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Reconsideration of the IS–LM model and limitations of monetary policy: a Tobin–Minsky model


The standard IS–LM model considers all types of financial assets, excluding money, as bonds. We construct a modified IS–LM model to better represent the characteristics of financial markets and investigate the stability of the economy. We present bank behavior explicitly and consider household portfolio preferences through the rate of return on financial assets. We build both static and dynamic models that incorporate the dynamic equation of monetary policy. In our model, an increase in the debt–capital ratio may have a negative impact on the profit rate and bring about the so-called “paradox of debt.” We indicate that factors such as the sensitivity of bank lending to the profit rate and the degree of substitutability between the household’s equity and money have a significant effect on the volatility of the profit rate and equity price. Particularly, the latter may lead to an unstable economy in the long run. We show that it is always possible for the economy to become unstable endogenously. The government and central bank must formulate loan regulations and adopt the appropriate monetary policy to stabilize the economy.

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  1. In addition, Nishi (2012) focuses on the Minskian taxonomy of firms’ financial structure (hedge, speculative, and Ponzi types) and analyzes its relationship with an economic-growth regime (debt‐led and debt‐burdened regimes).

  2. Bernanke and Blinder (1988) provide a model for analyzing the role of bank loans in macroeconomic activity. However, their intention is to reconsider the standard IS–LM model; consequently, they do not examine the instability of the economy.

  3. IS stands for investment/saving, while LM stands for liquidity preference/money supply.

  4. In Keynes’ (1936) words, “In my Treatise on Money (vol. ii, p. 195) I pointed out that when a company’s shares are quoted very high, so that it can raise more capital by issuing more shares on favorable terms, this has the same effect as if it could borrow at a low rate of interest” (p. 151).

  5. Tobin (1969) illustrates a general framework for monetary analysis. Our model is similar to Tobin’s model in that he abandoned the perfect substitutability assumption in relation to financial assets. However, there are some differences between our model and that of Tobin: we do not adopt the q-theory of investment for two reasons. First, the validity of the q-theory of investment has not been fully verified despite much empirical research [Chrinko (1993) and Oliner et al. (1995)]. Second, our model separates the investment decision from the price of equity. This is a corollary derived from our model, which treats the financial behaviors of households and firms independently. Our model also differs from Tobin’s model in that it considers the role of banks in credit creation. Finally, we extend a static model and perform a dynamic analysis.

  6. Asada (2014) formulates a series of mathematical macro dynamic models that contribute to the theoretical analysis of financial instability, resulting in a four-dimensional model of flexible prices with a central bank’s monetary stabilization policy. Our model, by contrast, is a dynamic model of fixed prices.

  7. The choice of interest rate, rather than money supply, as a monetary policy instrument is common in the recent literature. For example, Asada (2014), Isaac (2009), and Lavoie (2006) analyze the effect of monetary policy from the post-Keynesian viewpoint. The same trend can also be seen in new-Keynesian literature. Romer (2000) proposes the IS–MP model as a substitute for the IS–LM model. One potential reason for this is that the central banks in almost all industrialized countries have recently been controlling the real interest rate. For a given inflation rate, the real rate rule is a horizontal line in the output-real rate space. Romer refers to this line as the MP curve, different from the LM curve.

  8. See Hicks (1956).

  9. Hein (2007) investigates the stability conditions in the long run and then focuses on the analysis of the steady state. He finds that the long-run equilibrium value of the debt–capital ratio is positive and stable only if interest rates are extremely high and if the short-run equilibrium exhibits the ‘debt-led’ growth regime. However, this conclusion triggered some debates. Sasaki and Fujita (2012) point out that Hein’s conclusion crucially depends on the assumption that the retention ratio of firms equals unity. In addition, although Hein (2013) replaces a given retention rate with a given dividend rate, Franke (2016) reveals that in the model, the retained earnings of the firms will be non-positive in a long-run financial equilibrium.

  10. The balance sheet shows that the central bank controls the interbank rate through the call market.

  11. Under these assumptions, in our model, we can ignore the retained earnings of the bank and the central bank.

  12. Symbols with plus signs describe sources of funds and those with negative signs indicate uses of funds.

  13. Based on the stock-flow consistent (SFC) approach, it has been pointed out that traditional models such as Taylor and O’Connell (1985) often assume oversimplified hypotheses that do not do justice to Minsky’s literary analysis. Examples of such works include Dos Santos (2005, 2006).

  14. This assumption of the firm’s behavior follows Lavoie and Godley (2001).

  15. This formulation is different from that of Asada (1999). Asada formulates a model in which real and financial decisions are simultaneously determined to maximize the value of the firm. By contrast, since we follow Lavoie and Godley (2001), the firm’s real and financial decisions are separately determined. Therefore, the budget constraint shown as Eq. (12a) plays no role in the investment decision. These assumptions of Lavoie and Godley are often used [e.g., Franke and Semmler (1991) and Ryoo (2013a, b)].

  16. With regard to the analysis of the investment decision, Minsky insists “[t]he capitalization of the prospective yields to generate a demand price for capital assets is a more natural way to approach the problem of fluctuating investment than the marginal efficiency of capital schedule” (Minsky 1975, p.98). However, we use the marginal efficiency of capital approach based on Keynes (1936), who writes, “the rate of investment will be pushed to the point on the investment demand schedule where the marginal efficiency of capital in general is equal to the market rate of interest” (p. 136–137). Although our model is similar to that of Adachi and Miyake (2015), there is difference in the definition of the marginal efficiency of capital. See footnote 18.

  17. By contrast, Asada (1999) focuses on the theory of the “principle of increasing risk” proposed by Kalecki (1937), and does not consider the state of expectations. Asada presents the borrower’s risk as an increasing function of the debt–capital ratio and substitutes it into the model as an additional cost function. The increase in the debt–capital ratio influences investment via the cost function.

  18. Keynes argues, “[i]f there is an increased investment in any given type of capital during any period of time, the marginal efficiency of that type of capital will diminish as the investment in it is increased, partly because the prospective yield will fall as the supply of that type of capital is increased, and partly because, as a rule, pressure on the facilities for producing that type of capital will cause its supply price to increase; the second of these factors being usually the more important in producing equilibrium in the short run, but the longer the period in view the more does the first factor take its place” (Keynes 1936, p. 136). In the model, \(\phi\) corresponds to what Keynes called the marginal efficiency of capital; we assume that \(Q/pI\), the marginal efficiency of capital decreases as \(k\) increases. The assumption \({\phi }_{k}<0\) is nothing but a formulation of the first factor.

  19. This assumption ensures that the maximization problem has a meaningful solution.

  20. Keynes (1936) writes, “[t]he considerations upon which expectations of prospective yields are based are partly existing facts which we can assume to be known more or less for certain, and partly future events which can only be forecasted with more or less confidence.” We focus on “existing facts” and denote them using the present profit and the debt–capital ratio. For simplicity, we ignore “future events.”

  21. It may be said that this formulation also expresses the borrower’s risk. See also footnote 25

  22. The characteristics of the investment function in our model are to a large extent the same as those in Asada’s model (1999, 2001). However, there are some differences in the approach and derivation. In addition, Asada focuses only on the investment decision. The model simultaneously includes both the borrower’s risk and the lender’s risk in the investment decision. By contrast, we formulate the lender’s risk as part of bank behavior.

  23. The bank does not hold excess reserves, because they do not yield interest.

  24. For simplicity, in our model, the central bank supplies the call loans that are requested by the bank.

  25. Keynes (1936) stressed the importance of the lender’s risk. We note the following remarks made by Keynes: “But where a system of borrowing and lending exists, by which I mean the granting of loans with a margin of real or personal security, a second type of risk is relevant which we may call the lender's risk. This may be due either to moral hazard, i.e., voluntary default or other means of escape, possibly lawful, from the fulfillment of the obligation, or to the possible insufficiency of the margin of security, i.e., involuntary default due to the disappointment of expectation.” In our model, the lender’s risk has an indirect influence through the bank’s cost function.

  26. To allow banks to make profits, we assume that the loan rate exceeds the deposit rate, \(i>{i}^{d}\).

  27. For simplicity, we assume that \({i}^{b}\) remains constant throughout this study.

  28. We can express the demand for deposits as \({\dot{D}}^{d}=\lambda \dot{{M}^{d}}\). \(\lambda\) is constant.

  29. The portfolio behavior functions follow Tobin (1969).

  30. \(\frac{dq}{{di^{a} }} = \frac{{k_{{i}^{a}} \left[ {\alpha_{r} \cdot s^{h} + l_{r}^{s} - \left( {1 - \alpha } \right)s_{1} \left( {\frac{1}{\tau } + 1 - v} \right)} \right] - l_{{i}^{a}}^{s} \left\{ {k_{r} - [s_{1} \left( {\frac{1}{\tau } + 1 - v} \right) + v]} \right\}}}{{\left( {1 - s_{2} } \right)e\Delta }}.\)

  31. Taylor (1993) proposes that the nominal interest rate should respond to the divergence of actual inflation rates from target inflation rates and of actual GDP from potential GDP.

  32. \(\dot{e}_{e} = \frac{{ - q_{e} \left( {k^{*} - vr - l^{s} } \right)}}{{q^{2} }} - k^{*} .\) Considering Eqs. (19e) and (22b), we obtain \(\dot{{e}_{e}}=0\).

  33. Refer to Fazzari and Greenberg (2008), Charles (2016), and others.


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I wish to thank two anonymous referees and Shin Imoto (Onomichi City University) for their many valuable comments. Any errors remaining in this study are the authors’ sole responsibility.


This study was funded by Fukui Prefectural University.

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Correspondence to Toshio Watanabe.

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Watanabe, T. Reconsideration of the IS–LM model and limitations of monetary policy: a Tobin–Minsky model. Evolut Inst Econ Rev 18, 103–129 (2021).

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  • Financial instability hypothesis
  • Portfolio selection
  • Debt–capital ratio
  • Monetary policy

JEL Classification

  • E12
  • E44
  • E52