Assignment 4
1. The Phillips Curve
(a) The Output Gap and the Inflation Rate series are shown in figure 1. Using the Excel formula “=correl”, we find the correlation between these two variables to be -0.00206. The correlation coefficient ranges from -1 to 1, the closer the coefficient is to the extremes, the stronger is the linear relationship between the two variables. In this case, the correlation coefficient is close to zero, so there is almost no relationship between Ygap and Pi.
Figure 1
The Output Gap and the Inflation Rate series in 1955 – 2015
(b) Figure 2 shows the Output Gap and the change in the Inflation Rate series. Again, using the Excel formula “=correl”, we determine the correlation coefficient between Ygap and dPi to be 0.462757. This means that there is a moderate uphill relationship between the two series.
Figure 2
The Output Gap and the change in the Inflation Rate in 1955 – 2015
(c) The analysis above shows that dPi relates to Ygap better than the inflation rate Pi itself. The reason for this conclusion is that the absolute value of the correlation coefficient between the change in the inflation rate and the output gap is higher than that of the correlation between the GDP Gap and the inflation rate. The Phillips curve theory also suggests that there is a relationship between Ygap and dPi. Thus, the rate of inflation will remain the same when actual and potential output are equal. When output exceeds its potential, there is a positive change of inflation. Conversely, when GDP is below its potential, the inflation rate falls (Montoriol-Garriga).
(d) The summary output of the regression analysis in Excel with change in the Inflation Rate as the y-variable and the Output Gap as the x-variable is presented in figure 3. As we can see, the coefficient of determination R Square (r2) is equal to 0.214, or 21.4%. It states that 21.4% of variation in dPi is explained by the variation in Ygap.
The intercept coefficient is 0.259. This means that the regression line crosses the y axis at 0.259. The Output Gap coefficient is 0.309. It presents the slope of the regression function y (x).
The p-values for intercept and Output Gap variable are 0.207 and 0.0002 respectively. The p-value tests the null hypothesis that the related coefficient is equal to zero. If the p-value is less than 0.05, the null hypothesis may be rejected, otherwise, the coefficient is insignificant for the regression model (Frost). The relationship between dPi and Ygap is significant as the Output Gap p-value 0.0002 < 0.05. Conversely, the intercept coefficient p-value is rather large (0.207 > 0.05), so it has little importance for the model.
Figure 3
Regression analysis summary output
2. Monetary Policy
(a) The Federal Reserve is responsible for establishing the Federal Funds Rate (FFR) which affects production and inflation levels. When the inflation is high, the Fed should raise the FFR. As it is the short-term rate for the interbank loans, there will be less money available in the economy. This will lead to a decrease inGDP, employment, and inflation. On the contrary, decrease in FFR will lead to a larger money supply. In this case production level, investment, and inflation will rise while unemployment will fall (Mankiw 435).
The Taylor rule states that the nominal Federal Funds Rate = Inflation + 0.5 * (Inflation – 2.0) + 0.5 * GDP Gap (Mankiw 435). The real FFR is the nominal FFR minus inflation. The natural inflation rate is supposed to be 2%, so (Inflation – 2.0) in the equation above is the inflation deviation (tPi). So, in accordance with the Taylor principle, the rFFR rises by 0.5% when either the Inflation Deviation or the Output Gap rise by 1% (Mankiw 436). In other words, the policy coefficients are expected to be positive as there should be a positive relationship between tPi and rFFR as well as between Ygap and rFFR.
(b) Please see figure 4 for the dynamics of the real Federal Funds Rate and the Output Gap. The correlation coefficient between the two variables is 0.280705. This means that the relationship between rFFR and Ygap is positive, but weak. This is due to some exceptions from the Taylor rule in some years. For example, in 1980 – 1982 there was a significant increase of real FFR from -0.14 to 6.10 which was accompanied by a decrease of the Output Gap from -2.46 to -6.53.
Figure 4
The Output Gap and the real FFR in 1955 – 2015
(c) The real FFR and the Inflation deviation series are shown in figure 5. The correlation between them is -0.02504. As it is close to zero, there is almost no relationship betweem rFFR and tPi. The Taylor rule wasn’t observed on some time intervals, e.g. in 1980 – 1981, the real FFR increased from -0.14 to 6.00, while Inflation deviation slumped from 11.5 to 8.4.
Figure 5
The Inflation deviation and the real FFR in 1955 – 2015
(d) The regression analysis summary output with rFFR as the y-variable and Ygap and tPi as the x-variables is presented in figure 6. The coefficient of determination r2 is 0.079, or 7.9%. This means that only 7.9% of variation of the real Federal Funds Rate is explained by the variation in the two x-variables.
The intercept, Output Gap, and Inflation Deviation coefficients are 1.601, 0.245, and -0.019 accordingly. Thereby, the regression line may be presented as real FFR = 0.245 * Output Gap – 0.019 * Inflation Deviation + 1.601. The tPi negative coefficient doesn’t meet our expectations according to the Taylor rule.
The p-values for intercept, Output Gap, and Inflation Deviation variables are 0.00001, 0.03, and 0.847. Thereby, the null hypothesis is retained for the tPi variable as its p-value is greater than 0.05. In other words, for the given data, there is a very weak relationship between tPi and rFFR. The intercept and Ygap p-values do not exceed 0.05, so these coefficients are significant to the regression model.
Figure 6
Regression analysis summary output
Works cited
Frost, Jim. “How to Interpret Regression Analysis Results: P-values and Coefficients”. The Minitab Blog. Minitab, Inc., 1 July 2013. Web. 14 April 2016.
Mankiw, N. Gregory. Macroeconomics. 8th ed. New York: Worth Publishers, 2013. Print.
Montoriol-Garriga, Judit. “Growth without inflation: what does the Phillips curve tell us?” CaixaBank Research. Caixabank, S.A., 10 February 2015. Web. 15 April 2016.
