Flexibility in an inflation targeting regime under demand shocks:a model with endogenous potential output from the demand side

Ricardo Ramalhete Moreira1

Abstract: In the spirit of Sawyer (2002), Lavoie (2006) and Fontana & Palacio-Vera (2007), among others, this article aims to demonstrate that, under the hypothesis of an endogenous potential output from the demand side, there are social losses that are not analyzed by conventional inflation targeting models when central banks attack demand shocks. If there is an endogenous potential output from the demand side, central banks should take it into account when setting their strategy and monetary policy rule. By doing so, central banks attain higher economic performance, in comparison with central banks that do not implement the required changes in their instrument rule.

Key-words: inflation targeting; demand shocks; endogenous potential output.

JEL: E17; E52.

1 - Introduction

The conventional literature about the Inflation Targeting regime presents some motives for more flexible arrangements. A flexible regime could be justified, for example, under supply shocks (Ball, 1999a). In such a case, the reduction of the inflation rate implies a decreasing output level, or, in other words, reductions of inflation volatility imply increase of output volatility. There is a trade-off between these two variables (Clarida, Galí & Gertler, 1999). Hence, central banks have reasons to accommodate supply shocks, either partially or integrally, in order to maintain output and employment levels.

An additional reason central banks have for becoming a more flexible IT regime is interest rate smoothing, or the public preference for making interest rates more stable. This kind of preference occurs when the public is concerned about financial market health (Blinder, 2006). In cases in which financial institutions present some type of fragility, interest rate volatility may create a bankruptcy cumulative process. In such a context, central banks may prefer to accommodate inflationary shocks so as to avoid interest movements and financial disasters.

Another kind of motive in favor of IT flexibility is public preference for exchange rate stability. Interest rate movements have direct effects on exchange rate levels: the more volatile the former, the more volatile the latter, in a flexible exchange regime. Given the high velocity by which interest rate affects exchange rate, and the strong correlation between the latter and the inflation rate, if the IT regime is a strict or rigid regime, central banks are forced to counter inflationary processes affecting exchange rates as quickly as possible, creating exchange rate volatility. On the other hand, exchange rate volatility may complicate external trade and cause problems, especially in emerging economies, in which exports have a heavy impact on GDP, or when domestic agents have debts denominated in foreign currencies. Hence, as a means of avoiding exchange

1 Professor Adjunto no Departamento de Economia da UFES. Doutor em Economia pela UFRJ. ramalhete.s@gmail.com

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rate volatility in open economies, central banks look to accommodate part of the inflationary shocks, and by doing so minimize social losses (Ball, 1999b).

Additionally, the literature also presents arguments for the flexibility of an IT regime as a consequence of structural uncertainty (Brainard, 1969; Blinder, 2006). Uncertainty means that central banks have problems making forecasts about the future effects of current movements in interest rates. This happens because central banks simply do not know how economies work in an exact measure. In other words, there is uncertainty as to the parameters that define the direction and velocity of causal relationships. In a structural uncertainty environment, monetary authority prefers to be gradualist, adjusting its instrument with lower magnitude if compared with the suggestion of “optimal rules”.

In all of these cases above, the literature agrees with the notion of a flexible IT regime, and its corresponding adjusted instrument rule, as well as with additional mechanisms of decision making. However, it remains a special case to which the conventional literature sees no reason for flexibility: the case of demand shocks, or more specifically, the case in which the inflationary process is caused by output gaps. Clarida, Galí & Gertler (1999), Svensson (1997), Ball (1999a) and Bofinger, Mayer & Wollmershaeuser (2006) advocate an integral elimination of demand shock through interest rate responses. In their vision, demand shocks do not impose a trade-off between social objectives and monetary policy responses would eliminate inflation and output gaps simultaneously. There would be no social costs as a consequence of these responses.

This article is an attempt to reject the conventional theoretical result, according to which there is no social cost as an effect of a monetary policy that wholly (or partly) eliminates demand shocks. It will be demonstrated that this conventional conclusion requires the natural rate hypothesis: that is, the hypothesis by which potential output does not have a correlation with demand and current output fluctuations. It will be shown that, if the economic system operates under an endogenous potential output from the demand side, the IT regime should be flexible even in the case of demand shocks. A strict IT regime under such conditions imposes a social cost, translated by potential output losses in the long term. It will be assumed that endogenous potential output from the demand side is closer to the true structural model than the natural rate hypothesis.

Moreover, some preliminary words are convenient: in our view, following Svensson (2003), central banks in practice do not know the true structural model, and so they do not implement optimal instrument rules. Hence, in this article, we propose a structural model that will be considered an adequate approximation to the true structural model, borrowing Walsh’s (2003) words, under a policy process in which central banks have incomplete information about how the economic system actually works. Specifically, our short simulation will run two different ad hoc instrument rules. Although these two rules (a Taylor rule and an alternative rule) are not derived by optimization problems, they will be regarded as good approximations of how two distinct kinds of central bank implement their monetary policy. On the other hand, it is important to stress that this article is not an attempt to verify empirically or present eventual evidence concerning endogenous potential output by the demand side in the long term. This article intends specifically to test theoretically the effects of such an endogenous potential output by the demand side under demand

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shocks and their implications on inflation targeting regimes. Therefore, discussing the empirical appeal of this hypothesis is not under consideration, at least in this context. The general view of this article is compatible with recent kaleckian and post-keynesian works of Sawyer (2002), Lavoie (2006) and Fontana & Palacio-Vera (2007), among others, although specific assumptions or results may not be the same.

The article is structured in the following way: Section 2 presents a conventional inflation targeting model that will be used as a parameter for analysis of the main elements under consideration; Section 3 introduces the notion of endogenous potential output by the demand side in the model; Section 4 proposes a new instrument rule, rather than a strict Taylor rule, for central banks dealing with demand shocks; Section 5 stresses what may be called opportunity social cost and its implications for the social loss function behind monetary policy actions; Section 6 runs a small numeric simulation, and by doing so it compares economic performance under two alternative monetary policy regimes. Finally, the conclusions and references of the study are presented.

2 - A conventional Inflation Targeting model

The conventional models of inflation targeting follow a general pattern. The economic structure is translated by two stochastic dynamic equations, a dynamic IS curve and a Phillips curve, which are complemented by a monetary policy rule2 (Taylor, 1994; Ball, 1999a; Hall & Mankiw, 1994; Svensson, 1997; Bofinger, Mayer & Wollmershaeuser, 2006; Galí & Gertler, 20073). This type of model pays special attention to the lagged effects of monetary policy and the output and inflation inertia. The instrument rule or monetary policy rule is considered optimal when it minimizes a weighted sum of the inflation and output variances. Hence, the efficiency of a monetary policy rule could be measured by its effects on the volatility of those macroeconomic variables. Let the IS curve be:

(1) yt = m(yt-1) - n(rt-1) + t

The output gap (yt) depends on the lagged output gap (y t-1) and the lagged interest rate deviation (rt-1); there is a demand shock, , a stochastic process with zero mean and fixed variance (white noise process); all the parameters, m and n, are positives. Additionally, let us consider the output gap as a deviation of the effective output (Y t) in relation to potential output (Yp): yt = Yt - Yt

p4. In the conventional model, as will be better explained at a later point, potential output is constant in time, according to the natural rate hypothesis. It is easy to note that the interest rate affects output only with a

2 Some authors prefer to specify these equations in a forward-looking form, proposing a fundamental role to the public’s expectations which, in their turn, are constructed by information optimization (rational expectations) (in the same way as Clarida, Galí & Gertler, 1999). This article, on the other hand, adopts a backward-looking specification of those equations, by proposing more importance to the inertia effects on inflation and output.

3 Obviously, there are some differences with regard to specification among those works, but three structural equations may be understood as an essence of this family of models.

4 In the same way, let rt-1 be the deviation of the real interest rate (Rt-1) vis-à-vis the natural interest rate (Rn).

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one-period lag, and that output presents inertia increasing with m. Now, let the Phillips curve be:

(2) t = (t-1) + (yt-1) + gt

Equation (2) establishes that inflation rate deviation (t) is determined by its value in t-1 period (t-1), by the lagged output gap (yt-1) and by the supply shock (gt), defined as a stochastic process with zero mean and fixed variance (white noise process); the parameters, and , are positive. Here, inflation deviation means a divergence between inflation rate ( t) and inflation target (n). Hence, t = t – n.

It is possible to note from equation (1) that the policy decision made in the current period affects the output gap with a one-period lag, and the output gap affects inflation deviations with a one-period lag, through equation (2); hence, there are two-period lags between the modification in the real interest rate set by the central bank, and its effects on the inflation rate. Therefore, when the central bank decides what should be the new real interest rate in the economy, the authorities take inflation rate expectations relative to t+1 as a given, because the last one is not affected by monetary policy made in current period (t period). These lag properties are especially focused in Ball (1999a) and Svensson (1997; 1999), and express the backward-looking nature5 of the model.

The monetary policy, in its turn, is described trough an instrument rule, a typical Taylor rule, such as:

(3) rt = z1t + z2 yt + u1t

Rule (3) establishes that the monetary authority reacts to inflation deviation and output gap by adjusting the real interest rate; z1 and z2 are positives; u1t a random control error (zero mean and constant variance). We do not consider inertia components (or smoothing interest rates) in the policy instrument, but it does not alter qualitatively the results of our work. The conventional literature also attains this kind of optimal instrument rule by means of a first order condition for the minimization of a social loss function (see Svensson, 1997; 1999). The central bank decides what the interest rate should be based on information regarding current values of inflation and output, as well as potential output and the inflation target.

Furthermore, instrument rule (3) is defined in real values, not in nominal values. Implicitly, it supposes that central bank adjusts nominal interest rate in the exact magnitude necessary for a desired variation in the real interest rate. This is the Taylor principle, according to which the central bank reacts to inflation deviations by adjusting real and not only nominal interest rates.

It is essential to understand that this type of analytical model takes the potential output as given. In other words, the model assumes the natural rate hypothesis. This means that positive or negative output gaps don’t have any effect on the potential output, because the latter is considered as a variable without correlation with money and demand. Hence, when there is a positive output gap, for example, there are also inflation pressures through Phillips curve (2), but there is not any variation in potential output. In such a context, monetary authority does not have any reason to accommodate output

5 Questions concerning the difference between backward-looking and forward-looking models will not be analyzed here. A good reference that makes the issue clear is Clarida, Galí & Gertler (1999).

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and inflation deviations, and interest rate responses do not cause any social loss. The central bank sees no motives for implementing a more flexible monetary policy under demand shocks.

If the central bank increases real interest rates, there will be a decrease in output gap (1) together with reductions in inflation deviation (2). The conventional literature about the inflation targeting regime attempts to show that there is not a trade-off between output and inflation variances under demand shocks, although it occurs under supply shocks. Clarida, Galí & Gertler (1999) pose the issue as follows: “That policy should offset demand shocks is transparent from the policy rule. Here the simple idea is that countering demand shocks pushes both output and inflation in the right direction. Demand shocks do not force a short run trade-off between output and inflation .” (Clarida, Galí & Gertler, 1999, pp. 1674,5). In the same way, “Thus, the model shows that there is no trade-off between output and inflation in a situation of a demand shock.” (Bofinger, Mayer & Wollmershauser, 2006, pp. 100).

If potential output has no correlation with money, demand and actual output variations, it is true that the central bank is able to push both output and inflation in the right direction, without any social cost as a consequence of such a policy. However, if the output gap has effects on potential output, such as those by means of induced private investments, interest rate responses may imply some social cost that is not regarded by the conventional literature6.

3 - Introducing endogenous potential output by the demand side

There is an alternative literature, and here it will be referred to as heterodox literature, that considers potential output as endogenous from the demand side. It is endogenous because private investments - induced by money, demand and current production levels - inevitably have an effect on capital accumulation and productive trends, so on potential output. Authors such as Kaldor (1956), Pasinetti (1962), Robinson (1962), Kalecki (1971) and Dutt (1990; 1994) present private investment as a function of variables such as profits/income ratio, degree of utilization of productive capacity and capital productivity.

In the same way, Serrano (1995) aims to demonstrate how demand has an expressive impact on real variables in the long term. It is just as important to note that there are potential effects of demand and current output levels on production capacity, effects considered in a specific tradition of economic thought, although this issue will not be under an exhaustive analysis here.

More recently, Rowthorn (1999) and Sawyer (2002) have introduced endogenous capital accumulation and a kind of an endogenous NAIRU (non accelerating inflation rate of unemployment), under post-keynesian and kaleckian ideas, and have considered the implications for the economic dynamic.

Rowthorn (op. cit.), motivated by a desire to understand why European unemployment had remained persistently high since the shocks of the 1970s, proposed a model in which investments are endogenised in a variety of ways, such as by real profit and interest rates. The main conclusion Rowthorn (op. cit.) attains is that “a permanent

6 This literature is called the New Neoclassical Synthesis (as pointed out Goodfriend & King, 1997).

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reduction in the real interest rate leads to only a temporary acceleration in economic growth but a permanent fall in unemployment.” (Rowthorn, 1999, pp. 423), breaking off with mainstream results.

In the same line, Sawyer (2002) focuses on the role of aggregate demand on the determination of the dynamic of capital stock and employment within a context of some form of NAIRU. By assuming non mainstream assumptions, Sawyer (op. cit.) argues that there are long run relationships between inflation and unemployment, and between this last one and the capital accumulation. The author wants to demonstrate that a reduction in the NAIRU may be achieved with a sustained increase in the level of aggregate demand to stimulate investment; and that the ideas according to which a reduction of inflation (through control of the monetary policy instruments) can be achieved without any detriment to the real side of an economy and that there is no long run trade off between inflation and unemployment are both wrong.

Furthermore, Lavoie (2006) and Fontana & Palacio-Vera (2007), among others, represent interesting contributions to the theme of the endogenous potential output or endogenous natural rate of growth processes. Lavoie (2006), particularly, presents an amendment to the new consensus or mainstream model by taking into account that “The natural rate of growth is ultimately endogenous to the demand-determined actual rate of growth” (Setterfield, 2002, pp. 5).

Lavoie (2006) argues that, as León-Lesdema and Thirlwall (2002) have shown in an empirical study for fifteen developed countries over the post-war period, when actual demand growth diverges from the natural rate of growth it is created a change in the natural rate that will make its value converging to the actual demand growth.

This idea generates “the possibility of multiple equilibria, that make long-run supply forces dependent on short run disequilibrium adjustment paths induced by effective demand.” (Lavoie, 2006, pp. 177). This is compatible with the assumption posed by León-Lesdema and Thirlwall: “growth creates its own resources in the form of increased labour force availability and higher productivity of the labour force” (León Lesdema and Thirlwall, 2002, pp. 452).

Moreover, Fontana & Palacio-Vera (2007) study the implications of alternative assumptions, such as unit root processes, hysteretic systems and multiple equilibria, along with demand-led growth models, for the economic dynamic and monetary policy strategy; the results found by the authors show that “monetary policy does have long-run effects on output and employment” (Fontana & Palacio-Vera, op. cit., pp. 294) and “the demand side of the market does matter in both the short and the long run” (idem); the authors suggested a “‘flexible’ opportunistic approach which not only seeks to stabilize output in the short run and achieve price stability in the long run but that also makes an active contribution to the growth of output and employment” (idem).

In its turn, here, the main theoretical question is: if an endogenous potential output from the demand side is assumed, what are the implications for the inflation targeting regime, with respect to instrument rules, demand shocks and social costs? Initially, it is necessary to introduce the endogenous potential output in the conventional model expressed through equations (1) - (3). Such an introduction may be seen as the

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“amendment” of this work to the conventional inflation targeting model. Let the net investment in fixed capital rate function be:

(4) it = It/Yt – (It/Yt )* = (Yt-1 – Ypt-1)

Equation (4) shows that net investment rate deviations (it) are a positive function of the lagged output gap, given and Yp

t-1the potential output in period t-1; and given It/Yt – (It/Yt )* is the difference between the actual net investment rate (I t/Yt) in period t and the normal or desired net investment rate (It/Yt )* in the same period.

For simplicity, let the normal net investment rate be equal to zero ((It/Yt )* = 0), in such a way that if Yt-1 – Yp

t-1 is equal to zero so the actual net investment rate in period t is also zero (hence, if Yt-1 – Yp

t-1 = 0 then it = It/Yt = (It/Yt )* = 0)7. That is, there is an accelerator effect in the determination of net private investments, and on the other hand these same net investments are determining, one period ahead, the capital or potential output formation, such as:

(5) Ypt = Yp

t-1 + it-1 + t

Equation (5) illustrates the role of net investments in the potential output formation. Potential output in period t is a function of its value in period t-1, lagged net investment rate deviation (it-1) and a potential output shock (t), defined as a stochastic process with zero mean and fixed variance (white noise process), that represents productivity and net investment innovations.

If net investment rate deviation is zero, and shock is also zero, there is a constant potential output between two periods (only because (It/Yt )* = 0 for simplicity). In this case, there were only investments in the maintenance of the capital stock. By substituting (4) for (5), an endogenous potential output function is created:

(6) Ypt = Yp

t-1 + (Yt-2 – Ypt-2) + t

Equation (6) shows that the output gap affects potential output two periods ahead. It supposes that the output gap is caused by demand fluctuations, inducing higher net investment rates above that level considered desirable in past periods. Obviously, the model with an endogenous potential output from the demand side assumes > 0.

Hence, the model with exogenous potential output () may be thought of as a particular case of analysis. Conventional inflation targeting theory would be attached to the particular case in which there are no correlations between output gaps and potential output, that is, to the long term money neutrality hypothesis8. 7 In such a context, net investment is zero and there will be only investments in the maintenance of the capital stock. Adopting (It/Yt )* equal to zero makes simpler the equation (5). Indeed, if we assumed a positive value for normal net investment rate we would have to introduce a growth trend on potential output, which could be done by imposing a parameter higher than unity on Ypt-1. Note that in equation (5) implicitly this parameter is equal to unity, which is made possible only because we have assumed normal net investment rate equal to zero.

8 Conventional theory also assumes that potential output is endogenous, but not by the demand side. Potential output would be determined only by the supply side, or through real factors such as resources stocks and factors productivity. This perspective is implicit in Kohn’s (2003) words: “assessments of the

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In its turn, if we accept the non neutrality hypothesis (), the IS curve receives a new (implicit) specification9, because output is no longer subjected to a constant maximum level of production; this maximum level varies with demand and output fluctuations. Evidently, it is assumed that this hypothesis (non money neutrality) is closer to the true structural model than the neutrality hypothesis.

4 - A new instrument rule

The issue related to endogenous potential output from the demand side becomes especially important when considerations about demand shocks are proposed. These kinds of shocks are expressed through output gaps, even if the economic system was, in the previous periods, in an equilibrated trajectory. Output gaps and their inflationary consequences, in their turn, may be highly persistent, depending on inertia parameters (m e ), making the maintenance of price stability more difficult for the monetary policy. It is not surprising that conventional theory about the inflation targeting regime defends a rigid attack against demand shocks: as there is no correlation between output gaps and potential output in this theory, and the inflationary process implicates social costs, so monetary policy should not be benevolent with demand shocks and their effects on the economy. Modifications in interest rates do not result in any cost to the system and output and inflation volatilities are simultaneously eliminated.

However, if potential output is really under an effect of output gaps, interest rate responses should be adjusted, that is, if there is endogenous potential output from the demand side, the central bank should take into account, within the model for policy evaluation, the effects of lagged interest rate variations on potential output. On the other hand, if the central bank does not take these causal relationships into account, there will be real losses in the long term, translated by potential output losses.

The effect of output gaps on potential output contributes to endogenous elimination of inflation deviations. Under positive demand shocks, for example, the inflationary process would be partially stopped, by means of a higher potential output in future periods. If the central bank estimates this channel of transmission, increases in interest rates will be lower than the increase if central bank does not take endogenous potential output into consideration. It is not necessary to impose integral reduction of future inflation through future output contractions because current output gaps will impose potential output gains ahead. This channel of transmission requires an adjusted instrument rule for monetary policy under inflation targeting regime.

4.1 – New instrument for positive demand shocks

The central bank adjusts interest rates considering that potential output depends on the output gap with a two-period lag. Hence, facing positive demand shocks, let instrument rule be:

(7) rt = z1t + z2 yt – k{E[Ypt+2] – Yp

t} + u2t

level and growth of potential GDP must be revised frequently, and of course these variables are not under the control of the central bank”. 9 Implicitly, equation (6) is inside equation (1).

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Equation (7) is an extension of Taylor’s traditional rule (equation 3), by including – k{E[Yp

t+2] – Ypt}, where E[Yp

t+2] is the expected t+2 period potential output. This additional component shows that the central bank is aware of endogenous potential output from the demand side; u2t is a random control error (stochastic process with zero mean and constant variance) of this adjusted rule. Given k > 0, monetary authority becomes thriftier (less aggressive), as the difference between expected future potential output and current potential output is higher. Now, let the expected t+2 period potential output be:

(8) E[Ypt+2] = E[Yp

t+1] + (Yt - Ypt) = Yp

t + (Yt-1 - Ypt-1) + (Yt - Yp

t)

Substituting (8) in (7), let instrument rule be under positive demand shocks:

(9) rt = z1t + (z2 – k) yt – kit + u2t , given it = (Yt-1 - Ypt-1) = yt-1

In equation (9), the adjusted instrument rule presents two basic differences in relation to Taylor’s traditional rule (equation 3), facing positive demand shocks:

a) Facing positive demand shocks, with yt raising, the central bank increases interest rates by a lower magnitude (the central bank is thriftier); this difference is given as subtracted from z2;

b) Higher net investments in period t, under an economic expansion through the positive demand shock, lower interest rate chosen by the monetary authority because higher will be potential output in t+1. Hence, the central bank can make current monetary policy less tight, allowing effective output to expand in t+1.

Proposition 1: When the central bank is aware of endogenous potential output from the demand side, and takes it into account in its structural model used to evaluate policy, interest rate response facing positive demand shocks is less aggressive (more thriftier), if compared with a response that does not take endogenous productive capacity into consideration.

Proposition 1 means that the central bank, under positive demand shocks, increases real interest rates by a lower magnitude, if compared with a central bank that does not assume endogenous potential output from the demand side in its own model of guiding policy. The basic effect of such an adjusted instrument response is a higher potential output in the long term, in addition to price stability, because monetary policy is minimizing its negative effects on productive capacity formation.

4.2 – New instrument for negative demand shocks

Facing negative demand shocks, in their turn, let instrument rule be:

(7’) rt = z1t + z2 yt + k{E[Ypt+2] – Yp

t }+ u2t

Equation (7’) makes use of + k{E[Ypt+2] – Yp

t } instead of – k{E[Ypt+2] – Yp

t}, posed in equation (7). Contrary to what happens with positive demand shocks, negative demand shocks impose reductions in future potential output through induced lower investments with a two-period lag. Hence, monetary authority decreases interest rates more

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aggressively, under negative output gaps, in comparison with what happens in the case of a conventional central bank. As is known,

(8) E[Ypt+2] = E[Yp

t+1] + (Yt - Ypt) = Yp

t + (Yt-1 - Ypt-1) + (Yt - Yp

t)

Substituting (8) in (7’), let instrument rule be, under negative demand shocks:

(9’) rt = z1t + (z2 + k) yt + kit + u2t , given it = (Yt-1 - Ypt-1) = yt-1

In equation (9’), the adjusted instrument rule presents two basic differences in relation to Taylor’s traditional rule (equation 3), facing negative demand shocks:

c) Facing negative demand shocks, with diminishing yt, the central bank decreases interest rate in higher magnitude (central bank is more aggressive); this difference is given by added to z2;

d) Lower net investments in period t, under an economic contraction, lower interest rate chosen by monetary authority, because potential output will be lower in t+1. Hence, the central bank lets current monetary policy be loose, allowing effective output to expand in t+1 and investments and potential output in the long term. That means a counter-cyclical behavior.

Proposition 2: When the central bank is aware of endogenous potential output from the demand side, and takes it into account in its structural model used to evaluate policy, interest rate response facing negative demand shocks is more aggressive (less thriftier), if compared with a response that does not take endogenous productive capacity into consideration.

A consequence of Proposition 2 is an aggressive real interest response when the central bank deals with negative output gaps, as it is known that these negative gaps will reduce future potential output. The central bank, with such knowledge, does not only seek decreased real interest rates, but seeks them in greater magnitudes and more quickly. A summary of instrument rules in both positive and negative shocks, under a conventional and non-conventional central bank is given below:

Monetary policy conduction under two alternative central banks

CaseConventional central

bankNon-conventional central

bank

Positive demand shock

rt = z1t + z2 yt + u1t rt = z1t + (z2 – k) yt – kit + u2t

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Negative demand shock

rt = z1t + (z2 + k) yt + kit + u2t

5 – Opportunity social cost and the implicit adjusted social loss function

The conventional idea according to which there is no trade-off under demand shocks may be rejected: the strict response (equation 3) of the monetary policy to demand shocks pushes down inflation volatility, but it also implies an opportunity social cost (Cy), translated by what the positive impulse on potential output economy does not earn. This type of opportunity cost may be estimated through the difference between the potential output that would be verified under the flexible rule (rule 9 or 9’), E[(Yp

t)f], and the potential output that is actually observed under traditional rule (rule 3), (Yp

t)s, as such:

(10) Cyt = {E[(Yp

t)f] – (Ypt)s}

If there is public concern over this kind of opportunity cost while the central bank is adjusting its monetary policy instrument, the authority should take into account the trade-off between lower inflation volatility and higher opportunity social cost, when facing an attack decision on demand shocks. An adjusted social loss function that resembles these concerns may be:

(11) Lt = j1(Yt - Ypt)2

+ j2 (t - n)2 + j3 (Cy

t)2

Equation 11 above shows the case of public concerns with three types of social losses: output gaps, inflation deviations and opportunity social cost. Hence, the public is not looking only to minimize output and inflation deviations around their targets, as in the case of the natural hypothesis, but also to minimize opportunity social cost. For analytical simplicity, let j1 = j2 = j3 = 1, that is, the public gives the same weight to the three kinds of potential social losses when the central bank is deciding on interest rate levels.

6 – A small numeric simulation

The simulation aims to show that, under endogenous potential output from the demand side, the desirable instrument rule facing positive demand shocks10 becomes more thriftier (less aggressive), and that traditional Taylor’s rule imposes social losses translated by lower potential output levels in the long term.

The methodology of simulating follows broadly Ball’s (1999a) article and Walsh’s (2003) thoughts. As said by the latter, “since we can vary the parameters of our theoretical models in ways we cannot vary the characteristics of real economies, simulation methods allow us to answer a variety of ‘what if’ questions” (Walsh, 2003, p. 67).

10 For simplicity, the simulation is run only in the case of positive demand shocks, but it is believed that another simulation for negative demand shocks would bring results with the same essence or quality.

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The step-by-step in the current simulation was:

I) There was a simulation of interest rate responses to demand shocks under exogenous potential output () and consistent with Taylor’s traditional rule (equation 3), in order to verify real interest rates levels in line with conventional central bank;

II) These last values were applied to an economy subjected to endogenous potential output () in order to simulate the economic performance obtained by an orthodox central bank under endogenous potential output economy;

III) Equation (9) was applied to an endogenous potential output economy to verify economic performance along with a non-conventional central bank;

IV) The results of steps (II) and (III) above were compared.

The values chosen for m en are, respectively, 0.4, 0.8 and 1, these values the same as those adopted in Ball (1999a), based on empirical evidence. The inflationary inertia level is unitary (), but the qualitative results in the current analysis would not be changed if an inertia level lower than 1 were used. The others parameters and initial condition values were adopted freely. The only concern was to choose values that did not give hypersensibility to structural relations. Below, all values imposed to the simulation, including shocks, are listed.

Parameters, initial conditions and shocks

Y* Yp* R* Rn *

700 700 5 5 4

n m n 4 0.8 1 1 0.4

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z1 z2 tYt)*

0.5 1 0 or 0.5 0.2 0

tYt)0 t+5 t+18 t+20 t+28

0 20 45 500 35

Given Y*, Yp*, R*, * and tYt)0 initial conditions.

The results were as follows: Under rule 3 (or equation 3), by means of a conventional central bank, real interest rates achieved a maximum of 2.7 in log, as a consequence of demand shocks and their effects on inflation rates. Interest rates presented volatility – sum of square deviations – around 253,875; on the other hand, the non-conventional central bank, through rule 9, attained a maximum interest rate of 2.65, after the same observed demand shocks. In its turn, the interest rate volatility remained at around 208,853, much less than under rule 3. Hence, under potential output from demand side, rule 9, instead of rule 3, imposes less interest rate volatility and lower maximum levels of interest rate.

Likewise, under rule 3, simulation shows a maximum potential output of 964.00, while under rule 9 that measure was 966.00 monetary units (m.u.). Although the difference is too low, it is obvious that the latter rises as demand shocks rises. Moreover, average potential output is less under rule 3 if compared with rule 9: the former attains 675.75 monetary units and the latter 707.57.

In its turn, long term potential output presents some kind of trajectory that confirms the predictions of our hypothesis: when the endogenous output by the demand side operates, central banks that take it into account within their structural model used to evaluate policy reache higher long term levels of potential output. This variable reached 662.50 m.u. in the long term when by rule 3, but 700.00 when through rule 9. These worse results in terms of potential output under a conventional central bank are caused by its inadequate instrument rule (equation 3), through which interest rates responses and behavior are not satisfactory.

However, a prima facie analysis may guide to a wrong meaning of these results. The fact that, through rule 9, long term potential output reaches 700.00 m.u., that is, the initial potential output value, may be thought as a contradiction in relation to the proposition according to which “The basic effect of such an adjusted instrument response is a higher potential output in the long term”. Nevertheless, this apparent contradiction is eliminated if we analyze the long term potential output by rule 9 in comparison with the result attained through rule 3. In other words, if with the rule 9 the long term potential output is not higher than the initial potential output value11, on the other hand, with the rule 3, a conventional central bank, the result observed is lower than the initial potential output level. The Table 1 below presents the synthesis of the main results in the simulation.

Table 1

11 Note that this equality between long term potential output and the initial potential output value, in the case of rule 9, does not mean that a correlation between demand shocks and potential output does not exist. Indeed, the demand shocks impose endogenous fluctuations on potential output, under both regimes, as may be observed in Graph 1 and by the results in Table 1.

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Economic performance under rules 3 and 9 in the face of positive demand shocks    Rule (or equation) 3 Rule (or equation) 9Maximum interest rate 2.7 (log) 2.65 (log)Interest rate volatility* 253,875 208,853Maximum potential output 964.00 966.00Average potential output 675.75 707.57Long term potential output 662.50 700.00

* Sum of square deviations    

The dynamics of both inflation targeting regimes are shown in Graph 1 below, and correspond to the values discussed above.

Graph 1 - Potential output trajectory under rules 3 and 9

600

650

700

750

800

850

900

950

1000

t-2

t+3

t+8

t+13

t+18

t+23

t+28

t+33

t+38

t+43

t+48

t+53

t+58

t+63

t+68

t+73

t+78

Rule 9

Rule 3

In their turn, what are the impacts on inflation rates from both these different rules of monetary policy? Simulation shows that central banks following rule 3, operating under endogenous potential output from the demand side, impose a deflationary trend on the economic system. That is, as the interest rate rises in a more aggressive way by rule 3, so the lower potential output trend comes together with lower inflation rates in the long term: long term inflation rate of about – 26% (deflation), much lower than the inflation target (4%).

It is interesting to note that this deflationary trend is also verified in Khan, King & Wolman’s (2003) optimal policy modeling, albeit they find such a trend along with desirable real resources allocation, and thus a good or acceptable result. The same does not occur in our model because it takes into account endogenous potential output by the demand side. The latter implies calling for an adjusted instrument rule, introducing expected potential output modification as another important component facing monetary policy actions. By establishing rule 9 as a policy instrument, the central bank attained a long term inflation rate equal to the inflation target (4%), and, at the same time, higher potential output levels in the long term. The inflationary dynamic can be seen in Graph 2 below:

Graph 2 – Inflationary dynamic under rules 3 and 9

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Moreover, it is important to show that some long term results in the simulation are sensible to changes in specific structural parameters values; for example, changing , the coefficient that measures the sensibility of the potential output to lagged output gaps (equations 4 and 6), causes variations in the long term potential output under rule 3, although this variable is not altered when under rule 9, as the simulations have shown.

Graph 3 below presents the long term potential output, under rule 3, as a function of levels. It is easy to verify that: the higher the level, the lower is the long term potential output under rule 3, subjected to the same demand shocks and the same other parameters values in the simulation. It means that the higher the endogeneity of the potential output from the demand side (measured by ), under demand shocks, the lower is the potential output an economy attains if the monetary policy is conducted by the conventional instrument rule (rule 3).

Therefore, the higher the value, the higher the opportunity social cost (equation 10) if the central bank is conventional, because the difference between the potential output, observed under rule 3, and the result that would be verified, under rule 9 (700 m.u.), increases – as the potential output value under rule 9 does not change in the face of variations. As it may be seen from the Graph 3, when varies from 0.01 to 1.2, as a consequence long term potential output varies approximately from 699.00 to 610.00, if the demand shocks are attacked by rule 3.

Graph 3 – Long term potential output (m.u.) under rule 3 x

15

605

615

625

635

645

655

665

675

685

695

0.01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

7 - Conclusions

Conventional inflation targeting models are developed under the natural rate hypothesis. That is, the reasons for flexibility that are presented by the traditional literature depend on the hypothesis according to which output gaps have no impact on potential output over time, and there are no trade-offs when central banks are attacking demand shocks.

This article has introduced the hypothesis of an endogenous potential output from the demand side in a conventional inflation targeting model in order to evaluate the implications for monetary policy strategy and instrument rules, particularly when central banks are attacking demand shocks. Under endogenous potential output by the demand side, there exists a trade-off between inflation volatility and a kind of opportunity social cost. In other words, under demand shocks, pushing down inflation volatility may generate potential output losses in the long term, if the monetary policy rule does not take into account the appropriate changes.

It has been demonstrated by the numeric simulation that conventional instrument rules, in the Taylor rule tradition, are associated with worse economic performance if compared with an adjusted instrument rule which takes endogenous productive capacity into account. On the other hand, when the central bank calibrates its instrument rule for endogeneity by the demand side in the potential output, interest rate responses become more aggressive under negative demand shocks and more thriftier under positive demand shocks, taking the economic system to higher potential output levels in the long term – if compared with the results obtained by the conventional central bank –, along with the inflation rate equal to the target.

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