Phillips Curve Case Study

4. Data, Methodology and Results

As mentioned, the derivation of Phillips Curve requires the estimation of three variables i.e inflation, output gap and expected inflation. In order to estimate the expected augmented(Expectations Augmented) Phillips Curve, this study covers observations from time period 1961 to 2015 for both countries US and India.

The equation of Expected Augmented Phillips Curve(Expectations Augmented Phillips Curve) is
∏t = ∏et + β(Y-Yn) + et

where,
∏t = inflation at the time period t
∏et = expected inflation at the time period t
Y = Actual GDP
Yn = Potential GDP et = Supply Shocks

3.1 Inflation: GDP Deflator

GDP deflator, also called as implicit price deflator, has been used as a measure of inflation. (Appendix
Hodrick Prescott filter is a data smoothening technique that is commonly applied to remove short term fluctuations that are associated with the business cycles. Thereby, revealing long term trends. It is used to determine the long term trend of the time series by discounting the importance of short term fluctuations. The adjustment of the sensitivity of the trend to short-term fluctuations is achieved by modifying a multiplier λ.
It is a model-free based approach to decomposing a time series into its trend τt and cyclical components ct.
The HP filter is an algorithm that “smooths” the original time series yt to estimate its trend component, τt. The cyclical component is, as usual, the difference between the original series and its trend, i.e., yt = τt + ct where τt is constructed to minimize:
The filter is computed by applying the HP technique with λ equal 100 to actual GDP data, running it over a sample from 1961 to
Many time series exhibit serial autocorrelation i.e, linear association between lagged observations. This suggests past observations might predict current observations. An AR model is the one in which ∏t depends upon its past values ∏t-1, ∏t-2……
Thus ∏t = f(∏t-1, ∏t-2 ,……, εt)
The form of the AR(p) model is
∏te = β0 + β1∏t-1 + β2∏t-2 +……..+ βp∏t-p + εt ,where εt is an uncorrelated innovation process with mean zero and a constant variance.
In the given analysis, the current prediction is made using only one past observation i.e. last years inflation.
The stationary inflation series of both the countries is used to estimate the series of expected inflation using AR model. As mentioned,the given error term (ϵt) in AR model is assumed to be constant and close to zero because the average value appears to be zero