Any temporary “money illusion” however is corrected in the long run by agents revising their expectations. Once workers realised their real wages were not increasing due to the increase in inflation, any reduction in unemployment would remain temporary but that the rise in inflation would be permanent as it had been built into agents’ expectations. This implies the Long Run Phillips curve would be a vertical line with the horizontal intercept at the NAIRU and no trade-off between and unemployment and inflation being observed.
Suppose inflation expectations are formed according to the following information
(2)
- Expected Inflation in Period t, if then no short term relationship, - Unemployment in Period t, - Natural Rate of Unemployment - Random Error Term or “Supply Shock”
Assuming the Natural Rate of Unemployment is a constant as in Wooldridge (2006, pp. 391)
(3)
Where with asand
Assuming Expectations are determined via a Partial Adjustment Model
(4)
Plugging (2) into (4) gives us
(5)
Re-arranging (5)
(6)
This gives us the model to be tested for the short term
(7)
Where,,,
This model compares to a model utilised by Gordon (1989, pp. 221, Equation [1]).
Because the stochastic disturbance term is not correlated with the explanatory terms the OLS estimators remain unbiased. As such the model does not suffer from misspecification and can be estimated using OLS.
III. Data
The data chosen for this project was extracted from the OECD dataset “Country Statistical Profiles 2008”. I have no reason to suspect the data is unreliable as OECD statistics are widely used and well regarded.
The data used is annual data for the period 1967-2006. I chose this sample because there was a break in the data as defined by the OECD for Canada in the year 1967 and the year 2006 is the latest date for which the OECD has data available for access. I thus have 40 observations which is satisfactorily large enough to conduct statistical analysis.
The unemployment rate as defined by the OEDC is “The unemployment rates shown here use ILO Guidelines that provide common definitions of unemployment and of the labour force” – OEDC (2008). Further information is supplied in Appendix 2.
It is calculated using the formula (8)
The inflation rate is calculated from the Consumer Price Index or CPI as defined by the OEDC as “the change in the prices of a basket of goods and services that are typically purchased by specific groups of households” - OEDC (2008). Further information is supplied in Appendix 3.
Table 1: Variable Descriptions
In the OECD data the CPI has a value of 100 for the base year of 2000. The inflation rate is then calculated using the formula in Table 1 above. There may be questions over the validity of using 2000 as a base year but I find no evidence for it to be an unusual year for inflation in Canada.
Table 2: Summary Statistics
Points of interest from Table 2 include the much greater volatility of inflation as compared to unemployment as defined by the standard deviation (3.04 compared with 2.05). The average value of inflation as defined by the mean however is much lower than that of unemployment (4.59 compared with 7.96).
Figure 1: Inflation/Unemployment Time Series Plot
The interesting feature from Figure 1 to note is that except from periods 1973-1976 and 1978-1981 the rate of inflation has been lower than the rate of unemployment. This suggests that Canadian governments over the last 40 years have seen low inflation as a higher priority policy target rather than low unemployment.
This was explicitly stated in 1991 when inflation-control targeting was introduced by the Bank of Canada whose target rate of inflation is 2% with a 1% margin of error. This could well explain the much reduced volatility and lower mean value for inflation in the sample period 1991-2006. However as can be seen from the chart unemployment still remains stubbornly high throughout that period suggesting a trade-off between inflation and unemployment may still be in evidence.
“Since its introduction in 1991, inflation-control targeting has (…) helped keep the rate of inflation within acceptable limits. (…) The Bank of Canada aims to keep inflation at the 2 per cent target, the midpoint of the 1 to 3 per cent inflation-control target range.” - http://www.bankofcanada.ca/en/inflation/index.html
Bank of Canada (2008)
The first diagnostic test to be run is to ensure the error terms generated are not serially correlated. The null hypothesis is and that the errors are serially uncorrelated. This is indicated by a Durbin-Watson stat which is not significantly different from 2.
where is an estimator of first order correlation (9)
Testing for AR(1) serial correlation in the static Phillips curve (Equation 1) gives a Durbin-Watson statistic of 0.240187. This indicates evidence of positive first order serial order correlation and as such the t statistics and standard errors cannot be interpreted.
Testing for AR(1) serial correlation in the short term Expectations Augmented Phillips curve (Equation 7) a Durbin h statistic must be used as the equation contains a lagged variable as the DW stat is biased towards 2.
(10)
Where DW is the Durbin Watson statistic, T is the number of observations and is the variance of the lagged variable.
The h stat calculated was 0.238093 and is compared against the critical values of the normal distribution.
No Serial Correlation which is not rejected if -1.96 < h <1.96 at the 5% significance level.
This indicates there is no evidence of AR(1) serial correlation. Therefore the static Phillips curve can be disregarded in the short term for this study and the Expectations Augmented Phillips curve will now undergo further testing.
To avoid the possibility of running a spurious regression as outlined in Granger and Newbold (1974) the stationarity of the data must be determined. A data series is said to be integrated of order zero I(0) if it is stationary. A data series is said to be integrated of order one I(1) if it is non stationary and contains a unit root. A spurious regression occurs if a data series of I(0) is regressed with a data series of I(1). This can be corrected by differencing the I(1) data series into an I(0) data series.
The unit root test to be conducted in this study is the Augmented Dickey Fuller test (Dickey and Fuller, 1981). The augmented version of the earlier Dickey Fuller test (Dickey and Fuller, 1979) corrects the problem of autocorrelation which is common in time series data.
statistic (11)
statistic (12)
statistic (13)
Equations (11), (12) and (13) are used to test for a unit root if the variable is of the form random walk, random walk with constant or a constant with trend respectively.
Table 3: ADF Unit Root Tests
**Denotes the null hypothesis is rejected at the 1% level. Critical Values at the 1% level are -2.62, -3.58 and -4.15 for None, Constant and Constant with Trend respectively.
The results in Table 3 indicate that both inflation and unemployment are integrated order one I(1) and contain unit roots for each test statistic. Because both variables are integrated of the same order neither statistic needs to be differenced to avoid a spurious regression.
Dickey and Fuller (1981) calculated statistics to test the deterministic nature of the data.
(14)
Where is the restricted residual sum of squares, is the unrestricted residual sum of squares, T is the number of observations, r is the number of restrictions and k is the number of parameters to be estimated
statistic Random Walk with Drift (15)
Trend
statistic Pure Random Walk (16) Random Walk with Drift
Table 4: Joint Hypothesis Tests
*Denotes the null hypothesis is rejected at the 5% level, Critical Values at the 5% level for 50 observations are 6.73 and 3.94 for and respectively.
Since I cannot reject the null hypothesis for both and the results indicate that both inflation and unemployment are of the form pure random walk. Since neither has a trend the data does not need to be de-trended.
IV. Econometric Model
The Model to be tested is equation (7)
Table 5: OLS Regression Output
**Denotes the null hypothesis is rejected at the 1% level, R2=0.82, F-Stat= 82.64474, T-stats in parentheses.
All of the co-efficient estimates were significant at the 1% level and an F stat of 82.64474 indicates joint significance of the explanatory variables. An R2of 0.82 is high and suggests a high goodness of fit for time series data.
These values can then be placed into the econometric model
(17)
To test for a long term causal relationship a co-integration test has been used as outlined by Engle and Granger (1987).
The Static Model in equation (1) will now be tested to see if it holds in the long term
An ADF test is run on the residuals from the regression
(18)
Schwarz Information Criterion, No of Lags = 2, t-stat Obtained = -1.46, Critical Values for 50 observations are -4.12, -3.461 and -3.13 for the 1%, 5% and 10% levels respectively
Checking against the critical values of Mackinnon (1991) I cannot reject the null hypothesis as the t-stat -1.46 is greater than the critical values. This means there is no co-integration and no long term causal relationship between inflation and unemployment.
V. Interpretation
Referring back to equation (17)
The -0.38 represents the short term change in inflation caused by unemployment. If unemployment were to decrease by 1% then inflation would increase by 0.38% in the short term.
Now the estimated values can be reinterpreted in relation to equation (6)
(19)
(20)
(21)
50% of the total change in is accomplished in 6.58 years. This suggests that Canadians adjust their expectations of inflation relatively slowly.
(22)
Using the values found in equation (21) I can now estimate the NAIRU of Canada.
(23)
%
The natural rate for unemployment in Canada is estimated to be a high 9.11%. Laubach (2001) estimates the NAIRU to be 8.64% in 1998Q4 for Canada in his Bivariate model and my estimate is well within his 95% confidence interval. Only France and Italy have greater NAIRU estimates than Canada for 1998Q by Laubach (2001, pp. 228 Table 3).
VI. Conclusion
This study establishes there to be no long term causal relationship between inflation and unemployment in the long term as hypothesised by Friedman (1968, 1977) in his development of the long term Phillips curve. This study therefore accepts the Monetarist interpretation of the relationship between inflation and unemployment in the long term and rejects the Keynesian interpretation of the relationship.
In the short term the Canadian government may well be able to reduce unemployment by allowing inflation to increase. But in the long term people’s expectations will adjust and the economy will find equilibrium at a higher inflation rate but at the existing natural rate of unemployment.
This establishes the policy recommendation that Canada need not concentrate on one policy objective, keeping inflation low and stable as outlined by the Bank of Canada’s policy objective, but can also enact measures to reduce unemployment.
The natural rate of unemployment was found to be 9.11% which is very high for a country within the G7. Laubach also found evidence that the NAIRU in Canada has barely changed in the last 30 years, this means the assumption of the NAIRU as a constant in my modelling holds. For Canada to reduce the NAIRU and hence its unemployment level it must implement measures to reduce wage and price rigidities otherwise known as “supply side measures”.
This can include de-regulation of labour and product markets, trade union power reduction and reducing the tax burden on individuals and firms as outlined by Coe (1989). He places particular emphasis on the Canadian Government reducing unemployment benefits, eliminating extended regional benefits for individuals and on maintaining a low relative minimum wage to reduce the NAIRU in Canada.
VII. Bibliography
Bomhoff, E.J. (1980) “Inflation, the Quantity Theory, and Rational Expectations” North Holland Publishing Company, Amsterdam
Coe, D.T (1989) “Structural Determinants of the Natural Rate of Unemployment in Canada” IMF Working Paper, IMF Western Hemisphere Department
Dickey, D.A. and Fuller, W.A. (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root” Journal of the American Statistical Association, Vol. 74, pp. 427-431
Dickey, D.A. and Fuller, W.A. (1981), “Likelihood Ratio Statistics for Autroregressive Time Series with a Unit Root” Econometrica, Vol. 49, No. 4, pp. 1057-1072
Engle, R.F and Granger, C.W.K. (1987), “Co-integration and Error Correction: Representation, Estimation, and Testing” Econometrica, Vol. 55, No. 2, pp. 251-276
Friedman, M. (1968) “The Role of Monetary Policy” The American Economic Review, Vol.58, No.1, pp. 1-17
Friedman, M. (1977) “Nobel Lecture: Inflation and Unemployment” The Journal of Political Economy, Vol. 85, No. 3, pp. 451-472
Granger, C.W.K and Newbold, P. (1974) “Spurious Regressions in Econometrics” Journal of Econometrics, Vol. 2 pp.111-120
Gordon, R.J. (1989) “Hysteresis in History: Was There Ever a Phillips Curve?” The American Economic Review, Vol. 79, No. 2, pp. 220-225
Haldane A. and Quah D. (1999) “UK Phillips curves and monetary policy” Journal of Monetary Economics Vol. 44, Issue 2, pp. 259-278
Lahiri, K. (1981) “The Econometrics of Inflationary Expectations” North Holland Publishing Company, Amsterdam
Laubach, T. (2001) “Measuring the NAIRU: Evidence from Seven Economies” The Review of Economics and Statistics, MIT Press, Vol. 83, No. 2, pp. 218-231
Mackinnon, J.G. (1991) “Critical Values for Cointegration Tests” Long-run economic relationships: Readings in Cointegration, Oxford University Press, pp. 267-276
OECD (2007) “Main Economic Indicators” OECD, Paris
Phelps, E.S. (1967) “Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time” Economica, New Series Vol. 34, No. 135, pp. 254-281
Phillips, A. W. (1958) “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957” Econometrica, New Series, Vol.25, No. 100, pp. 283-299
Phillips, A. W. (1962) “Employment, Inflation and Growth” Economica, New Series, Vol. 29, No. 113, pp. 1-16
Wooldridge, J. (2006) “Introductory Econometrics: A Modern Approach” Toronto, Thomson South-Western
http://www.bankofcanada.ca/en/inflation/index.html - Accessed 30/04/2008
VIII. Appendices
Appendix 1: Data Access Log
http://stats.oecd.org/wbos/viewhtml.aspx?queryname=459&querytype=view&lang=en
Current Query: Canada
Dataset: Country statistical profiles 2008
Data extracted on 17:08 at 24/04/2008 from
Appendix 2: Definition of Unemployment Variable by the OECD
Unemployed persons are defined as those who report that they are without work, that they are available for work and that they have taken active steps to find work in the last four weeks. The ILO Guidelines specify what actions count as active steps to find work and these include answering vacancy notices, visiting factories, construction sites and other places of work, and placing advertisements in the press as well as registering with labour offices.
The unemployment rate is defined as the number of unemployed persons as a percentage of the civilian labour force, where the latter consists of the unemployed plus those in civilian employment, which are defined as persons who have worked for one hour or more in the last week.
Appendix 3: Definition of Inflation Variable by the OECD
Consumer price indices measure the change in the prices of a basket of goods and services that are typically purchased by specific groups of households. For the indices in these tables, the groups of households have been broadly defined and cover virtually all households except for "institutional" households – prisons and military barracks for example – and, in some countries, households in the highest income group.
