic (4) p-value A: Split by reputation High reputation 0.2506 28.77$$\%$$ 9.043 0.17 Low reputation 0.1748 43.14$$\%$$ 7.687 0.25 B: Split by compensation High equity 0.2248 27.61$$\%$$ 7.91 0.24 High cash 0.1499 39.94$$\%$$ 6.503 0.37 C: Split by tenure Long tenure 0.2003 30.40$$\%$$ 9.23 0.16 Short tenure 0.1708 37.96$$\%$$ 10.09 0.12 D: Split by time Early 0.2169 23.85$$\%$$ 11.44 0.09 Late 0.1682 36.46$$\%$$ 7.619 0.26 In this table, I report the subsample estimation results. Reputation is measured using a firm’s average earnings decile within the industry from two years previous to the year when the executive first joins the firm; Compensation structure is measured by the ratio of total cash- versus stock-based compensations; Tenure measures the number of years that an executive holds office; and Time is split by the year 2003. Career concern$$\%$$ measures the percentage of dividend smoothing due to executive career concerns. The J-statistic and p-value test the overidentification constraint for the moment conditions. Table 10 Subsample results (1) SOA (2) Career concern$$\%$$ (3) J-statistic (4) p-value A: Split by reputation High reputation 0.2506 28.77$$\%$$ 9.043 0.17 Low reputation 0.1748 43.14$$\%$$ 7.687 0.25 B: Split by compensation High equity 0.2248 27.61$$\%$$ 7.91 0.24 High cash 0.1499 39.94$$\%$$ 6.503 0.37 C: Split by tenure Long tenure 0.2003 30.40$$\%$$ 9.23 0.16 Short tenure 0.1708 37.96$$\%$$ 10.09 0.12 D: Split by time Early 0.2169 23.85$$\%$$ 11.44 0.09 Late 0.1682 36.46$$\%$$ 7.619 0.26 (1) SOA (2) Career concern$$\%$$ (3) J-statistic (4) p-value A: Split by reputation High reputation 0.2506 28.77$$\%$$ 9.043 0.17 Low reputation 0.1748 43.14$$\%$$ 7.687 0.25 B: Split by compensation High equity 0.2248 27.61$$\%$$ 7.91 0.24 High cash 0.1499 39.94$$\%$$ 6.503 0.37 C: Split by tenure Long tenure 0.2003 30.40$$\%$$ 9.23 0.16 Short tenure 0.1708 37.96$$\%$$ 10.09 0.12 D: Split by time Early 0.2169 23.85$$\%$$ 11.44 0.09 Late 0.1682 36.46$$\%$$ 7.619 0.26 In this table, I report the subsample estimation results. Reputation is measured using a firm’s average earnings decile within the industry from two years previous to the year when the executive first joins the firm; Compensation structure is measured by the ratio of total cash- versus stock-based compensations; Tenure measures the number of years that an executive holds office; and Time is split by the year 2003. Career concern$$\%$$ measures the percentage of dividend smoothing due to executive career concerns. The J-statistic and p-value test the overidentification constraint for the moment conditions. I also examine how dividend smoothness changes across time by running a time-series regression of dividend smoothing on realized executive turnovers.20 The coefficient (untabulated) on executive turnover is -4.354 and significant at the 0.1$$\%$$ level, suggesting that a one percentage point increase in executives’ turnover risk is associated with a 25$$\%$$ change in the realized SOA of dividends. Motivated by this finding, I split the full sample by time and reestimate the model based on the different time periods. The purpose of this exercise is twofold. I want to test whether the baseline model can fit the time-series patterns of executive turnover rate and dividend smoothing. Conversely, I use the model to determine whether some economic fundamentals, such as production technologies and earnings noisiness, change over time and have the potential to influence executive turnover and dividend smoothing simultaneously. In panel D of Table 10, the Early subsample contains all firm-year observations prior to 2002. The Late subsample contains all observations from 2003 onwards. The sample is split in this way so there is roughly the same number of years on each side of the cutoff. More importantly, there is a major tax reform in 2003 that changes the relative tax disadvantage of individual income to capital gains. Breaking the sample at 2003 ensures that I can parameterize the effects of the tax change, so that the estimation is not confounded by the structural break in the tax code. I then reestimate the model. Using the sub-sample-specific estimates, I find that the career-concern-based dividend smoothing is 13$$\%$$ higher in the Late subsample. This result links the time-series changes in executive turnover to that of dividend smoothness and suggests that, over time, managers face more severe career concerns, and they attempt to mitigate this effect by smoothing dividends even further. 5. Robustness In the baseline model discussed above, the key friction that I consider is the inseparability between a firm’s dividend payout and the information revelation, combined with managerial career concerns. I impose a list of simplifying assumptions with respect to how the executive compensation and turnover decisions are formed to make the model tractable and estimable. To allay concerns that the results are due to these simplifications, I relax these simplifying assumptions, one by one. All of the results reported below are documented in detail in the Internet Appendix.21 First, I extend the baseline model to include size-dependent executive compensation, $$log(W_t) = 0.3\times log(SIZE_t)$$, following Gabaix and Landier (2008). Second, I account for managers’ outside options by using their wage decreases upon firing as a measure for managerial rent income, which captures how much more they are able to extract above and beyond their second best options. I also separate the executives’ stock holdings, vested and nonvested stock options. Despite some changes in the parameter estimates, the magnitude of career-concern-based dividend smoothing remains significant and quantitatively similar in all three specifications. Next, I relax the assumption that managers are risk-neutral by introducing risk-averse managers with habit formation. Managers are assumed to be risk-averse about their rent income and the firm’s stock price. In addition, they have no access to personal savings or investment opportunities, so that their per-period consumption equals their income. Managers’ salaries are modeled to be fully performance-dependent and proportional to the shareholders’ perceived match-specific profitability, $$\hat{z}_t$$. Consistent with Lambrecht and Myers (2012, 2017), risk-averse, habit-persistent managers tend to smooth dividends more aggressively in order to smooth their marginal utility. The managers’ utility maximization incentive alone accounts for roughly 50$$\%$$ of the observed dividend smoothing in the data. These findings, combined with the counterfactual results in Table 8, define the range of excessive dividend smoothing in cases where the managers can smooth their income stream to some degree, but not perfectly. In the baseline model, I make the assumption that the manager’s match quality varies over time and is identically equal to the persistent part of firm earnings. In the robustness exercise, I explore more general cases where the match quality only influences a fraction, $$\rho$$, of firm earnings. I let $$\rho$$ vary from 20$$\%$$ to 100$$\%$$ and reestimate the model (the baseline model can be viewed as a special case, where $$\rho=100\%$$). The (untabulated) results suggest that all parameters remain quantitatively the same in all cases, except the turnover cost, $$c$$, which scales proportionately with $$\rho$$. This result occurs because the moments used in the identification are only able to pin down the ratio, $$\frac{c}{\rho}$$, but not the two parameters separately. Therefore, changes in $$\rho$$ will be completely absorbed by proportional changes in the turnover cost, $$c$$, leaving other parameter values unchanged. This result also suggests that the main takeaway of the paper is unlikely to be hardwired by the specific mapping between firm profit and managers’ match quality. Will the model’s prediction disappear if the persistent component in firm earnings is totally unrelated to managers’ match quality? To answer this question, the key assumption in the model is that the executive turnover decision is tied to firm fundamentals ($$z_t$$), which can be signaled by the firm’s earnings and dividend policy. The underlying mechanism could be that either 1) firm fundamentals are determined by certain executive characteristics, or 2) firm fundamentals have nothing to do with the executives, but the board/shareholders blame the executives when the fundamentals deteriorate. I have focused on the first explanation throughout the paper, but the interpretation of all results would follow through if we have the second, turnover for luck (Jenter and Kanaan, 2015), mechanism in place. In the baseline model, I also assume that the investors update their belief about managers’ match quality in a linear fashion following Equation (7). More rigorously speaking, while I should track the investors’ entire belief distribution, $$P(z)$$, as a state variable and specify the conditional distributions of firm policies $$P({\it{\Omega}}|z)$$ to allow the investors to update their belief in a Bayesian fashion, this algorithm is computationally infeasible given the complexity of the manager’s problem. To analyze the robustness of the linearity assumption, I first expand the investors’ prediction Equation (7) by introducing quadratic terms and cross-products. Second, I consider asymmetric learning by allowing the investors to extract a different amount of information from dividend increases versus cuts. The added terms contribute little to the investors’ forecasting accuracy, and they do not alter the quantitative results. 6. Conclusion In this paper, I provide a framework to study the interaction of dividend smoothing, firm value, and managers’ well-being. I build and estimate a dynamic agency model in which managers distribute dividends not only to signal the persistence of firm earnings, but also to influence their own turnover risk. This framework departs from most of the dividend-signaling literature by explicitly modeling the difference in the agent and principal’s payout incentives. The model can be employed to disentangle how different stakeholders’ incentives influence dividend smoothness and explore the consequences on firm value. Estimating the model yields three major findings. First, a model that embeds the managers’ career-concern-based dividend smoothing fits the data much better than a model ignoring this channel. This model can be used to understand the variations of dividend smoothing across a wide spectrum of firms, as well as across time. Second, I parameterize the model according to the estimations obtained from the actual data and use it to disentangle the underlying forces behind the observed smooth dividends. The results suggest that 60$$\%$$ of the smoothness is driven by the shareholders’ preferences to stabilize prices and 40$$\%$$ by the managers’ attempts to ease their career concerns. Third, and most importantly, I analyze the welfare implications of this career-concern-based dividend smoothing and find that it distorts firm policy and lowers the equilibrium firm value by 2$$\%$$. This result, however, does not necessarily imply an ex ante inefficiency. The observed dividend smoothing could be ex ante efficient if the costs of eliminating the agency friction, for example by establishing a different contract with the managers, exceed 2$$\%$$. Finding the ex ante optimal amount of dividend smoothing entails incorporating the current model into a dynamic contracting framework, which could be an interesting topic for future research. I am deeply indebted to my advisor, Toni Whited, for her continuous support. I thank an anonymous referee, Heitor Almeida, Guojun Chen, Dave Dennis (editor), Theodosios Dimopoulos, Ruoyan Huang, Olga Itenberg, Ron Kaniel, Jay Kahn, Oliver Levine, Boris Nikolov, Robert Parham, Robert Ready, Bill Schwert, Mihail Velikov, and Jerry Warner and all seminar participants at Baruch College, Johns Hopkins University, Indiana University, Washington University in St. Louis, University of South Carolina, University of Illinois, University of Rochester, University of Utah, and University of Washington for helpful discussions and comments. I am very grateful to Dirk Jenter and Charlie Hadlock for sharing their data on CEO turnovers with me. Supplementary data can be found on The Review of Financial Studies Web site. Footnotes 1 I extend the model to include risk-averse and habit-persistent agents in Section 5. Mathematically, making such an extension is equivalent to introducing a concave transformation on the managers’ utility function. Doing so gives managers stronger incentives to smooth. 2 This assumption is imposed to maintain tractability. I discuss the robustness of this assumption in Section 5. 3 In Equation (7), I focus on predicting $$z_t$$ only because $$s_t$$ is iid across time. 4 Consistent with the literature, Grullon et al. (2005) also find that including dividend change does not add to a model’s predictive power on future earnings changes. These findings jointly suggest that the informativeness of dividends is more about the persistence of earnings than about the levels. 5 This section deals with a case in which the board and outside investors share the same information about firm future profitability, and they perceive the same cost for firing a top executive. In the Internet Appendix, I extend the model by (1) adding an information asymmetry between the board and the outsiders and (2) allowing the board of directors to bear a personal cost from executive turnover. 6 Notice that $$\underline{z}$$ is the board of directors’ choice variable. The strict monotonicity of a firm’s market value in $$\hat{z}$$ ensures the existence and uniqueness of the boards’ choice of $$\underline{z}$$. 7 In the Internet Appendix, I show that the model-predicted patterns in Figure 3 are consistent with what is observed in the actual data. 8 Managers still allow dividends to covary positively with earnings because they care about firm value, but the covariance becomes a lot weaker because of the perceived turnover risk. 9 This finding also has been documented by Skinner (2008) and Leary and Michaely (2011). 10 Table 2 reports the detailed calibration of these two parameters. I first compute the stock ownership and per-period compensation at the executive-year level, and then I calibrate $$\kappa_I$$ and $$\eta$$ to the sample average. 11 I only target the five-day CARs surrounding dividend cuts because the price reaction at dividend increases is statistically insignificant. If I introduce asymmetric adjustment costs, the CARs at dividend cuts and increases both could be matched precisely. Since the price reaction to dividend increases is relatively small and statistically insignificant in the data, this alternative estimation strategy yields qualitatively very similar results. 12 $$\rho_z$$ and $$\sigma_z$$ are the persistence and standard deviation of a firm’s match-specific shock, respectively; $$\sigma_s$$ is the standard deviation of the transitory shock; $$\theta$$ is the curvature of a firm’s production function; $$\delta$$ is the depreciation rate of physical capital; $$\{\nu_1, \nu_2\}$$ represents the linear-quadratic cost for net equity issuance; $$\kappa_M$$ measures to what extent managers care about the firm’s market value; and $$c$$ captures the opportunity cost for executive turnover. 13 A step-by-step derivation of the auxiliary equation is provided in the appendix. 14 In the Internet Appendix, I present an alternative way to demonstrate the relation between an estimator and the moments of the data it depends on using the algorithm described in Andrews, Gentzkow, and Shapiro (2017). 15 Bazdresch, Kahn, and Whited (2017) argue that an estimator based on moments fails to match policy function slopes, and vice versa. In my estimation, the model fit also becomes less precise if I focus on the policy function slopes, which is an inevitable shortcoming of the model. 16 In this exercise, I use executive-year instead of firm-year as the unit of observation and treat each turnover or retention of the top five executives as a separate observation. The coefficients of turnover on earnings and dividends become slightly more significant if I restrict the sample to the top three executives or the Chief Executive Officers (CEOs). 17 Here, I focus on the regression coefficients, but not the R-square. This is because the baseline model has only two profitability shocks, which means the noisiness of firm value (or return) is not comparable to the level in the actual data. One mechanical way for the model to generate a lower R-square is to introduce some nonfundamental shocks that are independently distributed across time. This approach will increase the noisiness of returns without affecting other major model predictions. 18 In the model, managers mainly accommodate this career-concern-based dividend smoothing by cutting investments and adjusting cash holdings, a response inconsistent with Farre-Mensa, Michaely, and Schmalz (2016), who find that firms typically increase debt to finance their payouts. This is because, first, Farre-Mensa et al. examine the joint determination of dividends and capital structure, whereas here, I abstract from firms’ capital structure decision by consider all-equity financed firms. Therefore, firms are unable to fund dividends through external debt financing. Second, Farre-Mensa et al. examine aggregate payouts, whereas I exclusively focus on the fraction of dividend payments that is driven by managers’ career concerns. Farre-Mensa et al. find that firms devote more external capital to finance share repurchases than dividends. 19 The dashed lines in Figure 4 correspond to a case in which the shareholders extract information from the dividends, but the managers ignore this effect on their tenure. 20 The dependent variable is the SOA estimated for each year, as reported in Figure 5. The independent variable is the proportion of top executives who are fired in a given year. 21 The Internet Appendix also includes robustness results regarding managers’ horizon and firms’ investment/ financing frictions. Appendix A.1 Numerical Solution In this appendix, I describe how the equilibrium allocation is solved. Figure A1 presents a graphical illustration of the solution algorithm. Figure A1 View largeDownload slide Numerical strategy Figure A1 illustrates how the model described in Section 2 is solved numerically. The process starts by conjecturing a forecasting rule for the productivity processes and assigning it to the investors. Taking this rule as given, managers set the firm policies to maximize their utility. In anticipation of the managers’ decision-making process, the investors choose the optimal forecasting rule so that they make the best possible predictions of the underlying productivity processes. An equilibrium is achieved when both the managers’ policies and the investors’ forecasting decisions converge simultaneously, a scenario that guarantees that no party has any incentive to deviate from their current strategies. Figure A1 View largeDownload slide Numerical strategy Figure A1 illustrates how the model described in Section 2 is solved numerically. The process starts by conjecturing a forecasting rule for the productivity processes and assigning it to the investors. Taking this rule as given, managers set the firm policies to maximize their utility. In anticipation of the managers’ decision-making process, the investors choose the optimal forecasting rule so that they make the best possible predictions of the underlying productivity processes. An equilibrium is achieved when both the managers’ policies and the investors’ forecasting decisions converge simultaneously, a scenario that guarantees that no party has any incentive to deviate from their current strategies. The algorithm is similar to that described in Krusell and Smith (1998). As a preliminary step, I descritize the five state variables $$\{z,s,K,L,D\}$$. The net asset value lies between 0 and $$\bar{K}$$, where $$\bar{K}$$ is the maximal capital that a firm will hold in the first-best case. A firm’s dividends lie between 0 and $$(0.1\times\bar{K})$$. The shocks to a firm’s productivity are transformed into discrete states using the quadrature method described in Tauchen and Hussey (1991). After defining the grids, I solve the equilibrium via the following steps: (1) I conjecture the investors’ optimal forecasting rule, $$\Gamma=\left\{ \gamma_{0}, \gamma_\pi, \gamma_{{\it{\Omega}}},\gamma_\mathcal{F} \right\}$$. Taking this rule as given, I solve the managers’ optimal policy, $$\{I', E', L', D'\}$$. In equations (5) and (8), managers’ utility and the firm’s value are interdependent, so they have to be determined simultaneously. (2) To achieve this, I first set the firm’s value function to the first-best case: \begin{equation}\label{A.1} V_{FB}(K,L,D,z,\pi) = \max_{\{I',E',L',D'\}} (1-\tau_p) D'-E'+ \beta \times {\mathbb E} V'_{FB}(K',L',D',z',\pi'), \end{equation} (A1) subject to the sources and uses of funds constraint: \begin{equation}\label{A.2} Y-I'+\tau_c\delta K' +L\times\left[1+r_f(1-\tau_c)\right]-L'+\Lambda(E')-D'-W\geq 0. \end{equation} (A2) Because the model does not include any adjustment cost, I can collapse a firm’s holdings of liquid assets and physical capital into a single state variable, $$A$$: \begin{equation}\label{A.3} A=L\times[1+r_f\times(1-\tau_c)]+K\times(1-\delta), \end{equation} (A3) and I refer to $$A$$ as the firm’s net worth. I can rewrite Equations (A1) and (A2) as functions of this new state variable: \begin{eqnarray}\label{A.4} V_{FB}(A,D,z,\pi) = \max_{\{K',A',E',D'\}} (1-\tau_p) D'-E' + \beta \times {\mathbb E} V'_{FB}(A',D',z',\pi'),\\ \end{eqnarray} (A4) \begin{eqnarray} \label{A.5}s.t. \quad Y+A+(\delta\tau_c-\frac{r_f\times(1-\tau_c)}{1+r_f\times(1-\tau_c)})K'+\delta\tau_cK'+ \Lambda(E') -D'-W-\frac{1}{1+r_f\times(1-\tau_c)}A'\geq 0. \end{eqnarray} (A5) Conditional on $$V_M = V_I=V_{FB}$$, I solve the managers’ value function, $$U(.)$$, using value function iteration: \begin{align}\label{A.6} U(A,D,z,\hat{z},\pi) &= \max_{\{K',A',E',D'\}} {\mathbb E}\{\beta(1-\Phi)W+\beta(1-\Phi)U(A',D',z',\hat{z}',s') \nonumber \\ &\quad+\kappa_I[V_I(A,D,z,\pi)-\beta(1-\Phi)\times V_I(A',D',z',\pi')] \nonumber \\ &\quad+\kappa_M[V_M(A,D,\hat{z},\pi)-\beta(1-\Phi)\times V_M(A',D',\hat{z}',\pi')]\} , \end{align} (A6) in which $$\Phi$$ represents the executive turnover decision: \begin{equation}\label{A.7} \Phi = \left\{ \begin{array}{ll} 1, & \hat{z}'\leq \underline{z} \\ 0, & \text{otherwise.} \end{array} \right. \end{equation} (A7) If the firm decides to dismiss its incumbent executives, it takes a random draw from the initial unconditional distribution: $$z_{new} \sim N(0,\frac{\sigma_z^2}{1-\rho_z^2})-c$$ and resets: $$z = z_{new}$$. Solving Equation (A6) subject to the constraint (A5) yields the managers’ optimal decision, $$\{K',A',E',D'\}^!$$. Based on this optimal decision, I can update the firm’s value function: \begin{eqnarray}\label{A.8} V_I(A,D,z,\pi) = (1-\tau_p)D'-E' -\lambda|\triangle D'| + \beta {\mathbb E} V'_I(A',D',z',\pi'), \\ \end{eqnarray} (A8) \begin{eqnarray} \label{A.9}V_M(A,D,\hat{z},\pi) = (1-\tau_p)D'-E' -\lambda|\triangle D'|+ \beta {\mathbb E} V'_M(A',D',\hat{z}',\pi'). \end{eqnarray} (A9) I iterate until the value functions $$\{U,V_M,V_I\}$$ converge. (3) I then generate a panel of firms according to the optimal policy, $$\{K',A',E',D'\}^!$$, and calculate what forecasting decision best describes the simulated data: \begin{equation}\label{A.10} \hat{z}' = \gamma_{0} + \gamma_{\pi}\times \pi' + \gamma_{{\it{\Omega}}}\times{\it{\Omega}} + \gamma_{\mathcal{F}}\times\mathcal{F}. \quad \left\{ \gamma_{0}, \gamma_{\pi}, \gamma_{{\it{\Omega}}}, \gamma_{\mathcal{F}}\right\} = \arg\min{\mathbb E}|\hat{z}'- z|. \end{equation} (A10) Obtaining the optimal forecasting rule is essentially finding the least absolute deviation estimates in the following regression: \begin{equation}\label{A.11} {z} = \gamma_{0} + \gamma_{\pi}\times \pi' + \gamma_{{\it{\Omega}}}\times{\it{\Omega}} + \gamma_{\mathcal{F}}\times\mathcal{F} + \epsilon. \end{equation} (A11) Estimating the regression also provides a measure for the goodness-of-fit. (4) I stop if the estimates converge to the initial guess and the process yields a reasonable goodness-of-fit. If the estimates converge, but the goodness-of-fit is poor, I add in additional determinants and try different functional forms of Equation (A11). A.2 Estimation Procedure In this section, I briefly outline the estimation procedure. Let $$x_{i,t}$$ represent the real data vector and $$y_{i,t,s}(\beta)$$ represent the simulated data, where $$i = (1,2,3...n)$$ denotes the number of firms, $$t = (1,2,3...T)$$ indicates the number of time periods, and $$s =(1,2,3...S)$$ represents the number of simulated data sets. I explicitly write $$y_{i,t,s}$$ as a function of $$\beta$$ to emphasize the dependence of simulated data on the deep structural parameters. Michaelides and Ng (2000) find that good finite-sample performance of a simulation estimator requires a simulated sample that is approximately ten times as large as the actual data sample. I set $$S=10$$ following their suggestion. Equation (A12) contains the first two moments in the estimation process. As Cooper and Haltiwanger (2006) argue, this equation can be derived as an auxiliary equation from the firm’s production function and the profitability shock processes. The detailed procedures are illustrated as follows: I take the log of a firm’s production function: \begin{equation}\label{A.12} \ln Y_t=\ln z_{t}+ \ln s_{t} +\theta \times \ln K_{t}. \end{equation} (A12) I substitute $$z_{t}$$ and $$z_{t-1}$$ with $$(\rho\times z_{t-1}+\epsilon_{z,t})$$ and $$(\ln Y_{t-1} - \theta\ln K_{t-1} - \ln s_{t-1})$$, respectively and rewrite Equation (A12) as: \begin{equation}\label{A.13} \ln Y_t=\rho\times(\ln Y_{t-1} - \theta\ln K_{t-1} - \ln s_{t-1} + \epsilon_{z,t})+ \ln s_{t} +\theta \times \ln K_{t}. \end{equation} (A13) I rearrange terms in Equation (A13) to obtain: \begin{equation}\label{A.14} \ln Y_t=\rho\times\ln Y_{t-1} + \theta \times \ln K_{t} - \rho\times\theta\times\ln K_{t-1} + ( \ln s_{t} - \rho\times \ln s_{t-1} + \epsilon_{z,t}). \end{equation} (A14) Equation (A14) is in the same format as Equation (12), which can be directly estimated on the simulated data. For the actual data, I remove the firm fixed effects by focusing on the first difference, and I include a complete set of year dummies to absorb the aggregate shocks. Following the suggestion in Cooper and Haltiwanger (2006), I estimate Equation (A14) as a nonlinear GMM system, and I use lagged and twice-lagged capital, as well as twice-lagged profit as instruments. I add another set of 13 moments to pin down the 9 underlying parameters: $$\{\rho_z, \sigma_z, \sigma_s, \theta, $$$$\nu_1, \nu_2,\delta, \kappa_M, c\}$$. The choice of moments and the corresponding parameter estimates are reported in Table 3. The model is estimated using simulated method of moments (SMM). SMM chooses the parameter values to minimize the distance between simulated moments and the corresponding actual moments. Let $$m(x_{i,t})$$ and $$y_{i,t,s}$$ denote the moments calculated based on the real and simulated data, respectively. I can write the sample moment condition as: \begin{equation}\label{A.15} g(x_{i,t}, \beta) = \frac{1}{nT}\sum_{i = 1,n}\sum_{t = 1,T} \left[ m(x_{i,t}) - \frac{1}{S}\sum_{s = 1,S}m(y_{i,t,s}(\beta)) \right]. \end{equation} (A15) The simulated method of moment estimator $$\hat{\beta}$$ is then obtained by solving: \begin{equation}\label{A.16} \hat{\beta} = \arg\min_{\beta} g(x_{i,t}, \beta)'\hat{W}g(x_{i,t}, \beta), \end{equation} (A16) in which $$\hat{W}$$ is a positive definite matrix that converges in probability to a deterministic positive definite matrix W. I use the inverse of the sample covariance matrix of the moments to construct $$\hat{W}$$. The calculation follows the influence-function approach described in Erickson and Whited (2002). 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TI - What’s behind Smooth Dividends? Evidence from Structural Estimation
JO - The Review of Financial Studies
DO - 10.1093/rfs/hhx119
DA - 2018-10-01
UR - https://www.deepdyve.com/lp/oxford-university-press/what-s-behind-smooth-dividends-evidence-from-structural-estimation-ceITxZXRa4
SP - 3979
VL - 31
IS - 10
DP - DeepDyve
ER -