Sacri ce ratio in a medium-scale New Keynesian model

Transcription

1 Sacri ce ratio in a medium-scale New Keynesian model Guido Ascari y University of Pavia Tiziano Ropele Bank of Italy and IfW June 4, 0 Abstract A medium-scale macroeconomic model, with a number of nominal and real frictions that have be shown to be important for explaining observed aggregate uctuations, is capable to quantitatively account for the empirically estimated sacri ce ratio after a disin ationary monetary policy. This nding, however, is sensitive to the degrees of price and wage indexation to past in ation and, to a less extent, to the price and wage Calvo probabilities. JEL classi cation: E3, E5. Keywords: Disin ation, Sacri ce ratio Ascari thanks the MIUR for nancial support through the PRIN 05 and PRIN 07 programme, grant 007P8MJ7P. The views expressed herein are those of the authors and do not necessarily re ect those of the Bank of Italy. The usual disclaimer applies. y Address: Department of Economics and Quantitative Methods, University of Pavia, Via San Felice 5, 700 PAVIA, Italy. Tel: ; guido.ascari@unipv.it

2 Introduction In this article we assess the ability of a medium-scale macroeconomic model to account for the output response to a permanent monetary policy shock, namely a disin ationary monetary policy shock. Speci cally, we employ a standard workhorse model with a number of nominal and real frictions that the literature has shown to be suitable to explain observed aggregate uctuations and the response of several macroeconomic variables to a temporary monetary policy shock. Our objective is to quantitatively assess whether this model can also replicate the empirically estimated sacri ce ratio after a disin ation. We believe that our research objective is important because, on the one hand, the empirical evidence makes it clear that disin ations are costly in terms of foregone output while, on the other hand, basic fully forward-looking New Keynesian models have been criticized for not being able to account for these costs. First, existing empirical studies have shown that successful disin ations have come with notable economic downturns (e.g., Gordon and King, 98, Ball, 994b, or Cecchetti and Rich, 00). The indicator that has been commonly used in the literature to measure the output costs of disin ation is the so-called sacri ce ratio (henceforth, SR), calculated as the cumulative percentage output loss (i.e. the di erence between actual and trend output) divided by the size of disin ation. Although exhibiting considerable variation across countries, historical episodes and use of di erent estimation methods, estimates of the SR in general lie in a range from to 3 (see the discussion in footnote 8). Second, in the theoretical literature, several authors have criticized the inadequacy of the basic New Keynesian model to account for a costly disin ation. Taylor (983) was the rst to show the possibility of a disin ation without recession in a nominal rigidity model. Ball (994a) even showed that a disin ation could also be followed by a boom rather than a slump (see also Burstein, 006). In a subsequent paper, Ball (995) introduces imperfect credibility as a necessary device to explain the observed output costs after a disin ation. More recently, Erceg and Levin (003) and Goodfriend and King (005) introduce imperfect credibility in a standard New Keynesian model to explain the famous Volcker disin ation (see also Nicolae and Nolan, 006). Mankiw

3 (00) also forcefully expresses the view that standard sticky price models cannot deliver in ation persistence and thus justify the costs of disin ation. Mankiw and Reis (00) proposed a di erent model of price stickiness based on sticky information to tackle this issue. The literature has then rationalized the output costs of a disin ation by appealing to some form of imperfect credibility/information/rationality. In this article, therefore, we check whether the numerous nominal and real rigidities present in our medium-scale macroeconomic model are su cient per se to generate empirically plausible costs of disin ation and see whether some frictions are more important than others. Our key ndings are as follows. First, a cold-turkey disin ation implemented through a simple interest rate rule leads to a prolonged decline in output. Output remains below its steady-state level for nearly quarters whereas in ation reaches its new, lower steady state in about 6 quarters. Second, the SRs calculated from the model simulation are coherent with the empirical evidence, standing on the low side of the range of SR estimates. Numerically, SRs are equal to, meaning that for each percentage point of permanent reduction of in ation the economy has to sacri ce a cumulative decline in output of one percentage point (in deviation from steady state). According to our numerical simulations, however, an important caveat applies to our ndings as our theoretical SRs are sensitive to the calibration of some parameters of the model. In particular, the SR varies is pretty much sensitive to the degrees of indexation in price and wage and to the Calvo probabilities of not being able to optimally change price and wage. When price and wage indexation is reduced to (from ) the SR drops to 0.5 whereas when the price and wage Calvo probabilities are increased to 5 from and 4, respectively, the SR jumps to nearly 6. Analysing the e ects of a cold-turkey disin ation. The model We use a workhorse medium-scale macroeconomic model (see, e.g., Christiano et al., 005, Smets and Wouters 003, 007) that extends the standard textbook, one-sector dynamic stochastic growth model by adding various real and nominal frictions. Real

4 frictions embed monopolistic competition in goods and labor markets, habit formation in preferences for consumption, variable capital utilization and adjustment costs in investment. Nominal frictions include Calvo-style nominal price and wage contracts. As in Smets and Wouters (003, 007), we assume that rms (wage setters) that cannot re-optimize their prices (wages) use a hybrid indexation rule, partly to lagged in ation ( t ) and partly to steady-state in ation (), i.e., ( t ) (), with : We also abstract from money, so our economy is a cashless one. We assume that the central bank is a pure in ation targeter and sets the nominal interest rate i t according to the following Taylor-type rule + i t + + i = t, () + with > and where t, and i represent the in ation rate, the in ation target and the nominal interest rate target, respectively. It is worthwhile to note that this simple rule neither responds to the output gap nor to lagged nominal interest rate. We chose this speci cation because we view the implementation of a cold-turkey disin ation as a moment in which the monetary authority is uniquely focussed on reducing in ation. Hence, having a countercyclical or inertial policy rule would con ict with the central bank s major intention to quickly disin ate the economy. We simulate a cold-turkey disin ation as an unanticipated (and perfectly credible) downward shift in the central bank s in ation target, say from high to low. Agents acknowledge that this shift is permanent and do not expect any future change. Furthermore, we assume that before the disin ation takes place the economy is in a high in ation steady state, characterized by = high. After the disin ation is implemented the economy will converge to the new steady state, characterized by = low. From a methodological perspective, we numerically simulate the dynamic adjustment path of all variables by solving the model in its non-linear form, without approximating the structural equations of the model around steady state. A complete description of the structural equations and of the parameter calibration used in this paper is contained in an Appendix available from our website. Note that through the standard consumption Euler equation the nominal interest rate target is pinned down by the in ation target ( ) and the representative household s subjective discount factor (), i.e., + i = ( + ) =. 3

5 Our model-consistent SR is then constructed coherently with the de nition in Ball (994b). In particular, the denominator of this ratio is the change in trend (steady-state) in ation over a disin ation episode, while the numerator is the sum of output losses, i.e., the deviations between actual output and its trend (steady-state) level. Thus, we measure the SR by totaling up the output losses from the moment that the disin ation begins up until the point output fully recovers, in the sense of getting back to its steady-state level. Formally, P T t=0 Y t=y SR = high low, () where Y represents the steady-state level of output and T is the number of quarters output takes to return to Y. Before proceeding, it is important to clarify that we tie our hands by calibrating the structural parameters that enter our medium-scale operational New Keynesian model using exactly the same parameters values reported in Christiano et al. (005). 3 For the purpose of our analysis, it is worth reporting some of these values. In particular, the point estimate of the Calvo probability of not being to able to re-optimise prices is equal to, while that of not being to able to re-optimize wages is equal to 4. 4 Estimates of the parameters of habit in consumption and of investment adjustment cost are 5 and.48, respectively. Finally, in Christiano et al. (005) prices and wages that are not re-optimized are fully indexed to past in ation (i.e., is calibrated to be equal to ).. Cold-turkey disin ation We now study the short-run e ects of disin ation, measuring the output costs in terms of the SR. We experiment di erent moderately high and low steady-state in ation rates, namely high = f4%; 6%; 8%g and low = %. Two comments are in order. First, we examine disin ations aimed at achieving an in ation target of % for two reasons: () it approximates well many central banks 3 For those parameters that are estimated in Christiano et al. (005) we use the values reported in the row labeled benchmark in table at page7. 4 According to these estimates price contracts last, on average,.5 quarters while wage contracts last, on average,.8 quarters. 4

6 actual in ation objectives, e.g. the Reserve Bank of New Zealand, the Bank of Canada, the Bank of England and the European Central Bank; 5 () it is also in line with recent estimates of the US Federal Reserve s implicit in ation target. 6 Second, we focus on disin ations of small size because: () our medium-scale model employes the timedependent Calvo staggered adjustment mechanism, and thus it would be inaccurate to evaluate the e ects of large disin ations as in this case the average frequency of price (and wage) changes should not be treated constant; and () the aim of this paper is to assess the quantitative prediction of this model to a disin ation relevant for monetary policy in the recent period, preceding the current economic crisis. Qualitative Considerations. Figure illustrates the dynamics of output, in ation, and nominal and real interest rates when = :5. In our medium-scale New Keynesian model, cold-turkey disin ations come with a sizable recession. In ation gradually decreases to the new lower target. Nominal and real interest rates increase on impact and then slowly revert to their respective steady-state levels. What is the main economic mechanism behind this nding? Due to the Calvo nominal price rigidity 7 when the central bank shifts downwards the in ation target not all rms are allowed to optimally set prices. Optimizing rms slow down the increase of their prices in the prospect of a declining output, which is needed to reduce in ation. Non-optimizing rms on the contrary raise prices by + high because of the indexation to lagged in ation. As a result in ation slightly diminishes. As in ation does not instantly adjust to the new target, and therefore 0 low > 0 (where 0 is the in ation rate in period 0), the central bank raises the nominal interest rate, though the downward shift in in ation target implies a lower steady-state nominal interest rate. The exante real interest rate increases and households postpone consumption and decrease 5 In New Zealand and Canada the in ation target extends from to 3%. In the United Kingdom the explicit in ation objective is currently %, while in the euro area the European Central Bank s in ation objective is below, but close to, %. 6 Leigh (008) nds that in the period the Federal Reserve s implicit in ation target varied in the range of -3%. 7 Clearly, the same reasoning also applies to wage setters behavior. Here, however, we primarily comment on rms behavior and in ation dynamics. 5

7 investment. Real wage drops, households supply less labor and rms reduce capital utilization. Output falls. Afterwards, in ation progressively diminishes adjusting to the new lower target and the central bank lowers the nominal interest rate. The ex-ante real interest rate stays above steady state for several quarters. The economy runs through a recession, in which output reaches the trough after two quarters. Output is back to steady state after quarters, while in ation in about 6 quarters. Figure also shows that neither the qualitative adjustments of output, in ation, nominal and ex-ante real interest rates nor the time length for in ation to converge to the new lower target are a ected by the initial level of in ation target. The level of high does quantitatively a ect the size of the fall in output throughout the recession. Table reports the decline of output (in percentage deviation from steady state) at the trough and illustrates that the severity in contraction of output substantially worsens as high increases. Intuitively, higher levels of high make optimizing rms cut prices more forcefully hence yielding a larger reduction in in ation and a greater rise in the ex-ante real interest rate. Having a more hawkish central banker, i.e. = 3, entails a relatively more contractionary monetary policy (the nominal interest rate would increase more) and a deeper contraction in output (see Table ). As a result, disin ation is slightly quicker, but the behaviour of rms and the adjustment path of in ation are qualitatively the same as in Figure. Quantitative Considerations. So we have shown that in our medium-scale New Keynesian model cold-turkey disin ations entail a notable decline in output, but how large is this decline? To answer this question, we compute the SR as de ned in (). Results are reported in Table. Two ndings are worth noting. First, SRs implied by our model lie on the lower side of the range of estimates obtained in empirical studies, i.e. from to 3. 8 However, in a recent research, Goncalves 8 Empirical researchers have used di erent methods to estimate the SR. Early measures of SR relied on the estimate of linear Phillips curve regressions (e.g., Gordon and King, 98, Andersen and Wascher 999, or Cuñado and Gracia, 003). Successively, other authors measured the costs of disin ation by rst detecting a disin ation episode, identi ed by statistically locating peaks and troughs in trend in ation, and then cumulating the deviation of actual output from the trend (e.g., Ball, 994b, and Zhang, 005). More recently, the issue of measuring the costs of disin ation has also been examined 6

8 and Carvalho (009) examine 6 disin ations that have taken place in OECD countries in the period with the aim to establish di erences in the disin ation costs between in ation-targeting and non-in ation-targeting countries. Their nding is striking: while their reported average SR is about 5.6, this value drops to for in ation-targeting countries. Moreover, the average duration of a disin ation in in ation-targeting countries is about quarters. 9 In an earlier work, Corbo et al. (00) have studied a group of 9 countries that adopted in ation targeting from the early 990s onwards and found an average SR of. Recall that our simulated SRs in Table are derived assuming an implicit in ation targeting interest rate rule as (). Our results are therefore remarkably in line with the estimated SRs found for in ation-targeting countries in the two studies above. Indeed, our model-based SRs are approximately equal to 0:95 and : when = :5 and = 3, respectively. Second, according to our results, SRs implied by the model are barely a ected by the disin ation size: varying the size of disin ation leads to a roughly proportional rescaling of the dynamic adjustment of output, thus leaving the SR basically unchanged. In summary, in our medium-scale macroeconomic model, cold-turkey disin ations entail sizable output costs which yields SRs of nearly, meaning that for each percentage point of permanent reduction in in ation the economy has to bear a cumulative output loss of percentage point. 3 Which frictions drive the results? In this section we assess which frictions are crucial to deliver empirically relevant output costs of disin ation. To this end, we recalculate the SR by perturbing the values of some structural parameters. Figure graphically reports the results in terms of contour plots. 0 In panel A, we through the use of structural VAR models, which also has provided a description of the dynamic adjustment of key macroeconomic variables (e.g., Cecchetti and Rich, 00, Durand et al., 008). 9 See Brito (00) for a critique of this study. 0 In the gures in this Section, we report the results for a cold-turkey disin ation from 4 to %. Results do not qualitatively change for disin ations that start from larger levels of steady-state in ation and are aimed to % or 0. 7

9 investigate the sensitivity of our results to the degrees of price and wage indexation to past in ation, varying both of them in the range [0:5; ]. It turns out that lower degrees of indexation to lagged in ation worsens the ability of the model to match the empirical estimates of the SRs. What is striking is the rapidity with which the theoretical SR decreases: for degrees of price and wage indexation equal to the SR falls to 0.5. Furthermore, between these two indexation parameters, the SR appears to be more sensitive to the price indexation. In panel B, we report the e ects of modifying two other important parameters, namely the Calvo probabilities for rms and wage setters to re-optimize prices and wages in the range [0:3; 0:9]. In this case, the SR shows a great variability, ranging from 0.3 for low values of nominal price and wage rigidity to 6 when prices and wages display a high degree of stickiness. Also, it turns out that as the nominal price rigidity increase the e ect of wage rigidity becomes progressively weaker and eventually disappears. Finally in Panel C, we experiment with the parameters governing the backwardlookingness of the consumption and investment dynamic equations. Speci cally, we varied the habit formation parameter in the range [0; 0:9] and the investment adjustment cost in the range [0:5; 3:5]. It turns out that these two structural parameters do not a ect much the SR, which in this case varies between 0:8 and :5. What is more interesting to note is the fact the SR is decreasing in these two parameters, suggesting that a more inertial dynamic in consumption and investment (and therefore output) is associated with a lower decline of output and only a longer time for output to return to steady state. In sum, the SR appears to be particularly sensitive to the degrees of price (and wage) indexation and to the nominal price (and wage) stickiness. To get the intuition, it is 8

10 useful to consider the (log-)linearized New Keynesian Phillips curve (NKPC), t = + t + + E t t+ + ( ) ( ) mc t (3) ( + ) where is the subjective discount factor, is the degree of indexation to lagged in ation, is the Calvo probability of not being able to re-optimize price and mc represents rms real marginal costs. Thus, the parameter governs the backward-lookingness of the NKPC. So, lower values of make the in ation dynamics less backward-looking and therefore the adjustment of in ation towards the new level is quicker. In other words, this means that at the time the disin ation is implemented, non-optimizing rms increase prices relatively less and therefore the in ation rate decreases more. The in ation gap 0 low is smaller and the central bank rises the nominal and ex-ante real interest rate less. As a result, the output decreases less, thus generating a smaller output cost. The Calvo probability a ects instead the slope of the NKPC. And it is easy to show that the larger the smaller the slope of the NKPC, i.e. the NKPC attens. Thus, in this case to achieve a given reduction in in ation the real marginal cost (which is roughly proportional to output) has to decrease more. The ability of the model to replicate empirically realistic values of the SR rests on the assumption of full indexation. Indexation is by now a standard assumption in New Keynesian macromodels, because it improves their empirical t. However, this is just a reduced form mechanism lacking any convincing microfoundations and structural interpretation (see, e.g., Benati, 009). In addition, this reduced form assumption can be observationally equivalent to other more structural phenomena, so that a similar e ect can actually come from irrational price setters (rule of thumbers, e.g., Galí and Note that this is the standard formulation of the hybrid NKPC. This formulation is not a ected by the presence of trend in ation, because the hybrid indexation rule takes the form: ( t ) (), as in Smets and Wouters (003, 007). It follows that whatever the value of, prices are fully index in steady state. Hence, trend in ation does not a ect the steady state value of the variables, and it does not enter the log-linearized coe cient at rst-order of the NKPC. It is worth to recall however, that we do not log-linearize the model in our simulations, but we use the original non-linear equations of the model. This is done with DYNARE, see Ascari and Merkl (009) for more details. This would not be true, however, if monetary policy was conducted by using the money supply as an instrument (see Ascari and Ropele, 00). 9

11 Gertler, 999), inattentive price setters (Mankiw and Reis, 003) or lack of credibility (Erceg and Levin, 003), and more generally to any mechanism that delivers sluggish expectation adjustment. This paper suggests that further empirical investigation is needed to determine which is the most likely structural mechanism that determines a positive SR after a disin ation. 4 Conclusions In this article we have tested a medium-scale operational New Keynesian model, with nominal and real frictions to see whether it can account for the output e ects of a permanent monetary policy shock, namely a disin ation. We nd that this mediumscale model passes also this test. More precisely, the model implies a recession during a disin ation and is able to quantitatively match the empirical estimates of the cost of disin ation, namely the sacri ce ratio. In particular, our numerical results return a value for the sacri ce ratio roughly equal to, which is a number that stands on the low side of currently available estimates but which is also very close to the estimated output costs for in ation-targeting countries. An important caveat applies to our ndings. More speci cally, the degrees of price and wage indexation to past in ation and, to less extent, the price and wage Calvo probabilities are the crucial frictions that drive our results and even small variations in these parameters may lead to very di erent results for the sacri ce ratio. 0

12 References Andersen, P. S. and W. L. Wascher (999). Sacri ce ratios and the conduct of monetary policy in conditions of low in ation. BIS wp No. 8. Ascari, G. and C. Merkl (009). Real wage rigidities and the cost of disin ations. Journal of Money Credit and Banking 4, Ascari, G. and T. Ropele (00). Implementing disin ations in a mediumscale dynamic general equilibrium model: Money supply vis-à-vis interest rate rules. Quaderni del Dipartimento di economia politica e metodi quantitativi, No. 40 (07-0), Univeristy of Pavia, Ball, L. (994a). Credible disin ation with staggered price-setting. American Economic Review 84, Ball, L. (994b). What determines the sacri ce ratio? In N. G. Mankiw (Ed.), Monetary Policy, pp Chicago: University of Chicago Press. Ball, L. (995). Disin ation with imperfect credibility. Journal of Monetary Economics 35, 5 3. Benati, L. (009). Are "intrinsic in ation persistence" models structural in the sense of Lucas (976)? ECB working paper No Brito, R. D. (00). In ation targeting does not matter: Another look at OECD sacri ce ratios. Journal of Money, Credit and Banking 4(8), Burstein, A. T. (006). In ation and output dynamics with state-dependent pricing decisions. Journal of Monetary Economics 53, Cecchetti, S. G. and R. W. Rich (00). Structural estimates of the U.S. sacri ce ratio. Journal of Business and Economic Statistics 9, Christiano, L. J., M. Eichenbaum, and C. L. Evans (005). Nominal rigidities and the dynamic e ects of a shock to monetary policy. Journal of Political Economy 3 (), 45.

13 Corbo, V., O. Landerretche, and K. Schmidt-Hebbel (00). Assessing in ation targeting after a decade of world experience. International Journal of Finance and Economics 6, Cuñado, J. and F. P. D. Gracia (003). Sacri ce ratios: Some lessons from EMU countries, International Review of Applied Economics 7, Durand, J.-J., M. Huchet-Bourdon, and J. Licheron (008). Sacri ce ratio dispersion within the Euro Zone: What can be learned about implementing a single monetary policy? International Review of Applied Economics, Erceg, C. J. and A. T. Levin (003). Imperfect credibility and in ation persistence. Journal of Monetary Economics 50, Galí, J. and M. Gertler (999). In ation dynamics: A structural econometric analysis. Journal of Monetary Economics 44, 95. Goncalves, C. E. (009). In ation targeting matters: Evidence from OECD economiesš sacri ce ratios. Journal of Money, Credit and Banking 40 (), Goodfriend, M. and R. G. King (005). The incredible Volcker disin ation. Journal of Monetary Economics 5, Gordon, R. J. and S. King (98). The output cost of disin ation in traditional and vector autoregressive models. Brookings Papers on Economic Activity, Leigh, D. (008). Estimating the Federal Reserve s implicit in ation target: A state space approach. Journal of Economic Dynamics and Control 3, Mankiw, G. N. (00). The inexorable and mysterious tradeo between in ation and unemployment. The Economic Journal, C45 C6. Mankiw, N. G. and R. Reis (00). Sticky information versus sticky prices: A proposal to replace the New Keynesian Phillips Curve. Quarterly Journal of Economics 7, Mankiw, N. G. and R. Reis (003). Sticky information. Quarterly Journal of Economics.

14 Nicolae, A. and C. Nolan (006). The impact of imperfect credibility in a transition to price stability. Journal of Money, Credit, and Banking 38(), Smets, F. and R. Wouters (003). An estimated dynamic stochastic general equilibrium model of the euro area. Journal of the European Economic Association, Smets, F. and R. Wouters (007). Shocks and frictions in US business cycles: A bayesian DSGE approach. American Economic Review 97 (3), Taylor, J. B. (983). Union wage settlement during a disin ation. American Economic Review 73, Zhang, L. H. (005). Sacri ce ratios with long-lived e ects. International Finance 8,

15 5 Figures and Tables OUTPUT 8 ANNUALIZED INFLATION RATE From 8% to % From 6% to % From 4% to % quarters quarters 3 NOMINAL INTEREST RATE EX ANTE REAL INTEREST RATE quarters quarters Figure : Cold-turkey disin ations aimed at achieving new = % with = :5. 4

16 Degree of habit persistence.45 Nominal price rigidity 3 (A) (B) Degree of price indexation to π t Degree of wage indexation toπ t Nominal wage rigidity (C) Adjustment cost of investment. Figure : Sensitivity analysis. In each panel we report contour plots of the sacri ce ratio. 5

17 = :5 = 3 old new Output at the trough Sacri ce ratio (T=) Output at the trough Sacri ce ratio (T=) 4% % % % % % Table : Short-run costs of disin ation. Output at the trough is expressed as a percentage deviation from its steady-state level. 6