Chapter 10: New Keynesian Models of Monetary Policy PDF

Chapter 10 New Keynesian models of monetary policy 10.1 Introduction In the previous chapter, we analysed the effects of monetary policy which utilises monetary aggregates as the monetary policy instrument. However, modern macroeconomic research and actual monetary policy implementation suggest th...

Chapter 10 New Keynesian models of monetary policy 10.1 Introduction In the previous chapter, we analysed the effects of monetary policy which utilises monetary aggregates as the monetary policy instrument. However, modern macroeconomic research and actual monetary policy implementation suggest that the current policy instrument is the short-term interest rate controlled by the central bank via open market operations. Pure classical models suggest that money has no real effects at any horizon. If we introduce nominal and real frictions or relax some other key assumptions of the classical model, such as rational expectations, then monetary policy can have real effects in the short run. In this chapter we will examine the efficacy of a monetary instrument, the short-term interest rate, using a small scale new Keynesian macro model. 10.2 Aims This chapter aims to introduce models with nominal (price) frictions where the monetary policy instrument are short-term interest rates. We find short-term real effects of monetary policy under certain conditions. 10.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: explain key ingredients of the New Keynesian macro-model describe the monetary policy reaction function or the Taylor rule analyse the impact of demand shocks on macroeconomic outcomes analyse the impact of supply shocks on macroeconomic outcomes discuss the relevance of financial frictions in such models. 137 10. New Keynesian models of monetary policy 10.4 Reading advice This chapter follows on directly from Chapter 8 and Chapters 3 and 5 of Carlin and Soskice (2006) so you should familiarise yourself with the material presented in these chapters. You should read these while working through this section. The articles by Carlin and Soskice (2005) and by Taylor (1998) are also essential reading. Bernanke et al. (1999) discusses the role of financial accelerator in new Keynesian models. 10.5 Essential reading Books Carlin,W. and D. Soskice Macroeconomics: Imperfections, Institutions and Policies. (Oxford: Oxford University Press, 2006) Chapters 3, 5 and 15. Journal articles Aksoy, Y. H.S. Basso, J. Coto-Martinez ‘Lending relationships and monetary policy’, Economic Inquiry 51 2013, pp.368–393. Bernanke, B., M. Gertler and S. Gilchrist,‘The financial accelerator in a quantitative business cycle framework’, Chapter 21, in ‘Handbook of Macroeconomics’, Volume 1, Edited by J.B. Taylor and M. Woodford, 1999, Elsevier. Carlin, W. and D. Soskice ‘The 3-equation New Keynesian model – A graphical exposition’, BE Journals in Macroeconomics: Contributions, 5(1) 2005, pp.1–38. Clarida, R., J. Gali and M. Gertler ‘The science of monetary policy: A new Keynesian perspective’, Journal of Economic Literature 37 1999, pp.1661–1707. Clarida, R., J. Gali and M. Gertler ‘Monetary policy rules and macroeconomic stability: evidence and some theory’, Quarterly Journal of Economics 115(1) 2000, pp.147–80. Kiyotaki, N. and J. Moore ‘Credit cycles’, Journal of Political Economy, 105 1997, 211–248. Kuttner, K. and T. Robinson ‘Understanding the flattening Phillips curve’, North American Journal of Economics and Finance, 21 2010, pp.110–125. Taylor, J.B. ‘Discretion versus policy rules in practice’, Carnegie-Rochester Conference Series on Public Policy, 39 1993, pp.195–214. Taylor, J.B. ‘An historical analysis of monetary policy rules’, National Bureau of Economic Research working paper, w6768, (1998). 10.6 Further reading Romer, D. Advanced Macroeconomics. (Boston; London: McGraw Hill, 2012, fourth edition), Chapter 7. 138 10.7. IS-PC-MR model of new Keynesian economics 10.7 IS-PC-MR model of new Keynesian economics Up to end of 1980’s macro-monetary analysis was dominated by IS/LM models starting with a graphical analysis. Although standard Keynesian models were under constant attack from rational expectations economists led by Robert Lucas and Edward Prescott, among others. They argued that the theoretical foundations of Keynesian models were weak even absent. It took a long time to bring in some microeconomic foundations into Keynesian economics. In the last 20 years or so the focus turned into the Dynamic Stochastic General Equilibrium (DSGE) models with optimising behaviour of households, firms and sometimes policy makers. This literature uses methodological foundations of the Real Business Cycle (RBC) research. At the same time it incorporates: imperfect competition in the goods market nominal rigidities, that is, firms cannot adjust their prices continuously in the face of shocks and/or nominal wage contracts cannot be changed continuously in the face of the shocks hitting the economy. This literature, now labelled as the new Keynesian Macroeconomics, is still under construction. The model implies that the monetary policy conducted by means of short-term rates can be effective to stabilise inflation and real output in the short run. It is important to note that the policy is neutral long run. Thus classical dichotomy between real and nominal variables are still valid under new Keynesian assumptions. In its simplest form these models have three building blocks: an IS curve (IS) a New Keynesian Phillips curve (PC) an optimal monetary policy reaction function or a simple monetary policy rule (also known as the Taylor rule) (MR). In this chapter we will follow closely Carlin and Soskice (2005, 2006) when describing the key mechanisms of the model. Typically, the model develops a framework of forward looking households and firms and therefore both IS and Phillips curves are forward looking, that is, expectations about future real output and inflation matter when setting optimal consumption and production. For the sake of simplicity, Carlin and Soskice present a case with a backward looking IS and Phillips curves (that is, looking at what has happened in the previous period when decisions are made). This is of course an important simplification and departure from the standard analysis of New Keynesian models. Other than its usefulness for simplicity, backward looking IS and Phillips curves can be to some extent justified by the presence of consumers who form habits in their consumption decisions. That is consumers care about how much they consumed in the previous periods when they decide about their current consumption. However, the policy maker, in other words, the central bank, is forward looking when deciding the level of short-term interest rates by taking the Phillips and IS curves as constraints. Key assumptions are the presence of nominal rigidities (wages and/or prices do not adjust instantaneously to shocks hitting the economy) and imperfect competition. 139 10. New Keynesian models of monetary policy The IS curve is given as: y1 = A − ar0 (10.1) where y1 is the actual real output in period 1, A is an autonomous expenditure variable and r0 is real interest rate set in period 0. The simplified Phillips curve is given as: π1 = π0 + α(y1 − ye ) (10.2) where π1 is the rate of inflation in period 1, where π0 is the rate of inflation in the previous period. ye describes the ‘trend’ or long-term output and is the level of output associated with constant rate of inflation. ye reflects the level of real output associated with the structural features of the economy such as the degree of competition in the goods market and the nature of the labour markets. The presence of π0 is ad hoc and based on empirical observations of inflation persistence. Inflation persistence may be a reflection of backward looking expectations, lags in wage/price setting behaviour, consumption habits and other types of real/informational imperfections not discussed here. The central bank minimises a loss function such that next period inflation (π1 ) is close to a target inflation level (π T ) and next period real output (y1 ) is close to the ‘trend’ output (ye ) subject to IS and PC equations. L = β(π1 − π T )2 + (y1 − ye )2 . (10.3) Note that the parameter β describes the importance of inflation against output gap for the central bank. The assumption that the central bank can control real rates ensures that the central bank uses forecasts of the future inflation rate when setting the policy instrument. We show the precise timing in the 3-equation model in Figure 10.1 (Carlin and Soskice (2005, 2006)). To derive the optimal interest rate rule (or the monetary reaction function), Carlin and Soskice introduce a variable called the short-term interest rate relative to the natural real rate of interest rs that the central bank chooses when the rate of inflation deviates from its target or the real output deviates from its trend output. Let us define the real rate of interest, the interest rate that would prevail when the economy functions at the full employment level and compatible with trend (or long-term) output as: ye = A − ars . (10.4) Subtracting this expression from the IS curve, gives us the IS curve defined in terms of output gap, i.e. y1 − ye . y1 − ye = −a(r0 − rs ). (10.5) The central bank minimises the loss by choosing the (r0 − rs ). After substituting the IS and PC equations into the central bank loss function, the loss function becomes: L = β(π0 + α(−a(r0 − rs )) − π T )2 + (−a(r0 − rs ))2 . (10.6) The central bank chooses (r0 − rs ) optimally. Therefore first order condition with respect to (r0 − rs ) is given by: ∂L = 2β(π0 − aα(r0 − rs ) − π T ) · (α(−a)) + 2(−a(r0 − rs )(−a)) = 0. ∂(r0 − rs ) 140 (10.7) 10.8. Analysing demand shocks Figure 10.1: Timing: Source (Carlin and Soskice (2005)). Solving for (r0 − rs ) yields: (r0 − rs ) = 1 a(α + 1 (π0 ) αβ − π T ). (10.8) This is the interest rule (IR) as a response to deviations from target inflation and output gap. For a = α = β = 1 the rule becomes simply: (r0 − rs ) = 0.5(π0 − π T ). (10.9) Essentially, by setting the interest rates, the central bank needs to forecast inflation and output gap next period. Even though the central bank observes the shock in period 0 (we will define in the following sections), due to lagged effect of interest rates on aggregate demand it cannot fully offset the impact of the shock in the current period. According to the ‘rule’ interest rates need to increase whenever actual inflation exceeds target inflation and vice versa. In the following we present a graphical exposition how the demand-side stabilisation works with respect to demand or supply shocks (Carlin and Soskice, (2005)). 10.8 Analysing demand shocks Following Carlin and Soskice (2005, 2006) Figure 10.2 exhibits the vertical (long-run) Phillips curve at the equilibrium output level, ye , under imperfectly competitive product and labour markets so that the equilibrium output level is where both wageand price-setters make no attempt to change the prevailing real wage or relative prices and each Phillips curve is indexed by the pre-existing or the past rate of inflation, 141 10. New Keynesian models of monetary policy π I = π1 . The economy is in a constant inflation equilibrium at the output level of ye ; inflation is constant at the target rate of π T . In the upper panel of Figure 10.2 is the goods market equilibrium characterised by the IS equation: the stabilising interest rate, rs , will produce a level of aggregate demand equal to equilibrium (trend) output, ye . Figure 10.2: IS and Phillips curves: Source (Carlin and Soskice (2005)). Figure 10.3 shows the case when the economy is subject to an aggregate demand (IS shock) shock when the target inflation (π T ) is 2 per cent (Carlin and Soskice 2005)). A positive shock to demand will lead to a positive output gap above the trend output, which in turn leads to an increase in price inflation above the target level. This is shown in the lower panel of Figure 10.3. It shows that given the prevailing short-term rate, rs , there will be a positive output gap (y > ye ) and associated inflation rate will be π0 > π T (Point A). The central bank conducts the monetary policy by manipulating the interest rate r0 . As in Carlin and Soskice (2005), it does so by forecasting the Phillips curve for next period. Due to the past inflation, its forecast π I will be 4 percent as shown by the dashed line in the PC diagram. Note that, all points on the forecast Phillips curve with 142 10.9. Analysing supply shocks inflation below 4 per cent are associated with a negative output gap (y1 < ye ). It is clear that conducting disinflationary policies is costly in terms of real output output.1 How is the policy maker going to choose the r0 along the new (forecast) Phillips curve? This depends on the stabilisation preferences of the central bank. If the central bank cares more about inflation stabilisation relative the output gap, the higher the preference parameter, β, will be in its loss function. Given that the interest rate (r0 − rs ) determines output gap which in turn determines the rate of inflation, the more inflation averse the central bank is, the more it is willing to sacrifice output (below ye ) to achieve its inflation objective. In Figure 10.3 the central bank will choose point B where the central bank indifference curve (loss function) and the forecast PC will be tangent. Therefore the new desired output level y1 is the aggregate demand target according to the optimal monetary policy rule. The monetary reaction function connects point B and the zero loss point at Z. The next step is to forecast the IS curve (IS’) associated with desired output level y1 . The dashed line in the upper panel shows the central bank interest rate r0 in agreement with the new desired output to stabilise the inflation. Clearly, interest rate needs to increase. In the absence of further IS shocks, the increase in the interest rate leads to a fall in output to y1 and inflation starts to decrease. The central bank repeats the steps above to achieve the target inflation. Essentially, both preferences of the central bank and the Phillips curve represent the inflation output trade-off the central bank faces. Given the policy instrument, the short-term rate, the central bank stabilises the economy through aggregate demand management following an IS (demand) shock. Temporary or permanent demand shocks According to our example the central bank needs to decide whether the demand shock is a temporary or permanent one. If the central bank believes that the shock is permanent (would persist for another period), central bank policy rate r00 should be higher than the new stabilising interest rate, rs0 . If the central bank’s forecasts are such that the output will revert to its initial level, then it will increase the interest rate by less since the stabilising interest rate would have remained equal to rs (i.e. its chosen interest rate would have been on the IS pre-shock curve in Figure 10.3 rather than on the IS curve). 10.9 Analysing supply shocks Structural changes in the economy may lead to a shift in the trend output therefore a shift in the vertical (long-run) Phillips curve. Prominent examples of such structural changes are changes in the wage- or price-setting behaviour (curbing labour union power for instance), a change in tax regime or benefits or changes in the nature of the goods market competition such that price mark-up changes. Suppose that the degree of competition intensifies which leads to a shift in the vertical Phillips curve to the right. Equilibrium output shifts from ye to ye associated with a 1 It is worth mentioning that in other versions of the New Keynesian models demand shocks do not lead to a trade-off between output and inflation. The central bank can stabilise inflation by stabilising the output gap. (See, for instance, Clarida et al. (1999). 143 10. New Keynesian models of monetary policy Figure 10.3: New Keynesian model and demand shocks: Source (Carlin and Soskice (2005)). stabilising interest rate rs decline at Z’. Short-run Phillips curve corresponding to inflation equal to the target (shown by the Phillips curve (π I = 2, ye )) shifts to the right as well. Some observations are in order: first inflation falls from target inflation level of 2 percent to zero percent as the economy moves from equilibrium point A to B. Second, monetary policy maker should forecast the Phillips curve constraint (Phillips curve (π I = 0, ye )) for the next period. Corresponding optimal level of output is shown by point C. To raise output to this level, it is necessary to cut the interest rate in period zero to r as shown in the IS diagram. The economy is then guided along the MR–AD curve to the new equilibrium at Z. The positive supply shock is associated initially with a fall in inflation and a rise in output – in contrast to the initial rise in both output and inflation in response to the aggregate demand shock. In other words, according to the model, a supply shock leads to countercyclical inflation, whereas an aggregate demand shock as in the previous section leads to a procyclical inflation. 144 10.10. Financial accelerator models Figure 10.4: New Keynesian model and supply shocks: Source (Carlin and Soskice (2005)). 10.10 Financial accelerator models This section briefly discusses issues that may arise between banks and real economic activity. Banks are important for economic activity as they often provide much needed external funding for entrepreneurial activity. It has also been long recognised that credit-market conditions may themselves be the source factor depressing economic activity. Bernanke et al. (1999) study a new Keynesian model with a modification for financial intermediation process that captures credit market imperfections. There are several ways of doing this within the general equilibrium setting. One is to assume collateral constraints as in Kiyotaki and Moore (1997), or the existence of lending relationships as in Aksoy, Basso, Coto-Martinez (2013). Bernanke et al. assume asymmetric information. They formulate a model where asymmetries of information play a key role in borrower–lender relationships. In this model, financial contracts reflect the costs of gathering information about the quality of borrower’s investment 145 10. New Keynesian models of monetary policy project. Several problems can occur in credit markets that may lead to a worsening of informational asymmetries and increases in the associated agency costs and thereby lead to fewer projects get external financing. These then will have widespread real effects.2 In their model, there are three types of agents, called households, entrepreneurs, and retailers. Entrepreneurs play a key role in their model. These individuals are assumed to be risk-neutral and have finite horizons: Specifically, they assume that each entrepreneur has a constant probability of surviving to the next period (implying an expected lifetime of 1/(1 − γ)). In each period t entrepreneurs acquire physical capital that is financed by either wealth (profits plus labour income) and borrowing that is subject to external finance premium. If the wealth or net worth is high, this allows for internal finance therefore entrepreneurs will be able to finance their investment rather cheaply, or equivalently if they seek external finance they can post these as collateral, therefore financing the project is less risky. As the external finance needs should be met via some form of lending contract and there are informational problems about the quality of the entrepreneurial project (agency problem – uncertain returns on capital that are subject to both aggregate and idiosyncratic risk), uncollateralised external finance should be more expensive than collateralised one. j j j Bt+1 = Qt Kt+1 − Nt+1 . (10.10) The expression above formalises the need to borrow from some credit institution. At time t, the entrepreneur who manages firm j purchases capital for use at t + 1. The j quantity of capital purchased is denoted Kt+1 , with the subscript denoting the period in which the capital is actually used, and the superscript j denoting the firm. The price paid per unit of capital in period t is Qt . Capital is homogeneous, and so it does not matter whether the capital the entrepreneur purchases is newly produced within the period or is old, depreciated capital. At the end of period t (going into period t + 1) j entrepreneur j has an available net worth, Nt+1 . To finance the difference between his j expenditures on capital goods and his net worth he must borrow an amount Bt+1 . The entrepreneur borrows from a financial intermediary that obtains its funds from households. The financial intermediary faces an opportunity cost of funds between t and t + 1 equal to the economy’s riskless gross rate of return, Rt+1 . The riskless rate is the relevant opportunity cost because in the equilibrium, the intermediary holds a perfectly safe portfolio (it perfectly diversifies the idiosyncratic risk involved in lending). Because entrepreneurs are risk-neutral and households are riskaverse, the loan contract the intermediary signs has entrepreneurs absorb any aggregate risk. Lenders have to pay a fee (auditing, accounting, legal and so on) to verify the state of the entrepreneur, so they incur costs by lending. In equilibrium, Bernanke et al. show that for an entrepreneur who is not fully self-financed, the return to capital will be equated to the marginal cost of external finance, i.e. ! j  k  Nt+1 Rt+1 . (10.11) Et Rt+1 = s j Qt Kt+1 The ratio s(·) of the cost of external finance to the safe rate – which is the discounted return to capital but may be equally well interpreted as the external finance premium – 2 Remember that Modigliani–Miller theorem implicitly states that the source of funding of a particular project does not matter for the outcome, be it by firm’s internal resources using, for instance, equity or by external resources, for instance, using bank loans. When credit markets are characterised by asymmetric information, the Modigliani–Miller irrelevance theorem is violated. 146 10.11. Simple monetary policy rules depends inversely on the share of the firm’s capital investment that is financed by the entrepreneur’s own net worth. It shows that capital expenditures by each firm are proportional to the net worth of the owner/entrepreneur, with aproportionality factor  that is increasing in the expected discounted return to capital s j Nt+1 j Qt Kt+1 . A high s reduces default probability and entrepreneurs can take on more debt and expand the size of the firm, thus economy expands, and vice versa. In other words, financial (or equivalently credit) constraints can lead to stronger downturns than when these constraints are absent; hence it works as a financial accelerator. 10.11 Simple monetary policy rules We conclude this chapter by a brief discussion of the simple policy rules, that is where monetary authorities implementing policy according to a rule or formula that is chosen to be applicable over a large number of periods. These are simple rules thus by definition not reflecting optimal choice of the monetary policy instrument given the state of the economy as done in the previous sections. Despite reducing the inflation bias which we will discuss in the chapter, possibly to zero, depending on the rule, such policy will not be able to counter the productivity shocks that hit the economy. If the economy is prone to productivity shocks so its variance of was large, it may be desirable for the monetary authorities to lean against the wind using expansionary monetary policy in a time of negative productivity shocks, for example. However, to do so will require discretion on the part of the authorities, but this will naturally lead to the inflation bias. In the argument of rules versus discretion we have to weigh up the cost of using discretion (the inflation bias) with the cost of using a rule (inability to counter productivity shocks).3 Two possible rule scenarios are discussed next. Taylor rules Taylor rules are simple monetary policy rules that prescribe how a central bank should adjust its interest rate policy instrument in a systematic manner in response to developments in inflation and macroeconomic activity. Following a rule is transparent. By committing to follow a rule, policy makers can communicate and explain their policy actions easily and should at least in principle enhance the accountability and credibility of the central bank. In Taylor (1998) an interest rate rule of the form: Rt = πt + g(yt − y ∗ ) + h(πt − π ∗ ) + r∗ (10.12) was argued to be a valid representation of how nominal interest rates respond to economic variables for a number of different monetary regimes. Rt is the nominal interest rate, πt is inflation, π ∗ is the target level of inflation, yt − y ∗ is output deviations and r∗ is the estimate of the real interest rate. (10.12) can be rewritten, by collecting terms together to obtain: Rt = (r∗ − hπ ∗ ) + g(yt − y ∗ ) + (1 + h)πt . 3 (10.13) Note that next chapter discusses inflation bias problem in detail. 147 10. New Keynesian models of monetary policy When fitting this model to US data from 1987, quarter 1, to 1997, quarter 3, the g coefficient was found to be 0.765 and the coefficient on inflation was found to be 1.533. The fact that these are positive, and for the case of the coefficient on inflation, greater than unity, is important for the stability of the economy. Activity 10.1 Consider (10.12). If inflation was equal to the desired/target rate of inflation and output deviations were zero (yt − y ∗ ), to what does the equation collapse? Consider a fall in demand that causes output to fall below y ∗ with no immediate impact on inflation. A positive g coefficient implies that nominal interest rates set by the monetary authorities should fall, since yt − y ∗ is now negative. With no change in inflation, the fall in nominal rates will decrease real rates and so encourage investment spending and aggregate demand. Output should then return to the full employment level. Now consider the case where inflation has increased above the target rate. If the coefficient on inflation in (11.1) is greater than unity, then the increase in nominal interest rates will be greater than the increase in inflation. This causes real interest rates to increase, leading to reduced investment spending and so reduces the inflationary pressure in the economy. With positive coefficients for g and h (causing 1 + h, the coefficient on inflation in (11.1), to be greater than unity) we should see stability in the economy, with output tending to be at its full employment level and inflation staying close to the target rate. If the coefficient on inflation in (11.1) was found to be less than one (h < 0), then an increase in inflation will be met by a less than one-for-one rise in nominal rates. This will cause real rates to fall, encouraging investment and aggregate demand that will cause further inflationary pressure. The economic system in this case would be unstable. Friedman’s rule of constant money growth Due to the long and variable lags associated with the formulation and implementation of monetary policy, Milton Friedman suggested that trying to control the economy through changing monetary variables, would purely lead to greater instability. Consider Figure 10.5. At date t0 a shock occurs that causes output to start to fall. The first recorded data of such an event may become available at date t1 . However, the authorities need more than just one data observation before changing their policy. After all, the data reading could be a blip or involve considerable measurement error. At date t2 enough data are available for the authorities to determine that a downturn is indeed happening and the decision is made to implement an expansionary monetary policy. Since it takes some time for the monetary policy decision to take effect, output is only affected at date t3 , but this is the point when the economy is starting to recover. The monetary expansion at a time when the economy is naturally starting to accelerate could lead to a more volatile path for output. Hence, Friedman suggested monetary policy should not be used to combat output fluctuations, not because of neutrality arguments but because of the long and variable lags involved with such an activist policy. 148 10.12. A reminder of your learning outcomes Figure 10.5: 10.12 A reminder of your learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: explain key ingredients of the New Keynesian macro-model describe the monetary policy reaction function or the Taylor rule analyse the impact of demand shocks on macroeconomic outcomes analyse the impact of supply shocks on macroeconomic outcomes discuss the relevance of financial frictions in such models. 149