Dynamic model and cost of disinflation
Dynamic model: cost of disinflation (Lecture 18) Martin Berka
Is there a Phillips curve in the data? • Phillips curve tells us that, ceteris paribus, changes in inflation are, in short run, inversely related to changes in the unemployment rate. • Does Phillips curve theory accord with the data? • We will look at a few scatter plots for New Zealand • 1960-1977: data begins, medium inflation • 1978-1998: centered around the main disinflation • 1989-2011: π targeting
Inflation in New Zealand • Disinflation: fall in the rate of inflation • Deflation: inflation < 0 • 1970 – 1980: inflation acceleration • Unsuccessful attempts to disinflate through price, wage and other controls in 1982 – 1984 • Early disinflation (1985 – 1988): search for stable monetary indicators • RBNZ Act 1989: inflation targeting, major disinflation • Ongoing low inflation
Short-run and Long-run Phillips curves in NZ
Short-run and Long-run Phillips curves in NZ
Short-run and Long-run Phillips curves in NZ
Introduction: Okun’s law • We now introduce a new dynamic aspect • Growth rate of output, and changes in growth rate • We base this on Okun’s “law” • A reduced-form relationship between the changes in unemployment and changes in growth rate of output • Increases in output growth tend to be associated with decreases in unemployment rate: 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅ 𝑦 )
• Where 𝑔𝑦𝑦 : actual GDP growth rate • 𝑔̅ 𝑦: average GDP growth rate • 𝛽 ∈ (0,1)
(1)
Add two more equations • Phillips curve • Expectations-adjusted Phillips curve with backward-looking expectations: 𝜋𝑡 − 𝜋𝑡−1 = −𝛼 𝑢𝑡 − 𝑢 𝑛 , if 𝜋 𝑒 =𝜋𝑡−1 (2) • Trade-off: if country lowers inflation, it “pays” for it by a temporarily higher unemployment rate.
• Simplified AD relationship M • Simplify Y = Y , G, T by ignoring government for now: • 𝑌𝑡 = 𝑌
𝑀𝑡 𝑃𝑡
P
=𝛾
𝑀𝑡 𝑃𝑡
• Re-write in terms of changes: 𝑔𝑦𝑦 = 𝑔𝑚𝑡 −𝜋𝑡
(3)
• Where 𝑔𝑚𝑚 is the nominal money supply growth rate
• Now we have a 3-equation dynamic system
Three-equation system • Our three-equation system is 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅ 𝑦 ) 𝜋𝑡 − 𝜋𝑡−1 = −𝛼 𝑢𝑡 − 𝑢 𝑛
𝑔𝑦𝑦 = 𝑔𝑚𝑚 −𝜋𝑡
(1) (2) (3)
• This system defines how variables change in the short run • But it does not define the medium-run equilibrium (the equations assume the medium run equilibrium is exogenous) • So before we look at the short-run dynamics of the adjustment to medium run, we need to define the medium run
Medium run • Recall that in the labour market, 𝑢 = 𝑢𝑛 in medium run
• Therefore, Okun’s law (equation (1)) implies that output must grow at the normal rate 𝑔𝑦𝑦 = 𝑔̅𝑦 • Using the simplified AD relationship (3), this implies that 𝜋𝑡 = 𝑔𝑚𝑚 − 𝑔̅𝑦
• In the medium run, inflation is equal to nominal money growth minus normal output growth • Thus, a change in 𝑔𝑚𝑚 only causes changes in 𝜋𝑡 in the medium run • Money is neutral
Disinflationary adjustment • Countries regularly undergo periods of temporarily high inflation. • Cost of disinflation • Phillips curve: in order to lower inflation, country must have a temporarily higher unemployment rate. • After reaching new equilibrium inflation rate, unemployment rate returns to 𝑢 𝑛
• The cost is a consequence of nominal rigidities: • If wage contracts were instantaneously adjustable, adjustment would be feasible without laying off workers • Downward nominal wage rigidity: people do not like wage cuts. Some contracts are inflation-adjusted.
Disinflationary adjustment • Nominal rigidity in our textbook: sticky price expectations • But, since we are using a theory in which Pe enters wage negotiations, wages are also rigid in our model. • Let’s quantify the costs of the disinflationary adjustment • Assume π0=14% while the target π=4%, un=6% and 𝒈𝒚 = 𝟑%
• Need parameter values for Phillips curve and Okun’s Law. Let β=0.4 and α=1. Finally, assume the disinflation has to occur in 1 year • Substitute into equation (2) 𝜋𝑡 − 𝜋𝑡−1 = −𝛼(𝑢𝑡 − 𝑢𝑛 ) −10% = −(𝑢𝑡 − 6%) • ut must rise to 16% during the adjustment
Disinflationary adjustment • Now use Okun’s law equation (1) and substitute into it ut=16% 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅𝑦 ) 16% − 6% = −0.4(𝑔𝑦𝑦 − 3%) • Thus, gy = - 22% in order for the adjustment to happen • It seems very unlikely that such drastic adjustment would be politically feasible in a period of 1 year. • Gradualism: spread the adjustment over more years. But that has its disadvantages, also: prolonged misery
Lucas critique • Robert Lucas showed how changes in policy influence behaviour of people • People try to make optimal decisions, given the economic environment we live in. • Changes in government policy change the economic environment • Changes in our environment lead to changes in behaviour of people • Therefore, we cannot assume that parameters in our models, even when estimated from historical data, stay unchanged after a policy change. • A change in policy will cause people to re-optimize their behaviour to best take advantage of the new opportunities • This will cause parameters to take on new values
Lucas critique – in our model • We cannot address Lucas critique fully here, because our model does not feature optimizing people and firms. • You will learn how to do this in the third year and later • But we can improve our model to better reflect reality, by allowing inflation expectations to be less rigid • Furthermore, we will allow a policy-maker (central bank) to influence how inflation expectations are formed • A credible policy-maker will have a larger impact on inflation expectations than a non-credible policy maker • Assume inflation expectations are formed as:
πte = λπt + (1- λ)πt-1 • λ=0 implies rigid expectations, λ=1 implies expectations which are not rigid at all
Lucas critique – in our model • Phillips curve equation (2) is now in more general: 𝜋𝑡 = 𝜆𝜋𝑡 + (1 − 𝜆)𝜋𝑡−1 − 𝛼 𝑢𝑡 − 𝑢 𝑛 , which implies: −𝛼 𝑢𝑡 − 𝑢 𝑛 𝜋𝑡 − 𝜋𝑡−1 = 1−𝜆 • Assume that λ=0.5, and solve the model again −1 𝑢𝑡 − 6% −10% = 0.5 5% = 𝑢𝑡 − 6% • ut must now rise only 11% during the adjustment • Finally, using Okun’s law 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅𝑦 ) 11% − 6% = −0.4(𝑔𝑦𝑦 − 3%) 5% = (𝑔𝑦𝑦 − 3%) −0.4 • Now, gy = - 9.5% only
Nominal rigidities • Slow changes in expectations are only one form of nominal rigidities • Even if expectations adjust optimally and instantaneously, there exist other types of nominal (price) rigidities • Wage contracts are written for medium-time horizons • Thus wages cannot change instantaneously. • Costs of nominal adjustment (prices, wages, …): 1. Menu costs: managerial, information, implementation 2. Negotiation costs: managerial, information, implement. 3. Staggering of wage contracts: not all signed at the same time • Therefore, change to expectations need not lead to faster adjustment and therefore lower cost (unemployment and ouptut) of disinflation
Is there a Phillips curve in the data? • Phillips curve tells us that, ceteris paribus, changes in inflation are, in short run, inversely related to changes in the unemployment rate. • Does Phillips curve theory accord with the data? • We will look at a few scatter plots for New Zealand • 1960-1977: data begins, medium inflation • 1978-1998: centered around the main disinflation • 1989-2011: π targeting
Inflation in New Zealand • Disinflation: fall in the rate of inflation • Deflation: inflation < 0 • 1970 – 1980: inflation acceleration • Unsuccessful attempts to disinflate through price, wage and other controls in 1982 – 1984 • Early disinflation (1985 – 1988): search for stable monetary indicators • RBNZ Act 1989: inflation targeting, major disinflation • Ongoing low inflation
Short-run and Long-run Phillips curves in NZ
Short-run and Long-run Phillips curves in NZ
Short-run and Long-run Phillips curves in NZ
Introduction: Okun’s law • We now introduce a new dynamic aspect • Growth rate of output, and changes in growth rate • We base this on Okun’s “law” • A reduced-form relationship between the changes in unemployment and changes in growth rate of output • Increases in output growth tend to be associated with decreases in unemployment rate: 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅ 𝑦 )
• Where 𝑔𝑦𝑦 : actual GDP growth rate • 𝑔̅ 𝑦: average GDP growth rate • 𝛽 ∈ (0,1)
(1)
Add two more equations • Phillips curve • Expectations-adjusted Phillips curve with backward-looking expectations: 𝜋𝑡 − 𝜋𝑡−1 = −𝛼 𝑢𝑡 − 𝑢 𝑛 , if 𝜋 𝑒 =𝜋𝑡−1 (2) • Trade-off: if country lowers inflation, it “pays” for it by a temporarily higher unemployment rate.
• Simplified AD relationship M • Simplify Y = Y , G, T by ignoring government for now: • 𝑌𝑡 = 𝑌
𝑀𝑡 𝑃𝑡
P
=𝛾
𝑀𝑡 𝑃𝑡
• Re-write in terms of changes: 𝑔𝑦𝑦 = 𝑔𝑚𝑡 −𝜋𝑡
(3)
• Where 𝑔𝑚𝑚 is the nominal money supply growth rate
• Now we have a 3-equation dynamic system
Three-equation system • Our three-equation system is 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅ 𝑦 ) 𝜋𝑡 − 𝜋𝑡−1 = −𝛼 𝑢𝑡 − 𝑢 𝑛
𝑔𝑦𝑦 = 𝑔𝑚𝑚 −𝜋𝑡
(1) (2) (3)
• This system defines how variables change in the short run • But it does not define the medium-run equilibrium (the equations assume the medium run equilibrium is exogenous) • So before we look at the short-run dynamics of the adjustment to medium run, we need to define the medium run
Medium run • Recall that in the labour market, 𝑢 = 𝑢𝑛 in medium run
• Therefore, Okun’s law (equation (1)) implies that output must grow at the normal rate 𝑔𝑦𝑦 = 𝑔̅𝑦 • Using the simplified AD relationship (3), this implies that 𝜋𝑡 = 𝑔𝑚𝑚 − 𝑔̅𝑦
• In the medium run, inflation is equal to nominal money growth minus normal output growth • Thus, a change in 𝑔𝑚𝑚 only causes changes in 𝜋𝑡 in the medium run • Money is neutral
Disinflationary adjustment • Countries regularly undergo periods of temporarily high inflation. • Cost of disinflation • Phillips curve: in order to lower inflation, country must have a temporarily higher unemployment rate. • After reaching new equilibrium inflation rate, unemployment rate returns to 𝑢 𝑛
• The cost is a consequence of nominal rigidities: • If wage contracts were instantaneously adjustable, adjustment would be feasible without laying off workers • Downward nominal wage rigidity: people do not like wage cuts. Some contracts are inflation-adjusted.
Disinflationary adjustment • Nominal rigidity in our textbook: sticky price expectations • But, since we are using a theory in which Pe enters wage negotiations, wages are also rigid in our model. • Let’s quantify the costs of the disinflationary adjustment • Assume π0=14% while the target π=4%, un=6% and 𝒈𝒚 = 𝟑%
• Need parameter values for Phillips curve and Okun’s Law. Let β=0.4 and α=1. Finally, assume the disinflation has to occur in 1 year • Substitute into equation (2) 𝜋𝑡 − 𝜋𝑡−1 = −𝛼(𝑢𝑡 − 𝑢𝑛 ) −10% = −(𝑢𝑡 − 6%) • ut must rise to 16% during the adjustment
Disinflationary adjustment • Now use Okun’s law equation (1) and substitute into it ut=16% 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅𝑦 ) 16% − 6% = −0.4(𝑔𝑦𝑦 − 3%) • Thus, gy = - 22% in order for the adjustment to happen • It seems very unlikely that such drastic adjustment would be politically feasible in a period of 1 year. • Gradualism: spread the adjustment over more years. But that has its disadvantages, also: prolonged misery
Lucas critique • Robert Lucas showed how changes in policy influence behaviour of people • People try to make optimal decisions, given the economic environment we live in. • Changes in government policy change the economic environment • Changes in our environment lead to changes in behaviour of people • Therefore, we cannot assume that parameters in our models, even when estimated from historical data, stay unchanged after a policy change. • A change in policy will cause people to re-optimize their behaviour to best take advantage of the new opportunities • This will cause parameters to take on new values
Lucas critique – in our model • We cannot address Lucas critique fully here, because our model does not feature optimizing people and firms. • You will learn how to do this in the third year and later • But we can improve our model to better reflect reality, by allowing inflation expectations to be less rigid • Furthermore, we will allow a policy-maker (central bank) to influence how inflation expectations are formed • A credible policy-maker will have a larger impact on inflation expectations than a non-credible policy maker • Assume inflation expectations are formed as:
πte = λπt + (1- λ)πt-1 • λ=0 implies rigid expectations, λ=1 implies expectations which are not rigid at all
Lucas critique – in our model • Phillips curve equation (2) is now in more general: 𝜋𝑡 = 𝜆𝜋𝑡 + (1 − 𝜆)𝜋𝑡−1 − 𝛼 𝑢𝑡 − 𝑢 𝑛 , which implies: −𝛼 𝑢𝑡 − 𝑢 𝑛 𝜋𝑡 − 𝜋𝑡−1 = 1−𝜆 • Assume that λ=0.5, and solve the model again −1 𝑢𝑡 − 6% −10% = 0.5 5% = 𝑢𝑡 − 6% • ut must now rise only 11% during the adjustment • Finally, using Okun’s law 𝑢𝑡 − 𝑢𝑡−1 = −𝛽(𝑔𝑦𝑦 − 𝑔̅𝑦 ) 11% − 6% = −0.4(𝑔𝑦𝑦 − 3%) 5% = (𝑔𝑦𝑦 − 3%) −0.4 • Now, gy = - 9.5% only
Nominal rigidities • Slow changes in expectations are only one form of nominal rigidities • Even if expectations adjust optimally and instantaneously, there exist other types of nominal (price) rigidities • Wage contracts are written for medium-time horizons • Thus wages cannot change instantaneously. • Costs of nominal adjustment (prices, wages, …): 1. Menu costs: managerial, information, implementation 2. Negotiation costs: managerial, information, implement. 3. Staggering of wage contracts: not all signed at the same time • Therefore, change to expectations need not lead to faster adjustment and therefore lower cost (unemployment and ouptut) of disinflation
