Stabilization Policy and Expectations
EC 324: Macroeconomics (Advanced) Stabilization Policy and Expectations Nicole Kuschy
March 4, 2011
Lecture 7: Stabilization Policy and Expectations
Main reading: SWJ, chapter 21 1
Stabilization Policy
2
Adaptive Expectations
3
Rational Expectations and Policy Ineffectiveness
Taking Stock So far, our model of business cycle fluctuations and persistence is based on sticky wages, static expectations and shocks to the demand and supply sides of the economy. We have to deal with two more issues if we really want to explain the business cycle: 1
Introduction of uncertainty: So far, private agents were surprised by a shock because nominal wages were negotiated one period in advance, for example. But there is uncertainty for one period only - period t = 0; after that, agents cannot be surprised by further shocks.
2
Expectations formation: So far, private agents expected future inflation would be the same as in the current period; this generated much of the persistence. But is this a plausible way to model expectations?
Adaptive Expectations When expectations are static it is as if we play ‘catch-up’ each period. And we keep making the same old mistake. Maybe a better assumption is that expectations adapt. That is, each period we use information from all the past periods - not just the previous one: e e = (1 − φ) πt−1 − πt−1 , (1) πte − πt−1 | {z } | {z } revision of π e
previous forecast error
where 1 > φ ≥ 0. The parameter φ is a measure of the ‘stickiness’ of expectations. When φ = 0, we are back at static expectations: πte = πt−1
Adaptive Expectations Another way of expressing (1) is: e πte = φπt−1 + (1 − φ) πt−1
(2)
Iterating on (2) yields: πte =
∞ X
φn−1 (1 − φ) πt−n
n=1
Equation (3) expresses πte as a weighted sum of past inflation rates. Since φ < 1, adaptive expectations put more weight on recent events. This seems realistic. However, agents still make systematic mistakes because they always look to the past to figure out the future.
(3)
A different weight φ affects our previous results on business cycle dynamics: Table 19.1: The stochastic AS-AD model and stylized business cycle facts
Figure: Business cycle statistics for the stochastic AD/AS model.
©The McGraw-Hill Companies, 2005
Slide 1/11
AD/AS Model with Adaptive Expectations We have the following equations for AD, AS and expectations formation: yt − y = γ (π ∗ − πt ) + Dt
(4)
πt = πte + λ (yt − y) + St
(5)
e + (1 − φ) πt−1 πte = φπt−1
(6)
We solve the model exactly as before.
Solution of the AD/AS Model with Adaptive Expectations The AD and AS equations are now: ybt = −γb πt + Dt
(7)
π bt = π bt−1 + λb yt − φλb yt−1 + St − φSt−1
(8)
where ybt ≡ yt − y and π bt ≡ πt − π ∗ . When φ = 0 we are back at the model version with static expectations. The difference for φ > 0 is that there are extra lagged variables due to the way expectations about the future are formed.
The Implications of Adaptive Expectations I
Added lags change the degree of persistence. Again, we can calculate the half-live. We can use exactly the same technique as before (try this at home): Forward the AD and AS equations by one period. Set Dt = St = 0 for all t > 0. Use the current AD in the future period AS to eliminate π bt . Combine this expression with the future AD to eliminate π bt+1 .
The Implications of Adaptive Expectations II This implies: 1 + φλγ ybt + ... 1 + λγ | {z } ybt+1 =
t∗SE . Why? Static expectations imply that we care about what happened one period ago. Adaptive expectations imply that we care about this, and the period before, and the period before etc. with a lower and lower weight. [The weight is φt , and φt falls as t rises.] The extra insight is not great. How far can we really go with this approach? This question was addressed in the 1970’s.
Backward-Looking Versus Forward-Looking Expectations I
Neither static nor adaptive expectations fit well with a forward-looking model. The IS curve implies current investment depends on expectations of the future interest rate etc. In a stable economy it may seem reasonable to suppose: πte = Π (πt−1 , πt−2 , πt−3 , ....) Then, expectations based on past patterns of economic behavior are a good guide to the future.
Backward-Looking Versus Forward-Looking Expectations II But what if the economy is not stable? We may then be worried about the future: e e e πte = Π πt+1 , πt+2 , πt+3 , .... This represents the opposite extreme. Rational Expectations (RE) start from the second idea: Private agents use all available information to make a guess about future inflation. Importantly, this information is based on an understanding of the economic structure. From this we generate e , π e , π e , .... πt+1 t+2 t+3
Rational Expectations The RE assumption therefore flips everything around. We are no longer backward-looking making systematic mistakes. We are forward-looking and we know how the model works. Obviously, this is a strong assumption. Suppose inflation is high. The central bank attempts to reduce inflation to a lower level. This disinflation policy involves a change in the inflation target π ∗ . How long does it take for us to figure out what the central bank is trying to do? Clearly, it depends on the way expectations are formed: Adaptive expectations: a very long time. Rational expectations: immediately (we will show this).
Forecast Error with Static Expectations Static expectations imply πte = πt−1 and neglect the structural information on π ∗ . Figure 21.1: The inflation forecast error during a disinflation
e Thus, the inflation forecast error π with static expectations (simulation t − πt is )very persistent.
Figure: Static expectations: Inflation forecast error during Slide a 1/1 ©The McGraw-Hill Companies, 2005 disinflation.
The Lucas Critique I Suppose you are an econometrician. Assuming agents’ expectations are backward-looking, you estimate a structural model in order to predict the effects of a new policy regime (e.g. a change in π ∗ ). The problem is that your parameter estimates apply to the previous economic policy regime. You cannot use these estimates to infer (predict) economic behavior under the new policy regime. Example: Suppose we lower π ∗ to zero. If we had a model with consistent expectations, π e = π ∗ = 0 (we’ll show this). But the econometrician is assuming π e > 0, as expectations take time to catch up. In this case, he will miscalculate the impact of the policy.
The Lucas Critique II The Phillips Curve (rel: inflation and unemployment) is the most famous application of the Lucas Critique. Another example are temporary tax changes (rel: disposable income and consumption). Punch line: Expectations are important for aggregate relationships - they are likely to change them. But changes in policy are likely to affect expectations. So, policy can change aggregate relationships. If a policymaker tries to take advantage of such relationships, expectational mechanisms may cause those relationships to break down.
Rational Expectations Idea: Agents may be surprised by the latest news, but they won’t make systematic errors, i.e., on average agents will be correct. So, for any macroeconomic variable, say, Xt : e Xt,t−1 = E {Xt |It−1 } , {z } | | {z }
subj. exp’n
conditional exp’n
where It−1 is the information available to the agent (household or firm) at the end of period t − 1. e Notation: The term Xt,t−1 is then the expectation of X in period t made in period t − 1. E is the mathematical expectations operator. e Terminology: We sometimes say Xt,t−1 is the forecast of Xt .
Information Structure The monetary rule is: e + h (πt − π ∗ ) + b (yt − y) it = r + πt,t+1
or:
rt = r + h (πt − π ∗ ) + b (yt − y)
Case 1: Assume that neither the central bank nor the public know what shocks will occur. The central bank sets the interest rate rule using information in period t − 1: e h πt,t−1 − π∗ Case 2: Assume, more realistically, that central bank has more information than the trade unions: h (πt − π ∗ ) , where πt is known. e In each of the two alternative cases, πt,t−1 enters into the Phillips Curve.
Three Equation Model with Rational Expectations We use the same Three Equation Model - that is, IS, AS and monetary policy rule. yt − y = −γ2 (rt − r) + Vt e πt = πt,t−1 + λ (yt − y) + St
e e rt = r + h πt,t−1 − π ∗ + b yt,t−1 −y Fiscal policy is assumed to be at trend, i.e., gt = g. Vt is an additive shock (we have simply assumed that).
Shock Terms The final thing we need to do is describe Vt and St . Now Vt and St are random variables and change in each period, unpredictably. We assume the following: E {Vt } = E {St } = 0 : On average agents are correct. They can make mistakes, however. E V2t = σv2 and E S2t = σs2 : Forecast variance is constant. E {St , Sj } = E {Vt , Vj } = 0 for j 6= t : Shocks are uncorrelated over time. E {Vt , St } = 0 : Shocks are independent of each other.
Shocks with above properties are sometimes referred to as ‘white noise’.
Solving the Model with Rational Expectations
SE and AE: Take IS and AS and substitute them together. Conditional on the predetermined expectations, this gives the equilibrium values of the endogenous variables as a function of exogenous ones, i.e., inflation and output as a function of the shocks. With RE we need to know what agents should e e rationally expect: πt,t−1 and yt,t−1 . Only after we have figured this out can we perform the next step and solve for the actual values of inflation and output, i.e. πt and yt .
Three Step Procedure
1
What we usually do: Put the monetary policy rule into the IS curve to eliminate rt and get the AD curve. Substitute this expression into the AS curve to eliminate the output gap, ybt .
2
Given the first step, calculate the rational expectation of yt and πt . This amounts to taking expectations of the answer e e to stage 1 to find πt,t−1 and yt,t−1 .
3
e Use the result from the second step to eliminate πt,t−1 and e yt,t−1 from AD and AS. This gives us the equilibrium value of yt and πt .
More Details I Use the IS, monetary policy rule and AS equations. Step 1: The AD and SRAS, respectively, are: e e − y + Vt − π ∗ + b yt,t−1 yt = y − γ2 h πt,t−1 e e e − π ∗ + b yt,t−1 πt = πt,t−1 − λγ2 h πt,t−1 − y + λVt + St Step 2: Take expectations: e e e yt,t−1 = y − γ2 h πt,t−1 − π ∗ + b yt,t−1 −y e e 0 = h πt,t−1 − π ∗ + b yt,t−1 −y e e Note: E {Vt } = E {St } = 0, E yt,t−1 = yt,t−1 , and e e E πt,t−1 = πt,t−1 .
More Details II Simplifying: e yt,t−1 =y
It must also be that: e πt,t−1 = π∗
Interpretation: Once we have taken the model into account, we expect that output will be at its natural rate. We also expect inflation to be at its target level. There may be a shock that makes this expectation incorrect. But, on average, we will be correct.
More Details III Step 3: Use these results in the original AD and AS equations: ybt = yt − y = Vt π bt = πt − π ∗ = λVt + St This is the solution to the model. It looks very different to our previous solution under static expectations.
Under rational expectations, the expression for output does not contain policy variables. This is the Policy Ineffectiveness Proposition (PIP) - systematic policy cannot affect output. All that drives output under rational expectations are the shocks.
Intuition on Policy Ineffectiveness Rearranging AS and setting St = 0: e ybt = (1/λ) πt − πt,t−1 {z } |
surprise inflation
Monetary policy only affects output if expected and actual inflation differ. However, agents know the monetary policy rule and they also know the rest of the economy’s structure. Conclusion: If private agents know the monetary policy rule and have access to the same information as the central bank, the central bank cannot (systematically) affect output.
Changing the Information Structure In our PIP example, the central bank sets the interest rate using information in period t − 1. The same information is available to wage setters. That is not entirely realistic. Wage contracts tend to fix the nominal wage for a considerable period ahead, and many firms change their prices only at infrequent intervals. Conversely, the central bank can change the interest rate quickly in response to new information. This means that the central bank has more information at its disposal when setting interest rates. Since private agents are temporarily locked into nominal contracts, the central bank effectively acts after wages and prices have been fixed.
Three Equations Model with Different Information Structure The three equation model is: yt − y = −γ2 (rt − r) + Vt e πt = πt,t−1 + λ (yt − y) + St
rt = r + h (πt − π ∗ ) + b (yt − y) , That is, the monetary policy rule is now like that used in previous lectures. But private agents still need to form expectations about inflation. We now need to solve the model again, i.e., we need to employ the three step solution. We skip the details.
New RE Solution Using the three step procedure we find the following: ybt =
(1 + γ2 b) St + λVt 1 + γ2 (b + λh)
π bt =
Vt − γ2 hSt 1 + γ2 (b + λh)
Now monetary policy can systematically affect output. For example, different values of h affect the way shocks impact on output. The stems from the central bank’s different reaction to the shocks: When h is higher the real interest rate is more sensitive to inflation; as h rises, for a given shock to the supply side, the output gap is lower.
Another Reason Why PIP Fails: Wage Contracts Regardless of the information structure, PIP can fail. So far, we have considered very simplistic wage setting behavior. Essentially everyone sets the wage at the same time. Now consider the following: Suppose the workforce is made up of two different groups, say group ‘A’ and ‘B’. Each has a trade union. Both A and B sign wage contracts which are fixed for two years. However, they don’t sign contracts at the same time; ‘A’ contracts in ‘odd years’ (1,3,5...) and ‘B’ in ‘even years’ (2,4,6...). Such overlapping wage contracts are sometimes referred to as staggered wage setting.
Timing of Wage Contracts
Clearly, each group has a different set of information at the time they sign a contract, e.g. It−1 or It . Graphical illustration. The preferences of the trade union are defined over the real wage. Thus, as before, the trade unions need to figure out what the price level will be when they contract. We can also derive a Phillips Curve from this.
Implications of Staggered Wage Setting Is that realistic? Not totally. But wages are negotiated and set in advance. And different groups will inevitably do this at different times in the year. So our assumption captures the right idea. Also, this applies to some countries more than others. For example, the US tends to have a low union presence, but countries such as Germany and Denmark have a very high union presence. Monetary policy is effective at changing output, and due to overlapping wage contracts the economy asymptotically approaches the long-run (new equilibrium) after a shock. This makes the RE model appear like a model with adaptive expectations, even though agents do not make systematic mistakes. Thus, staggered wage setting can help generate persistence.
Figure Curve 18.4: Theand expectations-augmented Phillips curve Phillips Cost of Disinflation
Figure: The expectations-augmented Phillips Curve. ©The McGraw-Hill Companies, 2005
Slide 1/6
The Empirics of PIP: The Cost of Disinflation Disinflationary policies are one way we can test PIP. Ball (1994) looks at disinflation episodes in a number of OECD countries. He calculates the sacrifice ratio - the cumulative output loss associated with a permanent reduction in inflation that arises from a policy of disinflation. If the PIP holds, we would expect the sacrifice ratio to be zero. Empirically, Ball finds: For quarterly (annual) data, the average sacrifice ratio is 5.8% (3.1%). The sacrifice ratio is larger when disinflation is slower. The sacrifice ratio is larger in countries where the degree of nominal rigidity is higher.
Ball (1994): Sacrifice Ratio
March 4, 2011
Lecture 7: Stabilization Policy and Expectations
Main reading: SWJ, chapter 21 1
Stabilization Policy
2
Adaptive Expectations
3
Rational Expectations and Policy Ineffectiveness
Taking Stock So far, our model of business cycle fluctuations and persistence is based on sticky wages, static expectations and shocks to the demand and supply sides of the economy. We have to deal with two more issues if we really want to explain the business cycle: 1
Introduction of uncertainty: So far, private agents were surprised by a shock because nominal wages were negotiated one period in advance, for example. But there is uncertainty for one period only - period t = 0; after that, agents cannot be surprised by further shocks.
2
Expectations formation: So far, private agents expected future inflation would be the same as in the current period; this generated much of the persistence. But is this a plausible way to model expectations?
Adaptive Expectations When expectations are static it is as if we play ‘catch-up’ each period. And we keep making the same old mistake. Maybe a better assumption is that expectations adapt. That is, each period we use information from all the past periods - not just the previous one: e e = (1 − φ) πt−1 − πt−1 , (1) πte − πt−1 | {z } | {z } revision of π e
previous forecast error
where 1 > φ ≥ 0. The parameter φ is a measure of the ‘stickiness’ of expectations. When φ = 0, we are back at static expectations: πte = πt−1
Adaptive Expectations Another way of expressing (1) is: e πte = φπt−1 + (1 − φ) πt−1
(2)
Iterating on (2) yields: πte =
∞ X
φn−1 (1 − φ) πt−n
n=1
Equation (3) expresses πte as a weighted sum of past inflation rates. Since φ < 1, adaptive expectations put more weight on recent events. This seems realistic. However, agents still make systematic mistakes because they always look to the past to figure out the future.
(3)
A different weight φ affects our previous results on business cycle dynamics: Table 19.1: The stochastic AS-AD model and stylized business cycle facts
Figure: Business cycle statistics for the stochastic AD/AS model.
©The McGraw-Hill Companies, 2005
Slide 1/11
AD/AS Model with Adaptive Expectations We have the following equations for AD, AS and expectations formation: yt − y = γ (π ∗ − πt ) + Dt
(4)
πt = πte + λ (yt − y) + St
(5)
e + (1 − φ) πt−1 πte = φπt−1
(6)
We solve the model exactly as before.
Solution of the AD/AS Model with Adaptive Expectations The AD and AS equations are now: ybt = −γb πt + Dt
(7)
π bt = π bt−1 + λb yt − φλb yt−1 + St − φSt−1
(8)
where ybt ≡ yt − y and π bt ≡ πt − π ∗ . When φ = 0 we are back at the model version with static expectations. The difference for φ > 0 is that there are extra lagged variables due to the way expectations about the future are formed.
The Implications of Adaptive Expectations I
Added lags change the degree of persistence. Again, we can calculate the half-live. We can use exactly the same technique as before (try this at home): Forward the AD and AS equations by one period. Set Dt = St = 0 for all t > 0. Use the current AD in the future period AS to eliminate π bt . Combine this expression with the future AD to eliminate π bt+1 .
The Implications of Adaptive Expectations II This implies: 1 + φλγ ybt + ... 1 + λγ | {z } ybt+1 =
t∗SE . Why? Static expectations imply that we care about what happened one period ago. Adaptive expectations imply that we care about this, and the period before, and the period before etc. with a lower and lower weight. [The weight is φt , and φt falls as t rises.] The extra insight is not great. How far can we really go with this approach? This question was addressed in the 1970’s.
Backward-Looking Versus Forward-Looking Expectations I
Neither static nor adaptive expectations fit well with a forward-looking model. The IS curve implies current investment depends on expectations of the future interest rate etc. In a stable economy it may seem reasonable to suppose: πte = Π (πt−1 , πt−2 , πt−3 , ....) Then, expectations based on past patterns of economic behavior are a good guide to the future.
Backward-Looking Versus Forward-Looking Expectations II But what if the economy is not stable? We may then be worried about the future: e e e πte = Π πt+1 , πt+2 , πt+3 , .... This represents the opposite extreme. Rational Expectations (RE) start from the second idea: Private agents use all available information to make a guess about future inflation. Importantly, this information is based on an understanding of the economic structure. From this we generate e , π e , π e , .... πt+1 t+2 t+3
Rational Expectations The RE assumption therefore flips everything around. We are no longer backward-looking making systematic mistakes. We are forward-looking and we know how the model works. Obviously, this is a strong assumption. Suppose inflation is high. The central bank attempts to reduce inflation to a lower level. This disinflation policy involves a change in the inflation target π ∗ . How long does it take for us to figure out what the central bank is trying to do? Clearly, it depends on the way expectations are formed: Adaptive expectations: a very long time. Rational expectations: immediately (we will show this).
Forecast Error with Static Expectations Static expectations imply πte = πt−1 and neglect the structural information on π ∗ . Figure 21.1: The inflation forecast error during a disinflation
e Thus, the inflation forecast error π with static expectations (simulation t − πt is )very persistent.
Figure: Static expectations: Inflation forecast error during Slide a 1/1 ©The McGraw-Hill Companies, 2005 disinflation.
The Lucas Critique I Suppose you are an econometrician. Assuming agents’ expectations are backward-looking, you estimate a structural model in order to predict the effects of a new policy regime (e.g. a change in π ∗ ). The problem is that your parameter estimates apply to the previous economic policy regime. You cannot use these estimates to infer (predict) economic behavior under the new policy regime. Example: Suppose we lower π ∗ to zero. If we had a model with consistent expectations, π e = π ∗ = 0 (we’ll show this). But the econometrician is assuming π e > 0, as expectations take time to catch up. In this case, he will miscalculate the impact of the policy.
The Lucas Critique II The Phillips Curve (rel: inflation and unemployment) is the most famous application of the Lucas Critique. Another example are temporary tax changes (rel: disposable income and consumption). Punch line: Expectations are important for aggregate relationships - they are likely to change them. But changes in policy are likely to affect expectations. So, policy can change aggregate relationships. If a policymaker tries to take advantage of such relationships, expectational mechanisms may cause those relationships to break down.
Rational Expectations Idea: Agents may be surprised by the latest news, but they won’t make systematic errors, i.e., on average agents will be correct. So, for any macroeconomic variable, say, Xt : e Xt,t−1 = E {Xt |It−1 } , {z } | | {z }
subj. exp’n
conditional exp’n
where It−1 is the information available to the agent (household or firm) at the end of period t − 1. e Notation: The term Xt,t−1 is then the expectation of X in period t made in period t − 1. E is the mathematical expectations operator. e Terminology: We sometimes say Xt,t−1 is the forecast of Xt .
Information Structure The monetary rule is: e + h (πt − π ∗ ) + b (yt − y) it = r + πt,t+1
or:
rt = r + h (πt − π ∗ ) + b (yt − y)
Case 1: Assume that neither the central bank nor the public know what shocks will occur. The central bank sets the interest rate rule using information in period t − 1: e h πt,t−1 − π∗ Case 2: Assume, more realistically, that central bank has more information than the trade unions: h (πt − π ∗ ) , where πt is known. e In each of the two alternative cases, πt,t−1 enters into the Phillips Curve.
Three Equation Model with Rational Expectations We use the same Three Equation Model - that is, IS, AS and monetary policy rule. yt − y = −γ2 (rt − r) + Vt e πt = πt,t−1 + λ (yt − y) + St
e e rt = r + h πt,t−1 − π ∗ + b yt,t−1 −y Fiscal policy is assumed to be at trend, i.e., gt = g. Vt is an additive shock (we have simply assumed that).
Shock Terms The final thing we need to do is describe Vt and St . Now Vt and St are random variables and change in each period, unpredictably. We assume the following: E {Vt } = E {St } = 0 : On average agents are correct. They can make mistakes, however. E V2t = σv2 and E S2t = σs2 : Forecast variance is constant. E {St , Sj } = E {Vt , Vj } = 0 for j 6= t : Shocks are uncorrelated over time. E {Vt , St } = 0 : Shocks are independent of each other.
Shocks with above properties are sometimes referred to as ‘white noise’.
Solving the Model with Rational Expectations
SE and AE: Take IS and AS and substitute them together. Conditional on the predetermined expectations, this gives the equilibrium values of the endogenous variables as a function of exogenous ones, i.e., inflation and output as a function of the shocks. With RE we need to know what agents should e e rationally expect: πt,t−1 and yt,t−1 . Only after we have figured this out can we perform the next step and solve for the actual values of inflation and output, i.e. πt and yt .
Three Step Procedure
1
What we usually do: Put the monetary policy rule into the IS curve to eliminate rt and get the AD curve. Substitute this expression into the AS curve to eliminate the output gap, ybt .
2
Given the first step, calculate the rational expectation of yt and πt . This amounts to taking expectations of the answer e e to stage 1 to find πt,t−1 and yt,t−1 .
3
e Use the result from the second step to eliminate πt,t−1 and e yt,t−1 from AD and AS. This gives us the equilibrium value of yt and πt .
More Details I Use the IS, monetary policy rule and AS equations. Step 1: The AD and SRAS, respectively, are: e e − y + Vt − π ∗ + b yt,t−1 yt = y − γ2 h πt,t−1 e e e − π ∗ + b yt,t−1 πt = πt,t−1 − λγ2 h πt,t−1 − y + λVt + St Step 2: Take expectations: e e e yt,t−1 = y − γ2 h πt,t−1 − π ∗ + b yt,t−1 −y e e 0 = h πt,t−1 − π ∗ + b yt,t−1 −y e e Note: E {Vt } = E {St } = 0, E yt,t−1 = yt,t−1 , and e e E πt,t−1 = πt,t−1 .
More Details II Simplifying: e yt,t−1 =y
It must also be that: e πt,t−1 = π∗
Interpretation: Once we have taken the model into account, we expect that output will be at its natural rate. We also expect inflation to be at its target level. There may be a shock that makes this expectation incorrect. But, on average, we will be correct.
More Details III Step 3: Use these results in the original AD and AS equations: ybt = yt − y = Vt π bt = πt − π ∗ = λVt + St This is the solution to the model. It looks very different to our previous solution under static expectations.
Under rational expectations, the expression for output does not contain policy variables. This is the Policy Ineffectiveness Proposition (PIP) - systematic policy cannot affect output. All that drives output under rational expectations are the shocks.
Intuition on Policy Ineffectiveness Rearranging AS and setting St = 0: e ybt = (1/λ) πt − πt,t−1 {z } |
surprise inflation
Monetary policy only affects output if expected and actual inflation differ. However, agents know the monetary policy rule and they also know the rest of the economy’s structure. Conclusion: If private agents know the monetary policy rule and have access to the same information as the central bank, the central bank cannot (systematically) affect output.
Changing the Information Structure In our PIP example, the central bank sets the interest rate using information in period t − 1. The same information is available to wage setters. That is not entirely realistic. Wage contracts tend to fix the nominal wage for a considerable period ahead, and many firms change their prices only at infrequent intervals. Conversely, the central bank can change the interest rate quickly in response to new information. This means that the central bank has more information at its disposal when setting interest rates. Since private agents are temporarily locked into nominal contracts, the central bank effectively acts after wages and prices have been fixed.
Three Equations Model with Different Information Structure The three equation model is: yt − y = −γ2 (rt − r) + Vt e πt = πt,t−1 + λ (yt − y) + St
rt = r + h (πt − π ∗ ) + b (yt − y) , That is, the monetary policy rule is now like that used in previous lectures. But private agents still need to form expectations about inflation. We now need to solve the model again, i.e., we need to employ the three step solution. We skip the details.
New RE Solution Using the three step procedure we find the following: ybt =
(1 + γ2 b) St + λVt 1 + γ2 (b + λh)
π bt =
Vt − γ2 hSt 1 + γ2 (b + λh)
Now monetary policy can systematically affect output. For example, different values of h affect the way shocks impact on output. The stems from the central bank’s different reaction to the shocks: When h is higher the real interest rate is more sensitive to inflation; as h rises, for a given shock to the supply side, the output gap is lower.
Another Reason Why PIP Fails: Wage Contracts Regardless of the information structure, PIP can fail. So far, we have considered very simplistic wage setting behavior. Essentially everyone sets the wage at the same time. Now consider the following: Suppose the workforce is made up of two different groups, say group ‘A’ and ‘B’. Each has a trade union. Both A and B sign wage contracts which are fixed for two years. However, they don’t sign contracts at the same time; ‘A’ contracts in ‘odd years’ (1,3,5...) and ‘B’ in ‘even years’ (2,4,6...). Such overlapping wage contracts are sometimes referred to as staggered wage setting.
Timing of Wage Contracts
Clearly, each group has a different set of information at the time they sign a contract, e.g. It−1 or It . Graphical illustration. The preferences of the trade union are defined over the real wage. Thus, as before, the trade unions need to figure out what the price level will be when they contract. We can also derive a Phillips Curve from this.
Implications of Staggered Wage Setting Is that realistic? Not totally. But wages are negotiated and set in advance. And different groups will inevitably do this at different times in the year. So our assumption captures the right idea. Also, this applies to some countries more than others. For example, the US tends to have a low union presence, but countries such as Germany and Denmark have a very high union presence. Monetary policy is effective at changing output, and due to overlapping wage contracts the economy asymptotically approaches the long-run (new equilibrium) after a shock. This makes the RE model appear like a model with adaptive expectations, even though agents do not make systematic mistakes. Thus, staggered wage setting can help generate persistence.
Figure Curve 18.4: Theand expectations-augmented Phillips curve Phillips Cost of Disinflation
Figure: The expectations-augmented Phillips Curve. ©The McGraw-Hill Companies, 2005
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The Empirics of PIP: The Cost of Disinflation Disinflationary policies are one way we can test PIP. Ball (1994) looks at disinflation episodes in a number of OECD countries. He calculates the sacrifice ratio - the cumulative output loss associated with a permanent reduction in inflation that arises from a policy of disinflation. If the PIP holds, we would expect the sacrifice ratio to be zero. Empirically, Ball finds: For quarterly (annual) data, the average sacrifice ratio is 5.8% (3.1%). The sacrifice ratio is larger when disinflation is slower. The sacrifice ratio is larger in countries where the degree of nominal rigidity is higher.
Ball (1994): Sacrifice Ratio
