Debt cycles, instability and fiscal rules: a Godley-Minsky model

Transcription

1 Faculty of usiness an Law Debt cycles, instability an fiscal rules: a Goley-Minsky moel Yannis Dafermos Department of Accounting, Economics an Finance, University of the West of Englan, ristol, UK Yannis.Dafermos@uwe.ac.uk Economics Working aper Series 509

2 Debt cycles, instability an fiscal rules: a Goley-Minsky moel Yannis Dafermos Department of Accounting, Economics an Finance, University of the West of Englan, ristol, UK, Yannis.Dafermos@uwe.ac.uk Abstract: Wynne Goley an Hyman Minsky were two macroeconomists who saw the crisis coming. his paper evelops a simple macroynamic moel that synthesises some key perspectives of their analytical frameworks. he moel incorporates Goley s financial balances approach an postulates that private sector s propensity to spen is riven by a stock-flow norm (the target net private ebt-to-income ratio) that changes enogenously via a Minsky mechanism. It also inclues two fiscal rules: a Maastricht-type fiscal rule, accoring to which the fiscal authorities ajust the government expenitures base on a target net government ebt ratio; an a Goley-Minsky fiscal rule, which links government expenitures with private inebteness following a counter-cyclical logic. he analysis shows that (i) the interaction between the propensity to spen an net private inebteness can generate cycles an instability; (ii) instability is more likely when the propensity to spen respons strongly to eviations from the stock-flow norm an when the expectations that etermine the stock-flow norm are highly sensitive to the economic cycle; (iii) the Maastricht-type fiscal rule is estabilising while the Goley-Minsky fiscal rule is stabilising; an (iv) the paraox of ebt can apply both to the private sector an to the government sector. Keywors: Goley, Minsky, ebt cycles, instability, fiscal rules EL Classification: E0; E0; E3; E6 September 05 Acknowlegements: A previous version of this paper was presente at the Cambrige Keynes Seminar of the ost-keynesian Economics Stuy Group in May 0. I am grateful to Marco assarella an Graham Gugin for valuable comments. he paper has also benefite from comments an suggestions by Giorgos Galanis, Annina Kaltenbrunner, Anrew Mearman, o Michell, Maria Nikolaii, Christos apatheoorou, Engelbert Stockhammer an Rafael Wilauer. Any errors are mine.

3 . Introuction Debt cycles, instability an fiscal rules: a Goley-Minsky moel Wynne Goley an Hyman Minsky were two macroeconomists who saw the crisis coming. In 999 Goley publishe his well-known article on the seven unsustainable processes in the US economy (Goley, 999). In this article he argue that the rising inebteness of the US private sector was unsustainable an, therefore, private expenitures coul not be consiere as a source of steay growth in the meium run. He also pointe to the unsustainability of the rising US net foreign inebteness. Using a stock-flow consistent analytical framework, Goley argue that without a change in fiscal policy stance or an important rise in net exports, the US economy was oome to witness a severe recession an a sharp rise in unemployment. hese warnings were repeate in his publications as a hea of the Levy Economics Institute s macro-moelling team (see, e.g. Goley, 003, 005; Goley et al., 005). he crisis verifie Goley s fears: the US economy contracte sharply an the unemployment rate increase substantially. Minsky (975, 98, 008) evelope a theory that explains how inebteness can increase in perios of tranquillity as a result of enogenous forces that reuce the esire margins of safety of economic units. his graual reuction in the esire margins of safety was consiere by Minsky as the reason behin the increasing financial fragility that accompanies economic expansion an perios of stability. Accoring to his financial instability hypothesis, the increasing fragility makes the macro systems more prone to shocks that reuce the ability of borrowers to repay their ebt. hese shocks can lea to severe economic recessions. he processes escribe in Minsky s analysis are broaly in line with the pre-crisis evelopments in the US an other avance economies that ultimately le to the Great Recession. he emphasis that Goley an Minsky place on financial relationships as sources of cycles an instability enable them to provie some very important insights into the ynamics of moern macroeconomies. However, they i so from quite ifferent angles. Goley concentrate more on the macroeconomic relationships between the private, the government an the foreign sector an postulate that in the meium to long run the fluctuations in financial balances an growth are riven by some exogenous stock-flow norms. Minsky, on the other han, focuse more on the relationships within the private sector (primarily on the financial relationships between firms an banks) an explaine the macroeconomic fluctuations by consiering enogenous changes in norms an valuations of risk. Although it is wiely hel that Goley s an Minsky s perspectives are both important for the explanation of macroeconomic ynamics, there is still a lack of a formal See, for example, Whalen (008), Wolf (008), ezemer (00) an Wray (0, 0). Accoring to Goley et al. (007) an Zezza (009), the slowown of economic growth in 00- was a first sign of the unsustainable processes in the US economy. However, a severe recession was then prevente ue to accommoative fiscal an monetary policies.

4 framework that synthesises them. On the one han, there is a large literature on formal Minskyan moels that capture various ynamics relate to Minsky s financial instability hypothesis. Recent contributions to this literature inclue Ryoo (00, 03a), Chiarella an Di Guilmi (0), Eggertsson an Krugman (0), assarella (0), Sori an Vercelli (0), Keen (03), Nikolaii (0) an hattacharya et al. (05). However, none of these moels inclue explicitly insights from Goley s projection analyses. On the other han, there are some theoretical stock-flow consistent moels that utilise aspects of Goley s projection approach, but make no explicit links to Minskyan ynamics (e.g. Goley an Lavoie, 007; Martin, 008; Leite, 05). he purpose of this paper is to evelop a simple macroynamic moel that makes a Goley-Minsky synthesis. he moel concentrates on certain aspects of Goley s an Minsky s approaches that are eeme more important for a simplifie explanation of ebt cycles an instability in a national macroeconomy. he key features of the moel an the principal results of the analysis are the following. First, as in Goley s projection analyses, the moel economy consists of three sectors: the private sector, the government sector an the foreign sector. his permits an explicit consieration of Goley s financial balances approach that explains the interlinkages between these sectors an the resulting effects on ebt accumulation an growth. Remarkably, Goley s financial balances approach is broaly in line with Kalecki s profit equation that was use by Minsky. Secon, rawing on Goley, the private sector s propensity to spen is riven by a stock-flow norm (the target net ebt-to-income ratio). It is shown that, uner certain conitions, the interaction between the propensity to spen an net private inebteness generates cycles an instability. Instability is more likely when the propensity to spen respons strongly to eviations from the stock-flow norm. A paraox of ebt result arises: the more the private sector an its leners attempt to put net private inebteness uner control, by ajusting private expenitures, the more the net private ebt ratio estabilises. hir, following Minsky, it is assume that the stock-flow norm varies enogenously as a result of changes in the expectations an the conventions of borrowers an leners uring the economic cycle. It is shown that this enogeneity can give rise to Goley- Minsky ebt cycles an it is a source of instability. Instability is more likely when the stock-flow norm is highly sensitive to the economic cycle. Fourth, two ifferent fiscal rules are introuce: a Maastricht-type fiscal rule, accoring to which the fiscal authorities ajust the government expenitures base on a target net government ebt ratio; an a Goley-Minsky fiscal rule, which links government expenitures with private inebteness following a counter-cyclical logic. Simulation analysis illustrates that the Maastricht-type fiscal rule is estabilising while the Goley- Minsky fiscal rule is stabilising. Apart from supporting the view that counter-cyclical fiscal policy has positive effects on the stabilisation of output, this result suggests that countercyclical fiscal policy is also conucive to the stabilisation of government inebteness. Moreover, it is shown that the paraox of ebt can apply to the government sector: the more the fiscal authorities attempt to target a specific government ebt ratio, by ajusting the government expenitures, the more this ratio estabilises. he paper procees as follows. Section lays out the structure of the moel. Section 3 explores the interaction between private sector s propensity to spen an net private

5 inebteness when the target net private ebt-to-income ratio an government expenitures are exogenous. Section enogenises the target net private ebt-to-income ratio an stuies how Goley-Minsky cycles can arise. It also examines the implications of this enogeneity for instability. Section 5 introuces fiscal rules an analyses their (e)stabilising effects. Section 6 summarises an conclues.. Structure of the moel able portrays the transactions matrix of our three-sector economy. National accounting implies: Y C I G X M () Y Y rd () S Y C (3) D Y () D G G G rdg (5) D F F X M rd DG (6) D DG DF 0 (7) D D D (8) G F 0 G F where Y is the output of the economy, C is consumption, I is omestic investment, G enotes primary government expenitures, X enotes exports, M enotes imports, Y is the isposable income of the private sector, S is private sector s saving, enotes the total private expenitures ( C I ), D is the net private ebt, is the balance of the private sector, G is the balance of the government sector, enotes taxes, r is the interest rate, D G is the net government ebt, F is the balance of the foreign sector an D F is the net foreign ebt. he net ebt of each sector is equal to its financial liabilities minus its financial assets. A sector is a net ebtor when its net ebt is positive an a net creitor when its net ebt is negative. A ot over a variable x is use to enote time erivative ( x x / t ). For simplicity, the following assumptions have been mae: the interest rate is exogenously etermine by the monetary authorities an is the same for both the private an the government net ebt; 3 the primary government expenitures refer only to the purchase of goos prouce by the private sector; the price level is set equal to unity; there are no changes in asset prices an exchange rates that coul affect the value of assets an liabilities (an, thus, the value of net ebt). 3 he assumption that the interest rate is exogenous, an thus inepenent of the level of (private an government) inebteness, seems quite restrictive. However, this assumption has been aopte because one of the purposes of this moel is to show that inebteness can be a source of cycles an instability even when it has no irect impact on the interest rates. Note, though, that the averse effects that high inebteness can have on the new ebt inflow (by causing a rise in the interest rates) are implicitly incorporate in Eqs. (6) an (8a) below. 3

6 able. ransactions matrix. rivate sector Current Capital Government sector Foreign sector otal Government expenitures +G -G 0 axes Exports +X -X 0 Imports -M +M 0 Domestic investment +I -I 0 rivate sector's saving -S +S 0 Interest -rd -rd G -rd F 0 Change in net ebt D D G D F 0 otal articular attention shoul be pai to ientity (8). his ientity reflects Goley s financial balances approach. It states that the sum of the balances of the three sectors of the economy is equal to zero. his ientity has been wiely use by Goley himself an other economists to analyse the macroeconomic evelopments in various countries (see e.g. Goley, 995, 999, 003, 005; Goley et al., 007; Zezza, 009; Sawyer, 0; recht et al., 0; Wolf, 0). he important implication of this ientity is that the balance of one sector cannot improve without a eterioration in the balance of at least one of the other two sectors. herefore, if, for example, the government sector esires to ecrease its eficit to a specific level then the private sector an/or the foreign sector shoul be willing to accept a eterioration of their balances in an accurately offsetting manner. Otherwise, the intene ecline in eficit cannot be attaine. Moreover, since most components of the financial balances are also components of the aggregate eman, any attempt of the sectors to improve their balances may lea to lower output if the other sectors o not esire to experience lower balances. A istinguishing feature of the financial balances approach is the consoliation of househols, firms an banks into one single private sector. his implies that in our moel the transactions between househols, firms an banks are not taken explicitly into consieration. Moreover, the assets an the liabilities of the private subsectors that are counterparts of the assets an liabilities of other private subsectors are nette out in the estimation of the net private ebt. he net private ebt refers, therefore, solely to the net liabilities of the private sector that are net assets of the government an the foreign sector. Although this consoliation is a great simplification with various limitations (see Dos Santos an Maceo e Silva, 00 an Martin, 0 for a iscussion), it has prove quite useful in Goley s projections an other empirical analyses that focus on the interaction between private sector s behaviour, fiscal policy an foreign balance. Moreover, it serves the purposes of our simple skeleton that intens to capture the ynamics of a national macroeconomy by using a high-level aggregation. We have that: For an analysis of this approach see Goley an Cripps (983), Goley (995), Zezza (009), Dos Santos an Maceo e Silva (00), Kregel (0), recht et al. (0) an Wray (0).

7 p Y G Y D Y DG Y (9) g (0) () G () where p is private sector s propensity spen out of its income, 5 g is the government expenitures-to-output ratio, is the net private ebt-to-income ratio an G is the net government ebt-to-output ratio. Eqs. (3) an () imply that the taxes an the imports are proportional to the output of the economy (, m 0). Y (3) M my () Eq. (5) shows that, for simplicity, the exports grow at an exogenously given rate, g X. his rate relies on factors such as the economy s structural competiveness an the income of the foreign sector, which are taken as given. (5) X g X X Goley argue that the private sector targets in the long run a specific stock of net financial assets as a proportion of its isposable income (a stock-flow norm). He also postulate a formula which states that the balance of the private sector ajusts in orer for this esire stock to be attaine (see Goley an Cripps, 983; Goley, 999; Goley an Lavoie, 007). 6 In our moel this iea is capture by the following equation: p (6) In Eq. (6) expresses the target net private ebt-to-income ratio. It is eeme that this target in not only set by the private sector itself. It is also set by the government an, most importantly, by the foreign sector that are potentially leners of the private sector. For instance, it may capture the willingness of foreign investors to len to the private sector of a national economy (househols, firms or banks). herefore, this target is affecte by the ecisions of both borrowers an leners. 7 5 For simplicity, in Eqs. (9) an () we use the private sector s income after taxes, but before the interest payments. 6 See also Martin (0) an Shaikh (0). 7 Recall that the private sector can be either a net ebtor (when the net private ebt is positive) or a net creitor (when the net private ebt is negative). 5

8 Formula (6) implies that the private sector s propensity to spen increases (ecreases) when the actual net ebt ratio is lower (higher) than the targete one (i.e. 0). A change in the propensity to spen may express the ecisions of both the private sector an its leners. Importantly, although a change in the propensity to spen is the primary means through which the private sector can affect its net inebteness, it may not have the esire outcomes. As will become clear below, the ecision for spening affects the output of the economy an, therefore, has feeback effects on the net private ebt-toincome ratio. Eq. (6) can capture changes in private expenitures cause by capital inflows an capital outflows. For example, the inequality may reflect perios in which the net ebt of the private sector is consiere by foreign leners as sufficiently small. In such perios the existence of a low perceive lener s risk inuces higher capital inflows that lea to higher private expenitures relative to income. On the other han, the inequality may capture perios of capital outflows in which the lener s risk is perceive to be high. Interestingly, formula (6) shares some similarities with the recent macroeconomic analysis of Koo (03) about what he calls a balance sheet recession. In this analysis Koo makes a istinction between perios in which the private sector maximises profits ( Yang phases ) an perios in which the private sector minimises its ebt ( Yin phases ). In our moel, the reuction in the private sector s propensity to spen when resembles a Yin phase à la Koo. Similarities also exist between Eq. (6) an the formalisation in the moel of Eggertsson an Krugman (0) in which it is assume that borrowers-leners relationships are riven by a ebt limit. Although Goley postulate that the stock-flow norm is exogenous, it is clear that such an assumption can be consiere satisfactory only as a first approximation. In reality, economic units esire margins of safety, which etermine the stock-flow norm, change enogenously uring the economic cycle. Minsky (008, pp. 93, 09) argue that uring perios of expansion when the outstaning ebts are service without significant problems the esire margins of safety of borrowers an leners ecline. his happens because the recent goo performance of the economy an the favourable creit history inuce economic units to accept financial structures that were previously assesse as risky. he opposite hols in perios in which the economic performance an creit history are not favourable. 8 his enogenous responsiveness of the perceptions of risk to the economic fluctuations is in line with the empirical features of financial cycles (see orio, 03). Although Minsky s arguments primarily refer to the behaviour of firms an banks, they can be applie to any borrower-lener relationship an, therefore, to the financial relationships between the private sector of a national economy an its leners/borrowers (the government an the foreign sector). herefore, rawing on the above-mentione perspectives, we postulate the following specification: g g (7) Y Y0 8 See also Kregel (997), ymoigne (009), Vercelli (0) an Lavoie (0, p. 6). 6

9 Eq. (7) states that when economic growth ( g Y ) is higher (lower) than a benchmark growth rate ( g Y 0 ), the target net ebt-to-income ratio of the private sector increases (ecreases); note that 0.9 y enogenising the target net private ebt-to-income ratio, Eq. (7) can be viewe as a Minskyan extension of Goley s exogenous stock-flow norm for the private sector. In Section it will be shown that this enogeneity can increase the amplitue of the cycles an can be conucive to higher instability. Although our moel abstracts from asset price inflation, it shoul be pointe out that the postulate impact of economic growth on the target net ebt-to-income ratio of the private sector is compatible with the role that asset prices play in Minskyan ynamics. 0 Higher economic growth can inuce househols to take more risky positions by increasing the proportion of their assets that is hel in the form of equities or by increasing their investment in the housing market. he resulting rise in asset prices can lea to a higher target ebt ratio either irectly (by improving the state of confience) or inirectly (by affecting positively various economic variables, such as consumption, investment, the profitability of firms an the value of collateral). herefore, although our moel oes not explicitly incorporate asset price inflation, Eq. (7) can implicitly capture the estabilising role of asset prices, which is important in Minsky s analyses. However, economic growth is not the only river of the target net ebt ratio in our moel. Accoring to Eq. (7), this target is also partially attracte by a benchmark net ebt ratio,, which epens on eep economic, institutional an social factors (e.g. the egree of financialisation, the egree of openness of the omestic financial system, the prevailing consumption an investment norms, the society s perception of the role of ebt, etc.); note that 0. When 0, the private sector has a net ebtor benchmark position; when 0, it has a net creitor benchmark position. he benchmark net ebt ratio is expecte to change over a long-run horizon. For example, over the 990s an the 000s many avance economies experience a sustaine reuction in the balance of their private sector (see, for example, ymoigne an Wray, 0, pp. 07-). It is very likely that this reuction partially reflecte eep economic, institutional an social economic changes that took place over this perio, such as financial eregulation, financial globalisation an the graual prevalence of norms that were conucive to higher levels of consumption an ebt. hese funamental changes probably move the private sector in these countries towars a net ebtor benchmark position. Overall, accoring to Eq. (7), the target net ebt-to-income ratio epens on (a) cyclical changes in economic growth an (b) eep long-run economic, institutional an social factors. Following the istinction that alley (0) has mae between Minsky basic cycle an Minsky super cycle, it coul be argue that the cyclical changes effects are relate to the Minsky basic cycle, while the eep long-run factors have to o with the Minsky super cycle which has a longer time horizon. In this paper, is eeme constant 9 For a similar formulation that focuses on the enogeneity of the esire margins of safety of firms an banks see Nikolaii (0). 0 For recent Minskyan moels that incorporate explicitly this role see Ryoo (00, 03a), Chiarella an Di Guilmi (0) an assarella (0). 7

10 an, therefore, emphasis is place on the ynamics linke with the basic Minsky cycle. However, future extension of this moel coul allow to change enogenously permitting thereby the combination of the Minsky basic cycle with the Minsky super cycle. In our moel the ynamic behaviour of g is etermine by fiscal rules. Fiscal rules have been wiely aopte over the past two ecaes or so. hese rules impose constraints on fiscal aggregates, such as government ebt an eficit (see IMF, 009; Schaechter et al., 0; Chortareas, 03). We first consier a simple Maastricht-type rule which states that government expenitures (relative to output) ecline when the net government ebt-tooutput ratio is higher than a specific target ( G ). Formally, this rule is written as follows: g G G (8a) where 0. Note that the essence of this rule woul not change if the tax rate was use as a tool instea of the government expenitures. We then consier an alternative fiscal rule that eparts from the conventional approach since it places no limits on any specific fiscal aggregate. On the contrary, its rationale is that fiscal policy shoul stabilise the macroeconomy by increasing (ecreasing) government expenitures when the private sector exerts contractionary (expansionary) pressures as a result of its attempts to reuce (increase) its inebteness. Formally: g (8b) where 0. Eq. (8b) is consistent with the perceptions of both Goley an Minsky who emphasise that the government shoul intervene to offset fluctuations in economic activity that stem from the inherently unstable behaviour of the private sector. We thus call Eq. (8b) a Goley-Minsky fiscal rule. Combining Eqs. (), (9), (0), (3) an (), we get: gy X my Y py (9) Solving the above equation for Y, yiels: X Y m p g (0) For a Minsky moel that formalises these two cycles in a single framework see Ryoo (00). His moel relies on a Harroian perspective an concentrates on the interactions between househols, firms an commercial banks. For a fiscal rule that relies on a similar rationale see Nikolaii (0). Interestingly, the Goley-Minsky fiscal rule is in line with Koo s (03) proposition that uring Yin phases fiscal expansion is necessary in orer to avoi eep recessions. 8

11 he enominator in Eq. (0) must be positive (i.e. m p( ) g 0 ) to ensure goos market stability. Differentiating Eq. (0) with respect to time an iviing through by Y, gives the growth rate of the economy: Y g Y Y g X p m g p g () Using Eqs. (), (), (9), (), (3) an (), we get: D Y p r g Y Y Y () Employing Eqs. (5), (0), (), (3) an (), we get: G g r g (3) G D Y G Y Y Y G Eqs. () an (3), in conjunction with (), show that when the private an the government sector ecie to spen less (relative to income) the impact on their net ebtto-income ratios epens on whether they are net ebtors or net creitors. When the net ebt is positive, there are two counteracting effects. On the one han, the ecline in expenitures (i.e. in p an g) tens to reuce the net ebt-to-income ratios. We call this the spening effect. On the other han, such a ecline reuces g Y which in turn places upwar pressures on the positive net ebt-to-income ratios by reucing their enominator. We call this the growth effect. However, when the net ebt is negative, these two effects are mutually reinforcing. he reason is that a lower g Y reuces the enominator in the negative net ebt-to-income ratios making them more negative. Combining Eqs. ()-(6) an (9)-(), we can write the balances of the three sectors as a proportion of output: b ( p r )( ) Y () G bg g rg Y (5) F X bf m r G Y Y (6) Note that b bg bf 0. 3 Eqs. (6), (7), (8), () an (3) constitute a 5D ynamic system, which is reprouce below for convenience: 3 his can be easily shown by substituting the ratio X/Y from Eq. (0) into Eq. (6) 9

12 p r g Y () p (6) gy gy 0 (7) G g r g Y (3) G g G G (8a) (8b) g he system has a unique steay state. he steay-state values (enote by the subscript 0) for the state variables of the system are: 0 0 G0 G p g 0 0 g g X X r r G gyo g X Note that b 0 g X ( ) b g G0 b F0 X G an g [ ( ) X G are parameters. At the steay state we also have that: G ] rior to proceeing to the analysis of the ynamic macro system an its subsystems it is useful first to briefly examine the law of motion of private an government net inebteness when economic growth is exogenous. his can be one by assuming that p, g an are at their steay-state values, an thereby p g 0. Eq. (0) suggest that in this case economic growth is equal to the growth rate of exports (i.e. gy g X ). Uner these conitions, from Eqs. () an (3) we get: G G r g X r g X herefore, the net private ebt-to-income ratio an the net government ebt-tooutput ratio are stable when g X r. his implies that when economic activity is exogenous, the stability of the net ebt ratios relies on the export performance of the economy an the stance of monetary policy. he lower the interest rate set by monetary When Eq. (8b) is utilise instea of (8a), the whole macro system is inee a D system since G has no feeback effects on the other state variables. 0

13 authorities an the higher the export growth of the national macroeconomy, the higher the likelihoo that the ebt ratios will stabilise. In the ynamic analysis an the simulations that follow it will be assume that g X r. his will allow us to confine our attention to the estabilising forces that stem from the Goleyan an Minskyan mechanisms escribe above. he parameter values use in the simulation exercises an their justification are reporte in Appenix A he D subsystem: interaction between private sector s propensity to spen an net private inebteness his section analyses the D subsystem consisting of Eqs. (6) an (). Our aim is to examine the ynamic interaction between private sector s propensity to spen an net private inebteness when the target net private ebt-to-income ratio an government expenitures are exogenous. Hence, g an are kept at their steay-state values (i.e. g g 0 an ); G is not necessary to be kept at its steay-state value since it oes not fee back into the law of motion of an p. he following proposition hols. roposition. Consier the system consisting of Eqs. (6) an (). (a) If 0, the steay state of the system is locally stable. (b) If 0, there exists a parameter value 0 that satisfies the following properties: (i) the steay state of the system is locally stable for all (0, ). (ii) the steay state of the system is locally unstable for all (, ). (iii) the system unergoes a Hopf bifurcation at (in other wors, there exists a limit cycle aroun the steay state for some range of the parameter value which is sufficiently close to ). roof. See Appenix. roposition suggests that when the private sector has a net creitor benchmark position, Eq. (6) oes not prouce estabilising forces: the stabilising impact of a change in the propensity to spen is reinforce by the associate growth effect (see Section ). 6 On the contrary, when the private sector has a net ebtor benchmark position, the likelihoo that the system is unstable is higher the higher is the responsiveness of the propensity to spen to the ivergence between the actual an the target net private inebteness. he rationale behin this result is straightforwar: when the net private ebt ratio is higher (lower) than the target one, any attempt of the private sector to reuce (increase) its inebteness by reucing (raising) the propensity to spen has an averse (favourable) impact on economic growth. For sufficiently high values of, this growth effect 5 he MALA coes for the simulations of this paper raw on Nikolaii (0). 6 Stability also arises in the marginal case in which the private sector is in a zero net ebt benchmark position (i.e. 0 ).

14 ominates the spening effect leaing to instability. It is interesting to note that, as shown in Appenix, becomes higher when the interest rate eclines or the growth rate of exports increases. his implies that aequate monetary an trae policy can, until some limit, prevent the estabilising forces that stem from the behaviour of the private sector Figure presents the limit cycle that is generate when an 0. Suppose that the economy is initially in phase I. Since, the private sector increases its propensity to spen, proucing higher than steay-state growth. Simultaneously, net private inebteness eclines because the propensity to spen is not high enough. hase I can be interprete as a phase of recovery. As the net private ebt-to-income ratio eclines, p continues to increase an eventually the economy enters phase II in which the propensity to spen is high enough to generate a rise in inebteness. In this phase the economy continues to exhibit a high growth which, however, is accompanie by higher fragility. At some point, becomes higher than. At that point the inebteness of the private sector is conceive to be extremely high from the borrowers an/or leners perspective. his causes a reuction in private sector s propensity to spen. he economy enters a perio of stagnation (phase III) where low growth coexists with rising net inebteness. his rising inebteness reuces further the private sector s propensity to spen. Inebteness starts eclining only when the propensity to spen is low enough to outweigh the averse affects of low growth on the ebt ratio. When this happens, the economy enters a new phase (phase IV) where economic growth remains low (since is still higher than ). However, eclining inebteness sets the stage for the recovery that occurs when falls short of. When this happens, a new cycle begins. he cycles epicte in Fig. coul be characterise as Goley cycles, since they stem from private sector s attempt to achieve an exogenous stock-flow norm by moifying its propensity to spen. hese cycles are broaly in line with the empirical evience provie by Koo (03) accoring to which the saving behaviour of the private sector (motivate by the willingness to leverage or eleverage) was the principal river of expansions an contractions in many avance economies over the last ecaes.

15 Fig.. Limit cycle in the D subsystem; private sector in a net ebtor benchmark position ( 0 ); Fig. illustrates that when, the amplitue of the Goley cycles graually increases an the economy becomes unstable. 7 his happens because the propensity to spen respons strongly to eviations of the actual ebt ratio from its target value. herefore, the more the private sector an its leners attempt to put net private inebteness uner control, by ajusting private expenitures, the more the private ebt ratio estabilises. Arguably, this is a paraox of ebt result. Although the ajustment of the propensity to spen seems to be a sensible behaviour for the control of private inebteness, the resulting macroeconomic effects prevent the realisation of the esire inebteness. 8 7 For a very wie range of parameter values above, the iscriminant of the D subsystem (evaluate at the steay state) remains negative. Hence, the system exhibits oscillatory instability. 8 For the paraox of ebt in the case of firms see Steinl (976), Lavoie (995), Hein (007), assarella (0) an Ryoo (03b). 3

16 Fig.. Dynamic ajustments of the D subsystem to a 5% positive shock in the net private ebtto-income ratio; private sector in a net ebtor benchmark position ( 0 ); (a) Net private ebt-to-income ratio ( ) (b) rivate sector s propensity to spen ( p ) (c) arget net private ebt-to-income ratio ( ) () Fiscal variables (e) Growth rate ( g Y ) (f) Financial balances (in proportion of output)

17 Since g is constant in the D subsystem, net government inebteness is exclusively riven by the growth effect : when economic growth is high (low) enough the net government ebt-to-output ratio eclines (increases). As shown in Fig., this growth effect, which in the D subsystem is exclusively linke to the behaviour of the private sector, is sufficient to estabilise the net government ebt-to-output ratio. herefore, private sector s attempt to achieve its esire stock-flow norm can estabilise public inebteness espite the fact the government sector is passive. However, the constancy of g has as a result that the government financial balance oes not change significantly relative to the other two balances. Consequently, any eterioration or improvement in the financial balance of the private sector is almost entirely mirrore in the balance of the foreign sector.. he 3D subsystem: enogenising the targete net private inebteness We now allow the target net private ebt-to-income ratio to change enogenously accoring to Eq. (7); g is still kept at its steay-state value. he following proposition hols. roposition. Consier the system consisting of Eqs. (6), (7) an (). Suppose that the steay state of the subsystem of Eqs. (6) an () is stable. hen, there exists a parameter value 0 that satisfies the following properties: (i) the steay state of the system is locally stable for all (0, ). (ii) the steay state of the system is locally unstable for all (, ). (iii) the system unergoes a Hopf bifurcation at (in other wors, there exists a limit cycle aroun the steay state for some range of the parameter value which is sufficiently close to ). roof. See Appenix C. roposition suggests that the introuction of an enogenous change in the target net private ebt-to-income ratio can transform an otherwise stable system of an p into an unstable one. Instability arises when the responsiveness of the target net private ebt-to-income ratio to changes in economic growth is sufficiently high. Fig. 3 illustrates this in our simulations. 9 he figure refers to a private sector that has a net creitor benchmark position (similar results arise when a net ebtor benchmark position is consiere). It can be seen that the stability properties of the 3D subsystem change as increases: although the system is stable for low values of, it becomes unstable when is higher than For similar figures that show how changes in specific parameters affect the stability properties of ynamic systems, see Chiarella et al. (0) an Nikolaii (0). 5

18 Fig. 3. Dynamic ajustments of the 3D subsystem to a 5% positive shock in the net private ebtto-income ratio for varying values of ; private sector in a net creitor benchmark position ( 0 ). (a) Net private ebt-to-income ratio ( ) (b) rivate sector s propensity to spen ( p ) (c) arget net private ebt-to-income ratio ( ) () Net government ebt-to-output ratio ( G ) (e) Growth rate ( g ) Y (f) Government balance-to-output ratio ( b G ) 6

19 he unerlying mechanism can be explaine as follows. In perios of low growth, when net private inebteness is high, the eterioration in borrowers an leners expectations inuces them to target a lower net ebt ratio than the benchmark one ( ); recall that in the D subsystem. herefore, the ifference between the actual an the target ratio increases, proucing a greater ecline in the propensity to spen (an therefore in economic growth) compare to the D subsystem. Inversely, in perios of high growth, in which net private inebteness is low, the favourable expectations ue to the goo performance of the economy make the perceive risk lower. his leas to a higher target net ebt ratio than the benchmark one an, hence, to a more important rise in the propensity to spen. his results in higher economic growth. he greater fluctuations in both the propensity to spen an economic growth are reflecte in the law of motion of the net ebt ratio. If is sufficiently high, these fluctuations ultimately lea to instability. When 0. 56, the enogeneity of the target net private ebt-to-income ratio gives rise to a limit cycle. his is shown in Fig. where the magnitue of the estabilising forces, associate with the changes in euphoria an the perceptions of risk, is slightly lower than the magnitue that is necessary to prouce instability. he persistent cycles that are generate reveal that an otherwise stable Goley system can exhibit cyclical behaviour when it is combine with the Minskyan enogeneity of the stock-flow norm. Fig.. Limit cycle in the 3D subsystem; private sector in a net creitor benchmark position ( 0 ); he 5D system: introucing fiscal rules We now turn to examine how the stability of the macro system changes when fiscal rules are introuce. Fig. 5 illustrates the ynamic ajustment of the system when fiscal 7

20 authorities aopt a Maastricht-type fiscal rule (Eq. 8a). Fig. 6 shows the ynamic ajustments when a Goley-Minsky fiscal rule is implemente (Eq. 8b). In both simulation exercises the parameter values that refer to Eqs. (6), (7) an () are the same with those use in the simulations presente in Fig. 3. Moreover, the same range of values for has been employe an the case in which 0 has again been consiere. his allows us to specify how the ynamic ajustments of the macro system are moifie as a result of the introuction of fiscal rules. Consier first the Maastricht-type fiscal rule. Comparing the simulation results between Fig. 3 an Fig. 5, it can be observe that instability increases as a result of the implementation of this fiscal rule: first, for high values of the cycles become much more intense; secon, instability graually arises even for low values of. Intuitively, the following mechanisms are at play. Whenever economic growth is low (as a result of high net private inebteness) there is a tenency for the net government ebt-to-output ratio to increase. At some point uring the perio of low growth, the government ebt ratio becomes higher than G. o guarantee fiscal iscipline the government respons by reucing the expenitures-to-output ratio. his magnifies the contractionary effects that stem from the behaviour of the private sector: at a first place, economic growth is aversely affecte by the ecrease in g ; at a secon place, this aitional ecline in growth enhances the eterioration in the expectations reucing further ; other things equal, the ivergence between an increases with estabilising effects on growth, private expenitures an net private ebt. When the private sector has a net ebtor benchmark position there is an aitional channel through which the ifference between an increases: lower growth resulte from fiscal stance places upwar pressures on. he inverse mechanisms are at work when economic growth is high. his implies that the Maastricht-type fiscal rule increases the amplitue of ebt an economic cycles. 0 Importantly, the inuce instability refers not only to the private sector but also to the government sector. Fig. 5 illustrates that, as time passes, the Maastricht-type fiscal rule generates significant fluctuations in both the net government ebt-to-output ratio an the government balance (as a proportion of output). hese fluctuations are much more severe than those observe in Fig. 3. his result stems from the amplification of the economic cycles escribe above. herefore, in an economy in which the private expenitures respon to changes in net private inebteness an the targete inebteness is enogenous, the currently fashionable ebt brake rules o not only seem to estabilise the private sector but they may also be ineffective in ensuring fiscal pruence. Actually, a paraox of ebt result arises: the more the fiscal authorities attempt to target a specific government ebt ratio, by ajusting the government expenitures, the more this ratio estabilises. 0 For the estabilising effects of Maastricht-type fiscal rules see also Charpe et al. (0, ch. 9). he potential application of the paraox of ebt to the government sector has been briefly pointe out by Lavoie (0, p. 9). 8

21 Fig. 5. Dynamic ajustments of the 5D system to a 5% positive shock in the net private ebt-toincome ratio for varying values of ; private sector in a net creitor benchmark position ( 0 ); Maastricht-type fiscal rule. (a) Net private ebt-to-income ratio ( ) (b) rivate sector s propensity to spen ( p ) (c) arget net private ebt-to-income ratio ( ) () Net government ebt-to-output ratio ( G ) (e) Growth rate ( g Y ) (f) Government balance-to-output ratio ( b G ) 9

22 On the other han, the Goley-Minsky fiscal rule suggeste here is capable of stabilising both the private economy an the government sector for high values of. Fig. 6 inicates this. After some fluctuations in the initial perios (which are much less intense than the fluctuations in Fig. 5) all macro variables converge towars their steay-state values. Economically, this can be explaine as follows. When economic growth is low ue to high net private inebteness, the implementation of the Goley-Minsky fiscal rule prouces a rise in the government expenitures-to-output ratio. his has favourable effects on economic growth since it tens to reuce the ivergence between an by placing upwar pressures on. As allue to before, the reuction of this ivergence is conucive to stability. In high-growth phases the government expenitures-to-output ratio falls, slowing own the economic growth that is cause by the behaviour of the private sector. his again tens to reuce the ifference between an via the impact on. Consequently, fiscal policy reuces the amplitue of the cycles by suppressing the estabilising forces that stem from the enogenous changes in the esire margins of safety. his is also beneficial to the government sector itself. Since after some perios the fluctuations in economic growth ecline, the same happens to the government balance (as a proportion of output) an the net government ebt ratio. herefore, although at a first place there might be some averse evelopments in the fiscal performance, in the meium to the long run fiscal pruence is safeguare uner the Goley-Minsky fiscal rule. Interestingly enough, the simulations in Fig. 6 inicate that the Goley-Minsky fiscal rule is not stabilising when is close to zero, i.e. when the target net ebt ratio of the private sector oes not change enogenously (or changes only slightly). he reason is that Fig. 6 refers to a private sector that has a net creitor benchmark position. As mentione above, in this case a higher (lower) growth rate places upwar (ownwar) pressures on the net ebt ratio. Hence, the counter-cyclical effects of the Goley-Minsky fiscal rule are not conucive to stability. his, however, oes not hol when the private sector has a net ebtor benchmark position ( 0 ). In this case, the Goley-Minsky fiscal rule is stabilising even when is close to zero. 0

23 Fig. 6. Dynamic ajustments of the 5D system to a 5% positive shock in the net private ebt-toincome ratio for varying values of ; private sector in a net creitor benchmark position ( 0 ); Goley-Minsky fiscal rule. (a) Net private ebt-to-income ratio ( ) (b) rivate sector s propensity to spen ( p ) (c) arget net private ebt-to-income ratio ( ) () Net government ebt-to-output ratio ( G ) (e) Growth rate ( g Y ) (f) Government balance-to-output ratio ( b G )

24 Fig. 7 compares the relationship of the net private ebt ratio with the net government ebt ratio between an economy that implements the Maastricht-type rule an an economy in which government expenitures change accoring to the Goley-Minsky rule. It can be observe that the nature of the ebt cycles is very ifferent in these economies. In the economy that implements the Maastricht-type rule, there are perios in which both the private an the government net ebt ratio ecline. However, these ostensibly tranquil perios of eclining net inebteness are followe by perios where both the government an the private net ebt ratio increase. Contrariwise, uner the Goley-Minsky fiscal rule the relationship between the two ratios is always inverse (before the steay state is reache): in perios in which the net private ebt ratio eclines (increases), the net government ebt ratio increases (eclines). his is the consequence of the attempts of the fiscal authorities to mitigate the contractionary (expansionary) effects that stem for the esire of the private sector to reuce (increase) its inebteness. Fig. 7. Relationship between net private an net government inebteness in the 5D system; private sector in a net creitor benchmark position ( 0 ); (a) Maastricht-type fiscal rule b) Goley-Minsky fiscal rule 6. Conclusion his paper evelope a simple macroynamic moel that synthesises certain aspects of Goley s an Minsky s analytical frameworks. Using this moel, it was first shown that Goley ebt cycles are likely to arise as a result of the responsiveness of private sector s propensity to spen to ivergences between the actual an the target net private ebt ratio (the stock-flow norm). hese cycles are generate when the private sector has a net ebtor benchmark position. Instability emerges when the responsiveness of the propensity to spen is sufficiently high. his is a paraox of ebt result: the more the private sector an its leners attempt to put net private inebteness uner control, by ajusting private expenitures, the more the net private ebt ratio estabilises. his result is associate with the economic growth consequences of this ajustment which have estabilising feeback effects on net private inebteness. Furthermore, the analysis inicate that when the target net private ebt ratio is allowe to change enogenously via a Minsky mechanism an otherwise stable macro

25 system can be transforme into an unstable one. his happens, in particular, when the expectations that etermine the stock-flow norm are highly sensitive to the changes in economic performance. Goley-Minsky ebt cycles can also be generate. hese cycles are riven by the changes in euphoria an the perceptions of risk that affect Goley s stock-flow norm. Lastly, the paper examine the implications of the evelope framework for fiscal policy. he (e)stabilising effects of two ifferent fiscal rules were compare. he first rule is a Maastricht-type fiscal rule accoring to which the government expenitures-tooutput ratio ecreases (increases) when the net government ebt ratio is higher (lower) than a target level. he secon rule is a Goley-Minsky fiscal rule which states that fiscal authorities shoul increase (ecrease) government expenitures when the private sector attempts to ecrease (increase) its inebteness. Simulation analysis illustrate that the Maastricht-type fiscal rule is estabilsing while the Goley-Minsky fiscal rule is stabilising. he paraox of ebt appears to apply to the government sector: the more the fiscal authorities attempt to target a specific government ebt ratio, by ajusting the government expenitures, the more this ratio estabilises. Moreover, the two fiscal rules prouce ifferent results as far the relationship between the private an the government net ebt ratio is concerne. Uner the Maastricht-type fiscal rule, there are perios in which these ebt ratios move together proucing both tranquil times of ecreasing inebteness an turbulent times of increasing inebteness. Uner the Goley-Minsky fiscal rule, the net government ebt ratio always moves inversely with the net private ebt ratio an, therefore, there are no perios in which private an government net inebteness both increase. he moel of this paper an the results presente above bring to the fore the importance of Goley s an Minsky s perspectives on the inherent instability of the macroeconomy, the generation of ebt cycles an the stabilising role of fiscal policy. ase on these perspectives, the paper provie a new look at the ynamics of the moern macroeconomies in which the financial relationships between the private, the government an the foreign sector play a crucial role. An important line of research woul be to combine the Goley-Minsky cycles prouce here which focus on the role of sectoral ebt with the traitional Goowin cycles that concentrate on the intra-private sector relationships an the role of income istribution. For the presentation of the Goowin cycles an the combination of Goowin s moel with Minskyan ynamics see Keen (995), Sori an Vercelli (0) an Stockhammer an Michell (0). 3