Does the Barro-Gordon Model Explain the Behavior of Inflation in Romania?

MSc Student: Ana AlexeSupervisor: Professor Moisă Altăr

The Academy of Economic Studies

Doctoral School of Finance and Banking

Bucharest, July 2008

Topics

1. Introduction2. Literature review

3. Barro-gordon time consistency model 4. Input data5. The natural rate of unemployment

estimations6. Inflation and unemployment estimations

according to barro-gordon model7. Unit root tests8. Cointegration tests9. Conclusions

1. Introduction

There are many situations in which one economic agent (the government for example) has an incentive to deceive another economic agent.

Intuitively, the policymaker, who aims to bring the unemployment rate closer to its natural rate, is tempted to do so by creating surprise inflation. Households, being rational agents, perfectly anticipate this temptation to inflate and adjust their decisions accordingly. As a result, the equilibrium outcome is a situation with no reduction in unemployment and higher inflation than before (the `inflation bias' result).

The purpose of this paper is to analyze the time-inconsistency problem between inflation and unemployment rate series for Romania, using unit root tests and co-integration tests, Hodrick-Prescott filter and Kalman filter as estimation techniques, in order to test the Barro-Grodon model’s implications.

2. Literature review

In the literature there are known different types of time-inconsistency: time-inconsistency due to changes in preferences over time (Strotz (1956)) time-inconsistency of government plans when agents have rational

expectations (Lucas (1976), Kydland & Prescott (1977), Barro & Gordon (1983)).

The idea that the proper design of monetary policy is crucial to achieve good inflation outcomes was first proposed by Kydland and Prescott (1977). A key result is that if policymakers cannot commit to future policies, inflation rates are higher than if they can commit.

Barro and Gordon (1983) further developed this idea. They argue that an optimal punishment mechanism is in place and that no intervention is necessary.

Ireland (1999) initially conducted time series tests for the United States based on the modified Barro-Gordon model. He shows that Barro and Gordon’s (1983) model of time-consistent monetary policy imposes long-run restrictions on the time series properties of inflation and unemployment that are not rejected by the data in the US.

3. Barro-Gordon Time Consistency Model

BG model’s assumption:

inflation varies positively with the natural unemployment rate

inflation will inherit the persistency of the natural rate of unemployment when the central bank cannot commit to a monetary policy rule

Ireland (1999):

the actual unemployment rate is non-stationary

control errors for inflation – which permits the model to account for transitory deviations between the actual unemployment rate and the natural rate

3. Barro-Gordon Time Consistency Model

The equations of the model

expectations Phillips curve (1)

the natural rate (2)

the actual inflation rate (3)

minimize a loss function that penalizes variations of unemployment and inflation around target values: k*Unt and 0

(1) and (3) => the policymaker’s problem becomes:

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3. Barro-Gordon Time Consistency Model

The solution of the model

the first-order condition (4)

in equilibrium

using (4) => (5) the inflationary bias resulting from the policymaker’s inability to commit depends positively on the expected natural rate

from (1), (3) and (5) => (6) which shows how the control error for inflation (ηt) allows the actual unemployment rate to fluctuate, in equilibrium, around the natural rate

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3. Barro-Gordon Time Consistency Model

The solution of the model

combining (6) and (2) => (7)

combining (2), (3) and (5) => (8)

separately, (7) and (8) indicate that both inflation and unemployment are non-stationary, inheriting unit roots from the natural rate of unemployment

together, they imply that a linear combination of inflation and unemployment is stationary (9)

Equation (9) summarizes the constraint that Barro and Gordon’s theory imposes on the long-run behavior of inflation and unemployment: according to the model, these variables should be non-stationary but co-integrated.

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4. Input Data

Variable Period Analyzed Source Observations

Unemployment rate

Jan 1999 – March 2008 (monthly observations)

Website of the National Bank

registered monthly unemployment rates in %

Inflation rate For the CPI: National Institute of Statistics

measured as the first difference in the logarithm of the monthly CPI (Consumer Price Index)

The relationship between the two variables is a positive one, meaning that an extra one percentage point of unemployment pushes the inflation rate up.

The relationship between initial inflation and unemployment rates

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unemployment (%)

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5. The natural rate of unemployment estimations

A disadvantage of this representation is that it includes the unobserved natural rate of unemployment and there are no direct measures of the natural rate.

Statistical approaches to estimate time-varying natural rate of unemployment:

Hodrick Prescott filter - widely used among macroeconomists to obtain a smooth estimate of the long-term trend component of a series

Kalman filter - the most commonly used reduced form filtering technique for estimating the natural rate of unemployment due to its simplicity of estimation

5. The natural rate of unemployment estimations

Hodrick-Prescott (HP) filter

HP filter is a two-sided linear filter that computes the smoothed series s of y by minimizing the variance of y around s, subject to a penalty parameter

The penalty parameter controls the smoothness of the series (λ=14.400 for monthly data).

The trend estimated here counts for the natural rate of unemployment.

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UNEMPLOYMENT Trend Cycle

Hodrick-Prescott Filter (lambda=14400)

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5. The natural rate of unemployment estimations

Kalman filter I use the Kalman filter of Kalman (1960) and Kalman and Bucy (1961), since it

has the major advantage of allowing a time-varying natural rate of unemployment to be estimated jointly with a Phillips curve.

The general specification:

Equation (1) is a Phillips curve – it models unexpected inflation as a function of: shocks (xt) and the unemployment gap (Ut - Unt) The natural rate of unemployment (Unt) is time varying and its movement is modeled by Equation (2) The forecasts from the exponential smoothing method are used to track the seasonal movements in the actual series as it gives good results

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5. The natural rate of unemployment estimations

Hodric-Prescott filter versus Kalman filter

The key difference between the HP filter and the Kalman filter is that the HP filter natural rate of unemployment estimates move more closely with the actual level of unemployment => the size of unemployment gaps is smaller than those estimates based on the Kalman filter.

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5. The natural rate of unemployment estimations

Unit root tests for the estimated natural rate of unemployment

6. Inflation and unemployment estimations according to Barro-Gordon model

Equations (7) and (8) show that according to the model, both inflation andunemployment rate ought to be unit root processes.

Unit root tests for inflation – HP filter case

=> πt = 0.1343*Unt-1 + 5.6319*ΔUnt-1+ ηt (15.54) (6.08)

From the table above one can see that the inflation determined by BG has a unit root, which is according to the model.

*Critical points of 1%, 5% and 10% levels of significance: 1.98, 2.63, 3.39

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INFLATION

6. Inflation and unemployment estimations according to Barro-Gordon model

Unit root tests for inflation – Kalman filter case

=>πt = 0.0885*Unt-1 -0.0344*ΔUnt-1 + ηt (17.31) (-3.81)

From the table above one can see that the inflation determined by BG has a unit root, which is according to the model.

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INFLATION

6. Inflation and unemployment estimations according to Barro-Gordon model

Unit root tests for unemployment – HP filter case

=> Ut = Unt-1 +1.7344*( Unt-1- Unt-2) + εt (2.62)

From the table above one can see that the unemployment rate determined by BG has a unit root, which is according to the model.

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UNEMPLOYMENT

6. Inflation and unemployment estimations according to Barro-Gordon model

Unit root tests for unemployment – Kalman filter case

=> Ut = Unt-1 -3.2745*( Unt-1- Unt-2) + εt (-3.006)

As a conclusion, we can not say if the unemployment rate is in accordance with the model’s hypothesis that the unemployment is non-stationary if the natural rate of unemployment is non-stationary.

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7. Unit root tests

Unit root tests results

In the case when the natural unemployment rate is determined by Hodrick Prescott filter, both inflation and unemployment seem to be unit root processes, which is consistent with the model’s implication.

In the case when the natural unemployment rate is determined using Kalman filter, inflation is a unit root process, but it is difficult to say if unemployment is stationary or non-stationary, so we can not say whether this case is or not in accordance with the Barro-Gordon model.

8. Cointegration tests Equation (9) implies that the linear combination of unemployment rate and inflation is stationary, even though these two variables are non-stationary independently.

Phillips-Ouliaris (PO) co-integration test The tested hypothesis is H0 – no co-integration between inflation and

unemployment rate

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8. Cointegration tests

Phillips-Ouliaris (PO) co-integration test

HP filter case: the t-statistic > critical values* at 1%, 2.5% and 5% levels of significance, we reject H0: there is no co-integration between inflation and unemployment rate, which means that the data appear to be consistent with the Barro-Gordon model’s implication that inflation and unemployment are cointegrated, according to the PO co-integration test.

Kalman filter case: the t-statistic << critical values at 1%, 2.5% and 5% levels of significance, in this case we can’t reject H0: no co-integration between inflation and unemployment rate, which means that the linear combination of inflation and unemployment rate is non-stationary.

*t - critical values at 1%, 2.5% and 5% are -3.39, -3.05 and -2.76 respectively

8. Cointegration tests

Engle Granger (EG) Method

This method involves estimating the long-run Equation (9) by the standard regression method and then the residuals are recovered and tested for stationarity by applying the ADF and the PP unit root tests.

8. Cointegration tests Johansen co-integration test

The analysis below assumes that there is no constant in the co-integration relation (as implied in the BG model) and that there are no deterministic trends in the data; under this assumption, no constant terms are included in the preliminary regression.

There are two statistics to take into account; the trace and maximum eigenvalue.

Given that for both tests, the test statistic exceeds its critical value (5%) when the null is r = 0, we can conclude that at least one co-integration vector is present.

For more than one co-integration vector, the test statistic is less than the critical value so we conclude only a single co-integration vector is present.

Co-integrating Vector: πt=0.085486*ut

8. Cointegration tests Johansen co-integration test

Given that for both tests, the test statistic is less than its critical value (5%) when the null is r = 0, we can conclude that no co-integration vector is present.

8. Cointegration tests Johansen co-integration test

According to Maximum Eigenvalue statistic, only 1 co-integration vector exists. We compute the likelihood ratio:

Tested hypothesis: H0 – no co-integration between inflation and unemployment rate.

As the calculated likelihood ratio=10,2418 < likelihood critical values at 1%, 2.5% and 5% levels of significance, we cannot reject H0: no co-integration between inflation and unemployment rate.

* Likelihood critical values at 1%, 2.5% and 5% are 15.69, 13.27 and 11.44 respectively.

8. Cointegration tests Cointegration tests results

The co-integration vectors determined using the three co-integration tests are similar.

As a conclusion: I can say that the co-integration implication of the Barro-Gordon model can only

be proved in the case when the natural unemployment rate is estimated using the Hodrick-Prescott filter.

In the other case, when the natural unemployment rate is estimated using the Kalman filter, the co-integration implication can not be proved, this is mainly because we were not able to prove that the unemployment rate is non-stationary or not.

8. Conclusions The model implies that both inflation and unemployment rate processes depend on

the evolution of the natural rate of unemployment

Under the assumption that the natural rate of unemployment follows a unit root process, inflation and unemployment rate should be non-stationary while in the long-run, these two variables are co-integrated.

8. Conclusions

Looking at the results presented and analyzing the Barro-Gordon model’s implications, I conclude that:

inflation and unemployment are unit root processes – which is in accordance with the model: both inflation and unemployment are non-stationary in both of the cases presented for the estimation of the natural rate of unemployment

I could prove that the two variables are co-integrated only in the case when I’ve made the estimation of natural rate of unemployment using Hodrick Prescott filter – this is in accordance with the model’s implication of co-integration

The results in this paper support the Barro-Gordon model to explain long-term inflation behavior in Romania. The results indicate that the policymaker’s inability to commit in advance to a monetary policy could explain the evolution of inflation.

Thank you!