Inflation Targeting as a Tool To Control Unemployment

Transcription

1 Inflation Targeting as a Tool To Control Unemployment - Using the Phillips Curve to study its effectiveness - Manchit Mahajan Subhashish Bhadra St. Stephen s College Delhi University

2 Abstract An Inflation Targeting (IT) Central Bank is one whole sole objective is to maintain inflation at a low and steady level. The first Central Bank to adopt IT as its only objective was the central bank of New Zealand in Subsequently, it was adopted by the UK, Canada and Australia in quick succession. The basis of Inflation-Targeting (IT) lies in neoclassical macroeconomics, particularly the Phillips Curve relationship. We study this underlying economic rationale in Section 1 of this project. Whether Inflation-Targeting is s good option has been a matter of public debate for long. Several Chairpersons of the US Federal Reserve have suggested that the US Federal Reserve also adopt IT as its only objective. In Sections 2,3 and 4, we empirically test whether IT makes the conduct of monetary policy easier by testing for differences in the sacrifice ratio between a non-it economy (the US) and an IT economy (Australia). Our objective in this project is to test whether IT makes a difference to the sacrifice ratio. If it does, then it makes a case for transition to IT central banks. However, if it doesn t, then we are unable to say anything for sure. Contents 1. The Phillips Curve - Pg The United States of America - Pg Australia - Pg The Sacrifice Ratio - Pg Appendices - Pg. 21 2

3 Section 1 The Phillips Curve We will derive a particular functional form of the Phillips Curve equation that uses the wage-price bargaining between firms and workers to derive an inflation-unemployment tradeoff The Wage Setting Equation The wage-setting equation gives the wages demanded by workers in the economy. The wage demanded by the workers in the economy is a function of: Price Expectations: Since prices are not known at the time of setting the wages, price expectations are important. Since workers care only about the real wages, a rise in the expected price level will cause a proportional rise in the wage demanded by workers. Unemployment Level: A higher unemployment rate reduces the bargaining power of workers. Hence, an increase in unemployment rate reduces the wages demanded by the workers. Catch-All Factor: The catch-all factor z captures the effects of all other variables, such as unemployment benefits, etc. By definition, the catch-all variable is defined such that an increase in the variable reduces the wage demanded by workers. Thus, the wage-setting equation is given as follows: W t = P t e. F (u, z) The signs of the partial derivatives are given as follows: W t P t e > 0, W t u < 0, W t z > 0 The particular functional form of the wage-setting equation that we consider is given below. This equation satisfies all the partial derivatives that we have discussed above. W t = P t e. (1 α.u + z) 3

4 The Price-Setting Equation The price-setting equation gives the price that firms demand. The factors that affect the price-setting equation are as follows: Price Level: Since firms have perfect information about the price of their product, price expectations are not important. Wage Rate: The wage rate leads to a one-for-one increase in the price demanded by the firm. For example, a 100% rise in wages will lead the firm to demand a 100% increase in the price of its product Mark-Up: Under perfect competition, a firm will make zero economic profits. To introduce an element of imperfect competition in our model, we allow the firm to mark up its price over its wage bill by a factor (1+μ). μ will capture the degree of monopoly power that the firm enjoys. Hence, the price setting equation for the firm is given by: P = (1+μ).W The Phillips Curve In any equilibrium, both the equations must be satisfied. Combining both equations, we get: P t = P t e. (1 + μ). (1 α.u + z) It can be shown that after simple but tedious mathematical treatment, the previous equation can be converted into the Phillips Curve Equation 1 : π t = π t e + (μ + z) α.u Empirically, it was observed that the expected inflation, π t e, is equal to the last year s inflation rate π t-1. Hence, the final form of the Phillips curve is: π t - π t-1 = (μ + z) α.u At the Natural Rate of Unemployment, inflation is constant. Hence, u N = (μ + z)/ α Finally, the Phillips Curve can be written in terms of the Natural Rate of Unemployment as: π t - π t-1 = α (u t u N ) The Natural Rate of Unemployment 1 For the formal derivation, see Blanchard: Macroeconomics, Chapter 8. 2 For more details, refer to Foundations of Modern Macroeconomics, Ben Heijdra 3 What Makes the Output-Inflation Trade-off Change? E De Vierman 4

5 The natural rate of unemployment, U N, is a function of the sacrifice ratio, mark-up and catch-all variable. It can be derived from the Phillips Curve equation that we have derived. However, deriving U N using this Phillips Curve relationship requires non-linear estimation. We, instead, adopt another method to derive the natural rate of unemployment 2. Unemployment rate in this period is seen to be a function of last period s unemployment rate. Take a particular functional form given by: U t = α + β.u t-1 This is a first-order difference equation. We find the steady-state level of unemployment rate by take U t = U t-1 = U N. U N = α + β.u N (1-β) U N = α α U N = 1 β This is a steady-state level of unemployment around which there is no tendency to change. We take it as an acceptable proxy for the natural rate of unemployment as derived from the Phillips Curve equation. There are two countries in particular that we consider in this project USA and Australia. For both these countries, we run the above-mentioned regression and obtain the following results. Note that since our purpose here is to obtain point estimates of U N, we do not carry out rigorous statistical tests. Table 1.1: United States of America R 2 : Significance: Constant U t Table 1.2: USA - Heteroskedasticity Test Statistic: Significance: Constant U t U t For more details, refer to Foundations of Modern Macroeconomics, Ben Heijdra 5

6 The point estimate of U N thus obtained for the US economy is 6.51%. Table 1.3: Australia R 2 : Significance: Constant U t Table 1.4: Australia - Heteroskedasticity Test Statistic: Significance: Constant U t U t The point estimate of U N thus obtained for the Australian economy is 7.24%. We have similarly obtained the natural rate of unemployment, U N, for several other countries for which unemployment data over a sufficiently long period of time was available. While we have not used these values in our project, the reader may refer to Appendix 1 for these values The Sacrifice Ratio In macroeconomics, the sacrifice ratio is defined as the number of point-years of excess unemployment required to bring about a unit reduction in the inflation rate. Consider our specification of the Phillips curve: π t - π t-1 = α (u t u N ) A unit reduction in the inflation rate would correspond to the case when π t - π t-1 = -1. Substituting this value in the above equation, we get: (u t u N )= (1/ α) This value (1/ α) is known as the sacrifice ratio. The higher the sacrifice ratio, the more unemployment the economy must bear to be able to reduce its inflation rate. 6

7 The Lucas Critique Lucas suggested that the sacrifice ratio exaggerates the unemployment that the economy must undergo incase it wants to reduce unemployment. Lucas argument was that price expectations have a strong role to play in the Phillips curve. Hence, if the Central Bank is credible, then conduct of monetary policy becomes smoother, and hence the sacrifice ratio is reduced. The Lucas Critique was widely accepted in the world of central banking. For this reason, some central banks were designated as Inflation Targeting banks. It was believed that such inflation-targeting by the central bank would bring credibility to the monetary policy and hence reduce the sacrifice ratio. Data for the empirical work undertaken in the following sections was obtained from the World Bank website: The measurement units used are as follows: Unemployment Rate: Percentage of total labour force unemployed Inflation Rate: Annual GDP deflator. In percentage. The regressions carried out in Section 1 used GRETL. All other regressions and tests in Sections 2, 3 and 4 were undertaken on Microsoft Excel. This is because of some restrictions in GRETL, such as the inability to test for heteroskedasticity on heteroskedasticity-corrected data. 7

8 Section 2 The United States of America We use data for the US from the period , well after the original Phillips curve relationship had broken down. The particular functional form that we regress is the same as derived in Section 1, i.e. as follows: π t π t 1 = α U t U N The regression results are summarized in table 2.1. These results seem to confirm that the Phillips curve in its modified form is still valid for the US economy. The coefficient for excess unemployment is negative and significant, as suggested by the underlying theory. The overall fit of the regression line is also significant. Table 2.1: OLS estimates for US Data R 2 : Significance: U t -U N In order to check the robustness of the results that we have obtained, we must check for violations of the classical linear regression model (CLRM). Let us begin with a scatter plot, followed by tests for heteroskedasticity. 8

9 Figure 2.1: Phillips Curve for the US White s Test for Heteroskedasticity We now run the White s test for heteroskedasticity. The particular functional form that we use for this test is as follows: ε t 2 = β 1.(U t -U N ) + β 2.(U t -U N ) 2 + β 3.(U t -U N ) 3 The results of this regression are summarized in table 2.2. The null hypothesis that there is no heteroskedasticity is rejected at the 5% level of significance. The error term has a negative relationship with the square of excess unemployment, which is significant at the 5% level of significance. This means that as the excess unemployment rises, the error term reduces. The coefficients of the other powers of excess unemployment are not statistically significant. Table 2.2: White s Test R 2 : Test Stat:17.58 Significance: U t -U N (U t -U N ) (U t -U N )

10 Goldfeld Quandt Test for Heteroskedasticity To verify the results obtained through the White s test, we also run the GQ test on the available data. Since the total sample size is 30, we take two clusters with n 1 = n 2 = 12. We then run an F-test with the following test statistic: RSS 1 RSS 2 ~ F (11,11) The results of the GQ test are summarized in Table 2.3. The null hypothesis that there is no heteroskedasticity is rejected at the 5% level of significance. We conclude that the variance of the error term is significantly higher in the first sample (i.e. observations with lowest U t -U N ) than in the last sample. Hence, there is a problem of heteroskedasticity in our model. Table 2.3: GQ Test F-stat: Significance: 0.03 Value RSS RSS Chow s Test for Structural Break To further validate the significance of this result, we run the Chow Test for a structural break at the middle observation point, i.e The formula used for the Chow test is as follows: ( RSS pooled RSS A RSS B k ) ( RSS A +RSS B n 2k ) ~ F (k, n 2k) Note that since there is only one independent variable, U t -U N, the value of k is 1. There are 30 sample points ( ), and hence the value of n-2k is 28. With these values in mind, we obtain the following results for the Chow test: Table 2.4: Chow Test F-stat: Significance: 0.00 Value RSS pooled RSS A

11 RSS B 3.44 Note that the Chow Test is a test for structural breaks, and not for Heteroskedasticity. The Chow Test points to the fact that a single Phillips Curve (in its original form, without Heteroskedasticity correction) cannot be used for the US. We also ran the Chow Test at several other break points using GRETL, and obtained a significant F-statistic for most of the years in the 1990s Conclusions As we can see in this data, the Phillips Curve in its linear form cannot be applied to data from the US. Some researchers have commented that the Phillips Curve flattens out as the excess unemployment increases 3. The economic rationale is that price durations (i.e. price rigidities) are endogenous to the Phillips Curve model. When unemployment increases, prices become more flexible as companies are reluctant to fix prices for longer durations, fearing that a future reduction in unemployment would leave them with a bloated wage bill. For this reason, the error terms are lower as the excess unemployment increases. However, for the purpose of this project, we will correct the available data for heteroskedasticity, and then carry test for other violations of the classical linear regression model. As we saw in Table 2.2, the error terms are strongly negatively correlated to the square of excess unemployment. Hence, we divide both sides of our original Phillips curve relationship by (U t -U N ) to obtain heteroskedasticity-corrected estimates. π t π t 1 = α U t U N π t π t 1 = α U t U N The results of this Heteroskedasticity-corrected regression are as follows: Table 2.5: Heteroskedasticity-Corrected Estimates R 2 : Significance: U t -U N What Makes the Output-Inflation Trade-off Change? E De Vierman Journal of Money, Credit and Banking (Vol 41, No. 6, Sept 09) 11

12 We observe that the basic results of the original Phillips Curve are intact. Excess unemployment has a negative effect on the acceleration in inflation rate. Before we interpret the results of this regression, let us test this Heteroskedasticity-corrected model for other violations of the CLRM LM Test for Autocorrelation Since the Durbin-Watson test cannot be used for a zero-intercept model such as the Phillips Curve, we use the LM Test, a general test for higher order serial correlation 4. The functional form of the model used for the LM test is as follows: ε t = α 1.ε t-1 + α 2.ε t-2 + α 3.ε t-3 + β 1.(U t -U N ) + μ t We test for the linear restriction that α 1 = α 2 = α 3 = 0. For this, we run the restricted and unrestricted models and calculate the F-statistic according to the following formula. Note that m refers to the number of linear restrictions (3 in this case), whereas k is the number of independent variables (1 in our case) and n is the number of observations. ( RSS restricted RSS unrestricted m) ( RSS ~ F (m, n (m + k + 1)) unrestr icted n (m + k + 1) ) Given that the LM test is a large-sample test, we can approximate the F-distribution with the χ 2 distribution as given by the following equation: m. F ~ χ m 2 m.f follows a χ 2 distribution with m degrees of freedom. The results of the LM test are summarized Table 2.7. We conclude that there is no evidence of autocorrelation in the available data at even the 10% level of significance. This result is intuitively justifiable, since a high error term form some level of excess unemployment cannot possible affect the error term for the next value of excess unemployment. Table 2.7: LM Test F-stat: mf: Significance: Value RSS restricted RSS unrestricted Refer to Maddala, G.S and Kajal Lahiri, Pg

13 Multicollinearity: Since our model consists of only one independent variable, U t -U N, the problem of Multicollinearity does not arise Model Misspecification: The Phillips Curve as used in our project has a long history in macroeconomics. It is based on microeconomic foundations, i.e. the price-setting and wage-setting equations. It is thus a rigorously derived equation and hence, we believe that we do not need to suspect misspecification errors. We have estimated the Phillips Curve relationship for the US economy over the period as follows: π t π t 1 = U t U N The interpretation of this result is that for every 1 percentage rise in unemployment rate 5, the inflation this year is percent lower than last year s inflation rate. This is consistent with the prediction of the Phillips Curve equation. As summarized in Table 2.5, the R 2 value of the test is 0.071, which is significant at the 10% level of significance. The p-value of the coefficient is 0.071, which is also significant at the 10% level of significance. Elasticities The elasticity of this regression at the mean will be given by: y x x y For the regression that we have undertaken, this value is given by %. Hence, the elasticity of π t π t 1 w.r.t U t U N at the mean value is %. 5 Given our assumption of a time-invariant natural rate of unemployment, U N, this translated to a 1 percentage rise in excess unemployment, U t -U N. For a model of time-variant natural unemployment rate, refer to The Natural Rate, Hysteresis and the Duration Composition of Unemployment in the US (R Cross, H Hutchinson, S Yeoward) 13

14 Section 3 Australia Data for Australia was available for the period The model used for estimation of the Phillips Curve equation remains the same, i.e.: π t π t 1 = α U t U N The regression results are summarized in table 3.1. The results are in conformity with the underlying theory. While the fit of this regression result is not as good as that for the US, the overall regression and the coefficient for excess unemployment are significant at the 5% level of significance. Before we provide an economic interpretation of the regression results, let us test for violations of the CLRM assumptions. Table 3.1: OLS estimates for Australian Data R 2 : Significance: U t -U N We observed in Section 2.1 that Heteroskedasticity is typically a problem for the Phillips Curve equation. Let us test here whether there is a problem of Heteroskedasticity for Australian data too White s Test for Heteroskedasticity The functional form for White s Test is the same as that used in section 2.2.1, i.e: ε t = β 1.(U t -U N ) + β 2.(U t -U N ) 2 + β 3.(U t -U N ) 3 14

15 The results of this regression are summarized in table 3.2. We observe that the null hypothesis that there is no heteroskedasticity is not rejected at even the 10% level of significance. While the signs of the coefficients point to a reduction in variance w.r.t U t -U N, at a decreasing rate; however, none of the coefficients are significant at the 10% level of significance. We conclude that using the White s Test, there is no reason to reject homoskedasticity and hence, we carry out more tests to detect heteroskedasticity. Table 3.2: White s Test R 2 : Test Stat: Significance: U t -U N (U t -U N ) (U t -U N ) Goldfeld Quandt Test for Heteroskedasticity We also run the GQ test to verify our results for heteroskedasticity encountered in the White s test. The total sample size is 30 and we take two clusters with n 1 = n 2 = 12. We then run an F-test with the following test statistic: RSS 1 RSS 2 ~ F (11,11) The results of the GQ test are summarized in Table 3.3. We observe that the null hypothesis that there is homoskedasticity is not rejected at even the 10% level of significance. Moreover, unlike the data for the US, we see that the variance has increased with increasing value of U t -U N. However, this difference is not significant enough. Thus, we conclude that data for Australia does not show any significant heteroskedasticity, and hence we need not correct Australian data for heteroskedasticity. Table 3.3: GQ Test F-stat: Significance: Value RSS RSS

16 LM Test for Autocorrelation Once again, we must use the LM test, and not the Durbin tests, to test for serial autocorrelation. The functional form of the model used for the LM test is also the same as before: ε t = α 1.ε t-1 + α 2.ε t-2 + α 3.ε t-3 + β 1.(U t -U N ) + μ t Without getting into the details on the LM test (which have previously been covered in section 2.3.2), the results of the LM test are summarized Table 3.6. We observe that there is a severe problem of autocorrelation in the data. The linear restriction placed on the data, i.e. α 1 = α 2 = α 3 = 0, is statistically significant, and hence we must correct the data for autocorrelation. Table 3.4: LM Test F-stat: 8.54 mf: Significance: Value RSS restricted RSS unrestricted To correct for autocorrelation, we construct a Generalised Least Squares (GLS) model. To study the nature of autocorrelation, let us examine the summary results of the LM test that we undertook in the previous section. These results are summarized in Table 3.5. We observe that the error term ε t is positively and significantly dependent on a one-period lagged error term ε t-1. The other coefficients are not significant at the 5% level of significance and hence their effect can be ignored. Table 3.5: LM Test Summary (unrestricted model) R 2 : Significance: 0.00 U t -U N ε t ε t ε t For correcting for autocorrelation, we need the value of ρ. We cannot use the Durbin-Watson method of calculating ρ, since this method can only be used for models with intercept term. 16

17 For the purpose of this project, we will estimate the value of ρ from the OLS residuals, ε t. We run the following regression model: ε t = α.ε t-1 + μ t The result of this first-order autoregressive model is summarized in table 3.6. We observe that the error term shows significant autocorrelation. Also, we observe that the 95% confidence interval for the coefficient term is (0.51, 1.03). Also referring to Table 3.5, we conclude that the coefficient α is not significantly different from 1. Hence, we assume that ρ = 1, and then go on to estimate the GLS estimates using the First Difference Method. Table 3.6: AR (1) Estimate for ε t R 2 : Significance: ε t The First Difference Method Under the assumption that ρ = 1, which we discussed above, we construct a First Difference Model as follows: π t π t 1 = α U t U N + ε t (π t π t 1 ) = α U t U N + μ t We run a regression with the above model, and obtain the results as summarized in Table 3.7. We observe that, after correcting for autocorrelation, the fit of the regression line has deteriorated. The significance of the coefficient has also reduced. Table 3.7: Autocorrelation Corrected Estimates R 2 : Significance: U t -U N Multicollinearity: Since our model consists of only one independent variable, U t -U N, the problem of Multicollinearity does not arise. 17

18 Model Misspecification: As discussed in section 2.3.4, model misspecification is not a problem for our model as it is rigorously derived in economics. We have estimated the Phillip s Curve relationship for the Australian economy over the period as follows: π t π t 1 = U t U N The interpretation of this result is that for every 1 percentage rise in unemployment rate, the inflation this year is percent lower than last year s inflation rate. This is consistent with the prediction of the Phillip s Curve equation. As summarized in Table 3.7, the R 2 value of the test is not significant at even the 10% level of significance, and neither is the coefficient significant. 18

19 Section 4 The Sacrifice Ratio As derived in section 1.1.5, the sacrifice ratio is given by (1/α). To test for the significance of the difference between (1/α), it is sufficient to test for significance of the difference between α of the two countries. Let α US represent the coefficient of the Phillips Curve for the US, and α AUS represent the coefficient for the Phillips Curve for Australia. Under the null hypothesis that α US = α AUS, the following test statistic follows a standard normal distribution 6 : N (0,1) ~ α US α AUS σ US 2 +σ AUS 2 The results of this test are summarized in table 4.1. We observe that while there is a difference between the sacrifice ratio of the US and Australia, it is not significant at all. The standard errors of the coefficients are extremely high, and this prevents the mathematical difference between the sacrifice ratio from being significant enough. Table 4.1: Testing for Difference in α Test Stat: Significance: 0.42 Coefficient Standard α US α AUS Inflation-targeting was adopted as a goal by Australia in 1993 with the hope that it would be able to control unemployment better. However, as we have seen, there is no significant difference between the sacrifice ratio in America and in the US. In fact, other Inflation-targeting banks perform even more poorly, in that the Phillips curve equation does not even fit the data well. We summarise the results for two other IT countries, UK and Canada, in appendix 2. 6 For smaller samples, the test statistic follows a t-distribution. However, since our sample size for US and Australia is 30, we can approximate it by the standard normal distribution. 19

20 Appendix 1 The Natural Rate of Unemployment Country Name U N (%) Argentina Australia 7.24 Austria 4.03 Belgium 8.02 Brazil 9.66 Canada 8.8 Chile 8.32 China 2.94 Colombia Denmark 5.74 Estonia Finland 9.45 France Germany 8.9 Greece 9.35 Hong Kong 4.08 Ireland 8.81 Israel 8.42 Italy 9.73 Jamaica 8.86 Japan 5.9 Malaysia 3.8 New Zealand 6.81 Norway 4.02 Philippines 8.6 Portugal 7.18 Puerto Rico Singapore 4.03 Spain Sri Lanka 6.1 Sweden 7.48 Switzerland 3.66 Thailand 2.29 Trinidad and Tobago Uruguay Venezuela, RB

21 Appendix 2 Other Inflation Targeting Countries Table A1: OLS estimates for UK Data R 2 : 0.04 Significance: U t -U N Table A2: OLS estimates for Canada Data R 2 : Significance: U t -U N Note that both of these regressions are OLS estimates on the original Phillips Curve equation, without corrections for Heteroskedasticity and Autocorrelation. We observe that both these regressions are insignificant at the 5% level of significance. Hence, one of the basic premises of inflation-targeting bank, that the Phillips Curve relationship holds, is invalid. 21