Lecture 23 The New Keynesian Model Labor Flows and Unemployment. Noah Williams

Transcription

1 Lecture 23 The New Keynesian Model Labor Flows and Unemployment Noah Williams University of Wisconsin - Madison Economics 312/702

2 Basic New Keynesian Model of Transmission Can be derived from primitives: household consumption decisions, firm pricing decisions. Assumes monopolistic competition, sticky prices. Only labor input, C t = Y t. Unlike old Keynesian literature, assumes rational expectations. When firms set prices, forecast future demand and policy. Households also forecast future conditions when choosing consumption. Basic model has 2 key equations: a Euler equation which gives an IS relation between output and interest rates, and a Phillips curve which results from price setting decisions. Gives a relation between output and inflation. Along with a specification of monetary policy, these determine the evolution of output, inflation, and interest rates.

3 Basic Model Clarida-Gali-Gertler (1999), Woodford (2003). Let π t be inflation, E t π t+1 expected inflation, x t = y t y p t the output gap (deviation of output from potential ), R t the nominal interest rate. First equation relates output gap to real interest rate: x t = φ(r t E t π t+1 ) + E t x t+1 + g t Linearized consumption Euler equation/is curve. Second equation is the New Keynesian Phillips curve relating inflation and real activity: π t = κx t + βe t π t+1 + u t Linearized pricing decisions of firms with staggered price setting.

4 g t and u t are exogenous shocks. Demand (such as government spending) and cost-push (such as wage or markup fluctuations) Assume they re serially correlated: g t = ρ g g t 1 + ɛ g t u t = ρ u u t 1 + ɛ u t Note that timing of Phillips curve is different from previous expectations-augmented (Lucas suprise model): here inflation is fully forward looking. Can close model via an LM curve once we specify money demand. But since we ll analyze policy via setting interest rate R t, this will only pin down the stock of money.

5 Policy Implication of Forward-Looking Models The basic new Keynesian inflation adjustment equation without cost shocks is: π t = κx t + βe t π t+1 We can solve this equation forward to get an expression for inflation: π t = κ β i E t x t+i i=0 Inflation is a function of the present discounted value of current and future output gaps. The absence of a stochastic disturbance implies there is no conflict between a policy designed to maintain inflation at zero and a policy designed to keep the output gap equal to zero. Just set x t+i = 0 for all i; keeps inflation equal to zero.

6 Optimal Policy Thus, the key implication of the basic new Keynesian model is that price stability is the appropriate objective of monetary policy. No policy conflicts. When prices are sticky but wages are flexible, the nominal wage can adjust to ensure labor market equilibrium is maintained in the face of productivity shocks. Optimal policy should then aim to keep the price level stable.

7 Policy Implications of Price Stickiness Models that combine optimizing agents and sticky prices have very strong policy implications. When the price level fluctuates, and not all firms are able to adjust, price dispersion results. This causes the relative prices of the different goods to vary. If the price level rises, for example, two things happen. 1 The relative price of firms who have not set their prices for a while falls. They experience in increase in demand and raise output, while firms who have just reset their prices reduce output. This production dispersion is inefficient. 2 Consumers increase their consumption of the goods whose relative price has fallen and reduce consumption of those goods whose relative price has risen. This dispersion in consumption reduces welfare.

8 Optimal Policy The solution is to prevent price dispersion by stabilizing the price level. What is critical for this result is that nominal wages are assumed to be completely flexible. But the same argument would apply if wages are sticky and prices flexible. With sticky wages and flexible prices, monetary policy should stabilizes the nominal wage.

9 Woodford versus Friedman The basic new Keynesian model suggests price stability (i.e., zero inflation) is optimal. Zero inflation eliminates inefficient price dispersion. Friedman rule: zero nominal rate of interest is optimal. Zero nominal rate eliminates inefficiency in money holdings. Optimal inflation is negative (deflation) at rate equal to real rate of interest. Khan, King, and Wolman (2000) analysis model with both distortions. The conclude optimal inflation is closer to zero than to the Friedman rule.

10 Cost Shocks Now assume π t = κx t + βe t π t+1 + u t where u t represents an inflation or cost shock, which is serially correlated: Then u t = ρ u u t 1 + ɛ u t π t = κ β i E t x t+i + β i E t u t+i i=0 i=0 Cannot keep both x and π equal to zero. Trade-offs must be made.

11 Objective of Policy Policy objective in general is to maximize welfare of agents. In this model, can derive approximation of welfare giving loss function: L t = 1 ( ) ωxt 2 + π 2 t 2 Penalizes deviations of output relative potential, deviation of inflation from target (zero): Price stability and Full Employment goals. In deriving this expression, weight on output ω can be related to underlying parameters. If there are distortions in the economy (such as monopoly power), optimal level of output gap is positive so loss is: L t = 1 2 ( ) ω(x t x) 2 + π 2 t

12 Policy Problem Suppose central bank targets positive output gap x > 0. Chooses interest rate policy each period to minimize loss, taking as given private expectations. Easiest here to suppose central bank directly controls inflation and output gap, then use IS to back out optimal interest rate choice. Suppose also β = 1. Represent the central bank s problem as a Lagrangian: L = 1 2 ( ) λ(x t x) 2 + π 2 t + µ (κx t + βe t π t+1 + u t π t ) The first order conditions are: λ(x t x) + µκ = 0 and π t = µ or x t = κ λ π t + x

13 x t = κ λ π t + x Substitute back into Phillips: π t = κx t + βe t π t+1 + u t (1 + κ 2 /λ)π t = κ x + βe t π t+1 + u t Guess π t = k 0 + k 1 u t. Then E t π t+1 = k 0 + k 1 E t u t+1 = k 0 + k 1 ρu t. Substitute and use β = 1: λ π t = κ 2 + ω(1 ρ) u t + λ κ x Then from optimality get: x t = κ λ π t + x = κ κ 2 + λ(1 ρ) u t

14 Inflation Bias and Time Consistency Note Eπ t = λ κ x but Ex t = 0. Target gap x only affects mean inflation rate. If β < 1 then targeting x > 0 will result in x > Ex t > 0.) Government tries to push output above potential, in equilibrium only leads to higher inflation. This is just as in the earlier analysis, but more direct/explicit. Policymakers have an incentive to announce they will be tough on inflation to affect people s expectations, then actually to pursue loose policy. In equilibrium, people will come to expect this. With rational expectations (as we ve used), this only leads to higher inflation.

15 Optimal Discretionary Policy With x = 0 (for any β): π t = λ κ 2 + λ(1 βρ) u t, x t = κ κ 2 + λ(1 βρ) u t Can then get optimal interest rate response from IS: x t = φ(r t E t π t+1 ) + E t x t+1 + g t R t = E t π t+1 + (1/φ) (E t x t+1 x t + g t ) = γe t π t+1 + (1/φ)g t, where γ > 1. (i) Cost push shocks u t imply inflation/ouput tradeoff. (ii) If expected inflation rises, nominal interest rates should rise by more (γ > 1) so real rates increase. (iii) Policy should offset demand shocks g t, accommodate movements in potential output (say productivity shocks).

16 Commitment When forward-looking expectations play a role, discretion leads to a stabilization bias even though there is no average inflation bias. Under optimal commitment, central bank at time t chooses both current and expected future values of inflation and the output gap. Minimize [ ΩE t β i π 2 t+i + λ (x t+i x ) 2] i=0 subject to π t = βe t π t+1 + κx t + u t. Notice the IS imposes no constraint use it to solve for i t once optimal π t and x t have been determined.

17 Optimal Commitment The central bank s problem is to pick π t+i and x t+i to minimize E t i=0 [ ] β i π 2 t+i + λxt+i 2 + ψ t+i (π t+i βπ t+i+1 κx t+i u t+i ). The first order conditions can be written as π t + ψ t = 0 (1) E t ( πt+i + ψ t+i ψ t+i 1 ) = 0 i 1 (2) E t ( λxt+i κψ t+i ) = 0 i 0. (3) Dynamic inconsistency at time t, the central bank sets π t = ψ t and promises to set π t+1 = ( E t ψ t+1 ψ t ). When t + 1 arrives, a central bank that reoptimizes will again obtains π t+1 = ψ t+1 the first order condition (1) updated to t + 1 will reappear.

18 Discretion vs Commitment Responses of to a 1% inflation shock under the optimal commitment (solid) and discretion (dashed) policies.

19 Improved trade-off under commitment The difference in the stabilization response under commitment and discretion is the stabilization bias due to discretion. Consider a positive inflation shock, u > 0. A given change in current inflation can be achieved with a smaller fall in x if expected future inflation can be reduced: π t = βe t π t+1 + κx t + u t Requires a commitment to future deflation. By keeping output below potential (a negative output gap) for several periods into the future after a positive cost shock, the central bank is able to lower expectations of future inflation. A fall in E t π t+1 at the time of the positive inflation shock improves the trade-off between inflation and output gap stabilization faced by the central bank.

20 Gains from Commitment

21 Contemporary New Keynesian Models To capture the dynamics and persistence in the data, modern NK models add many real and nominal frictions Smets and Wouters (2003) model has the following features: - Sticky prices - Habit formation - Sticky wages - Variable capacity utilization - Price & wage indexation - Investment adjustment costs There are 10 structural shocks: - Productivity - Goods markup - Labor supply - Labor markup - Preference - Equity premium - Adjustment cost - Policy instrument - Government spending - Policy objective Later models add explicit financial sector

22 Estimation and Use Most of the literature uses Bayesian methods. Simulation based approach (MCMC) which allows to calculate posterior distribution of parameters. Use observations on (Y t, C t, I t, π t, w t, N t, R t ). Can be difficult to estimate: 7 time series, 32 parameters 16 structural parameters, 10 shock standard deviations, 6 autocorrelations. Standard of fit is a vector autorgregression (VAR): atheoretical, empirical model. Most modern NK models are comparable in fit. But unlike VAR, NK model can be used for policy analysis. Models of this type used by most central banks and policy institutions: Fed, ECB, Bank of England, IMF, etc.

23 Basic Facts About the Labor Market US Labor Force in Sept. 2012: 142 million people US working age population in 2012: million people Labor force participation rate of about 63.6%. Employment-population ratio of 58.7% Between 1967 and 1993 the average job loss rate was 2.7% per month, average job finding rate was 43%, and average unemployment rate 6.2%. In September 2012 job loss rate was 1.3% per month (with 2.5% going out of labor force), finding rate was 19%, and unemployment rate was 9.1%. Large differences in employment, unemployment, and their evolution in US and Europe.

24 Employment/Population and Participation Rates 67.5 Civilian Labor Force Participation Rate Civilian Employment-Population Ratio (Percent) research.stlouisfed.org

25 Separations and Hires Total Separations: Total Nonfarm (left) Quits: Total Nonfarm (left) Civilian Unemployment Rate (right) Hires: Total Nonfarm (right) Layoffs and Discharges: Total Nonfarm (right) (Rate) (Percent), (Rate) research.stlouisfed.org

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32 Length of Unemployment Spells Unemployment Spell 8/89 10/92 10/06 3/11 < 5 weeks 48% 35% 38% 18% 5-14 weeks 31% 28% 31% 22% weeks 11% 14% 14% 15% > 26 weeks 9% 23% 16% 46% Other countries: in Germany, France or the Netherlands about two thirds of all unemployed workers in 1989 were unemployed for longer than six months.

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35 Median Duration of Unemployment 30 Median Duration of Unemployment (Weeks) Source: US. Bureau of Labor Statistics research.stlouisfed.org

36 Distribution of Unemployment Duration 70 Of Total Unemployed, Percent Unemployed Less than 5 Weeks Of Total Unemployed, Percent Unemployed 5 to 14 Weeks Of Total Unemployed, Percent Unemployed 15 to 26 Weeks Of Total Unemployed, Percent Unemployed 27 Weeks and over (Percent) research.stlouisfed.org