# 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 .

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 . 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 . 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 . 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 , 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.