# What does the supply-side economy emphasize?

## Introduction to Macroeconomics: plural and interactive

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In the previous chapters we tried to develop an understanding of the fundamental relationships and mechanisms that can explain the emergence of three central macroeconomic variables. These three macroeconomic variables are:

- the gross domestic product (\ (Y \))
- unemployment (\ (U \)) or employment (\ (L \))
- and the inflation rate (\ (\ pi \))

To this end, we have developed simple models of the demand and supply sides of a model economy. We have assumed a closed economy here. The central elements of these models can be summarized using the individual illustrations of the respective model components. Figure 11.1 shows the macroeconomic overall 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 of the figure. The elements of the supply side can be found on the right. The key summarizing equations of the model are the IS curve and the Phillips curve. Realized employment is determined jointly by aggregate demand and the production function. The distribution mark equilibrium is shown in the WS-PS diagram. The illustration here shows a general equilibrium in all model components, which can be disturbed by supply or demand shocks.

This system is based on simple building blocks of the kind found in most introductory standard macroeconomics textbooks (e.g. in Carlin and Soskice (2015, Chapters 1–3)). It is largely compatible with a mainstream view of simple, short-term macroeconomic models The central components of the model are the IS curve diagram for the demand side and the Phillips curve diagram for the supply side.The other model components can to a certain extent be understood as connecting elements of these two diagrams.

We 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 want to deal with how economic policy can influence our overall system when exogenous demand and supply shocks occur. The aim of economic policy is to stabilize the economy at a high level of employment while at the same time ensuring a low level of inflation. We will see that we can add a third equation to the IS curve and Phillips curve, which describes an optimal policy response and thus makes the model the 3-equation model of the “New Consensus” in Macroeconomics (NKM).

**NKM: New Classic or New Keynesian?**

The New Consensus Model in Macroeconomics is based on the neo-classical and New-Keynesian macroeconomics of the 1980s and 1990s and represents a synthesis of both approaches. While the neo-classical model comes to the result on the assumption of rational expectations and flexible prices New Keynesian authors have presented various microeconomic approaches that explain why even in the absence of state intervention and trade unions, prices and wages are not always flexible (see Snowdon and Vane 2005, Chapters 5 and 7). It then follows from this that, at least in the short term, involuntary unemployment can arise and state economic policy can have real effects on the level of production and employment. The model of the New Consensus in macroeconomics thus has New Keynesian rather than New Classical properties (cf. Clarida, Gali and Gertler 1999; Goodfriend and King 1997).

Our previous and following presentation is based closely on Carlin and Soskice (2015, Chapters 1–3). As we will see below, their model can be converted into a model that delivers post-Keynesian results by a few changes in the assumptions and the behavioral equations. Post-Keynesianism is the attempt to make the essential messages of John Maynard Keynes (1936) and Michal Kalecki (1954; 1987) usable for modern macroeconomics (cf.Hein 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 in general to post-Keynesian theory, i.e. not only in the short term in the presence of price and wage rigidities. Demand-side economic policy therefore has effects not only on the level of income and employment in the short term, as in the New Keynesian theory and in the New Consensus, but also in the long term.

Before we turn to the model of the NKM, however, we should first make it clear which fundamental possibilities exist for an economic policy reaction to macroeconomic shocks in this model world.

### 11.1 How can politics react to demand and supply shocks?

The shocks introduced in Chapter 10, whether positive or negative, lead in the model economy without political intervention to a process of ever increasing or decreasing inflation. Economic policy should therefore not remain inactive, whereby the pressure to act in the event of a drop in demand is increased by the rise in unemployment. But which economic policy options arise in the event of supply or demand shocks in the standard model?

In principle, economic policy can influence events in our model economy either on the demand side or on the supply side. Regardless of its cause, a shock could in principle be countered through both political channels. In doing so, however, we have to distinguish whether politics tries to achieve an inflation target with a given distribution equilibrium and a given NAIRU or whether politics also want to influence the distributional equilibrium and thus the NAIRU itself. In the standard model, the latter would only be achievable through supply-side policy measures. We have already addressed this above in Chapter 9.5 and also emphasized that supply-side measures on the labor and / or goods market initially only increase inflation-stable employment or reduce the NAIRU without automatically increasing actual employment and the actual unemployment rate falls. Because the latter are determined by the effective demand on the goods market.

In this chapter we will now focus on the demand-side responses of economic policy. As a rule, these represent a more rapidly available means than supply-side changes, which instead often go hand in hand with more long-term institutional changes (on the goods market and / or the labor market, etc.). In the case of macroeconomic shocks, it is particularly important to intervene quickly, since the economy can move further and further from its starting point as a result of a shock; in our basic model, however, this only applies to the inflation rate. The necessary adjustment costs grow with the time between the shock and the political reaction. With the central bank (or monetary policy) and the ministry of finance (or fiscal policy), we now have two economic policy institutions that assess the aggregate demand with their respective decisions about the interest rate and government expenditure (and possibly taxes, which we here however will not be considered at first) directly and thus be able to react to shocks. Active state control of demand through these policy areas, with the aim of stabilizing the economy, is also called **Demand management** designated. But who should do this demand management in response to shocks? The central bank? The Treasury? Or both?

If we take a brief look back into the history of macroeconomics and the stabilization policy recommendations of various theories (cf.Hein 1998), we find that in the 1950s, 1960s and the first half of the 1970s, with the dominance of the neoclassical synthesis of the The focus was on a countercyclical fiscal policy (cf. Snowdon and Vane 2005, Chapter 3). The effectiveness of monetary policy was assessed as low, especially in phases of crisis and recession, because on the one hand interest rates that cannot be fallen below can be achieved relatively quickly through expansionary monetary policy ("liquidity trap") and, on the other hand, no expansive effects on the demand for goods are to be expected even when interest rates fall , since investments in particular become interest-rate inelastic (“investment trap”).

This focus on fiscal policy changed in the second half of the 1970s, 1980s and 1990s with the dominance of monetarism and then the neo-classical period (cf. Snowdon and Vane 2005, chapters 4–5). Since it was assumed here that market processes themselves always lead back to the equilibrium of full employment, there was no longer any stabilization policy task for fiscal policy and economic policy should rather be concerned with reducing equilibrium unemployment itself through supply policy measures. For monetary policy, the task of inflation control remained - here still through an adequate monetary policy as a policy instrument of the central bank. With the emergence of New Keynesianism in the 1980s and 1990s (cf. Snowdon and Vane 2005, Chapter 7), however, the optimism was called into question that free markets without state intervention (and also labor markets without trade union power) were always due to flexible prices tend quickly to equilibrium and therefore always full employment will automatically set in. In New Keynesianism and then in the New Consensus of Macroeconomics, monetary policy therefore plays a role in stabilizing policy in the short term, with the interest rate now being understood as an essential policy instrument. This is also the case in the 3-equation model presented here by Carlin and Soskice (2015, Chapters 1–3).

### 11.2 The central bank's interest rate policy and macroeconomic stabilization

In line with this approach, which became popular in many countries in the 1990s, we will first focus on the central bank as the main actor in demand management in response to demand or supply shocks. This already opens up an understanding of current economic policy debates, which often revolve around the interest rate policy of the central banks to control the economy, while the fiscal policy discussion today is often limited to maintaining a more or less "balanced" budget.^{39} However, we will see later that this specific economic and political role allocation can only be effective under certain model assumptions, which were and are repeatedly called into question, especially after the financial crisis of 2007-09, the euro zone crisis and the current corona crisis.

**The central role of inflation expectations**

In the 3-equation model of the NKM by Carlin and Soskice (2015, Chapters 1–3), inflation expectations form an important point of reference for the central bank's economic policy measures. Why? In Chapter 10 we saw that both demand and supply shocks mean that inflation expectations will steadily rise or fall and thus move further and further away from a target value set by the central bank (\ (\ pi ^ T \)). In our model, this leads to the Phillips curve shifting further and further, leading to ever increasing or decreasing inflation and thus wage-price spirals. From this model behavior we can already see that inflation expectations must play a central role in the central bank's response to macroeconomic shocks. Ultimately, the central bank's concern must be to bring inflation expectations back into line with its inflation target.

In order to understand how the central bank can succeed in reducing inflation expectations in this way with the help of interest rate policy, let us first concentrate on the example of a positive demand shock. This may have been triggered, for example, by an exogenous increase in autonomous consumption by private households. To repeat, Figure 11.2 illustrates this scenario in our overall model. The positive demand shock associated with a right shift in the IS curve means that if the interest rate level remains unchanged, employment will be higher, which will lead to rising nominal wage claims. The Phillips curve therefore shows an inflation rate that is above the target value.

Figure 11.2: Positive demand shock.

In this situation, without political intervention, the inflation rate would rise more and more, as inflation expectations, and with them the Phillips curve, would continue to shift upwards. What can the central bank do?

The best possible response from the central bank will only come about if the central bank could respond to the demand shock before the current wage round is over. Then it could neutralize the demand shock by raising the interest rate and thus simply prevent the inflation rate from deviating from its target value in the first place. In Figure 11.2, the central bank would have to choose precisely the interest rate that leads to the inflation-stabilizing level of employment on the IS curve, which has been shifted to the right by the demand shock. In the income-expenditure quadrant, the demand curve shifts back to its original position and the distribution equilibrium is not disturbed.

If the central bank responded immediately with an immediate impact on demand, there would be no further problem from the demand shock. The inflation rate would remain at its target value. However, this is not a particularly realistic case for at least two reasons. First, the central bank cannot (perfectly) foresee the demand shock and can therefore only react to it with a delay. The rise in nominal wage demands in the first wage round cannot then be prevented, and the dynamic we are familiar with arises from changes in the realized inflation rate and inflation expectations. Second, we have seen that realistically the interest rate will only have a lagging effect on investment demand. Even if the central bank could react immediately to the demand shock with a change in interest rates, the effect of this reaction on demand will only materialize later. Under these circumstances, the initial surge in inflation cannot be prevented directly. We will assume this constellation in the following. That is, the central bank does not foresee the shock and investment demand is delayed in reacting to a change in the interest rate. The first assumption means that the central bank does not set the interest rate until after a shock and after the respective wage round has closed. The second assumption can be modeled with a lag of the real interest rate in the investment function and thus the IS curve (see Section 7.4)

\ [\ begin {equation} Y ^ * = A - \ alpha r _ {- 1} \ tag {11.1} \ end {equation} \]

These two assumptions mean that inflation expectations will change in any case as a result of the positive demand shock. The central bank must therefore find a way to stabilize inflation expectations through demand management and ultimately bring them back to their target value. But how could she succeed in doing this in principle?

Intuitively, we can best answer this question using the IS curve and the Phillips curve diagram as shown in Figure 11.3. Whereby we show the Phillips curve with reference to output, instead of employment, in order to be able to show the two diagrams one above the other.

Figure 11.3: Demand shock in the IS and Phillips curve diagram.

If we now observe a positive demand shock, the IS curve in the above part of the figure shifts to the right. The current interest rate, which the central bank has not changed in the absence of a forecast of the shock, results in higher levels 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 rise in the inflation rate leads to higher inflation expectations. The central bank has now observed the shock and knows the new inflation expectation if we assume adaptive expectations in the private sector. The central bank estimates a Phillips curve, which represents the totality of the possible combinations of inflation and employment or employment correctly expected by the central bank.Represents output in employment and next round inflation. Since the first round is not yet fully completed (the last step is the determination of the new interest rate by the central bank), we also speak of the “predicted” Phillips curve of the central bank for the next round, i.e. \ (PC_2 \).

Now the central bank can use its interest rate control on this predicted Phillips curve (\ (PC_2 \)) to choose a point that will keep inflation expectations from rising any further and that is in line with the inflation target. On the IS curve, the central bank can read and set the necessary corresponding interest rate required to bring output and employment back to the equilibrium level, thus completing the round. The delayed effect of the new, higher interest rate will then be felt in the next round (round 2). Output, employment and the rate of inflation are falling, and as a result inflation expectations also fall. The Phillips curve predicted by the central bank for the following round shifts back to its original position and the central bank can again select an output on this curve that now corresponds to the long-term equilibrium of the economy and is in line with the inflation target. Since the inflation expectations in the second round coincide with the actually realized inflation rate, the economy stabilizes at the original level. Figure 11.4 shows this adjustment process in three steps.

Figure 11.4: Return to the inflation target as quickly as possible after a positive demand shock.

The first arrow illustrates the shock that leads to an initial rise 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 response, which is creating a level of output on the new predicted Phillips curve that is in line with the inflation target. After the central bank has set the desired interest rate and round 1 is completed, the Phillips curve predicted in round 1 (\ (PC_2 \)) is replaced by the Phillips curve that was current in round 2. The same procedure is then repeated in round 2. Finally, the Phillips curve shifts back to its original position and the central bank can end its restrictive policy and restore the long-term 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's reaction to a negative demand shock shows that the central bank can achieve its inflation target just two rounds after the shock. The only requirement is that it raises the interest rate enough. However, such a reaction by the central bank is by no means unproblematic.

In order to neutralize the effect of the positive demand shock on the inflation rate as quickly as possible, the central bank must lower output and thus employment well below the inflation-stabilizing level, \ (L ^ N \). The central bank can only combat the surge in inflation by significantly increasing the unemployment rate above the long-term equilibrium level (NAIRU) in order to return to the inflation target as quickly as possible. This is necessary in order to reverse the wage-price dynamics caused in the WS – PS diagram and to quickly bring the inflation expectations back to the target value. The significant increase in the unemployment rate is only temporary, but it is associated with a high loss of welfare and social costs.

In the interactive Figure 11.6, 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.

But does the central bank have to react in the manner discussed above? Or is there a “gentler” way to react? That depends crucially on what the central bank's goals are. If their aim were to achieve the inflation target on one side, then the reaction described above would be optimal from the central bank's point of view, since limiting unemployment itself would not be an economic policy aim of the central bank. Rather, unemployment would be a pure means to an end, with the sole aim of keeping the inflation rate constant. The situation is different if the central bank also includes the effects on unemployment in its monetary policy strategy.

### 11.3 Various objectives of the central bank: the central bank reaction function and the monetary policy rule

For a central bank that includes unemployment as well as the inflation target in its economic policy response, the approach outlined in Section 11.2 is by no means optimal. Instead, the central bank will try to strike a balance between restoring the inflation target as quickly as possible and avoiding an excessive rise in unemployment. To do this, the central bank must weigh up 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.

In fact, we can do both of those goals with one **Objective function** model for the central bank. This will later help us infer an optimal response function for the central bank. For this we define the "loss" of the central bank, \ (Loss \), as a function of unemployment and the inflation rate:

\ [\ begin {equation} Loss = Loss \ left (\ text {Inflation rate}, \ text {Unemployment} \ right) \ tag {11.2} \ end {equation} \]

If we assume that labor 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, however, the central bank is interested in the fluctuations of these two values around the respective target values. These fluctuations are given by \ ((Y - Y ^ N) \) for the output and \ ((\ pi - \ pi ^ T) \) for the inflation rate. We can therefore model the loss function even more precisely through the deviations of the realized values of inflation and output from their target values. If we also assume that positive and negative deviations generate the same loss for the central bank, then we can explicitly write this function as the sum of the squared deviations of the inflation target and inflation-stabilizing output.

\ [\ begin {equation} Loss = Loss (\ pi, Y) = (Y - Y ^ N) ^ 2 + (\ pi - \ pi ^ T) ^ 2 \ tag {11.4} \ end {equation} \]

Squaring the deviations simply means that both negative and positive deviations mean a higher loss for the central bank. The loss of the central bank will therefore increase both with the deviation of the inflation rate from the inflation target and with fluctuations in output around the inflation-stabilizing level. The optimal loss of zero is therefore only achieved if both target values are achieved.

In the loss function written down in equation (11.4), inflation and output fluctuations are included in the same way. We then speak of an equal “weighting” of the two goals. However, we could also assume that the central bank sees either of the two objectives as more important. For example, the central bank might be more concerned about an increase in unemployment than it would about an increase in inflation, or vice versa. We can integrate a different weighting of the goals into our loss function using a positive weighting parameter, \ (\ beta \ geq 0 \):

\ [\ begin {equation} Loss = Loss (\ pi, Y) = (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 one, \ (\ beta = 1 \), i.e. that the goals are weighted equally. If \ (\ beta> 1 \) then is the central bank **inflation averse**, Fluctuations in the inflation rate then generate a higher loss than fluctuations in output or unemployment. If \ (\ beta <1 \), then is the central bank **unemployment averse**.

We can now also visualize our loss function graphically. Since the loss can increase in two variables (inflation and output) we can illustrate it with a three-dimensional map. In doing so, we assume a simplification for the numerical examples and simulations in order to be able to retain the parameter constellation used so far for the other model elements. The simple loss function from equation (11.5) only applies if the inflation-stable output is normalized to 1. For the numerical simulation, we scale our central bank loss parameter by a factor of 100, so that the simulated loss function approximately follows equation (11.5). In order to be able to recalculate the numerical results of the central bank's loss in the following figures and simulations, the parameter \ (\ beta \) must be multiplied by a factor of 100.^{40}

Figure 11.7: Central bank loss function.

At the "bottom" of Figure 11.7, the loss is 0. This is the optimal value that is only achieved with the inflation target and inflation-stabilizing employment. For any higher loss, there are a number of combinations of inflation and output that can generate that specific loss value. These combinations lie on the rings that we would get if we were to cut through the loss functions on a horizontal plane (or if we were to look at the loss function from above). Each of these rings represents a specific level of loss and the combinations of inflation and output that generate that value. The higher the loss level, the larger the diameter of the respective ring.

We also refer to these rings as **Indifference curves**because the central bank is indifferent to the loss of the various combinations of inflation and output that lie on the ring. No combination is better than another on the ring.

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 11.8 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 realized loss, but are not possible due to the location of the short-term Phillips curve.

Figure 11.8: Central bank indifference curves.

Due to the unpredictability of the shocks and the delayed effect of interest rate changes on demand, the central bank cannot change the situation in the first round. However, it can try to use its interest rate policy to reduce the level of losses in the next round. To do this, she can choose from all possible combinations of inflation and output, which are given by the Phillips curve \ (PC_2 \) predicted in round 1 in Figure 11.9. Since the central bank wants to minimize the loss, it will choose a point on the Phillips curve \ (PC_2 \) that is tangent to as “small” a ring as possible.

Figure 11.9: Minimizing the anticipated loss after a positive demand shock: the best possible policy response to a positive demand shock.

The central bank is not (yet) at its target position (inflation target and inflation-stabilizing output level), but it can keep the loss in round 2 to a minimum.

The process of economic policy adjustment is not yet over. However, the central bank was 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 towards its original position. In order to keep the loss to a minimum, the central bank must also target the optimal combination of output and inflation on the new predicted Phillips curves (\ (PC_3 \)) in the following rounds. The procedure is the same as before. The central bank minimizes the loss for the Phillips curve by choosing the smallest possible diameter of the indifference curve. As a result, the inflation rate continues to move in the direction of 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 and thus steering the economy towards its inflation-stable equilibrium. This is shown in Figure 11-10.

Figure 11.10: Further adjustment in the direction of general equilibrium.

In Figure 11.11 we are in round 4. The central bank has reduced inflation expectations “almost” to the inflation target. The current inflation rate is 2.05% while the predicted inflation rate, which further minimizes the loss function, is 2.025%, very close to the inflation target of 2%.

Figure 11.11: Full adjustment to target inflation and inflation-stable output and employment levels.

Let us summarize: The decisive driver for the adjustment to the target inflation rate and inflation-stable output and employment level are here again the inflation expectations, which underlie the nominal wage demands of dependent employees. The central bank uses its options for controlling output and inflation in order to gradually bring inflation expectations back to their target value. This shifts the short-term Phillips curves and enables the central bank to stabilize the economy as smoothly as possible. This process continues until the central bank's targets are met again and its loss is zero again.

As can be seen in Figure 11.11, the adjustment process runs along a line (red arrow) that results from the connection of the optimal reaction points of each round. This shows that the optimal reaction of the central bank to a shock follows the same system or rule across all rounds. The same adjustment rule indicated by the line also applies in the event of a negative demand shock and, similarly, even in the event of supply shocks (more on this later). To generalize the rule for positive and negative demand shocks of any size, we simply have to continue the line in both directions. The optimal reaction point for any demand shock then lies precisely at the intersection of the reaction line and the short-term Phillips curve for each round. Figure 11.12 represents the **optimal reaction line** for a positive demand shock. We follow Carlin and Soskice (2015, chapter 3) and call this reaction line the **gel political rule**, MR (*English* monetary policy rule).

Figure 11.12: Monetary policy rule (MR) and positive demand shock.

In the interactive figure 11.13 the loss of the central bank is illustrated by indifference curves. The weighting parameter and the inflation target of the central bank can also be changed.

The graphical derivation of the MR curve is based on a minimization of the central bank loss in each round after a shock. We can use the same procedure for the formal derivation of the MR curve and the equation on which it is based. The intuition is as follows: in each round the central bank tries to use the loss function of the next round

\ [\ begin {equation} Loss _ {+ 1} = Loss (\ pi _ {+ 1}, Y _ {+ 1}) = (Y _ {+ 1} - Y ^ N) ^ 2 + \ beta (\ pi _ {+ 1} - \ pi ^ T) ^ 2 \ tag {11.6} \ end {equation} \]

to minimize. The possible combinations of output and inflation from which the central bank can choose are, however, given by the forecast short-term Phillips curve for the respective round:

\ [\ begin {equation} \ pi _ {+ 1} = \ pi + k (Y _ {+ 1} - Y ^ N) \ tag {11.7} \ end {equation} \]

The forecast Phillips curve is therefore the condition under which the central bank must minimize its loss. So we can simply insert the forecast 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 the central bank uses to minimize the loss function is the output of the next period, \ (Y _ {+ 1} \). It can influence this directly on the IS curve with the interest rate of the previous period, \ (r \). The minimization of the loss function should now produce the smallest possible diameter of the indifference curve, whereby the central bank directly selects the optimal output on the Phillips curve and the associated inflation rate adjusts itself according to the wage-price dynamics on the labor market and the Phillips curve.How can we mathematically minimize the loss function? For this we derive the loss function given by equation (11.8) simply according to the output of the next period, \ (Y _ {+ 1} \).

The minimum of the loss function is given when its first derivative equals zero. Therefore:

\ [\ begin {equation} Y _ {+ 1} = Y ^ N - k \ beta (\ pi _ {+ 1} - \ pi ^ T) \ tag {11.9} \ end {equation} \]

We get an equation for the output of the next period with a negative slope compared 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 NKM

The monetary policy rule, which is represented by the MR curve, forms the third central component of the 3-equation model of the New Consensus. The equation that formally depicts the MR curve is, besides the IS curve and the Phillips curve, the third central equation of the model and represents the economic policy rule or reaction function for the central bank, which gives the model a stabilizing element. The integration of a stabilizing economic policy into the model has resulted in the model economy not drifting further and further from its equilibrium after a shock. Instead, economic policy can restore the equilibrium situation and the inflation target through the use of interest rate policy. Before we formally derive the MR curve in the next step, we have shown the three central elements of the model again in Figure 11.14. The goods market equilibrium is represented by the IS curve, here once as a real interest rate IS curve and once as a nominal interest rate IS curve (see Chapter 7.5). The Phillips curves represent the supply side of the economy, with the vertical long-term Phillips curve marking the equilibrium of distribution. The MR curve represents the monetary policy stabilization function of the central bank. The combination of inflation target and inflation stabilizing output represents the target equilibrium of the central bank.

Figure 11.14: The three elements of the three equation model.

The 3-equation model of the New Consensus according to Carlin and Soskice (2015, Chapter 3) now 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 shows 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 macroeconomic demand components, \ (A \), ie that part of total demand that does not depend on income.^{41}

**Phillips curve (9.22):**

\ [\ pi = \ pi ^ e + k (L - L ^ N) \] The second equation is a short-term Phillips curve (PC). The Phillips curve relates the current inflation rate, \ (π \), to the inflation expectations (given by adaptive expectations: \ (π _ {- 1} \)) and the current employment gap, which is expressed as a deviation from the current employment level, \ (L \), is defined by 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-term optimal interest rate and serves as the central bank's reaction function.

### 11.5 Responses to shocks

We can now use the MR curve to discuss the optimal response of the central bank to any type of shock in the context of the 3-equation model.

**Demand shocks**

For a positive demand shock, we have already done this when deriving the MR curve in subsection 11.3. In the case of an exogenous decline in demand - a negative demand shock - the reaction is symmetrical to the adjustment described above after a positive demand shock.

Figure 11.15: Monetary policy rule (MR) and negative demand shock.

So far we have assumed that the central bank can control the real interest rate directly. Here we now introduce the more realistic case of nominal interest rate control. The nominal interest rate to be set by the central bank must now take inflation expectations into account. On this basis, the central bank has to estimate the nominal interest rate IS curve and can then use this to determine the optimal nominal interest rate.

Our interactive scenario in Figure 11.16 can be used to achieve the best possible adjustment path in response to demand shocks.^{42}

**Change the preferences of the central bank**

The level of the parameter \ (\ beta \) in the loss function of the central bank (11.5) determines the preferences of the central bank and thus the speed of the adjustment process in response to an economic shock. If \ (\ beta \) is greater than 1, the central bank places more emphasis on deviations in inflation from the target value than on deviations in employment from the target value. In this case, the central bank is considered to be inflation averse. If \ (\ beta \) is less than 1, the central bank is less interested in inflation than in 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 interactive scenario in Figure 11.17, different values of central bank preferences can be experimented with.

**Supply shocks**

The fundamental difference between demand and supply shocks with regard to the reaction of the central bank in the 3-equation model of the NKM is that supply shocks also influence the general equilibrium of the economy, while this remains unaffected by demand shocks in the model world presented here. In Chapter 10, we distinguished between two different types of supply shocks:

A labor market shock leads to a change in the position of the wage setting curve (equation (9.4)), which occurs either through a change in \ (\ mathbf {b} \), e.g. through a change in social benefits, or through a change in the conflict orientation, \ (k \) that can be caused by dependent employees.

A price-setting shock, for example due to a change in the intensity of competition on the goods market and an associated change in the premium rate, \ (m \), leads to a shift in the price-setting curve (equation (9.9)).

As an example, we are discussing the reaction to a positive supply shock using a labor market shock that shifts the wage-setting curve downwards (the differences between the various supply shocks are marginal, see Chapter 10). In Chapter 10 we already saw that a positive supply shock leads to an increase in inflation-stabilizing employment or production. However, since demand does not automatically adjust to this new value, there is initially a decline in the inflation rate and a sustained disinflation process. This is shown again in Figure 11.18.

Figure 11.18: Positive labor market shock and increase in inflation-stable employment.

What does the optimal central bank reaction look like here? Instead of the old general equilibrium at \ (L ^ {N_ {old}} \), the central bank must now lead the economy to the new equilibrium at \ (L ^ {N_ {new}} \). This means that the supply shock not only shifts the Phillips curve, but also changes the position of the MR curve, provided the central bank recognizes that the supply shock leads to a permanent increase in inflation-stabilizing output and that it therefore has to adapt its optimal reaction function accordingly.

What happens now in the individual steps of the adjustment? As can be seen in Figure 11.19, the Phillips curve shifts in round 1 due to the positive supply shock from \ (PC_0 \) to \ (PC_1 \), and the inflation rate falls to \ (\ pi_1 \) = 1.8% and thus below the target inflation rate of 2%. The output in round 1 remains unaffected. The central bank recognizes the permanent supply shock and adjusts its optimal reaction function in round 1 from \ (MR_ {old} \) to \ (MR_ {new} \). In the next step she will choose the optimal point on the forecast Phillips curve for round 2 (\ (PC_2 \)) and change her interest rate accordingly. This concludes round 1. In round 2, the delayed effect of the interest rate change leads to an increase in output and the inflation rate, which also shifts inflation expectations upwards. The projected Phillips curve shifts in the direction of the new general equilibrium and the central bank can target an output in the next round that is closer to the inflation-stabilizing level.

Figure 11.19: Adjustment after a positive supply shock.

Analogous to the scenario in Figure 11.16, the interactive scenario in Figure 11.20 can be used to understand the economic policy implications of a supply shock in the context of the 3-equation model. The users can decide under labor market shock and price setting shock.

### 11.6 Limits to stabilization through the central bank's interest rate policy: deflation trap, zero interest rate limit and investment trap

In the previous sections we saw that the central bank can always bring the economy back to its general equilibrium. It just has to follow its optimal reaction function.

However, within the 3-equation model presented here, it can also be shown that the central bank's demand management will only be sufficient to stabilize the economy under “normal circumstances”. In the event of a deep crisis, the central bank can quickly reach its limits. The expansionary measures that the central bank can then take may not be enough to lead the economy out of the crisis.

Such a severe crisis can be triggered, for example, by a strong negative demand shock, for example as a result of the financial crisis of 2007-09, the euro zone crisis from 2010 or the current pandemic-related crisis. This is illustrated in Figure 11.21. The collapse in demand leads to a strong left shift in the IS curve. At the current level of interest rates, output and employment fall to a very low level. If the drop in demand is so severe that the model economy slips into deflation in the first round, the central bank should now try to stimulate the economy by choosing a low interest rate level and create a positive output gap. This should then reverse the path of inflation expectations and gradually return to the target value. However, the central bank cannot do this in the example shown in Figure 11.21. How so?

Figure 11.21: Strong negative demand shock.

As can be seen in Figure 11.21, the sharp decline in inflation expectations shifts the predicted short-term Phillips curve far down for the next round. The optimal output would require a negative nominal interest rate on the IS curve (\ (i <0 \)). However, this is not possible for the central bank as it cannot lower the nominal interest rate into negative territory. We are also talking about the **Zero interest rate limit**. Instead of its optimal interest rate, the central bank will set an interest rate of zero and is therefore limited in its monetary policy reaction options. The best possible reaction (\ (i ^ {best} = 0 \)) leads on the IS curve to an output (and employment) well below the inflation-stable output and employment level (\ (Y (i = 0) = L (i = 0)

Is there a way out of the situation shown in the previous figure? The answer lies in fiscal policy. Stabilization can only succeed here if there is an additional demand stimulus from government spending. The central bank is therefore dependent on the help of fiscal policy here. Optimally, government spending must rise so much 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 reaching the zero interest rate limit and an impending deflation trap is illustrated in the "zero interest rate limit" scenario in the interactive scenario from Figure 11.16 when a deep crisis is triggered. In the scenario it becomes clear that the central bank no longer has the necessary economic policy instruments to stabilize the economy. Only with the help of an expansive fiscal policy can the economy be brought back to a long-term equilibrium of distribution at \ (L ^ N \). After an expansive fiscal policy has been pursued to a sufficient extent, the optimal central bank interest rate becomes positive again and the monetary policy is thus effective again.

In the interactive scenario “zero interest rate limit” it becomes clear that from the point of view of the “new consensus” in macroeconomics, monetary policy is an effective means of stabilizing the economy in the short term and under normal circumstances and only needs to be supported by fiscal policy in exceptional cases. It also shows that an expansionary fiscal policy is not an efficient way of reducing unemployment below the NAIRU level in the long term. A demand-driven rise in employment will lead to a rise in inflation and thus a central bank response aimed at reducing aggregate demand to a level consistent with the NAIRU. Fiscal policy therefore plays a subordinate role in the NKM. From the NKM's point of view, fiscal policy should therefore generally refrain from active demand management in order to help the central bank keep inflation under control.

### Investment trap in the 3-equation model

In addition to the zero interest rate limit, the occurrence of the investment trap from Chapter 7 within the 3-equation model can mean that the central bank can no longer stabilize the economy by means of interest rate policy. The investment trap has the effect that a change in the interest rate no longer leads to a change in the goods market equilibrium; so the IS curve is here *interest-inelastic*. This situation is shown in Figure 11.22. The central bank has no way of maintaining employment at the level necessary to reverse inflation expectations. This role can only be fulfilled by fiscal policy, which has to set an expansive demand impulse via government spending, \ (G \). The central bank will only be able to act again when the investment trap no longer exists and the investments become interest-elastic again.

Figure 11.22: Vertical IS curve in the 3-equation model.

### 11.7 Summary of the economic policy implications of the 3-equation model of the NKM

Finally, we can now briefly summarize the policy mix (or the assignment) of the 3-equation model of the New Consensus in Macroeconomics:

The **Monetary policy** the central bank is therefore responsible in the long term for controlling the inflation rate and achieving the inflation target. The central bank uses its interest rate policy as an instrument for this. Changes in interest rates by the central bank have short-term effects on employment and unemployment. Changes in the unemployment rate serve as a means of meeting the long-term inflation target. Long-term equilibrium unemployment, the NAIRU, is determined by the institutional structures and norms of the labor market and the goods market and cannot be directly influenced by the central bank.

The **Labor market, wage / income and competition policy** influences the labor market institutions and the intensity of price competition on goods markets. These are the main determinants of the equilibrium of distribution and inflation-stable employment, or the NAIRU. A reduction in e.g. social benefits, i.e. a generally lower bargaining power of the dependent employees and their unions, as well as higher price competition between the companies on the goods market, reduce the NAIRU. Whether a lower NAIRU made possible in this way and higher inflation-stable employment will actually be achieved then depends on the reaction of monetary policy.

The **Fiscal policy** of the state does not normally play a role in macroeconomic stabilization. The state should therefore strive for a balanced budget in the long term and thus support monetary policy in its policy of inflation control. If the state were to try to reduce unemployment through expansionary fiscal policy, this would only have an inflationary effect in the long term and would therefore have to be combated by monetary policy with high interest rates. The state should therefore concentrate on increasing inflation-stable employment and reducing the NAIRU through supply policies on the labor market and the goods market, i.e. through structural reforms.

An ex ante **Coordination of policy areas** is actually not necessary if every political actor consistently fulfills his task.The central bank pursues its inflation target in the long term and pursues a policy of inflation control that also has effects on employment and unemployment in the short term. The state pursues a policy of structural reforms in the labor market and the goods market, which reduce the NAIRU and increase inflation-stable employment. An active fiscal policy for macroeconomic stabilization is not necessary and would come into conflict with monetary policy. The state should therefore pursue a balanced budget policy in the long term. There is also no room for an independent, goal-oriented wage and income policy of the collective bargaining parties (trade unions and business associations). Rather, the aim of state structural policy must be to enable nominal wages to be as flexible as possible on the labor market and thus, in particular, to reduce the influence of trade union wage policy.

However, this policy mix and the role assignment contained therein presupposes that the main actor in the NKM, the central bank, can actually and unreservedly use its interest rate policy for domestic inflation control. In an open economy that is not dealt with here, it must therefore not be restricted, for example, by the obligation to comply with implicit or explicit exchange rate targets.

We have also shown in our model, and the crises 2007-9 and 2020 also provided empirical evidence for this, that the policy mix of the NKM presented here reaches its limits in deep recessions and crises. Interest-inelastic investments (investment trap), reaching a nominal lower limit of zero for the nominal interest rate controlled by the central bank, as well as uncontrollable deflation processes represent the limits of macroeconomic stabilization by the central bank in deep recessions. Here, an expansionary fiscal policy is required to avoid total collapse avert. Government deficit financed expenditure must stabilize the economy and return it to a “normal range” with positive inflation rates and interest-elastic investments so that the central bank's interest rate policy can be effective again.

In the last interactive scenarios 11.24 and 11.23, the functionality of the 3-equation model can be repeated. In the interactive scenario 11.23, the determination of the economic policy is left to the users. It is possible to change the values of the parameters and the exogenous variables as required. The results are presented with curves and impulse response functions.

In the interactive scenario 11.24, economic policy is determined endogenously. The users can determine the type of shock, the preferences of the central bank and the inflation target. The results of the simulation are only shown with impulse response functions.

### Further reading for chapter 11

**Textbooks:**

- Bofinger (2019, chapter 23)
- Carlin and Soskice (2015, chapter 3)
- Snowdon and Vane (2005, chap. 7)

### literature

Bofinger, P. 2019. *Fundamentals of Economics: An Introduction to the Science of Markets*. 5th edition Halbergmoos: Pearson.

Carlin, W. and D. W. Soskice. 2015. *Macroeconomics: Institutions, Instability, and the Financial System*. Oxford University Press.

Clarida, R., J. Gali, and M. Gertler. 1999. The Science of Monetary Policy: A New Keynesian Perspective. *Journal of Economic Literature* 37, No. 4: 1661-1707.

Goodfriend, M. and R. King. 1997. The New Neoclassical Synthesis and the Role of Monetary Policy. In: *NBER Macroeconomics Annual 1997, Volume 12*, 231-296. National Bureau of Economic Research, Inc.

Hein, E. 1998. Keynesianism - an economic theoretical and political obsolete model? Keynesian economic policy perspectives. *WSI announcements* 51, No. 12: 820-32.

Hein, E. 2008. *Money, Distribution Conflict and Capital Accumulation: Contributions to ’Monetary Analysis’*. New York: Palgrave Macmillan.

Kalecki, M. 1954. *Theory of Economic Dynamics: An Essay on Cyclical and Long-run Changes in Capitalist Economy*. London: George Allen; Unwin.

Kalecki, M. 1987. *Crisis and Prosperity in Capitalism: Selected Essays 1933-1971*. Marburg: Metropolis Verlag.

Keynes, J. M. 1936. *The General Theory of Employment, Interest, and Money*. London: Palgrave Macmillan.

King, J. E. 2015. *Advanced Introduction to Post Keynesian Economics*. Cheltenham: Edward Elgar.

Lavoie, M. 2006. *Introduction to Post-Keynesian Economics*. Basingstoke: Palgrave Macmillan.

Snowdon, B. and H. R. Vane. 2005. *Modern Macroeconomics: Its Origins, Development and Current State*. Cheltenham: Edward Elgar.

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