A post Keynesian theory for Tobin’s q in a stock-flow consistent framework

ABSTRACT

The paper proposes a post Keynesian framework to explain Tobin’s q behavior in the long run. The theoretical basis is informed by the Cambridge corporate model originally proposed by Kaldor (1966), which is reinterpreted here as a theory for q. The core of the “Kaldorian q theory” is a negative long-run relation between q and growth rates, a negative relation between q and propensities to consume, and the fact that q can be different from 1 in the long-run equilibrium. We generalize this model through a medium-scale stock-flow consistent (SFC) model, which introduces important post Keynesian aspects missing in the Kaldorian model, such as endogenous money, a financial system, and inflation. We extend the model to include a more realistic treatment of firms’ financial structure decisions and allow the interdependence between these decisions and dividend policy. Numerical simulations confirm that the original Kaldorian relations between q and growth rates and propensities to consume hold, but unlike the original model, in our model, q is not independent of how firms finance their investment. We also confirm the possibility of q being different from 1 in the long run. Finally, we contrast this “post Keynesian q theory” with the Miller–Modigliani dividend irrelevance proposition and the neoclassical investment and financial theory. It is shown that its validity depends crucially on the value taken by q: for q values different from 1 the proposition will not hold and dividend policy will be relevant for equity valuation. Therefore, post Keynesian q theory stands against the main predictions of mainstream finance and constitutes an alternative for developing a macroeconomic theory for equity markets.

KEYWORDS:

• Cambridge corporate models
• Miller–Modigliani dividend irrelevance proposition
• post Keynesian macroeconomic theory
• stock-flow consistent models
• Tobin’s q

JEL CLASSIFICATIONS:

• E12
• E22
• E44
• G10
• O42

Notes

¹In fact, the first person to propose this ratio at the macroeconomic level was Kaldor (1966), who called it the “valuation ratio.” In this paper, the term valuation ratio will refer not only to Tobin’s q but also to the price–earnings ratio. Tobin’s q and the price–earnings ratio will be the only two financial valuation metrics used in this paper.

²The insight that higher growth rates lead to lower valuation ratios has profound implications both for policymakers and market participants. The importance of market valuations for policymakers has been argued at length in Smithers (2009), who claims that central bankers should pay more attention to financial market valuations and not exclusively to price inflation. For market participants, it is useful to have an idea whether markets are “expensive” or not. However, at the macro level, traditional fundamental equity valuation methods applied to the valuation of whole indexes will not work if the Kaldorian insight applies—because these discounted cash-flow methods will tell you that higher growth rates should lead to higher valuations.

³Although Tobin and Brainard did not formally develop this reverse causation issue, they briefly hinted at this dependence of q on investment decisions; “We agree that q’s are partly endogenous variables, that investments can influence q’s as well as vice versa, and that the lags between exogenous changes in q and investment could be ‘long and variable’” (Tobin and Brainard, 1990, p. 548).

⁴For a discussion of a possible research agenda in common between post Keynesian economics and behavioral finance, see Jefferson and King (2010).

⁵This is the case in most real-business cycle and new Keynesian models. See, for instance, Christiano et al. (2005) and Smets and Wouters (2007). In these models, the institutional setup is irrelevant (it does not matter who owns what), so that capital structure and dividend policy are irrelevant. In addition, no clear picture of the role of financial intermediaries in the system is provided.

⁶For a discussion of the differences between Minsky and Brainard and Tobin’s framework, see Crotty (1990) and Palley (2001).

⁷However, Brainard and Tobin’s framework is quite different from the neoclassical one. As they admit: “We are so far from being thorough-going neoclassicals that we are quite comfortable in believing that corporate managers … respond to market noise and are in any case sluggish in responding to the arbitrage opportunities of large deviations of ‘q’ from par” (Tobin and Brainard, 1990, p. 548). Furthermore, Tobin (1984, pp. 6–7) expressed serious reservations about the “efficiency of financial markets,” approvingly citing Keynes’s idea of markets driven by noninformed, herding behavior.

⁸Under constant returns on the adjustment costs, it can be shown that marginal and average q coincide (Hayashi, 1982). Moreover, other influences such as monopoly power, downward-sloping product demand curves, and a large share of dated capital can produce discrepancies between the marginal and the average q (see Romer, 2012, p. 415).

⁹For a thorough review of the Cambridge model literature, see Baranzini and Mirante (2013).

¹⁰See Moss (1978) for a model with dual-class income distribution analysis in the framework of a corporate economy.

¹¹The terminology used in the Cambridge literature is misleading. What is labeled “the rate of interest” really is the equity yield. In fact, there is neither money nor debt in these models, thus no “rate of interest” in the Keynesian sense. The origin of this confusion could be due to the neoclassical institutional structure, where there are no households or firms, but a representative agent, so the difference between the rate of profit and equity yield vanishes, because the agent as household will equalize the equity yield to the rate of profit obtained as “entrepreneur”—the sort of arbitrage game that abounds in the Modigliani–Miller literature. In turn, the rate of profit is usually considered in the neoclassical framework to be the rate of interest (as in Solow’s model), given in principle that all firm’s liabilities can be treated alike. Therefore, in the neoclassical framework, the rate of profit, rate of interest, and equity yield can be used interchangeably.

¹²Kaldor (1966) assumed that households’ propensity to save was homogeneous across all income classes (i.e., wages, dividends, and capital gains). However, in a model with different propensities to save, the link between every propensity and the valuation ratio is still positive (Moore 1973, 1975).

¹³Full disclaimer: all these relationships should be properly understood in a long-run context.

¹⁴See the discussion in the previous section. Post Keynesians disagree on the neoclassical investment functions (those solely with q as an independent variable), on the grounds that the rationality imposed is absurd (e.g., radical uncertainty and animal spirits) or on the grounds that no quantities (e.g., cash flows, utilization) are included. Thus, q is not a key determinant of investment. Our point is that investment is a determinant of q.

¹⁵We do not claim completeness for the items recorded in the balance sheet. For instance, all the interesting links between the banking sector, the government, and the Central Bank often highlighted by the modern money theory (MMT) literature (Tymoigne and Wray, 2013; Wray, 2012) have been assumed away. Although they would certainly be needed in a more complete description of a modern economy, they do not change the essence of the argument presented here.

¹⁶For the post Keynesian debate on investment functions, see Hein et al. (2011, 2012) and Lavoie (2014, ch. 6).

¹⁷Household debt has been assumed away. Although it has played an important role in developed countries recently, our argument can proceed without it. For a model dealing with household debt dynamics in the Cambridge tradition, see Palley (1996).

¹⁸Real disposable income is not simply the deflated value of nominal disposable income, but has to be adjusted for the erosion in wealth produced by inflation. For a formal proof, see Godley and Lavoie (2007, pp. 293–294).

¹⁹For a more realistic banking sector in the SFC tradition, see Le Heron and Mouakil (2008) and Dafermos (2012).

²⁰Return on equity is defined as total profits divided by the previous period value of equity in firms’ balance sheets.

²¹Figures 1(b) and 2(b) should be understood as measuring consumption, disposable and real wealth in the new scenario in comparison to the baseline (steady-state) scenario.

²²A natural extension of the model would be to deal with financialization issues in depth. For SFC models dealing with financialization issues in detail, see Van Treeck (2008) and Caverzasi and Godin (2015).

²³Montier (2014b) presents additional evidence against shareholder value maximization, showing how equity returns were higher in the period 1940–90 than since then.

²⁴Moreover, there is nothing in our model (or in the post Keynesian tradition) to suggest that equity prices only incorporate the relevant information for managers so they can make “rational” investment decisions. In other words, no efficient market hypothesis is assumed here.

²⁵Most of them are based on market imperfections, among others: different tax rates for dividends and capital gains, asymmetric information (managers may want to signal corporate prospects through dividend policy), and other corporate imperfections such as inefficient managers who may squander cash—making it preferable to pay out dividends. Recently, experiments in the behavioral finance literature have shown that individuals pay attention to the source from which they receive income, engaging in mental accounting (Thaler, 1990, 1999): the way an investor receives his income matters. Finally, the M&M proposition, which is an argument derived from micro conditions, may not necessarily be applicable at a macro level, due to the well-known fallacy of composition problems (King, 2012; Taylor, 2004). For additional critiques of the M&M framework, see Gordon (1992, 1994), Glickman (1997), Pasinetti (2012), and Woods (2013).

²⁶A precision has to be made. For convenience, the q used in this section and computed with this formula is the “equity q”—that is, market value of equity to its replacement cost (assets net of debt). The equity q (or “leveraged q”) is related to the traditional q in the following way: $$q_e=\frac{q-l}{1-l}$$, where l is the leverage ratio (debt to total assets). As one would expect, when q is equal to 1, then equity q will be equal to 1 as well. Therefore, for the M&M discussion and its validity when q is different from 1, it does not matter whether one uses the traditional q or the equity q.

²⁷The example is taken from Penman (2011, ch. 2), but modified and adapted for our purposes. However, Penman does not explicitly discuss the case when r ≠ γ. The technical details of the four scenarios can be found in Appendix 2.

²⁸For brevity’s sake, only the case when r > γ is considered here.