Deviations of the Taylor Rule - a New Methodology with an Application to Australia - Case Study Example

UNDERSTANDING THE DEVIATIONS OF THE TAYLOR RULE: A NEW METHODOLOGY WITH AN APPLICATION TO AUSTRALIA By(Student’s Name) Code+ Course Name Professor’s Name University Name City Date Describe the aims, methodological innovations and finding of this paper The aim of the paper is to investigate the deviations of the Taylor Rule, with specific focus being on the Australian context. The authors point out that their investigation focuses on explaining and quantifying the deviations of the rule. The paper seeks to identify whether the deviations from the rule are systematic and the factors that explain these deviation it is systematic. Additionally, it seeks to investigate whether the factors can be identified as being international or domestic and whether the impact of these factors can be quantified. The paper adopts a qualitative design approach in which a three-step econometric procedure is used to analyze economic information from Australian databases in order to identify the deviations of the Taylor rule. The data used in the paper is quarterly, starting from 1994’s Q1 to 2013’s Q1. The authors point out that information on real time seasonally adjusted real GDP was sourced from the Australian Real time Macroeconomic database. The methods used in the econometric procedure are OLS regression, factor augmented analysis and LMA shapely decomposition. OLS regression is used in the first step to estimate the Taylor rule. Real time data is used in the OLS regression approach with the deviation from the Taylor rule being taken as the residual. In factor augmented analysis, the researchers collated a large macroeconomic data set made up of 229 series and 13 unique categories of domestic and international variables. They also implement the Eigenvalue Ration Test to determine the number of factors created from the principal components of each category of variables. The LMG-Shapely decomposition is used in the final step to quantify the explanatory power of each individual factor. OLS regression is a linear modeling technique that can be utilized to model a single response variable that has been recorded on an interval scale. The technique is used to find the function that best approximates the data. When observed data is provided, OLS attempts to fit a model into these data. In this paper’s case, the OLS regression is used to fit Taylors rule into the observed data in the Australian economy. Factor augmented analysis is generally used to measure the effectiveness of monetary policy. It is a relatively new econometrics method and has been used in a number of studies and in provision of important information to policy makers. In this paper, the authors utilize the principle component analysis to reduce the explanatory variables into single factors after which the Eigenvalue Ratio test is run. In the findings, it is reported that a big percentage of Australia’s deviation from the Taylor rule can be systematically explained. The paper reports that 65% of the deviation can be explained systematically while the rest of the deviation is as a result of international factor and domestic factors. Domestic factors are said to account for 22.5% of the total variation from the rule while international factors are reported to account for 41.9% of the deviation. The researchers point out that some domestic factors had a significant statistical impact on the deviation from the Taylor rule while others were found to be statistically insignificant. Domestic interest rate is identified as the factor that significant contributes to the deviation among domestic factors while the exchange rates are pointed out as the most significant international factor contributing to the deviation from the rule. The authors report that the findings from the study reveal that Australia is deviating from the rule in the same way as the US and that the country is following in the international monetary policies established by the US. The statistical and economic significance of outputs in table 1 (Equation Three) In the results presented in table 1 for the model equation 3, the following can be deduced. I. The coefficient for inflation rates for the previous year are statistically insignificant across all the two approaches used for modelling output ranging from -0.03 to 0.6. As for the linear trend, the weighted median CPI inflation is negative implying that for any percentage increase in the previous year’s inflation rates, the current interest rates would reduce by 0.03 per cent. Generally, the low coefficients for the previous year’s inflation rate imply that the current interest rates are either not affected by previous inflation rate or that the effect is very little. II. The coefficients for the output gap are positive but statistically insignificant, less than o.5 at the 1% level of significance. This implies that the average discrepancy between the real and expected output for the previous year does not influence the current interest rates. It is important to identify from the table that both the coefficients of output gap and previous inflation rate are significantly different from the parametization set by Taylor (1993) which specifies that the coefficients should be 1.5 and 0.5 for inflation rates and output gap respectively. III. The coefficients of the smoothing parameters are also positive but statistically insignificant which implies that interest rate smoothing does not influence the foregoing interest rates. IV. The coefficient of variation R and Adjusted R are very high i.e. 0.93 for all the approaches used. This implies that, in as much as the coefficients are very low, the variables, taken together, explain 93% of the variation in interest rates. However, this very high level of R and Adjusted R could also imply a problem of collinearity in the data used. V. The Schwarz Criterion is lowest for the Trimmed Mean model in which both the significance of the interest rate smoothing and output gap was tested at the 1% level of significance. This implies that the Trimmed Mean Model under the HP-Filter could be selected as the best model for determining the factors influencing interest rates. Statistical and Economic significance of outputs in table 2 (Equation four). With respect to equation four, the following results can be inferred from the table. I. The coefficients of the measure of deviation from the Taylor’s rule in the US are both positive and statistically significant at the 1% level of significance implying that the deviations observed in the US will significantly affect the Taylor rule of deviation as applied in Australia. II. Coefficients of the first principle component estimated factor of the domestic interest group are all positive and statistically significant at the 1% level of significance. The implication is that an increase in measures of the factor of domestic interest group will increase the deviation of Taylor rule. III. Coefficients of the first principle component estimated factor of the international interest group are all negative and statistically insignificant at the 1% level of significance. The implication is that an increase in measures of the factor of international interest group will decrease the deviation of Taylor rule. IV. Coefficients of the first principle component estimated factor of the domestic interest group are all positive and statistically significant at the 1% level of significance. The implication is that an increase in measures of the factor of domestic interest group will increase the deviation of Taylor rule. V. Coefficients of the first principle component estimated factor of the domestic interest group are all positive and statistically significant at the 1% level of significance. The implication is that an increase in measures of the factor of domestic interest group will increase the deviation of Taylor rule. VI. The first principal component estimated factor of commodities group coefficients exhibit a similar pattern in that they all are positive and statistically significant at the 5 % level of significance implying that an increase in the exchange rate group principals increases Taylor deviation. VII. The R and Adjusted R both over 0.60 which implies that taken together, deviation of Taylor rule in the US, the first principal component estimated factor of domestic, international, commodities and international group all account for over 60% of the deviations of Taylor rule. The principle finding of the research paper is that about 65 per cent of the deviations in the Taylor rule in Australia can be explained systematically (Hudson & Vespignani, 2014, 2) VIII. As for the output gap measurements, the lowest Schwarz Criterion is for the Headline CPI inflation of the linear trend in which the deviation of Taylor rule in the US, principle components estimated factor of the domestic and international groups were tested for significance at the 1% level of significance. Describing Outputs in table three Table Three provides the LMG-Shapley decomposition of Equation Six and it can be interpreted for the specific explanatory variables as follows. The deviation of Taylor rule in the United States The deviation of Taylor rule in the United States accounts for 8.6 per cent of the total variation in deviation of Taylor rule in Australia and 13.3 per cent of the explained variation in deviation of Taylor rule is accounted for by the deviation of Taylor rule in the United States Commodity Factor The commodity factor accounts for 12.5 per cent of the total variation in deviation of Taylor rule and of the total explained variation in Taylor rule, commodity factor accounts for 19.4 per cent of the same. International Interest Rates The first principal component estimated factor of international interest group explains 4.8 per cent of the total variation in deviation of Taylor rule and about 24.8 per cent of explained variation in deviation of Taylor rule is accounted for by the international interest rates. Domestic Interest Rates The first principal component estimated factor of domestic interest group explains 22.5 per cent of the total variation in deviation of Taylor rule and 34.9 per cent of explained variation in deviation of Taylor rule is accounted for by the domestic interest rates. Exchange Rate The first principal component estimated factor of exchange rate group explains 16 per cent of the total variation in deviation of Taylor rule and 24.8 per cent of explained variation in deviation of Taylor rule is accounted for by the domestic interest rates. Finally, the deviation of Taylor rule in the United States, Commodity Factors, Exchange rates, Domestic and International interest rates all account for 64.4 per cent of variation in the deviation of Taylor rule and all this factors taken together account for 100 per cent of the explained variation in deviation of Taylor rule. Essentially, this factors are responsible for the total variation in deviation of Taylor rule. In table three, the individual effects of the various explanatory variables can be ascertained since the decomposition techniques like the LMG-Shapley decomposition are often used to disentangle and quantify the impact of various causal factors (Shorrocks, 2013, 1) References Hudson, K. B., & Vespignani, J. (2014). Understanding the Deviations of the Taylor Rule: A New Methodology with an Application to Australia. IDEAS. Viewed on 7th May 2015 at 4.52pm Shorrocks, A. F. (2013). Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. Journal of Economic Inequality, 1-28. Read More