IS THE PHILLIPS CURVE ALIVE IN THE U.S? Neoclassical Views

ECON 2003Y (3) Principles of Econometrics

UOMIS THE PHILLIPS CURVE ALIVE IN THE U.S? Neoclassical Views

Submitted By:Phoolchund ReshmeeDorasamy Sebastien

Table of Contents1.0 Introduction .21.1 Statement of theory..32.0 Specification of the econometric model...42.1 Difficulties of estimating Phillips curve...........62.2 Assumption of our model..63.0 Obtaining the data for the United Sates and Empirical evidence.74.0 Estimation of the econometric parameters and hypothesis testing..104.1 Uncorrelated Phillips curve in U.S 1970s....114.2 Phillips curve chow test...124.3 Aftermath of 1970s..134.4 Recession 2008 and its impact on Phillips curve.134.5 Dummy variables to detect structural change: Recession144.6 Linear model of Phillips curve (2000-2013)155.0 Multiple Regression.165.1 When to add a new variable.165.1.1 The marginal contribution of Imports...175.1.2 The marginal contribution of Real GDP Growth Rate.185.1.3 The marginal contribution of real interest rates....195.2 Testing the overall significance f the model....206.0 Relaxing the assumption.....216.1 Multicollinearity..............................216.2 Autocorrelation226.2.1 Detecting autocorrelation..226.3 Heteroscedasticity........236.3.1 Detecting heteroscedasticity.....247.0 Forecasting...248.0 Using the model for control or policy purposes..259.0 Conclusion...2610.0 References..261.0 IntroductionInflation and unemployment are two key features of an economy. Inflation is simply a general increase in the average prices of goods over time and thus, leading to a fall in the purchasing power. Main causes of inflation are demand pull and cost push. It can be measured using Consumer Price Index (CPI). On the other hand, unemployment is the state of being unemployed when a worker is actually searching for a job. Causes could be structural, cyclical or even seasonal. One method of measuring unemployment rate is by using claimant count, that is, the number of people receiving unemployment benefits. High values of both show the poor health of an economy because they are the main key economic indicators. The opportunity cost of lower unemployment is higher inflation and vice versa. Thus, it is said that there exists a tradeoff between these two variables. This particular relationship between inflation and unemployment is known as the Phillips Curve. Our purpose in doing this report is to provide empirical evidence in the United States by having recourse to regression analysis. We have chosen the latter with a neoclassical school of thought with backward linear expectations. It is one having rational expectations. Throughout we will test if the present day Phillips Curve is consistent with the neoclassical beliefs.Part one is about theory and the other sections will concentrate on earlier and recent empirical evidence. What kind of relationship prevails? Inverse, positive or no relationship at all? Is the inflation rate or the unemployment the dependent variable? Well, it all depends on the researcher and weve decided to make the inflation rate the dependent variable. [The lower the unemployment rate the more people will demand more goods via an increase in wages leading to inflation]. Can we forecast inflation rate given the value of known unemployment rate? What policy must be used to exploit the trade off? To answer all these we will briefly go into the history of the Phillips Curve and know the different variables in the equation of the curve to be able to make statistical inferences and answer all these issues. However, there can be limitations but we will try as much as possible to resolve the problems such as multicolliearity, heteroscedascity and autocorrelation.

1.1. Statement of TheoryIn 1958, A.W. Phillips a New Zealand born economist, wrote a paper titledThe Relation between Unemployment and the Rate of Change of Money Wage Rates in the UK, 1861-1957, which was published in the quarterly journalEconomica and showed that nominal wage growth was negatively correlated with unemployment in the United Kingdom. Hence, the Phillips curve shows the short-run trade-off between inflation and unemployment. = -f(U)Two years later, in 1960, Paul Samuelson and Robert Solow found a negative correlation between United Sates inflation and unemployment rates, naming it the Phillips Curve. It is deduced that there are two frames for the Phillips curve: The short-run Phillips curve : an increase in inflation would lower unemployment The long-run Phillips curve : no trade off- positive relationshipThese are shown in figure 1 and 2 below:

Figure 1Figure 2Figure 1 shows the short run Phillips Curve (SRPC) which is drawn on the assumption of agiven expected rate of inflation.So if there were an increase in inflation caused by a monetary expansion and this has the effect of drivinginflationary expectationshigher causing an upward shift in the short run Phillips Curve. At low aggregate demand, inflation is low and since labour is a derived demand, demand for labour is low, therefore unemployment is high. Figure 2 shows the natural rate of unemployment hypothesis which states that unemployment eventually returns to its natural rate, regardless of the inflation rate based on the classical dichotomy (long run aggregate supply-LRAS). An inward shift in the long run Phillips Curve might be due to supply-side improvements to the economy and a reduction in thenatural rate of unemployment.

2.0 SPECIFICATION OF THE ECONOMETRIC MODELTo bridge the gap between theory and evidence, Friedman and Phelps introduced a new variable: expected inflation a measure of how much people expect the price level to change. The econometric model we will be using is:

The deviation of unemployment from the natural rate Error Term: e.g. supply shocks Actual inflation rate at time t, where

Inflation depends on expected inflation : being formed in year (t 1)

Given expected inflation, te, an increase in the unemployment rate leads to a decrease in inflation, t. The equation above denotes the inverse relationship between inflation rate and unemployment rate. The natural rate of unemployment is sometimes referred to as the Non Accelerating Rate of Inflation (NAIRU) where inflation rate remains stable. The other variables in the equation are notably: U: Unemployment RateUn: Natural Rate of UnemploymentU-Un: Unemployment Gap: measures the response of inflation to cyclical unemployment: the rate of change in the average value of t.It is to be noted that this equation is derived from the Aggregate Supply equation.Writing the Neoclassical Phillips curve equation: t = et - (Ut Utn) + ut .(1)t et = - (Ut Utn) + ut.(2) et = t1: the inflation expected this year is the inflation rate that prevailed in the last year. This is known as the random walk.

Rewriting the regression model in standard form, we obtain the following equation:

t t1 = -Ut+ Utn + ut..(3)t = -Ut + + ut..(4)t = - Ut +ut..(5)

Last equation states that the change in the inflation rate between two time periods is linearly related to the current unemployment rate. Throughout this report we will be using equation 5.2.1. Difficulties of Estimating Phillips Curve Estimation of et and Utn Such variables are difficult to estimate in real life. Dummy Variables: since the 1970s it has become common practice to include dummy variables and measures of supply shocks, such as the relative price of energy. Shocks to such variables arguably create positive correlation between ination and unemployment, and would thus, bias the estimate of if omitted. Accuracy of Data: Maybe the quality of data collected over the internet may be poor. The success of regression analysis depends on the availability of the appropriate data.

2.2. Assumption of Our Model Wages and prices are completely flexible with respect to changes in expected inflation. E(ut)=0 The errors have zero mean Var(ut)= 2 - The variance is constant and finite over all values of Xt Cov (ui,uj)=0 - Errors are statiscally independent of each other: No autocorrelation Cov(ut , Xt) =0 Zero covariance Normally Distributed-To make statistical inferences about the population parameters from the sample data. It will follow a t-distribution. The regression model is correctly specified- No specification bias or error There is no perfect multicollinearity- No perfect linear relationships among the explanatory variables. The regression would be linear in parameters.

3.0 Obtaining the Data for the United States and Empirical EvidenceWe have collected data for the United States on inflation rate and unemployment rate on an annual basis from 1960 to 2013. The size of the data is 54. The source is from Bureau of Labor Statistics. Inflation rate is measured by CPI. The unemployment rate is the civilian unemployment. Both are collected using monthly censuses. The summary results are as follows:Unemployment Rate: X Inflation Rate: Y

n=54n=54

Mean: 6.10Mean=3.96

Mode: 5.5Mode=1.6

Median: 5.75Median=3.2

Std Deviation=1.59Std Deviation=2.81

Kurtosis: -0.17Kurtosis= 2.62

On average unemployment rate was 6.1% and inflation rate was 3.96 over the last 54 years. The point estimators namely mean, mode and median is higher for unemployment rate. Standard deviation which is the measure of variability is higher for inflation rate by 1.22 thus, slightly further away from the mean. Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution.Thekurtosis of unemployment is less than zeroindicates a relatively flat distribution compared to inflation rate. Note: Test of normality: Kurtosis

Normally distributed value: 3 However, limitations of time series data is that it assumes data to be stationary, that is, mean and variance do not vary systematically over time. Plotting inflation rate and unemployment rate against time we get the graph below: Figure 3There has been some inverse relationship as well as positive ones over the last 54 years. Between 1979 and 1983, we see inflation fall from 15% to 2.5% and a rise in unemployment from 5% to 11%.This suggests there can be a tradeoff between unemployment and inflation.In 2008, the recession caused a sharp rise in unemployment and inflation became close to zero. Plotting the same data set but inflation rate against unemployment rate we get the resulting Phillips Curve. Note: We will use the level form because the percentages are small values. Therefore, we would not be using log in our approach. Only the linear neoclassical functional form will be tested throughout. The Phillips Curve for the period 1960-2013 referred as population regression function is shown on the next page.

SR Trade offNo trade off in the LR

Figure 4 Figure 5It is important to note that such a scatter graph may enable a labour economist to predict the average change in inflation rate given a certain unemployment rate.Figure 4 which is from 1960-2013, we do not see the well-known inverse relationship. But if we break down the same graph into shorter time periods we are able to see downward sloping graphs which are shown in figure 5. The US data from 19601969 and 1885-1990 both suggest a trade-off between inflation and unemployment rates. However, this is not always the case and it will be shown later that there can also be positive relationship between inflation and unemployment rates.

4.0 Estimation of Econometric Parameters and Hypothesis TestingWe start from earlier days when inflation rate was negatively related to unemployment rate. The sample consists of data from 1960-1969. As depicted, this is a downward sloping Phillips curve represented by the linear functional form.

Figure 6Linear model: t =8.0014 1.1802Ut+ ut df=8 SE = (1.29) (0.265) F(1,8)=19.90 t = (6.18) (-4.46) r2 = 0.7133 p = (0.000) (0.002) Regression results show that if the unemployment rate goes down by 1 percentage point, on average, the inflation rate goes up by about 1.18%, and vice versa. The intercept term shows that if unemployment rate is zero then the mean value of inflation rate is about 8%. The p values are significant at 5% significance level implying there is enough evidence against Ho.The F value is also significant at 5% significance level. r which measures the percentage of the total variation of inflation rate is about 71% is explained by unemployment rate. To sum up in the 1960s the sample supported the views of Williams Phillips. However, it is interesting to note that it is not always the case when the Phillips curve slopes downwards. There have been many occasions where this belief was broken. 4.1. Uncorrelated Phillips curve in U.S in 1970s

Figure 7In the 1970s, however, the relation broke down. In the USA and most other OECD countries, there was both high inflation and high unemployment, clearly contradicting the original Phillips curve. Hence, the relation broke down. This is a situation of stagflation where both the variables are increasing.The reasons were simply because of supply shocks. The United States was hit twice in the 1970s by large increases in the price of oil & rising expected inflation worsened the tradeoff. This could be referred to as structural change that is, the values of the parameters do not remain the same throughout the entire time period. Structural change can be a consequence of oil shocks, food crisis or even financial crisis. We will use the Chow Test to detect whether a structural change has occurred causing the negative relationship to turn out into a positive one.

4.2. Phillips Curve Chow testTime period 1960-1979: t = 0.745-0.61Ut+ ut n = 21 RSS=177.995 Time period 19601969: 1t = 8.0014 1.1802U1t+ u1t n1 = 10 RSS1=6.034Time period 19701979 2t = 5.037+0.333U2t+ u2t n2 = 10 RSS2=63.04The hypotheses would be as follows: H0: 1t = 2t = 0H1: at least one of 1t or 2t is non zeroIf 1t = 2t = 0, then there is no difference between the two time periods. It assumes that the intercept as well as the slope coefficient remains the same over the entire period.If at least one of 1t , or 2t are nonzero, the regression function changes at date t.The resulting F test would be as follows:

We reject Ho if Estimated F-value> Critical F-value at 5 % significance level.RSSUR = RSS1 + RSS2 with df = (n1 + n2 2k) =6.034+63.04 =69.074RSSR = 177.995 Estimated F=12.61 Critical F value for 2 and 17 df the 5% sig level is 3.59. Since 12.61> 3.59, we reject at 5 % significance level implying that a structural shift has occurred. However a limitation is that the null hypothesis allows for no differences at all between the groups.4.3 Aftermath of 1970

Figure 8 Figure 9Afterwards, the data no longer show any sign of a negative relationship between inflation and unemployment. A new relationship appeared in the form of change in inflation. 4.4 Recession 2008 And its Impact on Phillips Curve

Figure 10The only time it shown evidence of holding is before 2008 when unemployment increased significantly and inflation decreased. However, from 2009 onwards the relationship did not held well. In 2011 both inflation and unemployment fell and show little correlation and there are a number of data points that could defy the theory. The Feds excessive monetary policy and the fall in participation rate together are strong factors that can explain why the Phillips Curve relationship has not held as of late. This will allow us to investigate whether the recent nancial crisis can be considered a structural change in the Phillips curve.

4.5 Dummy Variables to Detect Structural Change: Recession Time period 2000-2013: t =1.29+ 1.84Dt -0.24Ut -0.01(DtUt) + ut Insignificant t values and insignificant F test!!R2 = 0.0357D=1 for observation 2008-2013 and 0 otherwiseThe mean function for the period 2000-2007 is:E(t /Dt =0, Ut)= 1.29 -0.24Ut The mean function for the period 2008-2013 is:E(t /Dt =1, Ut)= 1.84-0.25Ut Using F test the null hypothesis is not rejected, the regression lines will coincident. Hence, structural change has not happened in the form of recession. The results are below:

4.6. Linear Model of Phillips Curve (2000-2013)

Figure 11Linear model: t t1 = 0.824 - 0.137Ut + ut df=12 SE = (1.54) (0.232) F(1,12)=0.35 t = (0.54) (-0.59) r2 = 0.0283 p= (0.602) (0.566)

Regression results show that if the unemployment rate goes up by 1 percentage point, on average, the change in the inflation rate goes down by about 0.137 percentage points, and vice versa.The intercept term shows that if unemployment rate is zero then the mean value of inflation rate is about 8%. The natural rate of unemployment is about 6.01% All t values, p values and F test are insignificant leading us to conclude that the regression itself is insignificant and the independent variable is not actually explaining any change in the inflation rate.5.0. MULTIPLE REGRESSIONInflation is also affected by other variables such as: Labour costs Real GDP growth rate Import prices Costs of production Real interest ratesWe shall test how the inclusion of these variables namely real GDP growth rate, import prices and real interest rate will affect our dependent variable, inflation.

5.1. WHEN TO ADD A NEW VARIABLEResearchers choose the model that gives the highest adjusted R2. The question that arises is when adjusted R2 increases? It will increase if the t value of the coefficient of the newly added variable is larger than 1 in absolute value. Adjusted R2 will increase with the addition of an extra explanatory variable only if the F ( =t2) value of that variable exceeds 1.

5.1.1. The Marginal Contribution of Imports.Expectations: An increase in import prices will lead to higher imported inflation which will thereby lead to a rise in demand for local goods and hence reduce unemployment in US and vice versa.The results are as follows: Time Period: 2000-2013

Adding imports has increased our adjusted R2 by 0.073. The incremental contribution of the new variable can be conducted through F test:F Test = =1.90 >1

ANALYSIS OF RESULTS:Firstly, a positive relationship was found between inflation and import (0.41) as expected. Secondly the t value of the coefficient of the newly added variable is larger than 1. (1.38). Moreover the adjusted R2 has also increased by adding imports(From 0.0527 to 0.0203) This may be due to the absolute t value and F test which is also greater than 1. Next the VIF is less than 10 (1.13) and tolerance ratio is not that near 0 (0.88), so low multicollinearity exist, It would therefore be wise to include this variable in our model. 5.1.2. The Marginal Contribution of Real GDP Growth Rate:Expectations: The higher the real GDP growth rate the higher the inflation.The results are as follows:Time Period: 2000-2013

Adding real GDP growth rate has increased adjusted R2 by 0.0088. Incremental contribution of explanatory variable is denoted by the F test.F Test = 1.10 > 1

ANALYSIS OF RESULTS:There exists a positive relationship between the two (0.26) as expected. Then the t value of the coefficient of the newly added variable is larger than 1. (1.05). In addition, The F value of this variable exceeds 1. Thus the adjusted R2 will also increase.(From 0.0527. to 0.0439). Next the VIF is less than 10 and tolerance ratio is not near 0 (0.98) , so low multicollinearity exist, It would therefore be wise to include this variable in our model. 5.1.3. The Marginal Contribution of Real Interest RatesExpectations: The higher the expected inflation the higher the real interest rates. Time Period: 2000-2013

Adding real interest rates has decreased adjusted R2 by - 0.0759: Incremental contribution of explanatory variable F- Test = =0.1932 < 1 Any analysis of the Phillips Curve without the inclusion of real interest rates may generate a misleading result as any changes in the interest rate impacts the labour capital input mix in the production process, leading to a change in the level of employment in the economy. It is important to include interest rate in our model. ANALYSIS OF RESULTS:From the above results, it can be seen that due to significant multicollinearity the coefficient of interest rate is negative when according to theory it should have been positive. The tolerance ratio is near 0. The adjusted R2 has reduced significantly (F test and absolute t value less than 1). Here it would be preferred to drop the collinear variable as it would be impossible to isolate the individual impacts. The various variables have yield different results. However in our model it is highly favourable to include only those which are not highly correlated such as import prices and real GDP growth rate.5.2. TESTING THE OVERALL SIGNIFICANCE OF THE MODELIn fact it is important to further test whether it is favorable to add both imports prices and real GDP in our model including the first variable unemployment. Under assumptions of: Disturbances ut are normally distributed (CNLRM) H0: all slope coefficients are simultaneously zeroThen the F ratio is given by: ESS/k-1 RSS/n-kIf F > F(k 1, n k), reject H0 ( all slopes are not equal to zero)

MULTIPLE REGRESSION RESULTS:Regression Eqn: t t1 = + 1U1t + 2 X2t +3 X3t + ut X2t =Real GDP Growth RateX3t =Imports (% of GDP) Results after Regression:

t t1 = -6.834 -0.241U1t + 0.353X2t +0.508X3t + ut SE = (4.3) (0.23) (0.24) (0.29) F(3,10)=1.59 t = (-1.59) (-1.07) (1.5) (1.74) R2 = 0.3227 p= (0.143) (0.31) (0.17) (0.11) df=10 F value= 1.59Critical value: 3.71Since 1.59 < 3.71 we do not reject the null hypothesis and conclude that all slope coefficients are zero and conclude that there is no evidence that any of the predictors are linearly associated to Y. This is why it would have been better to make use of the reciprocal method which is a reason why maybe these results tend to be insignificant.6.0 RELAXING THE ASSUMPTION6.1 MulticollinearityAs discussed earlier we had so many insignificant values. Does it imply the sample is not good or have we missed some variables?When two X variables are highly correlated, they both convey essentially the same information. It misleadingly inflates the standard errors. Thus, it makes some variables statistically insignificant while they should be otherwise significant. It is detected by using Variance Inflation Factor (VIF) or Tolerance Ratio (1/VIF). Our sample has low degree of multicolinearity.

6.2. Autocorrelation Recall: Cov (ui,uj)=0 It occurs in time series data when the errors associated with a given time period carry over into future time periods. Cov (ui,uj) =/= 0 Cannot use t and F testSome Causes of Autocorrelation Excluded Variable Nonstationary mean and variance LagsWe used t = t t1 : One of the explanatory variables is the lagged value of the dependent variable: Autoregression

6.2.1. Detecting AutocorrelationA. Durbin Watson Test defined as:

Assumptions are: 1. No lagged version of dependent variable among explanatory variable.2. There is an intercept term in the regression model.The regression result for autocorrelation is as follows:

B. Breusch-Godfrey lm test allows for:1. Non schotastic regressors such as the lagged values of the regressand.The result using this approach is:

However, using Durbin Watson Test to detect autocorrelation revealed a value near 2 forcing us to conclude there is no serial correlation. A similar result is obtained using Breush Godfrey Langrange Multiplier Test.

6.3. HeteroscedasticityRecall: Var(ut)= - The variance is constant and finite over all values of Xt It is a case when the variance is not constant Heteroscedasticity causes standard errors to be biased. OLS estimators are no longer BLUESome Causes of Why Variance of the Error Will Vary: Misspecifications- Omitted Variables Measurement Error 6.2.2. DETECTING HeteroscedasticityThe Breusch-Pagan LM Test- Linear Model: H0: Homoscedascity: Equal Variance H1: Heteroscedascity: Unequal VarianceTest at 5% significance level with df=10

Critical= 3.94030

Since computed < 2 critical we do not reject the null and conclude that there is significant evidence of homoscedasticity. All these tests have shown that our sample is free from these problems. Yet, the regressions are insignificant. This makes us conclude that neoclassical views today are not representative of the earlier theory.

7.0. Forecasting Phillips curve model can prove useful for forecasting future rates of inflation and has already been exhaustively explored in the literature.According to Atkeson and Ohanian (2001) model present day Phillips curve contradicts the trade off theory. Thus, it does not successfully help to forecast inflation. But instead overestimate the forecast. We would try to forecast inflation even if it would not be accurate.According to the Market Watch, predicted average unemployment rate in the U.S for 2014 would be around 6.8%. If we plug in our regression equation of 2000 to 2013 we obtain expected value for change in inflation in 2014 which is around -0.11% However, according to Useconomy.com forecasted expected change in inflation is -0.1%. Thus, our Phillips curve model over predicts the forecasted inflation by about -0.01.

8.0 Using the Model for Control or Policy Purposes. Let us see the general use of Phillips curve. First, The Central Bank can use Phillips Curve for the setting of short-term interest rates. Secondly, forecasted inflation affects governments expected tax revenues. And finally inflation is everywhere and always a monetary phenomenon. It enables the monetary economists to predict the amount of money, as a proportion of their income, which people would want to hold at various rates of inflation. US monetary and fiscal policy in the 1960s were very expansionary implied that policymakers could exploit the trade off to influence the rate of economic growth and inflation. However, the relationship from 1970s stated that it was not usable for policy purposes. Once people came to expect the higher inflation, monetary policy could not keep the unemployment rate permanently below its natural level. Classical theory says that any monetary policy in the long run is ineffective as the unemployment rate will return to its natural rate despite higher rates of inflation. The new classical model indicates that the effect of expansionary policy depends on whether it is anticipated or unanticipated. It demonstrates that policy makers cannot know the outcome of their decisions without knowing the publics expectations regarding them. Once they figure out the publics expectations, they can know what effect their policies will have. It may be nearly impossible to find out what the publics expectations are, given that the public consists of over 300 million U.S. citizens. Public expectations do not remain fixed while policy makers are plotting a surprisethe public will revise its expectations, and policies will have no predictable effect on output only unanticipated policy matters.

9.0. ConclusionTo wrap up our regression analysis of our sample 2000-2013 we had some strength namely no autocorrelation it had low degree of multicolinearity and equal variance. However, the sample has unfortunately some weaknesses like low r2 and insignificant t test and p values.Nevertheless we have reached at a general conclusion that this particular sample does not exhibit the presence of Phillips curve.On a final note this particular sample refutes the backward linear expectations of neoclassical and could be referred to as misperception theory in modern days. Maybe the data would best suit the New Keynesian reciprocal approach. Gordon 2013 who followed the new Keynesian approach found that the Phillips curve is well alive in the U.S.

10.0. References1. Basics Econometrics-Damodar Gujrati 4th Edition2. http://en.wikipedia.org/wiki/Phillips_curve3. http://www.minneapolisfed.org/research/qr/qr2511.pdf4. web.uconn.edu/cunningham/econ309/phillipscurve.ppt5. http://ashleymac.econ.vt.edu/working_papers/ashley_verbrugge.pdf

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