| 17 | A model of fiscal and monetary policy |
| Thomas Michl |
Progressive economists agree that in a liquidity or deflation trap, fiscal stimulus is part of the solution, and perhaps even the only solution. There is some disagreement about the need for fiscal consolidation (active policy to stabilize or reduce the debt–income ratio) in the long run after the storm has passed, a position Paul Krugman (2011) succinctly summarizes as “jobs now, deficits later.” This paper attacks the problem using a model that has recognizably Keynesian components, but which has Classical characteristics as well, following an approach laid out in Foley and Michl (1999, ch. 10). The model descends with modification from a similar effort (Michl, 2008) devoted to analysis of inflation targeting. Since the basic model exhibits the paradox of thrift in the short run but not in the long run, it is not too inaccurate to describe it as “short-run Keynesian, long-run Classical.”
To keep the model focussed, we make several simplifying assumptions. First, we take the distribution of income between capitalists and workers to be parametric; we represent the profit share as π. Second, we assume workers do not save or pay taxes. These two assumptions let us abstract from the distributional consequences of public debt. Third, we assume that growth is constrained by capital, not labor, parallel to the Classical models with a conventional wage share described in Foley and Michl (1999, ch. 6). We briefly consider the implications of using fiscal policy to target employment. Fourth, we will argue that monetary policy devoted to stabilizing inflation creates a gravitational pull that guides utilization of capital, u, to a normal level (taken to be = 1) in the long run. Writing the output-capital ratio at normal utilization as ρ, these choices impose a long run rate of profit, π ρ, that does not reflect aggregate demand factors, even though the short run rate of profit, uπρ, does.
Among these assumptions the existence of a center of gravity at normal utilization has perhaps generated the most controversy among heterodox economists. The traditional argument for this assumption is that it is hard to see why capitalists would pursue accumulation in the presence of persistent unused capacity. There are three basic resolutions of this problem. First, some models essentially take capitalist saving to be the “primitive” and make investment adjust according to some economic, financial, or monetary mechanism, so that the system achieves long run growth at full or normal capacity utilization; Duménil and Lévy (1999) or Skott (2010) are examples. Second some models take investment (determined by profitability) to be primitive, and make the saving rate adjust, again achieving full capacity utilization; Rowthorn (1999) and Shaikh (2009) are examples. Third, some models regard the saving/investment distinction itself as primitive, and allow utilization to adjust through changing norms of desired utilization; Lavoie (1995) and Dutt (1997) are examples. The working premise in this paper is that one or both of the first two resolutions are closer to the truth. Yet it is hard on purely theoretical grounds to resolve these conflicts, and it is probably best just to admit that the alternative resolutions reflect underlying differences of Schumpeterian vision as much as anything else.
A central premise is that capitalist economies are subject to an inflation barrier. At high levels of utilization, the inflation process tends to generate a gradually rising inflation rate, and conversely at low levels, disinflation. Thus, we will write the Phillips-type curve as
|
(1) |
where p measures the inflation rate at time t, and u is normalized so that u = 1 represents normal or full capacity. Suppressing t subscripts and writing t + 1 as just +1 simplifies the notation. The system is assumed to be capable of producing above full capacity from a technological point of view, but at the cost of rising inflation. The coefficient a just measures the sensitivity of the change in inflation to slack. The lag structure is sometimes interpreted as an expression of adaptive inflation expectations or learning, but it can also reflect the inertial character of the inflation process. Modeling the inflation process relative to capacity utilization rather than the unemployment rate (which is undefined in this model) is not without precedent (Taylor, 2004).
A sensible way of containing the inflation process in models like this is to assume that the monetary authority actively pursues some inflation target, through a Taylor rule or reaction function for example. The Taylor rule is anchored by the natural or inflation-neutral rate of interest, r*. The monetary authority obeys this rule in setting the real rate of interest, r:
 |
(2) |
In the model we develop, the natural rate evolves along with the debt ratio. We will assume that the monetary authority knows the steady state value of the natural rate and uses that as its benchmark. We use “interest rate” and “real interest rate” interchangeably.
Since we are building a growth model, let us normalize everything we can by the capital stock K. (For simplicity, assume it does not depreciate.) The growth rate of capital will be represented by g. Government spending (normalized) is represented by γ, and policy is assumed to index spending to the capital stock. We will assume (and this is not an innocent assumption) that it consists entirely of consumption spending.
Taxes are lump-sum, and paid entirely by the capitalist class in our two-class world. But as a practical matter, the tax will be set as a percentage of the capital stock, τ, so that it is indexed to growth. This looks like a wealth tax, but each individual capitalist pays a fixed sum that is perceived, fallacy of composition style, to be independent of her own capital.
The government can also borrow and it uses one-period indexed bonds. Let b (for bonds) represent the debt–capital (B/K) ratio. The primary fiscal deficit is the difference between spending and taxing, or f = γ − τ. The actual fiscal deficit is ΔB/K = f + rb. The equation of motion for debt is:
 |
(3) |
Now it can be seen immediately that a steady state debt ratio, where b+1 = b, satisfies the following fiscal sustainability condition:
 |
(4) |
If growth exceeds the interest rate, a stable public debt ratio can coexist with a permanent primary fiscal deficit. Some economists (Galbraith, 2011) have argued on this basis that a primary fiscal deficit need not imply a future fiscal consolidation because the debt ratio will self-stabilize. We will borrow from Joan Robinson1 in spirit and refer to this happy state as a golden age.
On the other hand, if the interest rate exceeds the growth rate, a stable public debt ratio requires a primary fiscal surplus. We refer to this state as a leaden age. The denominator of equation (4) is sufficiently important to name it the growth—interest differential.
Since the debt ratio will affect aggregate demand, it will be necessary to include a fiscal policy reaction function in order to stabilize debt. We have two potential policy instruments (γ or τ), and we also have a potential objective or goal in the debt ratio (b), which could be chosen jointly with growth or other objectives. We’ve elected to set government spending, 
, using the tax parameter as instrument. We will also have to choose a debt ratio goal (
) to anchor the tax in the steady state; call that tax ratio τ*. Our fiscal reaction function is:
 |
(5) |
There is some loss of realism here, as we are forgoing the opportunity to model automatic stabilizers. We have solved the assignment problem by letting the monetary authority worry about managing the value of money and the fiscal authority focus on debt, which seems lifelike.
At the center of the model are an independent investment equation and a national saving equation. The underlying motivation for writing out an independent investment equation is that there is an implicit division of labor between capitalists in their capacity as owners of capital (who make saving decisions) and in their capacity as managers (who make investment decisions), and this presents a coordination problem. An alternative motivation might be that at a point in time, some capitalists are net savers and others are net investors. In either case, changes in the level of utilization coordinate the saving and investment decisions of the capitalists through the principle of effective demand: utilization changes to generate the right amount of saving to match the predetermined investment level.
To achieve a transparent, tractable model, we adopt a linear investment equation used in one form or another in many Kaleckian and Steindlian models:
 |
(6) |
Since g = I/K in equilibrium, this equation2 imposes restrictions on the relationship between the rates of interest and growth, as would any investment equation of general form g(r). From this equation, the condition for a golden age at normal utilization can be characterized as (d0 + d2)/(1 + d1) > r*.
It is worth commenting on the role that interest rates play in regulating investment, about which there is a long tradition of disputation. On the one hand, economists as diverse as Marx, Fisher, Keynes, and Minsky perceive the difference between the profit rate on capital and the interest rate on loans as central to the investment decision, whether because it measures the rate of “profit of enterprise” or the “marginal efficiency of investment (capital).” On the other hand are skeptics like Joan Robinson (1962, p. 43) who observes that a “model … in which monetary policy, via the interest rate, controls the level of investment, is a kind of day-dream that economists delight in.” Yet even she relies on monetary controls to bring some of her mythic metallic economies into line.
The most convincing theoretical argument for including the interest rate in the investment equation continues to be Kalecki’s (1937) principle of increasing risk, through which a lower interest rate relaxes the equity (finance) constraint on investment. The basic idea is that firms know the expected rate of profit on new investment, but as they expand their spending on illiquid capital goods, they are putting more of their own funds or the external funds of their creditors at risk. In this framework, the rate of investment will be determined when the cost of funding, equal to the rate of interest plus a risk or liquidity premium rising with investment, achieves equality with the expected rate of profit. A decrease in the interest rate will typically lead to a greater volume of investment spending, since it creates more room for a larger risk premium. In this framework, there is no need for an inverse relationship between the volume of investment and the return on investment which formed the basis for Keynes’s theory, heavily informed by his Marshallian interpretation of the law of diminishing returns. Indeed, Kalecki and others have subjected that theory to withering criticism for its internal inconsistencies and repetition of marginalist errors of logic.3
Yet Kalecki himself omitted the interest rate from his own investment equations. The reason had nothing to do with fundamental theory but was a “simplification … based on the fact that … the long-term rate of interest (as measured by yields of government bonds) does not show marked cyclical fluctuations” (Kalecki, 1969, p. 99). As Hicks (1989) has pointed out, Keynes, and by implication his contemporary Kalecki, were influenced by their experience with interest rates that up to that point had not exhibited much variability. There may be good reasons to question the limits of interest rate policy within a broadly Kaleckian framework, particularly related to the political and social determinants of investment stressed in Kalecki (1943), but there certainly is less basis in theory for omitting the interest rate from all consideration.
Given the self-imposed constraint that the normal rate of profit, π ρ, is unchanging, and that the system achieves normal utilization in the long run, the interest rate plays a key role here in that it allows for flexibility of the steady state growth rate.
National saving, S, is the sum of capitalist saving out of profits, at the rate s; capitalist saving out of net interest at the rate sb; and government saving, which is just the (negative of the) overall fiscal deficit, f + rb. The treatment of capitalist saving is somewhat eccentric. The idea is to preserve some flexibility, so that interest income and bond wealth are potentially treated differently from ordinary profit income or dividends. The saving rate, sb, could be interpreted to some extent as a measure of the degree of “Ricardian equivalence.” The idea is that while some capitalists may behave as if their planning horizons extend off to infinity, many or most do not.4 So we have:
 |
(7) |
Setting equations (7) and (6) equal and solving for utilization gives us an investment–saving equation,
 |
(8) |
where the multiplier, α is 1/c = 1/(sπρ−d2)and c > 0 is the well-known condition for stability of the multiplier process. Using the notation that ux = ∂u/∂x, we see immediately that ub, uγ > 0 and uτ < 0. But ur < 0 requires d1 > (1 − sb)b because an increase in the interest rate reduces investment demand but increases the demand for luxury consumption in what might be termed a Godley–Lavoie (2007) effect. In this model, public debt strengthens the rentier elements of the capitalist class who live off their bond holdings like characters in a Jane Austen novel. We will assume that the Godley–Lavoie effect does not predominate, so that a higher interest rate represents monetary tightening.
By setting u = 1, we can recover an equation for the natural rate of interest, r*:
 |
(9) |
Public debt tends to raise the natural rate of interest because it generates demand for luxury consumption goods among the rentier elements of the capitalist class. This does not mean that debt and deficits must increase the observed interest rate. As long as the system can expand in the short run, it is capable of generating the new saving required to finance a fiscal deficit through the Keynesian principle of effective demand. But once we impose the long-run restriction that utilization settles on its normal rate, this mechanism is no longer available.
Using equation (4), equation (6) specialized to u = 1, and equation (9) lets us solve for the steady state or long-run equilibrium values of the tax ratio, the growth rate, and the interest rate, or, using boldface to denote matrices, x′ = (τ*, g*, r*). Then the system can be written compactly as
x = y + Ax
where 
and
Solving this system (e.g., using Cramer’s rule or postmultiplying y by (I − A)−1), gives us the steady state values:
Note that the monetary and fiscal authorities are assumed to know the structure of the world well enough to solve these equations in order to set the benchmark real interest rate and the tax ratio.5
Since workers neither save nor pay taxes, their consumption (normalized by the capital stock) will be constant; call that cw, and call capitalist consumption (also normalized) ck.6 Because the system gravitates toward a long run with normal utilization (u = 1), we can write the basic income identity:
ρ = cw + ck + γ + g
This identity makes the growth effects of fiscal policy particularly transparent.
Recalling that our fiscal policy reaction function takes the tax parameter to be the instrument, we characterize the fiscal policy using (,). If we are interested in the pure effects of public debt, this policy ordering is appropriate.7 We can immediately see that public debt has an unambiguously negative effect on growth in this model in the long run.8 That is because it creates an incipient category of rentiers whose luxury consumption (ck) only adds to effective demand. When the system reaches the inflation barrier, there must be some offset to this demand, and that takes the form of a monetary response raising the interest rate sufficiently to reduce investment spending. Through this mechanism, public debt crowds-out private capital in the long run. But this need not happen at higher frequencies, and indeed, crowding-in is likely in the short run. The exception occurs, of course when the saving propensity out of interest achieves unity, in which case debt is neutral with respect to growth and interest.
Government consumption spending also has a negative effect on growth, which is consistent with some of the vast empirical literature on Barro equations (Barro and Sala-i-Martin, 2004, ch. 12). (One potential problem here is that this literature takes growth of per capita output rather than capital or output itself to be the object of interest.) Moreover, autonomous investment spending, d0, which is sometimes taken as a token of aggregate demand, has no effect on the long-run growth rate (although it does affect the long-run interest rate.).
We can also see that the model can be either in a golden age or a leaden age, with very different implications for fiscal policy. We will return to this theme in more detail but for now, let us write down the condition for g > r that defines the boundary between ages:
| Country | 1960s and 1970s | 1980s | 1990s | 2000s |
| g − r | ||||
| US | +2.8 | −2.2 | −1.4 | −0.3 |
| Germany | +0.8 | −3.1 | −2.4 | −2.2 |
| Advanced G-20 | n.a. | −2.7 | −3.1 | −0.8 |
| Emerging G-20 | n.a. | +9.0 | +8.9 | + 10.3 |
Sources: For US and Germany, Carlin and Soskice (2006, Table 6.1), except 2000s. All the rest, IMF (2010, Table A1.1).
The important point here is that fiscal policies that increase spending or the target debt ratio move the threshold to the right along the sπρ line. An economy that starts in a golden age can be relocated into a leaden age by policy. An increase in the animal spirits of managers represented by d0+d2 will also shift the threshold to the right, because it too increases the natural rate of interest. Finally, an increase in sπρ (which is the incipient laissez-faire growth rate) moves the economy toward the golden age region.
We now have enough structure to provide a preliminary answer to the question raised by the sustainability condition. Once the fiscal policy is chosen (i.e, any two of the trio (γ, τ, b)), so too is the rate of growth and the rate of interest in the steady state. Choosing a primary fiscal deficit pins down b, g, and r, for example; an exercise that takes the rates of growth, interest, and the fiscal deficit to be independent would be untenable in the world described by this model.
There is some evidence that neoliberal capitalism may have passed through the boundary from a golden age to a leaden age. The test for this would compare the steady state growth rate to the steady state real interest rate (on public debt). Absent an established method for measuring steady state values, the next best solution is to look at averages over time. Table 17.1 presents a brief sketch of the critical growth–interest differential (using growth of GDP rather than capital). Definitions of the decades differ slightly, so they are identified generically, with the 2000s ending in 2008.
For the advanced countries, it is clear that the neoliberal era does look leaden.9 For the emerging G-20 countries (basically, the BRICs — Brazil, Russia, India, China) it appears that golden age conditions prevail, even in the neoliberal era. This is consistent with the generalization that emerging G-20 countries carry lower debt ratios than the advanced countries, as well as their often high rates of accumulation. In 2006, for example, the emerging G-20 countries had a gross debt ratio of 36.9 per cent and a net debt ratio of 35.2 per cent; the advanced G-20 figures were 78.4 per cent and 50.3 per cent (IMF, 2010, Statistical Tables 8 and 9).
Using the steady state equations (which the monetary and fiscal authorities need), and equations (3)–(8), we can write down the four equations that describe the dynamics of the model. These form a system of autonomous, nonlinear difference equations:
 |
(10) |
Since the system is nonlinear, the first step in analyzing the stability properties is to obtain the Jacobian of equations (10), evaluated at the equilibrium. Adopting the notation that zj = ∂z(·)/∂j for z = p(·), b(·) and j = b, r, τ, we have
The stable space consists of all the (hm, hf) values that satisfy the condition that the roots (eigenvalues) of the Jacobian lie within the unit circle. This space identifies local asymptotic stability only; global stability of nonlinear systems can get tricky (Elaydi, 2005, ch. 5) and achieving any analytical results with a four-dimensional system presents a technical challenge. Below we demonstrate the possibility that the stable space can be nonempty with some numerical examples.
This model provides a natural environment for attacking the problem of stabilizing demand through debt financing. If the monetary authority remains committed to controlling inflation and the fiscal authority to hitting its target debt ratio, a temporary demand shock (say a one-period-only downward shift in the investment function, Δd0 < 0) will trigger a subsequent reflation, assuming the shock has not thrown the system into a deflation trap.10 The inflation dynamics process guarantees that a temporary decline in inflation requires a subsequent reflationary period with utilization above normal. Fiscal policy will initially tighten (because the debt ratio rises) but as the monetary stimulus raises the growth rate the debt ratio will decline and open up space for more fiscal stimulus (lower taxes) temporarily. The mathematics of the difference equations suggest that this shock will generate oscillations.
A severe shock (e.g., one which involves a deflation trap) might be attacked with a discretionary fiscal stimulus, such as a temporary increase in government spending financed by debt. This is the “jobs now” part of a stabilization plan referred to in the opening paragraph. (The implicit assumption here and in the next section is that the deflation or liquidity trap conditions are temporary, so that monetary policy returns to full strength in the recovery phase.)
If we impose the assumption that the system starts and remains in a golden age, we can use this occasion to consider an instructive thought experiment that sheds light on the possibility of growing out of a deficit. Let the fiscal authority be willing to switch off its reaction function (i.e., keep τ constant) and the monetary authority be willing to abandon its inflation target (i.e., keep r constant). The demand shock can be absorbed using a purely bond-financed increase in government spending (i.e., Δγ = −Δd0). The newly issued bonds then add to the public debt, but because growth exceeds the interest rate in a golden age, the debt ratio will eventually stabilize without further policy intervention. In this case, the utilization rate will remain elevated by the stimulus coming from the luxury consumption by rentier elements out of the (new) bond wealth. But because the capital stock is growing faster than public debt, this stimulus will be declining over time. Thus, inflation will rise as long as utilization is elevated, but will eventually stabilize at some level above the old target as the stimulus peters out.
It is worth drilling down further into this world. How are the bonds being serviced? Where do the resources come from to satisfy the rentiers’ demands for luxury consumption? The second question is easier: the system is producing real output by running the factories overtime. It can afford both more luxury consumption and higher accumulation because of the presumed elasticity of production (capacity barriers are not technologically binding).
To answer the first question, consider the bonds issued after the initial shock. They are being serviced by further borrowing. Each cohort of rentier-capitalists receives payments from the next cohort of capitalists, all intermediated by the state.11 This is a Ponzi game made sustainable by the rapid growth of capitalist wealth, revealing the underlying reason that this system demands a primary fiscal deficit to stabilize the debt ratio under golden age conditions.
Here we are encroaching on the nature of state fiat money. Recognizing that debt and (outside) money represent liabilities of the state, we need to ask what lies on the other side of the balance sheet. Foley (2003, p. 9) has argued that the value of fiat monies is an expression of the fiscal power of the state: “The ability of states (and central banks) to borrow rests on their holdings of offsetting assets. Every government has an asset in the tax liabilities of the public. … It is not true that a central bank note is a valueless token which is inconvertible into anything of value. As a liability of the government it can be used to pay taxes.”
Yet we know from experience (see Table 17.1) that governments are able to sustain positive growth–interest differentials, implying that Ponzi finance has been available to them ex post. For such financing to be available ex ante would require that capitalists are willing to lend to the state on the understanding that their bonds will be serviced out of further liabilities issued by the state. Such capitalists would be trusting their futures to the kindness of strangers, the implausibility of which for many economists rules out such a fiscal program ex ante. In addition, there is always the possibility that the structure of accumulation will shift unfavorably toward a leaden age, as indeed it seems to have done. It is clear from this angle that public debt acquires value from the contingent assets generated by the future taxing capacities of the state. The impression that permanent Ponzi finance may be possible is an artifact of the mechanical nature of the model, lacking deeper theoretical foundations. The argument here validates the conventional government intertemporal budget constraint equating the value of public debt with the present discounted value of future fiscal primary surpluses.12 Thus, the basic message of the fiscal sustainability condition (equation (4) above) that under leaden age conditions today’s fiscal deficits imply future primary fiscal surpluses would seem valid under general conditions. This is the “deficits later” part of a stabilization plan.
This need for a fiscal consolidation (“deficits later”) raises the question of its effects on growth. If the debt ratio is allowed to rise through a change in the debt target, we know that the long-run growth rate will decline. Even if the debt target is not altered, so that a temporary rise is followed by a return to the unchanged target ratio, the loss of capital accumulation caused by the shock (assuming it is offset by a debt-financed fiscal stimulus as above) will permanently lower the path of the capital stock even as it returns to its original trend growth rate. Yet the model suggests that fiscal consolidation can be part of a long-range plan to restore some desired level of capital and employment.
To illustrate the mechanisms, let us assume that the authorities want growth to keep up with the natural rate of population growth, n. In this case, fiscal policy needs to be adjusted so that the target debt ratio supports growth at the natural rate. From the solution for steady state growth, we can characterize the required debt target thus:13
Perhaps the system has accumulated a large reserve army of unemployed labor, and must now adjust to a population growth rate that is greater than the rate attached to the old debt target. In this case, the growth deficiency could be rectified by a fiscal consolidation that reduces the long-run debt ratio. Continuing to take the government spending ratio as constant, the fiscal consolidation at least initially requires a tax increase to slow the growth of debt. Let us assume the monetary authorities coordinate fully and switch to the new, lower natural interest rate target immediately. Thus, the transitional dynamics will involve a classic policy mix, with loose monetary policy partially compensating for tighter fiscal policy.
Initially, taxes need to go up to begin the process of fiscal consolidation, and without an extra measure of monetary stimulus the initial result will be a policy-induced decline in utilization. This seems to be the way real-life consolidations play out, even in small open economies in which monetary policy can offset the fiscal shock through both interest and exchange rate reductions (Guajardo, Leigh, and Pescatori, 2011). As the transition unfolds, the tax rate can be brought down toward its new steady state value.
During the transition dynamics going from low to higher growth, it is clear that the system will typically enjoy a period (or periods) of super-normal growth when it overshoots the natural rate of growth. This creates an opening for the policy makers to target the level of employment as well as its rate of growth. Using E to represent employment and L to represent the labor force (assumed to be a constant proportion of the population), we can write the employment rate, e = E/L, in terms of the capital–labor force ratio, κ = K/L, and the full-utilization capital–labor ratio, k:
Since the utilization rate gravitates toward u = 1, targeting the capital–labor force ratio is equivalent to targeting the employment rate, or achieving some desired path of employment. By applying discretion in their choice of policy reaction parameters (hf, hm, and 
), the authorities can influence the path of the capital–labor force ratio, κ. In doing so, they are exploiting the path dependent quality of this class of model.
We illustrate these properties in Figure 17.1 with some simulations in which we have chosen different values for . In one scenario, the target inflation rate is maintained at its original level, and fiscal consolidation proceeds with the amount of monetary accommodation provided by the Taylor rule. In the other, the monetary authority increases its inflation target modestly to provide additional accommodation. In these simulations, the target growth rate is increased, and the steady state debt ratio decreased (from 0.5 to 0.25).14
The path of κ is shown as an index number set to κ = 1 at t = 0. With the additional accommodation from an increased inflation target, the system gravitates toward a higher capital–labor force ratio. The more aggressive monetary support generates additional capital accumulation; the system enjoys a substantial period of super-normal growth. A less aggressive monetary policy results in less such super-normal growth.
There is a clear lesson here for confronting the challenges of Depression-level shocks. Full recovery requires a two-stage approach. Leveraged fiscal policies can be effective in restoring the level of demand and utilization in the first stage of recovery. But they leave behind a residual level of debt that will reduce the growth of capital and employment if allowed to grow pari passu, and this could create long-term problems in providing full employment to a growing population. In fact, restoring full utilization may not be sufficient to restore full employment of labor if the level of capital is insufficient, as is likely after a prolonged period of low investment during the depressed years. Full recovery requires a second stage of fiscal consolidation. The key to making this work is the use of the right monetary–fiscal policy mix. By calibrating the fiscal consolidation with monetary stimulus, it should be possible to generate a period of rapid accumulation that both reduces the debt ratio and increases the capital stock in relation to the labor force. This model, in a sense, underwrites the functional finance approach associated with Abba Lerner. The fact that we have eliminated, by assumption, any distributional complications
Figure 17.1 Debt consolidation with (solid line) and (dashed line). Using a more accommodating monetary policy to support debt consolidation results in an increase in the steady state employment rate, indexed by κ (bottom right panel). The debt consolidation reduces from 0.5 to 0.25. The parameter values are: n = 0.133, a = 1, s = 0.8, sb = 0.9, π = 0.3, ρ = 1, d0 = d1 = 0.1, d2 = 0.05, hf = 0.4, hm = 0.75, initial = 0.05, γ = 0.115.
across class lines demonstrates that such an approach can be implemented in principle without saddling workers with the burden of new taxes to service debt.
This model shows a way out for policy makers confronted by a major shock, and helps clarify the nature of the fiscal sustainability condition. The model can generate either a golden age in which the growth–interest differential is positive or a leaden age in which it is negative. There is some evidence that in the neoliberal era advanced capitalist countries have entered a leaden age. In either case, the model suggests that debt has a long-run negative effect on growth. It is also arguable that a temporary fiscal stimulus requires a future fiscal consolidation. Even in a golden age, when the formal possibility of growing out of a debt burden does present itself ex post in the model, that does not appear to be a convincing possibility ex ante.
Importantly, policy makers have the option of pursuing a long-run fiscal consolidation that lowers the debt ratio and raises the long-run growth rate. High growth during the transitional period even makes it possible for the authorities to guide the level of capital and employment toward some desired path. Whether this optimistic policy recommendation resonates with real economies depends on the validity of several key assumptions that give the policy makers more power in the model than they probably possess in life.
The author thanks J. W. Mason whose blog, The Slack Wire, provided some of the inspiration to write this chapter, and Peter Skott, who made several insightful comments that decisively shaped the results, while taking full responsibility for the views expressed and any errors of commission or omission.
1 To be precise, (Robinson, 1962, pp. 52–54) describes a growth path with full employment and mass prosperity as a golden age and a path with full employment achieved through “Malthusian misery” as a leaden age.
2 A more complete investment equation in this tradition would include the profit share, following Bhaduri and Marglin (1990). Thus, the term d0 + d2 captures the effect of the normal rate of profit (evaluated at u = 1) on accumulation. But it would be a mistake to ignore the voluminous literature that tries to get to grips with the investment equation. For recent critiques of the Kalecki–Steindl approach from Harrodian and Classical perspectives, see Skott (2010) and Shaikh (2009).
3 Sardoni (1987) provides a discussion with references to the relevant literature. We might also note the similarity between Kalecki’s treatment of investment and that of Minsky (1975), who uses Keynes’s “borrower’s risk” and “lender’s risk” in much the same fashion. In both frameworks, the investment function can be volatile, given the underlying instability of profit expectations and attitudes toward risk and liquidity. A full account of Kalecki’s views on the theory of investment can be found in Sawyer (1985).
4 If we must have some microeconomic foundation for capitalist saving, there are other ways to model the bequest motive besides the hypothesis of intergenerational altruism that underpins modern Barro–Ricardo equivalence, such as the hypothesis that capitalists derive utility from their end-of-life wealth for its own sake as in Michl (2009). In the latter case, their planning horizon would be finite.
5 If the monetary authority chooses the wrong value for the natural rate of interest, say 
, they will still wind up stabilizing the system through the Taylor principle but inflation will miss the target by:
Similar considerations apply to the fiscal authority’s choice of 
and the steady state debt ratio.
6 For a model that adopts the polar opposite assumption that workers pay all the tax so that debt works through cw, see Skott (2001).
7 An alternative ordering would take the tax as given and let spending be the policy instrument. In this case, a change in the debt target would involve changes in spending that would muddy the water.
8 There is surprisingly little empirical literature on debt and long-run growth. The best evidence for a negative relationship is probably Kumar and Woo (2010) which focusses on the effect of the debt ratio on subsequent growth (in per capita output), thus attenuating the problem of endogeneity.
9 More rigorous treatments show a similar pattern; see de Carvalho, Proano, and Taylor (2010, Figure 6) or Abbas, Belhocine, El-Ganainy, and Horton (2011). An alternative interpretation might emphasize the prevalence of financial repression (e.g., Regulation Q controls on bank interest rates) in the earlier period.
10 With a given inflation target anchoring inflation expectations, the model defines the condition for a deflation trap in which the natural rate of interest falls below the minimum rate of interest at the zero nominal interest rate bound, min r = −pe, which is:
In this case, an increase in the inflation target, if it were credible, could escape the deflation trap. Otherwise, fiscal policy remains the only solution to chronic stagnation. Note that these two boundary conditions are ordered so that as the saving rate increases, the system progresses from a leaden to a golden age and then to a deflation trap. Thus, being in a golden age is not necessarily desirable.
11 This point can be visualized more clearly by assuming there are no debts to begin with, no taxes are ever collected, and aside from the temporary stimulus, no government spending.
12 See Foley and Michl (1999, pp. 226–229) for a derivation and an explanation of the role of the no-Ponzi-game condition.
13 This expression brings out an important limitation on fiscal policy. Only if the laissez-faire rate of growth (sπρ) exceeds the natural rate of growth can the fiscal authority target growth using public debt as an instrument. If the laissez-faire growth rate is below the natural growth rate, the state must become a creditor (b < 0), using its fiscal authority to finance capital accumulation and holding net claims on the private sector. We will assume that the level of government consumption spending does not prevent the system from achieving the natural rate of growth with positive b, or that sπρ > sbγ + n.
14 The numerical examples are locally stable, based on the condition that the characteristic roots of the Jacobian, J, all lie within the unit circle. The eigenvalues here come in pairs of complex conjugates that are independent of the choice of inflation target. With = 0.5, the dominant eigenvalue is 0.851 ± 0.307i, while with , the dominant eigenvalue is 0.753 ± 0.331i. See the caption of Figure 17.1 for parameter values.
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