Welfare costs of shifting trend inflation: Staggered wage and price contracts

Nội dung text: Welfare costs of shifting trend inflation: Staggered wage and price contracts

1. WELFARE COSTS OF SHIFTING TREND INFLATION: STAGGERED WAGE AND PRICE CONTRACTS Ha Le*1 Abstract: We develop a New Keynesian model featuring Calvo price setting and Calvo wage setting to study welfare consequences of exogenous variations in trend inflation. We find that shifting trend inflation produces a large welfare cost, which can be mainly accounted not only by a reduction of the average level of consumption and working hours, but also by an increase in their volatility. When trend inflation is high, these variables become more volatile, which make up for an increasingly considerable proportion of welfare reductions. Further, the staggered wage contracts play a vital role in transmitting adverse impacts of shocks to trend inflation into economy. JEL classifications: C63, E31, E52. Keywords: Shifting Trend Inflation, Welfare Consequences, Staggered Prices, Staggered Wages, Second Order Approximation. 1. INTRODUCTION The New Keynesian Phillips curve (NKPC, henceforth), a key element of Dynamic Stochastic General Equilibrium (DSGE, henceforth) models, has been used widely for theoretical, empirical and monetary policy analysis. However, the assumptions of NKPC are sometimes restrictive that either trend inflation2 must be zero or firms must index their prices to past inflation or target inflation3. First, central banks in the real world have invariably selected positive inflation targets, thus the assumption of zero inflation target is exceedingly rare. Second, misleading conclusions could be drawn when we assume the zero steady-state inflation. For instance, a divine coincidence suggested by Blanchard and Gali (2007)4 or a highly non-linear and positive slope of the long run NKPC5 might not be true in the case of positive trend inflation. Moreover, Levin and Piger(2003) and Ireland (2007)6 indicate that trend inflation has the tendency to vary over time. The aforementioned reasons motivate the case for studying optimizing behavior without making an assumption of zero trend inflation. However, most existing versions of NKPC have focused on constant * Date of Submission: 5th September 2018, Topic of research: Development Economics, Numbers of words: 4060 Ph.d in Economics. Email: phd15202@grips.ac.jp, Department of Economics, National Economics University 2 It can be interpreted as central bank’s implicit inflation target and private sector’s long-run inflation expectation. 3 Yun (1996) derives the indexation rule. When firms cannot optimize their prices, they are still able to update their price according to this indexation rule. 4 Blanchard and Gali (2007) indicate that under a price stickiness, a monetary policy rule might be able to simul- taneously stabilizes the inflation rate and the output gap in the face of preference or technology shocks.Alves (2014), however, shows that this divine coincidence only holds when the inflation rate is stabilized at zero. Other- wise, there is a trade-off between stabilizing inflation and stabilizing output gap. 5 Ascari and Ropele (2009) indicate that due to a strong price dispersion effect, the slope turns quite rapidly negative for extreme values of trend inflation. 6 By using the model that allows inferences concerning the Federal Reserve’s inflation target, Ireland (2007) shows changes from 1959 (1.25 percent) to the late 1970s (8 percent) and in 2004 (2.5 percent).
2. 542 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA positive trend inflation1, while they have not paid enough attention to the property of its time-varying variation (shifting trend inflation). Few papers have recently investigated it to show necessities of the research on this field. For example, Kozicki and Tinsley (2001) explore implications of shifting trend inflation for the term structure of interest rates, while its effects on output and overall inflation are investigated by Ireland2007. Furthermore, Cogley and Sbordone (2008) and Cogley, Primiceri, and Sargent (2009) conduct research to examine implications of shifting trend inflation for estimated parameters and a predictability of inflation, respectively. Most recently, welfare consequences of shifting trend inflation are measured by Nakata (2014). The similar spirit of the existing literature is that the previous studies employ a highly persistent shock to trend inflation, regarded as the central bank’s moving implicit targets to model shifting trend inflation and they adapt only one form of rigidities. So far, these papers only discuss the sticky-price model with shifting trend inflation. To fill the gap in the literature, this paper also investigates welfare consequences of shifting trend inflation but we argue that the trend inflation process can adversely impact the economy by distorting output and labor allocations through staggered price and wage contracts. In particular, the Calvo mechanism generates the price and wage dispersion. They in turn induce a gap between the average price level and the price set by resetting firms, and a gap between the average wage level and the wage set by resetting households. The following reasons inspire an inclusion of both price and wage rigidities. First, a tendency to discuss price and wage rigidities as independent phenomena seems to be inappropriate at the macro-level as argued by Basu and House (2015). The price rigidities depend significantly on the wage rigidities since most models assume that target prices are set as a constant mark-up on nominal marginal cost. The inertia of the price levels then depends on the sluggish adjustment of marginal costs, in which wage accounts for the greatest proportion. As a result, wage stickiness reinforces price stickiness. Second, the empirical New-Keynesian model incorporating the wage rigidities is more successful in explaining cyclical fluctuations as argued by Christiano, Eichenbaum, and Evans (2005). In the scope of this study, we examine whether wage rigidities are quantitatively important in explaining welfare costs of shifting trend inflation. Erceg, Henderson, and Levin (2000) employ the model with both price and wage stickiness to show that variability of growth rates of nominal wages implies misalignment of wages, thus an inefficient utilization of labors. The inefficient utilization of labor then is magnified by constant positive trend inflation (Ascari, Phaneuf, & Sims, 2016). So far, researchers have not investigated impacts of shifting trend inflation in the model with staggered price and wage contracts. This paper, thus, expands the existing literature by incorporating both price and wage rigidities to quantify costs of shifting trend inflation. We address the following questions: (i) how large welfare costs of shifting trend inflation are? and (ii) do staggered price or wage contracts more importantly determine the welfare costs of shifting trend inflation? To solve these questions, we study the same model as Ireland (2007) but considerably expand by developing the model with a Calvo staggered price setting and a Calvo staggered wage setting. While the Calvo price setting is popular in literature, we follow Erceg, Henderson, and Levin (2000) for the Calvo wage setting. Trend inflation is supposed to follow an AR(1) process to model a sustained rise in inflation. We argue that exogenous variations in trend inflation can distort the economy by two channels: staggered prices and staggered wages. Moreover, we discuss two special cases: the model with staggered price contract and completely flexible wage, and the model with completely flexible price and staggered 1 For example, we can see in Ascari (2004), Amano, Ambler, and Rebei (2007), Ascari and Ropele (2007), and Coibion and Gorodnichenko (2011).
3. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 543 wage contract. This discussion is useful to analyse the role of each mechanism individually in transmitting impacts of exogenous alternations in trend inflation into the economy. With these extensions, we showed that the consequences of constant positive trend inflation and shifting trend inflation are severe, especially when trend inflation is high. Among two channels, staggered wage contracts play a vital role in transmitting adverse impacts of constant and shifting trend inflation into economy. This conclusion is aligned with findings in Ascari et al. (2016) who also measure welfare costs of trend inflation in the model with both staggered price and wage contracts. Our study provides other evidence that the costs of shifting trend inflation are signified when considering the staggered wage contracts. Without the staggered wage channel, welfare costs of constant and shifting trend inflation are modest as in Nakata (2014). The rest of this paper is organized as follows. The extended model will be discussed in section 2. Section 3 explains how to compute welfare and welfare costs. Calibrated parameters are presented in section 4 while section 5 shows main results. Some conclusion is provided in section 6. 2 THE MODEL The model is populated by five classes of agents: the final-goods producing firms, a continuum of intermediate-goods producing firms indexed by i [0 1], employment agencies, a continuum of household indexed by j [0 1], and the government. 2.1 The Final-Goods Producing Firm In each period t, perfectly competitive firms manufacture units of final consumption product by using units of intermediate goods at the nominal price according to the constant-return-to-scale technology as follows θ p θ − p 1 θ p−1 θ ∫=1 p (1) 0 Ytt() i di Y  where denotes price elasticity of demand for intermediate goods. Profit maximization and the zero profit condition imply the demand function of intermediate good i is given as −θ ptY Pi() Yi()= t (2) t P t and that the price of the final good, is a CES aggregate of the prices of the intermediate goods, 1 1−θ di −θ P= ∫1 Pi() p 1 p (3) tt0 2.2 The Intermediate-Goods Producing Firm Monopolistic firms produce the intermediate good i using the following production function (4) where denotes the labor input for the production good i and is an exogenous stochastic
4. 544 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA process capturing the productivity effects. In particular, follows stationary AR(1) process ε (5) Zt where is the serially uncorrelated innovation, which has a normal distribution with mean zero and standard deviation . The intermediate-goods producers are assumed to set nominal prices as in staggered Calvo price fashion. According to Calvo (1983), a fixed fraction of firms, which cannot re-optimize its nominal prices, still set their prices according to the indexation rule. Following Ascari (2004), the way that firms reset the price is given as (6) where and denote a degree of price indexation and the relative weight on lagged inflation, respectively. The inflation, , is defined as and is interpreted as the central bank’s inflation target. Subject to the usual cost minimization condition, re-optimizing firms maximize the present value of future profits by choosing their price (7) such that (8) where if s = 1,2,3, , is the same as the Lagrangian multiplier on the household’s budget constraints, and denotes the nominal wage. 2.3 The Employment Agency Firms are owned by a continuum of households indexed by . As assumed by Erceg et al. (2000), each household is a monopolistic supplier of specialized labor, . A large number of competitive “employment agencies” combines this specialized labor into a homogeneous labor input as given (9) where denotes the desired mark-up of the wage over the household’s marginal rate of substitution. The labor demand function is obtained by solving a profit maximization for the perfectly competitive employment agencies as given (10) where is the wage received from employment agencies by the supplier of labor of type j while the wage paid by the intermediate firms for their homogeneous labor input is expressed as (11) 2.4 The Household Households maximize the expected discounted utility sum of future period utility (12) where and denotes the discount factor and the habit formation parameter, which are restricted as , and is the inverse Frisch elasticity of labor supply.
5. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 545 The households budget constraint is given by (13) At the beginning of each period, the households provide units of labor to each intermediate- goods producing firm to earn . They also receive a nominal profit due to owning the intermediate goods firms. They also save by purchasing the one-period bond, , from the intermediate goods producers at the price . A lump-sum tax is imposed to finance government spending . During each period t, households purchase consumption goods, , from the final-goods producing firms at the nominal price, . Therefore, the households choose labor supply, , bond holding, , and consumption, to maximize the lifetime utility subject to the budget constraint. The first order conditions for the households utility maximization problem can be represented (14) (15) where is a non-negative Lagrange multiplier on the budget constrain. In term of wage setting, we follow Erceg et al. (2000) to assume that there is a fraction, , of firms who cannot freely set their wage but still can update their wage as follows (16) The remaining fraction of firms can choose an optimal wage by maximizing (17) subject to the labor demand function (18) 2.5 Authority’s policy 2.5.1 Monetary Policy The authority sets the short-term nominal interest rates following a Taylor rule. In particular, the rule allows for interest rate smoothing and interest rate responses to deviations of inflation from the central bank’s inflation target and deviations of output from the steady state (19) where are the steady state of and , respectively. The parameter illustrates the degree of interest rate smoothing. is an i.i.d monetary policy shock. The evolution of trend inflation is described as a persistent AR(1) process as (20) where denotes the degree of shock persistence and is a standard normally distributed shock which is independent of time. 2.5.2 Fiscal Policy The public spending is given by
6. 546 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA (21) where is an exogenous disturbance following the stochastic process (22) where represents the steady-state value of government spending relative to output. 2.6 Market Clearing Condition The market clearing condition in the labor market, the goods market and the bond can be expressed in turn as (23) (24) (25) 3 WELFARE AND WELFARE COST COMPUTATION We also use the perturbation method to compute the approximation to the policy functions around the deterministic steady-state, and use these to compute the welfare. We decompose the welfare into the three different components as given where ; and and are vector which contain the first and second derivative of u(.) evaluated at which are the deterministic steady state of . Three components consist of: the deterministic component, , the level component, , and the volatility component, . Then the welfare cost can be computed as where are consumption and labor supply in the economy with and are in economy with . 4 CALIBRATION Table 6 lists the baseline parameters, which are calibrated for the U.S. data during the 1954Q3- 2015Q1 period. There are two subsets of parameters. The first subset consists of parameter values that we can compute by using the data or parameter values are standard in the literature. In particular, the standard calibration bases on the steady-state target, such as the steady-state inflation ( ), the steady-state share of government expenditure ( ). Some parameters are taken from the literature. For example, the discount factor, , and the inverse Frisch elasticity, , are set to 0.9974 and 1.00, respectively. The parameters and are the elasticities for goods and labors which are both set at 10, common values in these models. Moreover, we follow Justiniano and Primiceri (2008) to set the values for parameters related to persistence level and standard deviation of structural shocks. Accordingly, the autoregressive parameters of productivity shock and the government expenditure shock are set to 0.4 and 0.98, respectively. We also base on Justiniano
7. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 547 and Primiceri (2008) to select parameter values for Taylor rule, including the smoothing parameter, , the coefficient on inflation, , and the coefficient on output growth, . They are in turn 0.81, 1.91 and 0.08, which are also common in the literature. Regarding the shock to trend inflation process, we set its persistence level, , and standard deviation, , to 0.995 and 0.0008 as in Cogley et al. (2009). The second subset includes parameters that are calibrated jointly to match selected moments in the 1954Q3-2015Q1 U.S. data. These parameters are the habit formation, , the probability of non-optimization for prices, , the degree of price indexation, , the probability of non-optimization for wages, , and the degree of wage indexation, . The five selected moments include the consumption volatility , the volatility of consumption relative to output , the volatility of labor relative to output , a correlation between output and consumption , and a correlation between output and labor . These moments are important for the subsequent welfare analysis because they closely reflect the dynamic behavior of consumption and labor supply. Based on the moment matching approach, the habit formation, , is set to 0.91. Both the probability of non-optimization for prices and wages, and , are calibrated at 0.69. There is also a fair degree of price and wage indexation (0.5), which is the same but smaller than Fernandez-Villaverde, Guerron-Quintana, and Rubio-Ramirez (2010) (between 0.62-0.63). Table 1: Moments Data 0.008 0.56 1.42 0.79 0.87 Calibration 0.007 0.62 1.42 0.77 0.75 Note: Moments in the second row are obtained from HP-filtered U.S. data (1954Q3-2015Q1). The last row is the moments from simulations for the calibrated model. Table 1 compares the moments generated by the parameterized model with moments computed by the data. The reported volatility and correlation statistics are for the HP-filtered U.S. data during 1954Q3- 2015Q1 period. Table 1 shows that the model does a good job for matching the volatility of consumption, the variance of consumption, labor to output, and the correlation between consumption, labor and output. In sum, the key features of the data are captured reasonably well by the calibrated model. Therefore, the calibrated model can provide an appropriate laboratory for the subsequent welfare analysis. 5 RESULTS 5.1 Welfare Costs of Constant Positive Trend Inflation General Case Table 2 compares the welfare of an economy in which central banks set constant trend inflation at 0 annualized percent and an economy in which central banks set constant trend inflation at 4 annualized percent. We firstly discuss the model featuring both staggered price and staggered wage contracts. Table 2 shows that the greater trend inflation results in large welfare costs (nearly 4.5 ). This result is aligned line with Ascari2016 who also discuss the costs of trend inflation in the model with both staggered price and wage contracts. These welfare costs come mainly from reduction of the mean and volatility component, especially the volatility component. Conversely, the changes in the deterministic component play a small role in explaining the welfare difference. When central banks raise their inflation targets from 0 percent to 4 percent, there are changes in the mean as well as the variance of consumption and working hours. It is worth
8. 548 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA noticing about a significant increase in variance of consumption and working hours. Table 2: Welfare Costs of Constant Trend Inflation: Model with Staggered Price and Wage Contracts Welfare Cost 4.46 Welfare -1242.2 -1281.4 -1219.5 -1219.6 -0.05 -0.24 -22.6 -61.5 E(C)(*) -0.015 -0.041 E(H)(*) -0.018 -0.050 1.33 2.17 2.50 3.22 Note: (*) expressed as percentage deviation from the deterministic steady-state. , and are the deterministic steady-state, level and volatility component, respectively. Two special cases: Staggered Prices and Staggered Wages In the next exercise, we compare welfare and welfare costs of constant trend inflation in two special cases: the model with staggered price contract and completely flexible wage ( ) and the model with completely flexible price and staggered wage ( ). We call them the staggered price model and the staggered wage model, respectively. Table 3 reports results of these two special cases. Some main findings could be listed here. First, welfare costs due to a constant and positive trend inflation level in the staggered price model is trivial (0.22 ) as compared to the staggered wage model (3.62 ). The modest cost of constant trend inflation in the first special case is consistent to those of Ascari (2004), Amano, Moran, Murchison, and Rennison (2009), and Nakata (2014) that discuss trend inflation distorting the economy solely by the staggered price contracts. The higher costs in the staggered wage model when trend inflation increases from 0 percent to 4 percent suggest that a staggered wage mechanism plays a vital role in transmitting adverse impacts of varying trend inflation levels into the economy. This conclusion is similar to those discussed by Ascari et al. (2016). The changes in the property of economy due to constant trend inflation are also reported in Table 3. In the staggered price model, changes in the mean and variance of consumption and working hours are very small, whereas there are significant movements in the staggered wage model. The higher dynamics of economy due to the staggered wage contracts in part explain high welfare costs due to a constant positive trend inflation through this channel. Table 3: Welfare Costs of Constant Trend Inflation: Two Special Cases Staggered Prices Staggered Wages Welfare Cost 0.22 3.62 Welfare -1232.6 -1234.3 -1240.2 -1271.7 E(C)(*) -0.0046 -0.0069 -0.014 -0.044 E(H)(*) -0.0001 -0.0001 -0.018 -0.057
9. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 549 0.92 0.93 1.28 2.02 2.14 2.23 2.44 3.07 Note: (*) expressed as percentage deviation from the deterministic steady-state. Staggered prices and wages correspond to and , respectively. In short, welfare consequences of constant positive trend inflation are severe in the model with staggered price and wage contracts. The staggered wage channel plays a vital role in transmitting adverse impacts of constant trend inflation into the economy. 5.2 Welfare Costs of Shifting Trend Inflation General Case Table 4 reports welfare costs of shifting trend inflation when central banks set the inflation target level to 2 annualized percent and 4 annualized percent, respectively. Trend inflation participates in the model as a shock and the presence of this shock creates welfare costs. This part discusses how this shock affects the economy in terms of welfare costs. First, we focus on the 2-percent-trend-inflation economy. The persistent trend inflation shock creates welfare costs, which is 0.6 . A reduction in welfare mainly comes from a decline of volatility component, while the deterministic steady-state component remains the same. A positive shock to trend inflation, therefore, drives the average levels of consumption and working hours down, while pushing their volatility up. In our exercise, the volatility component accounts for the largest proportion of welfare reduction, which shapes business cycle dynamics. Specifically, the standard deviation of working hours increases from 1.33 to 1.47, while an increase in those of consumption is from 2.52 to 2.62. Table 4: Welfare Costs of Shifting Trend Inflation: Model with Staggered Price and Wage Contracts Welfare Cost 0.60 4.27 Welfare -1242.4 -1246.7 -1243.9 -1281.4 -1219.6 -1219.6 -1219.6 -1219.6 -0.01 -0.03 -0.21 -0.23 -22.8 -27.8 -24.0 -61.5 E(C)(*) -0.016 -0.023 -0.031 -0.041 E(H)(*) -0.019 -0.028 -0.037 -0.050 1.33 1.47 1.35 2.17 2.52 2.62 2.51 3.22 Note: (*) expressed as percentage deviation from the deterministic steady-state. , and are the deterministic steady-state, level and volatility component, respectively. When trend inflation is 4 annualized percent, the costs of shock to trend inflation become more severe. This shock generates larger welfare costs (4.27 ). The welfare differences still result from reduction of volatility component. However, a fall in volatility component is more considerable when trend inflation is higher. The economy also becomes more volatile, which is reflected by a substantial rise in the standard
10. 550 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA deviation of consumption (1.35 to 2.17) and working hours (2.51 to 3.22). The changes in properties of economy suggest that the volatility component plays an increasingly important role in explaining a fall in welfare due to exogenous variations in trend inflation when trend inflation is high. Two special cases: Staggered Prices and Staggered Wages Subsequently, we discuss welfare costs of shifting trend inflation in two special cases: completely flexible price and staggered wage contract ( and ), and staggered price contract and completely flexible wage ( and ). Table 5 reports results of these two special cases. The most striking feature is that welfare costs of shifting trend inflation in the model with staggered wage contract (0.48 ) are significantly greater than one with staggered price contract (0.04 ). The modest costs of exogenous variation in trend inflation in the sticky price model is consistent with the results of Nakata (2014). Welfare differences in these two cases can be explained by changes in mean and variance of consumption and working hours, but through the staggered wage channel, any change is greater. The significant costs of shifting trend inflation in the model with sticky wage suggest that an existenceof staggered wage contract is a more vital channel in transmitting adverse impacts of shifting trend inflation into the economy as compared to the staggered price. Table 5: Welfare Costs of Shifting Trend Inflation: Two Special Cases Staggered Prices Staggered Wages Welfare Cost 0.04 0.48 Welfare -1232.9 -1233.2 -1240.3 -1244.3 E(C)(*) -0.0051 -0.0057 -0.0159 -0.0228 E(H)(*) -0.0001 -0.0001 -0.0205 -0.0294 0.92 0.92 1.29 1.41 2.17 2.17 2.41 2.52 Note: (*) expressed as percentage deviation from the deterministic steady-state. Staggered prices and wages correspond to and , respectively. In brief, shifting trend inflation produces large welfare costs especially in the high-trend-inflation economy. The welfare differences caused by shifting trend inflation can be mainly accounted by reduction in the volatility components. As trend inflation increases, the role of volatility component becomes increasingly important. Comparing two special cases, welfare costs created by shifting trend inflation through the staggered wage channel are more significant than those generated through the staggered price channel. The results suggest that the staggered wage is an important factor determining the welfare costs of shifting trend inflation1. 6 CONCLUSIONS The literature on shifting trend inflation has so far only considered the price rigidities. The present study, therefore, developed the model featuring a staggered price and wage contracts to fill the existing gap. Further, we assumed implicit inflation target to be positive and time-varying due to a lack of commitment in the policy implementations of central banks. Thus, trend inflation was modelled as a highly persistent 1 To support these two conclusions in this paper, we conduct additional analyses that use the asymmetric parameter values. The results of these exercises are reported in Appendix 9.
11. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 551 AR(1) process. We then compared welfare of an economy with zero and the other with positive variance of innovation to the trend inflation process. To analyse the role of each channel importantly determining welfare costs of shifting trend inflation, we discussed two special cases: the model with staggered price contract and completely flexible wage, and the model with completely flexible price and staggered wage contract.With these extensions, we showed that welfare consequences of constant positive trend inflation and shifting trend inflation are severe, especially when trend inflation is high. Furthermore, among the two channels, staggered wage contracts play a vital role in transmitting adverse impacts of constant and shifting trend inflation into economy. APPENDIX 7 PARAMETERS Table 6: Calibration Parameter Description Calibrated Value Discount factor 0.9974 Consumption habit 0.91 Labor supply disutility 1.00 Inverse Frisch elasticity of labor supply 1.00 Steady state share of Government expenditure 0.26 AR(1) coefficient for technology shock 0.40 AR(1) coefficient for government spending shock 0.98 Standard deviation of technology shock 1.10 Standard deviation of government spending shock 0.55 Monetary Policy Taylor coefficient on the inflation gap 1.92 Taylor coefficient on the output gap 0.08 AR(1) coefficient for monetary shock 0.81 Standard deviation of monetary shock 0.25 Calvo Price Setting Price elasticity 10.0 Probability of not being able to optimize [0.6,0.65,0.7,0.75] Degree of price indexation [0.0,0.33,0.67,1.0] Weight on lagged inflation 1.00 Calvo Wage Setting Wage elasticity 10.0 Probability of not being able to optimize [0.6,0.65,0.7,0.75] Degree of wage indexation [0.0,0.33,0.67,1.0]
12. 552 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA Weight on lagged inflation 1.00 Shifting Trend Inflation Steady-state level of trend inflation Persistence level of shocks to trend inflation Standard deviation of shocks to trend inflation [0.1,0.075,0.05,0.025,0] 8 THE MODEL 8.1 A List of Nonlinear Equilibrium Conditions in Stationary Variables (NL1) (NL2) (NL3) (NL4) (NL5) (NL6) (NL7) (NL8) (NL9) (NL10) (NL11) (NL12) (NL13) (NL14) (NL15)
13. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 553 (NL16) (NL17) (NL18) 8.2 A List of Steady-State Variables (ss1) (ss2) (ss3) (ss5) (ss6) (ss7) (ss8) (ss9) (ss10) (ss11) (ss12) (ss13) (ss14) (ss15) 9 THE ADDITIONAL ANALYSES To conduct a robust check of two conclusions, we consider another case that there are asymmetric parameter values for staggered prices and wages (the asymmetric case). We select Justiniano2008 for a comparison purpose since our model and theirs share many similar features. Details about parameter values are reported in 7.
14. 554 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA Table 7: Calibration: An Asymmetric Case Parameter Description Calibrated Value Discount factor 0.9974 Consumption habit 0.81 Labor supply disutility 1.00 Inverse Frisch elasticity of labor supply 1.59 Steady state share of Government expenditure 0.26 AR(1) coefficient for technology shock 0.28 AR(1) coefficient for government spending shock 0.98 Standard deviation of technology shock 1.10 Standard deviation of government spending shock 0.55 Monetary Policy Taylor coefficient on the inflation gap 1.92 Taylor coefficient on the output gap 0.1 AR(1) coefficient for monetary shock 0.81 Standard deviation of monetary shock 0.25 Calvo Price Setting Price elasticity 10.0 Probability of not being able to optimize 0.9 Degree of price indexation 0.84 Weight on lagged inflation 1 Calvo Wage Setting Wage elasticity 10.0 Probability of not being able to optimize 0.61 Degree of wage indexation 0.09 Weight on lagged inflation 1 Shifting Trend Inflation Steady-state level of trend inflation Persistence of trend inflation Standard deviation of shocks to trend inflation 0.08 The results for welfare cost computations are presented in Table 8. The results confirm two conclusions this paper. First, the consequences of constant positive trend inflation and shifting trend inflation are severe. Second, staggered wages more importantly determine costs of both constant and shifting trend inflation.
15. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 555 Table 8: Welfare Cost Results: An Asymmetric Case Constant Trend Inflation Shifting Trend Inflation Welfare Costs General Case 4.91 0.56 Staggered Prices 0.22 0.05 Staggered Wages 4.13 0.49 REFERENCES Amano, R., Moran, K., Murchison, S., & Rennison, A. (2009). Trend ination, wage and price rigidities, and productivity growth. Journal of Monetary Economics, 56 (3), 353-364. Ascari, G. (2004). Staggered prices and trend ination: Some nuisances. Review of Economic Dynamics, 7 (3), 642-667. Ascari, G., Phaneuf, L., & Sims, E. (2016). On the welfare and cyclical implications of moderate trend ination. Journal of Monetary Economics (Forthcoming). Ascari, G., & Ropele, T. (2007). Optimal monetary policy under low trend inflation.Journal of Monetary Economics, 54 (8), 2568-2583. Ascari, G., & Ropele, T. (2009). Trend ination, taylor principle and indeterminacy. Journal of Money, Credit and Banking, 41 (8), 1557-1584. Basu, S., & House, C. (2015). Challenges for new keynesian models with stick wages. Working Paper. Blanchard, O. J., & Gali, J. (2007). Real wage rigidities and the new keynesian model. Journal of Money, Credit and Banking, 39 (1), 35-65. Calvo, G. A. (1983). Staggered prices in a utility-maximizing framework. Journal of Monetary Economics, 12 (3), 383-398. Cogley, T., Primiceri, G. E., & Sargent, T. J. (2009). Ination-gap persistence in the us. American Economic Journal: Macroeconomics, 2 (1), 43-69. Cogley, T., & Sbordone, A. M. (2008). Trend ination, indexation, and inflation persistence in the new keynesian phillips curve. American Economic Review, 98 (5), 2101-2126. Erceg, C. J., Henderson, D. W., & Levin, A. T. (2000). Optimal monetary policy with staggered wage and price contracts. Journal of Monetary Economics, 46 (2), 281-313. Fernandez-Villaverde, J., Guerron-Quintana, P. A., & Rubio-Ramirez, J. (2010). Fortune or virture: Time-variant volatilities versus parameter drifting in u.s data. FRB of Philadelphia Working Paper(10-14). Ireland, P. N. (2007). Changes in the federal reserve’s ination target: Causes and consequences. Journal of Money, Credit and Banking, 39 (8), 1851-1882. Justiniano, A., & Primiceri, G. E. (2008). Time-varying volatilities and macroeconomic fluctuations. American Economic Review, 98 (3), 604-641. Kozicki, S., & Tinsley, P. A. (2001). Shifting endpoints in the term structure of interest rates. Journal of Monetary Economics, 47 (3), 613-652. Levin, A. T., & Piger, J. M. (2003). Is ination persistence intrinsic in industrial economies? NBER Working Paper. Nakata, T. (2014). Welfare costs of shifting trend ination. Journal of Macroeconomics, 41 , 66-78.