Chapter 11 Economic policy in the 3-equation model of the “new consensus” macroeconomics
In the previous chapters, we have develop an understanding of the basic relationships and mechanisms that explain the emergence of three key macroeconomic variables:
- gross domestic product (\(Y\))
- unemployment (\(U\)) and employment (\(L\))
- and the inflation rate (\(\pi\))
To this end, we have developed simple models of the demand and the supply side of our model economy.39 The key elements of these models can be summarised via the individual figures of the respective model components. The figure 11.1 represents the overall macroeconomic system developed so far.
Figure 11.1: The new consensus model without a policy reaction function.
The demand side is represented by the elements on the left side of the figure. The elements of the supply side are shown on the right side. The fundamental equations of the model are the \(IS\) curve and the Phillips curve. Employment is jointly determined by aggregate demand and the production function. The distribution equilibrium is shown in the \(WS-PS\) diagram. The figure depicts a general equilibrium in all model components. The equilibrium can be disturbed by supply or demand shocks as we will see later in this chapter.
This system is based on simple model building blocks found in most standard introductory macroeconomics textbooks (e.g. Carlin and Soskice (2015, chaps. 1–3). It is broadly compatible with a mainstream view of simple short run macroeconomic models. The central components of the model here are the \(IS\) curve diagram, for the demand side, and the Phillips curve diagram for the supply side. The other model components can be understood as “connecting” elements of these two diagrams.
In the previous chapters, we have modeled the two core equations of this macroeconomic model as follows:
IS curve (7.2):
\[Y^* = A - \alpha r\]
Phillips curve (9.22):
\[\pi = \pi^e + k(L^* - L^N)\]
In this chapter, we will look at how economic policy can influence our system when exogenous demand and supply shocks occur. The goal of economic policy is to stabilise the economy at a high level of employment while maintaining a low level of inflation. To the \(IS\) curve and Phillips curve, we will add a third equation that describes an optimal policy response. The complete set of equations represents the 3-equation model of the “new consensus” in macroeconomics, short NCM.
NCM: New classical or new Keynesian?
The new consensus model in macroeconomics is based on the new classical and new Keynesian macroeconomics of the 1980s and 1990s and represents a synthesis of both approaches. While the neoclassical model, under the assumption of rational expectations and flexible prices, concludes that the economy must actually always be in full employment equilibrium, and therefore government stabilisation policies are actually unnecessary, new Keynesian authors have presented various microeconomic approaches that justify why, even in the absence of government intervention and unions, prices and wages are not always flexible (see Snowdon and Vane 2005, chap. 5 and 7). It then follows that involuntary unemployment can arise, at least in the short run and that government economic policy can have real effects on the level of output and employment. This means that the new consensus model of macroeconomics has new Keynesian rather than new classical features (see Clarida, Gali, and Gertler 1999; Goodfriend and King 1997).
Our exposition so far and what will follow below is closely modeled along Carlin and Soskice (2015, chaps. 1–3). As we will see later on, their model can be transformed into a model that yields post-Keynesian results by making a few changes in the assumptions and in the behavioural equations. Post-Keynesianism is thereby an attempt to make the essential messages of John Maynard Keynes (1936) and Michal Kalecki (1954, 1971) applicable to modern macroeconomics (see Hein 2023, chaps. 2–3; 2008, chap. 6; King 2015; Lavoie 2006). The main difference between the post-Keynesian approach and the new Keynesian approach is that the principle of effective demand, which goes back to Keynes and Kalecki, applies generally in post-Keynesian theory, i.e. not only in the short run when price and wage rigidities are present. Demand-side economic policy therefore has effects on the level of income and employment not only in the short run, as in new Keynesian theory and the new consensus, but also in the long run.
Before turning to the description of the complete NCM model, we should first make clear how in this model economic policy works in response to macroeconomic shocks.
11.1 How can policies respond to demand and supply shocks?
Without policy intervention, the shocks introduced in chapter 10, whether positive or negative, lead to a process of ever increasing or decreasing inflation. Economic policy should not remain inactive, with the pressure to act being further increased by the rise in unemployment in the event of a decline in demand. But what are the options for economic policy action in the event of supply or demand shocks in the NCM model?
In principle, economic policy can influence events either via the demand side or via the supply side. A shock could be addressed via both policy channels regardless of its cause. However, we have to distinguish whether the policy response attempts to achieve an inflation target at a given distributional equilibrium and a given NAIRU or whether the policy also aims to influence the distributional equilibrium and consequently the NAIRU. In the standard model, the latter would only be achieved via supply-side policy measures. We have already addressed this point in chapter 9.5. We have also emphasised that supply-side measures in the labour and/or goods market only increase the inflation-stable employment level, or reduce the NAIRU, without automatically increasing actual employment and reducing the unemployment rate. This is because employment and unemployment are determined by effective demand in the goods market.
In this chapter, we will focus on economic policy reactions on the demand-side. These are usually faster than supply-side measures which are instead often accompanied by more long run institutional changes (in the goods market and/or the labour market, etc.). Rapid intervention is particularly important, since after a shock the economy can move quickly further and further away from its starting point. In our basic model, however, this only applies to the inflation rate. Thus, the necessary adjustment costs grow with the time that elapses between the shock and the policy response. We now have two economic policy institutions, the central bank (or monetary policy) and the ministry of finance (or fiscal policy) which can directly influence aggregate demand with their respective decisions on the interest rate and government spending (and possibly taxes, which we will not consider for now). Active government management of aggregate demand with the goal of stabilising the economy is also known as demand management. But who should carry out this demand management in response to shocks? The central bank? The ministry of finance? Or both?
If we take a brief look back at the history of macroeconomics and the stabilisation policy recommendations of different theories, we find that in the 1950s, 1960s and the first half of the 1970s, with the dominance of the neoclassical synthesis, the focus was on countercyclical fiscal policy (see Snowdon and Vane 2005, chap. 3). The effectiveness of monetary policy was considered to be low, especially in crisis and recession phases. On the one hand, expansionary monetary policy can quickly reach interest rates that cannot be undercut (“liquidity trap”). On the other hand, even if interest rates fall, an expansionary effect on goods market demand cannot be expected since, in time of recession, investment becomes inelastic to the interest rate (“investment trap”).
With the dominance of monetarism and then neoclassical economics starting in the second half of the 1970s and continuing until the 1980s and 1990s the focus on fiscal policy was abandoned (see Snowdon and Vane 2005, chaps. 4–5). Since it was assumed that market processes always lead back to full employment equilibrium by themselves, fiscal policy was no longer seen as policy tool necessary to stabilise the economy. The goal of economic policy was rather seen that of reducing equilibrium unemployment through supply-side measures. Monetary policy was left with the task of controlling inflation - in this case still through an adequate money supply policy as a policy instrument of the central bank. With the emergence of the new Keynesian paradigm in the 1980s and 1990s (see Snowdon and Vane 2005, chap. 7), however, the optimism that free markets without government intervention (and also labour markets without union power) will always tend quickly to equilibrium through flexible prices was questioned. In the new Keynesian school and then in the new consensus of macroeconomics, monetary policy takes on a stabilisation role in the short run, with the interest rate as the key policy instrument of the central bank. This is also the case in the 3-equation model of Carlin and Soskice (2015, chaps. 1–3) that we are going to discuss here.
11.2 Central bank interest rate policy and macroeconomic stabilisation
In line with the approach of the new consensus, which gained acceptance in many countries in the 1990s, we will first focus on the role of the central bank as the main actor responsible for demand management in response to a demand or a supply shock. Studying the role of the central bank helps to understand the current economic policy debate which often revolves around the effect of interest rate policy of the central banks in managing the economy. The discussion about fiscal policy is instead limited to the idea of the government maintaining a balanced budget over the cycle.40 We will see later, however, that this particular role assignment of economic policy can be effective only under certain model assumptions which have been and continue to be challenged after the financial crisis of 2007-09, the euro area crisis and the current Corona crisis.
The central role of inflation expectations
In the 3-equation model of the NCM by Carlin and Soskice (2015, chaps. 1–3), inflation expectations are an important reference point for the economic policy actions of the central bank. Why? In chapter 10, we had seen that both demand and supply shocks will cause inflation expectations to rise or fall continuously, moving further and further away from the inflation target of the central bank (\(\pi^T\)). In our model, this causes the Phillips curve to shift further and further leading to increasingly rising or falling inflation and to a wage-price spirals. From this behavior of the model, we can already see that inflation expectations must play a central role in the response of the central bank to the shock. Ultimately, the central bank must be concerned with bringing inflation expectations back in line with its inflation target.
We now study how the central bank manages inflation expectations with the help of interest rate policy. We first focus on the case of a positive demand shock. A positive shock to aggregate demand can be triggered, for example, by an exogenous increase in autonomous consumption of households. Figure 11.2 illustrates this situation in our overall model. After a positive demand shock and a rightward shift of the \(IS\) curve, higher employment sets in at an unchanged interest rate level, leading to rising nominal wage demands. The result is an inflation rate on the Phillips curve above the target value.
Figure 11.2: Positive demand shock.
In the absence of policy intervention, inflation would continue to rise as inflation expectations and with them the Phillips curve, would shift upward continuously. What can the central bank do to prevent this to happen?
The best possible central bank response arises only if the central bank could react to the demand shock before the current wage round is completed. More precisely, the central bank could neutralise the demand shock by raising the interest rate and by so doing preventing the inflation rate from moving away from its target value at all. In figure 11.2, the central bank would have to choose exactly the interest rate that leads to the inflation-stabilising level of employment on the \(IS\) curve shifted to the right after the demand shock. In the income-expenditure quadrant, the demand curve shifts back to its original position and the distributional equilibrium is not disturbed.
If the central bank had the possibility to react immediately and to effect demand with its interest rate policy, no further problem would arise after the initial shock and the inflation rate would remain at its target value. However, this is not a realistic, at least for two reasons. First, the central bank cannot (perfectly) anticipate the demand shock and can only react to the shock with a certain delay or lag. The rise in nominal wage demands taking place in the first wage round cannot be prevented and the wage-price spiral will start. Second, we have seen that it is realistic to assume that the interest rate will have only a lagged effect on investment demand. This means that even if the central bank could respond immediately to the demand shock by setting immediately the right interest rate, the effect of this response on demand will be delayed. Given these conditions, the initial surge in inflation cannot be prevented directly. In what follows, we will keep these assumptions. The central bank does not anticipate the shock and investment demand responds with a lag to a change in the interest rate. The first assumption means that the central bank sets the interest rate only after a shock and after the completion of the respective wage round. The second assumption can be modeled with a lag of the real interest rate in the investment function hence in the \(IS\) curve (see chapter 7.4):
\[\begin{equation} Y^* = A - \alpha r_{-1} \tag{11.1} \end{equation}\]
These two assumptions mean that inflation expectations will change as a result of the positive demand shock. The central bank must therefore find a way to stabilise inflation expectations via demand management and eventually bring them to its target value of inflation. How can the central bank succeed in doing so?
Intuitively, we can best answer this question by looking at the \(IS\) curve and the Phillips curve diagram as shown in figure 11.3. We plot the Phillips curve with reference to output rather than employment in order to plot the two diagrams on top of each other.
Figure 11.3: Demand shocks in the IS and Phillips curve diagrams.
If we now observe a positive demand shock, the \(IS\) curve in the above part of the figure shifts to the right. At the current interest rate, which the central bank has not yet changed not having predicted the shock, the result is a higher level of output and employment. This leads to an increase in the inflation rate from \(\pi_0\), where the inflation rate is equal to the inflation target, \(\pi^T\), to \(\pi_1\). The increase in the inflation rate leads to higher inflation expectations. The central bank has now observed the shock and is aware of the new inflation expectation if we assume adaptive expectations of the private sector. The central bank will now produce an estimate of a Phillips curve which represent the set of possible combinations of inflation and employment, or output, correctly expected by the central bank (after all the central bank knows how inflation expectations are formed) together with the correct estimate of the inflation rate in the next round. Since the first round is not yet complete (the last step is the central bank’s setting of the new interest rate), we refer to the Phillips curve for the next round as the central bank’s “predicted” Phillips curve, i.e. \(PC_2\).
At this point, the central bank can choose a point on this predicted Phillips curve (\(PC_2\)) that keeps inflation expectations from rising even further and that is also consistent with its inflation target. On the \(IS\) curve, the central bank can find the necessary interest rate required to bring output and employment back to the distributional equilibrium level. After the required interest rate is set, the round is complete. The effect of the new and higher interest rate is then observed in the next round (round 2). Output, employment and inflation will fall and inflation expectations will follow along. The Phillips curve predicted by the central bank for the following round shifts back to its original position and the central bank can again choose a level of output on this curve that is again in line with the long run equilibrium of the economy and consistent with the inflation target. As inflation expectations in the second round match the actual realised inflation rate, the economy is stabilised at its original level. Figure 11.4 shows this adjustment process in three steps.
Figure 11.4: Returning to the inflation target as quickly as possible after a positive demand shock.
The first arrow illustrates the shock leading to an initial increase in the inflation rate. The second arrow illustrates the change in inflation expectations and the central bank’s predicted Phillips curve. The third arrow represents the central bank’s interest rate policy response which establishes a level of output on the new predicted Phillips curve equal to the inflation target. After the central bank sets the desired interest rate and round 1 is completed, the Phillips curve predicted in round 1 (\(PC_2\)) is replaced by the current Phillips curve in round 2. The same process is then repeated in round 2. Finally, the Phillips curve then shifts back to its original position and the central bank can end its restrictive policy and restore the long run equilibrium output.
Of course, we can also represent this adjustment process in our overall model, as figure 11.5 shows.
Figure 11.5: Representation of the reaction in the overall model.
This first example of a central bank reaction to a positive demand shock shows that the central bank can bring the economy back to its inflation target just two rounds after the shock. The only precondition for this is that the interest rate is raised strongly enough. However, this kind of policy reaction of the central bank is not unproblematic.
In order to neutralise the effect of the demand shock on the inflation rate as quickly as possible, the central bank must reduce output, and with it employment, well below the inflation-stabilising level, \(L^N\). The only way the central bank can combat the inflationary surge is to raise the unemployment rate significantly above the long run equilibrium level (NAIRU) in order to return to the inflation target as quickly as possible. This is necessary to reverse the wage-price dynamics caused in the \(WS-PS\) diagram and to quickly bring inflation expectations back to the target. The significant increase in the unemployment rate is temporary but it is associated with a large welfare loss and social cost.
In the interactive app below, interest rate policy can be used to respond to a demand shock. The aim is to return to the inflation target as quickly as possible.
Does the central bank have to react in the way discussed above or is there a “softer” response that the central bank could adopt? The answer depends crucially on the objectives of the central bank. If the goal of the central bank is only to keep inflation at target, the reaction described above would be optimal, since limiting unemployment would not be one of the policy goals of the central bank. In this case, unemployment would rather be just a mean in the objective of keeping the inflation rate constant. The situation changes if the central bank takes into account the effects on unemployment in its monetary policy strategy.
11.3 Different central bank objectives: the central bank reaction function and the monetary policy rule
If the central bank includes unemployment in its economic policy response together with the inflation target, the approach outlined in section 11.2 is not optimal. Instead, the central bank will try to strike a balance between restoring the inflation target as quickly as possible and but the same time avoiding too high unemployment levels. To do so, the central bank must balance the welfare losses from fluctuations in the inflation rate around the inflation target and fluctuations in unemployment (or employment or output) around their inflation-stable levels.
We can model these two objectives with a target function for the central bank. This will help us later to derive an optimal reaction function for the central bank. To do this, we define the central bank’s loss (\(Loss\)), as a function of unemployment and the inflation rate:
\[\begin{equation} Loss = Loss \left( \text{Unemployment}, \text{Inflation rate} \right) \tag{11.2} \end{equation}\]
If we assume that labour productivity does not change, then we can also define the central bank’s loss as a function of the inflation rate, \(\pi\), and output, \(Y\):
\[\begin{equation} Loss = Loss (Y, \pi) \tag{11.3} \end{equation}\]
More precisely, the central bank is interested in the fluctuations of these two values around their respective target values. These fluctuations are given by \((Y - Y^N)\) for output and \((\pi - \pi^T)\) for the inflation rate. We can thus model the loss function even more accurately by the deviations of the realised values of inflation and output from their target values. If we additionally assume that positive and negative deviations generate the same loss for the central bank, we can write this function explicitly as the sum of the squared deviations from the inflation target and the inflation-stabilising output.
\[\begin{equation} Loss = Loss (Y, \pi) = (Y - Y^N)^2 + (\pi - \pi^T)^2 \tag{11.4} \end{equation}\]
Squaring the deviations means that both negative and positive deviations imply a higher loss for the central bank. The central bank’s loss will thus increase both with the deviation of the inflation rate from the inflation target and with fluctuations in output around the inflation-stabilising level. The optimal loss of zero will only be achieved when both target values are reached.
In the loss function written down in equation (11.4), inflation and output fluctuations enter in the same way. We then speak of an equal “weighting” of the two targets. We could also assume that the central bank considers one of the two objectives to be more important. For example, the central bank might be more concerned about an increase in unemployment than an increase in inflation, or vice versa. We can incorporate a different weighting of the objectives into our loss function via a positive weighting parameter, \(\beta \geq 0\), as follows:
\[\begin{equation} Loss = Loss (Y, \pi) = (Y - Y^N )^2 + \beta (\pi - \pi^T )^2 \tag{11.5} \end{equation}\]
For the previous loss function in equation (11.4), we had implicitly assumed that the weighting parameter is exactly equal to one, \(\beta = 1\), meaning an equal weighting of the targets. If \(\beta > 1\), the central bank is inflation averse and fluctuations in the inflation rate generate a higher loss than fluctuations in output or unemployment. If \(\beta < 1\), the central bank is unemployment averse.
We can now visualise our loss function graphically. Since the loss can increase in two variables (inflation and output) we can illustrate this situation using a three-dimensional figure. However, we assume a simplification for the numerical examples and simulations here in order to be able to retain the parameter constellation of the other model elements used so far. The simple loss function from equation (11.5) only applies if the inflation-stable output is normalised to 1. For the numerical simulation, we scale our central bank loss parameter by a factor of 100 for this purpose, which makes the simulated loss function approximate equation (11.5). To recalculate the numerical results of the central bank’s loss in the following figures and simulations, we need to multiply the \(\beta\) parameter by a factor of 100.41
Figure 11.6: Loss function of the central bank.
At the “bottom” of the figure 11.6, the loss has a value of 0. This is the optimal value which is reached only at the inflation target and inflation-stabilising employment. For any higher loss, there are a number of combinations of inflation and output that can generate this particular value. These combinations lie on the rings that we would obtain if we “cut” through the loss functions on a horizontal plane (or, if we looked at the loss function from above). Each of these rings represents a specific loss level and the combinations of inflation and output that generate that value. As the loss level increases, so does the diameter of each ring.
We also refer to these rings as indifference curves because the central bank is indifferent with respect to the loss to the various combinations of inflation and output that lie on the ring. Therefore, on the ring, no combination is better than another.
We can now also integrate the indifference curves into our representation of the Phillips curve, since they are determined by the values of inflation and output. Figure 11.7 again shows the situation shortly after a positive demand shock. In addition, we have now integrated the indifference curve on which this specific combination of inflation and output lies into the diagram. All other points on the indifference curve shown would also have generated the same realised loss but are not possible due to the location of the short run Phillips curve.
Figure 11.7: Indifference curves of the central bank.
Due to the unpredictability of shocks and the lagged effect of interest rate changes on demand, the central bank cannot change the situation in the first round. However, it can try to reduce the level of losses in the next round using its interest rate policy. To do so, it can choose from all possible combinations of inflation and output given by the Phillips curve \(PC_2\) in figure 11.8 predicted in round 1. Since the central bank wants to minimise the loss, it will choose a point on the Phillips curve \(PC_2\) that is tangent to the smallest possible ring.
Figure 11.8: Minimising anticipated losses following a positive demand shock: Best possible policy response following a positive demand shock.
The central bank is not (yet) at its target position (inflation target and inflation-stabilising output level), but it can minimise the loss in round 2.
The economic policy adjustment process is not over yet. However, the central bank has been able to reverse the surge in inflation by pursuing a restrictive monetary policy (i.e. interest rate policy). The decline in the inflation rate also reverses the path of inflation expectations and the Phillips curve shifts back toward its original position. To continue to minimise the loss, the central bank must continue to target the optimal combination of output and inflation on the new predicted Phillips curves (\(PC_3\)) in subsequent rounds. The procedure is the same as before. For the Phillips curve, the central bank minimises the loss by choosing the smallest possible diameter of the indifference curve. As a result, the inflation rate moves further toward the inflation target and output also rises while unemployment falls. The rise in output and the fall in the unemployment rate show that the central bank is gradually reducing its restrictive monetary policy steering the economy toward its inflation-stable equilibrium. This is shown in figure 11.9.
Figure 11.9: Further adjustment toward general equilibrium.
In figure 11.10, we are in round 4. The central bank has “almost” returned inflation expectations to the inflation target. The current inflation rate is 2.05% while the predicted inflation rate, which further minimises the loss function, is 2.025%, very close to the inflation target of 2%.
Figure 11.10: Full adjustment to target inflation and inflation-stable output and employment levels.
To sum up: Once again, the key driver of adjustment to target inflation rates and inflation-stable output and employment levels is inflation expectations which underlie the nominal wage demands of workers. The central bank uses its output and inflation management capabilities to bring inflation expectations back to its target value. This shifts the short run Phillips curves and allows the central bank to stabilise the economy in a gradual manner. This process continues until the central bank’s targets are reached and its loss is zero again.
As can be seen in figure 11.10, the adjustment process proceeds along a line (red arrow) obtained by connecting the optimal response points in each round. This shows that the central bank’s optimal response to a shock follows the same system or rule across all rounds. The same adjustment rule implied by the line also applies in the case of a negative demand shock and, similarly, in the case of supply shocks (more on this later). For the generalisation of the rule for positive and negative demand shocks of any size, we simply need to continue drawing the line in both directions. The optimal reaction point for any given demand shock is then exactly at the intersection of the reaction line and the short run Phillips curve for each round. Figure 11.11 again plots the line of the optimal reaction function for a positive demand shock. We follow Carlin and Soskice (2015, chap. 3) and call this reaction function the monetary policy rule, in short \(MR\) for monetary rule.
Figure 11.11: Monetary policy rule and a positive demand shock.
In the interactive app below, the loss of the central ban is illustrated with the indifference curves. The weighting parameter of the loss function and the inflation target of the central bank can be changed.
The graphical derivation of the \(MR\) curve is based on a minimisation process of the loss of the central bank taking place in each round after the shock. We can apply the same procedure to the formal derivation of the \(MR\) curve and its underlying equation. The intuition is the following: in each round, the central bank tries to minimise the loss function of the following round:
\[\begin{equation} Loss_{+1} = Loss ( Y_{+1}, \pi_{+1} ) = ( Y_{+1} - Y^N )^2 + \beta ( \pi_{+1} - \pi^T )^2 \tag{11.6} \end{equation}\]
However, the possible combinations of output and inflation from which the central bank can choose are predetermined by the forecast short run Phillips curve for the round in question:
\[\begin{equation} \pi_{+1} = \pi + k (Y_{+1} - Y^N) \tag{11.7} \end{equation}\]
The predicted Phillips curve is the condition under which the central bank must minimise its loss. We can therefore simply plug the predicted Phillips curve for \(\pi_{+1}\) into the central bank’s loss function:
\[\begin{equation} Loss_{+1} = \left( Y_{+1} - Y^N \right)^2 + \beta \left[ \pi + k \left(Y_{+1} - Y^N\right) - \pi^T \right]^2 \tag{11.8} \end{equation}\]
The variable over which the central bank minimises the loss function is the output of the next period, \(Y_{+1}\). It can directly influence this on the \(IS\) curve with the interest rate of the previous period, \(r\). Minimising the loss function should now generate for us the smallest possible diameter of the indifference curve, with the central bank directly choosing the optimal output on the Phillips curve and the associated inflation rate setting itself according to the wage-price dynamics in the labour market and the Phillips curve. How can we now mathematically minimise the loss function? To do so, we simply derive the loss function given by equation (11.8) according to the output of the next period, \(Y_{+1}\).
The minimum of the loss function is given when its first derivative is equal to zero. Therefore:
\[\begin{equation} Y_{+1} = Y^N - k \beta (\pi_{+1} - \pi^T) \tag{11.9} \end{equation}\]
We obtain an equation for the output of the next period with a negative slope with respect to the inflation rate of the next period. This is exactly what our \(MR\) curve corresponds to.
11.4 The 3-equation model of the NCM
The monetary policy rule represented by the \(MR\) curve forms the third central building block of the 3-equation model of the new consensus. The equation of the \(MR\) curve is the third central equation of the model, along with the \(IS\) curve and the Phillips curve. The \(MR\) curve represents the economic policy rule or reaction function of the central bank and adds a stabilising element to the model. Incorporating stabilising economic policy into the model implies that after a shock, the model economy does not drift further and further away from equilibrium. Instead, economic policy can restore equilibrium and the inflation target through the use of interest rate policy. Before we formally derive the \(MR\) curve, we show again the three central elements of the model in figure 11.12. The goods market equilibrium is represented by the \(IS\) curve, here once as a real interest rate \(IS^r\) curve and once as a nominal interest rate \(IS^n\) curve (see chapter 7.5). The Phillips curves represent the supply side of the economy with the vertical long run Phillips curve marking the distributional equilibrium. The \(MR\) curve represents the monetary stabilisation function of the central bank. The combination of inflation targeting and inflation-stabilising output depicts the central bank’s target equilibrium.
Figure 11.12: The three elements of the three-equation model.
The 3-equation model of the new consensus according to Carlin and Soskice (2015, chap. 3) results from the following three equations:
IS curve (7.2):
\[Y^* = A - \alpha r\]
The first of these three equations is the \(IS\) curve, which represents the equilibrium aggregate demand, \(Y^*\), of the closed economy as a function of the real interest rate, \(r\), and as a positive function of all autonomous aggregate demand components, \(A\), i.e., the part of aggregate demand that does not depend on income.42
Phillips curve (9.22):
\[\pi = \pi^e + k(L - L^N)\]
The second equation is a short run Phillips curve (\(PC\)). The Phillips curve relates the current inflation rate, \(\pi\), to inflation expectations (given by adaptive expectations: \(\pi_{-1}\)) and the current employment gap, which is defined as the deviation of the current level of employment, \(L\), from the level corresponding to the NAIRU, \(L^N\): \((L - L^N)\).
MR curve (11.9):
\[Y_{+1} = Y^N - k \beta (\pi_{+1} - \pi^T)\]
The third equation is the monetary policy rule or \(MR\) curve. The \(MR\) curve is used to calculate the short run optimal interest rate and serves as the reaction function of the central bank.
11.5 Reaction to shocks
We can now use the \(MR\) curve to discuss the optimal central bank response to each type of shock in the context of the 3-equation model.
Demand shocks
We have already worked out the case of a shock in aggregate demand in the context of deriving the \(MR\) curve in section 11.3. In the case of an exogenous decline in aggregate demand, the reaction of the central bank is symmetric to the adjustment described above after a positive shock.
Figure 11.13: Monetary rule and a negative demand shock.
So far, we have assumed that the central bank can directly control the real interest rate. We now introduce the more realistic case of the central bank controlling the nominal interest rate. The nominal interest rate to be set by the central bank must now take inflation expectations into account. The central bank must estimate the nominal interest rate \(IS^n\) curve on this basis and can then use it to determine the optimal nominal interest rate.
Our interactive scenario accessible via the link below can be used to achieve the best possible adjustment path in response to demand shocks.43
Change the central bank’s preferences
The size of the \(\beta\) parameter in the central bank’s loss function (11.5) determines the central bank’s preferences and thus the speed of the adjustment process in response to a shock. When \(\beta\) is greater than 1, the central bank places more weight on deviations of inflation from target than on deviations of employment from target. In this case, the central bank is considered inflation averse. If \(\beta\) is less than 1, the central bank is interested less in inflation than employment. In this case, the central bank is considered unemployment averse. When \(\beta\) equals 1, the central bank’s loss is equally affected by the deviation of inflation and employment from their respective targets. In the following interactive scenario, one can experiment with different values of preferences of the central bank.
Supply shocks
The fundamental difference between a demand and a supply shock with respect to the central bank’s response in the 3-equation model is that supply shocks also affect the general equilibrium of the economy whereas the the general equilibrium remains unaffected after a demand shock. In chapter 10, we had distinguished between two different types of supply shocks:
a labour market shock leads to a change in the location of the wage-setting curve (equation (9.4)). This can be caused either by a change in the parameter \(\mathbf{b}\), e.g., a change in social benefits, or by a change in the conflict orientation of workers, the parameter \(k\).
a price-setting shock, caused for example by a change in the intensity of competition in the goods market and the change in the markup rate, \(m\), leads to a shift in the price-setting curve (equation (9.9)).
As an example, we now illustrate the response of the central bank to a positive supply shock using a labour market shock that shifts the wage-setting curve downward (the differences between the various supply shocks are marginal, see chapter 10). In chapter 10, we had already seen that a positive supply shock leads to an increase in inflation-stabilising employment or output. However, since demand does not automatically adjust to this new value, there is initially a fall in the inflation rate and a continuing disinflation process. This is illustrated again in figure 11.14.
Figure 11.14: Positive labour market shock and increase in inflation-stable employment.
Now what is the optimal response of the central bank? Instead of moving to the old general equilibrium at \(L^{N_{old}}\), the central bank must now move the economy to the new equilibrium at \(L^{N_{new}}\). This means that the supply shock not only shifts the Phillips curve but that also changes the location of the \(MR\) curve, assuming that the central bank recognises that the supply shock leads to a permanent increase in inflation-stabilising output and that that the central bank adjust its optimal reaction function accordingly.
What happens now in each step of the adjustment? As can be seen in figure 11.15, in round 1, the positive supply shock shifts the Phillips curve from \(PC_0\) to \(PC_1\), and the inflation rate falls to \(\pi_1\)=1.8%, below the target inflation rate of 2%. Output in round 1 is unaffected. The central bank recognises the permanent supply shock and adjusts its optimal reaction function from \(MR_{old}\) to \(MR_{new}\) while still in round 1. In the next step, it will choose the optimal point on the predicted Phillips curve for round 2 (\(PC_2\)) and change its interest rate accordingly. This completes round 1. In round 2, the lagged effect of the interest rate change leads to an increase in output and inflation, which also shifts inflation expectations upward. The projected Phillips curve shifts toward the new general equilibrium and the central bank can target output closer to the inflation-stabilising level in the next round.
Figure 11.15: Adjustment following a positive supply shock.
Analogous to the first scenario, the interactive scenario below can be used to understand the economic policy implications of a supply shock in the context of the 3-equation model. Here, users can decide between a labor market shock or a price-setting shock.
11.6 Limits to stabilisation by the central bank’s interest rate policy: deflation trap, the zero lower bound and the investment trap
In the previous sections, we have seen that the central bank can always bring the economy back to the general equilibrium. To do so, the central bank has just to follow its optimal reaction function.
We now want to show that within the 3-equation model the central bank can play its economic stabilisation role only under “normal circumstances”. In the presence of a deep economic downturn, the interest rate policy can quickly reach its limits and the expansionary measures of the central bank may not be sufficient to bring the economy out of the crisis.
Such a severe crisis can be triggered by a strong negative demand shock following for example the financial crisis of 2007-09, the eurozone crisis started in 2010 or the current crisis caused by the pandemic. This is illustrated in figure 11.16. The collapse in aggregate demand leads to a strong leftward shift of the \(IS\) curve. At the current level of interest rates, output and employment fall to very low levels. If the collapse in demand is so severe that the model economy slips into deflation already in the first round, the central bank should try to stimulate the economy by choosing a low interest rate and establish a positive output gap. This should reverse the path of inflation expectations and gradually return inflation and employment back to their target values. However, the central bank cannot succeed in doing this in the example shown in 11.16. How is this possible?
Figure 11.16: A strong negative demand shock.
As it can be seen from figure 11.16, the sharp decline in inflation expectations shifts the predicted short run Phillips curve far downward. The optimal output would now require a negative nominal interest rate on the \(IS\) curve (\(i < 0\)). However, this is not possible because the central bank cannot lower the nominal interest rate below zero. We also refer to this as the zero lower bound of the interest rate. At this point, the central bank is constrained in its monetary policy response and can only set an interest rate of zero. The best possible response (\(i^{best} = 0\)) that the central bank can achieve leads to output (and employment) on the \(IS\) curve well below the inflation-stable output and employment level (\(Y(i = 0) = L(i = 0) < Y^N \space \text{or} \space L^N, \text{if} \space y = 1\)). The expansionary policy is not sufficient to lift the inflation rate above its previous value, the short run Phillips curve will continue to shift downward and the the economy to sink further into a deflationary spiral. The central bank cannot overcome the crisis because it cannot stimulate demand sufficiently with its resources. The economy is in a deflation trap.
Is there a way out of the situation depicted in the previous figure? The answer is yes and the solution lies in fiscal policy. Stabilisation can only succeed through an additional demand stimulus from government spending. The central bank is therefore dependent on help from fiscal policy. Optimally, government spending must increase so strongly that the \(IS\) curve is shifted so far to the right that the central bank is again able to target its optimal output at a positive interest rate (\(i \geq 0\)).
The case of the “zero lower bound” and of the deflation trap is illustrated in in the first interactive scenario that we have seen above when the option deep crisis is selected. In the interactive scenario, it will become clear that the central bank no longer has the necessary economic policy tools to stabilise the economy when monetary policy reaches the zero lower bound. Only with the help of an expansionary fiscal policy the economy can return to the long run distributional equilibrium at \(L^N\). After expansionary fiscal policy has been pursued to a sufficient extent, the optimal interest rate becomes positive and monetary policy is effective again.
In the interactive scenario when the economy reaches the zero lower bound, it becomes clear that, from the perspective of the new consensus in macroeconomics, monetary policy is an effective means of stabilising the economy in the short run but only under normal circumstances and that monetary policy needs to be supported by fiscal policy just in exceptional cases. It also turns out that expansionary fiscal policy is not an efficient way to reduce unemployment below the NAIRU in the long run. A demand-driven increase in employment will lead to a rising inflation rate triggering the response of the central bank which will reduce aggregate demand to a level consistent with the NAIRU. In the new consensus model, fiscal policy plays only a subordinate role and should refrain from active management of aggregate demand and by so doing helping the central bank in keeping inflation under control.
Investment trap in the 3-equation model
In addition to the case of the zero lower bound, the occurrence of the investment trap that we have seen in chapter 7 can lead to the situation of the central bank no longer being able to stabilise the economy with its interest rate policy. The investment trap means that a change in the interest rate no longer leads to a change in the goods market equilibrium; the \(IS\) curve is therefore interest rate inelastic. This situation is illustrated in figure 11.17. Here, the central bank has no way to guide employment to the level necessary to reverse inflation expectations. This role can only be fulfilled by fiscal policy. To restore employment and output, the only solution is to provide an expansionary demand stimulus via government spending, \(G\). The central bank will only be able to intervene again when the investment trap disappears and investment becomes interest rate elastic again.
Figure 11.17: Vertical IS curve in the 3-equation model.
11.7 Summary of the economic policy implications of the NCM 3-equation model
We conclude this chapter by summarising the policy mix (or assignment) of the 3-equation model of the new consensus:
The monetary policy of the central bank is responsible for controlling the inflation rate and maintaining the inflation target in the long run. The central bank uses its interest rate policy as an instrument for this purpose. Interest rate changes by the central bank have short run effects on employment (and unemployment). Changes in the unemployment rate serve as a means to achieve the long run inflation target. The long run equilibrium unemployment rate, the NAIRU, is determined by the institutional structures and norms of the labour and goods market and cannot be directly influenced by the central bank.
Labour market, wage/income, and competition policies influence labour market institutions and the intensity of price competition in the goods market. These are the key determinants of distributional equilibrium and inflation-stable employment, the NAIRU. A reduction in social benefits, for example weaker bargaining power of trade unions as well as higher price competition between firms in the goods market have the effect of lowering the NAIRU. Whether a lower NAIRU and higher inflation-stable employment are achieved depends on the response of monetary policy.
The fiscal policy of the government plays in normal circumstances no role in macroeconomic stabilisation. The government should aim for a balanced budget in the long run and by so doing supporting monetary policy in its inflation target policy. If the government were to try to reduce unemployment through expansionary fiscal policy, this would only have an inflationary effect in the long run that would have to be countered by monetary policy with high interest rates. The government should focus on increasing inflation-stable employment and reducing the NAIRU through supply-side policies in the labour and the goods market, i.e., through structural reforms.
Ex ante coordination of policy areas is not really necessary if each policy actor consistently fulfills its role. The central bank pursues its inflation target in the long run and pursues a policy of inflation control, which also has effects on employment and unemployment in the short run. The government pursues a policy of structural reforms in the labour and in the goods market which reduce the NAIRU and increase inflation-stable employment. Active fiscal policy for macroeconomic stabilisation is not necessary and would conflict with monetary policy. The government should pursue a balanced-budget policy in the long run. There is no room for an independent, goal-oriented wage and income policy by the collective bargaining parties (unions and business associations). Instead, the goal of structural policy must be to allow nominal wages in the labour market to be as flexible as possible and to reduce the influence of unions on wage policy.
This policy mix and the role assignment it contains presuppose that the key actor in the NCM, the central bank, can actually use its interest rate policy for domestic inflation control without restriction. In an open economy, something that we do not discuss here, the central bank cannot be constrained, for example, by the obligation to meet implicit or explicit exchange rate targets.
We have also shown, and the 2007-9 and 2020 crises have provided the empirical evidence, that the NCM policy mix presented here reaches its limits in deep recessions and crises. Interest-rate inelastic investment (investment trap), the reaching of a nominal zero lower bound for the nominal interest rate as well as uncontrollable deflation processes represent limits to macroeconomic stabilisation by the central bank in deep recessions. This is the case where expansionary fiscal policy should take place to avert total collapse. Government deficit-financed spending must stabilise the economy and return it to a “normal range” with positive inflation rates and interest rate elastic investment, so that the central bank’s interest rate policy can be effective again.
The two final interactive scenarios offer the opportunity to review the mechanics of the 3-equation model learned in this chapter. In the first scenario, it is possible to change the values of the parameters and the exogenous variables of the model as desired. The determination of economic policy is left to the users. The simulation is played round after round and results are displayed with curves and impulse response functions building as the rounds progress.
In the last interactive scenario, economic policy is determined endogenously. Users can determine the type of shock, the preferences of the central bank and the inflation target. In this scenario, results are shown only with impulse-response functions.
Further reading on chapter 11
Textbooks:
- Carlin and Soskice (2015, chap. 3)
- Snowdon and Vane (2005, chap. 7)
- Bofinger (2019, chap. 23) (in German)
Literature
We have assumed a closed economy.↩︎
This was true at least before the Corona crisis.↩︎
For example, we obtain the numerical loss given inflation of 2.4% and an employment level of 122 as in figure 11.7 by: \((122 - 118)^2 + 1 \cdot 100 \cdot ( 2.4 - 2 )^2\). The inflation rate is given here in percentage units as in the figures. The mathematically exact loss function would instead be \(loss = \left( \frac{Y - Y^N}{Y^N} 100 \right)^2 + \beta ( \pi - \pi^T )^2\), where inflation would be expressed in percentage units and output in output units.↩︎
\(A\) and \(\alpha\) thereby also include the goods market multiplier, \(m\) (see chapter 7).↩︎
We have referred to interactive applications of partial model elements as “interactive figures” throughout the text. For full models, on the other hand, we refer to them as “interactive scenarios.”↩︎