The UK Bank of England - Research Paper Example

The UK Bank of England Monetary Policy Committee The UK’s Monetary Policy Committee (MPC) is a specialized economic advisory panel whose role is to set short term base interest rate. The MPC is made up of nine members namely the Bank's Governor, the two Deputy Governors, the Chief Economist, the Executive Director for Market Operations and four external members appointed by the Chancellor of the Exchequer (Bank of England, 2012). The MPC sits on a monthly basis to announce revised decisions on interest rates based on a range of economic data. The decisions on what rate to be announced are made on a majority vote. The committee also publishes quarterly inflation report (Politics.co.uk, 2013). The Evolution of Exchange Rate in UK Figure 1: Trend of Exchange Rate The results show a turbulent exchange rate trend for the period 1992 – 2012. As noted in Figure 1, the lowest exchange rates were observed in 2007; just the same time the global financial crisis started being more pronounced. As shown, it shot to the highest levels ever the subsequent year suggesting that the global financial crisis negatively impacted on the exchange rate levels are led to weaker currency. Figure 2 shows the trend by season. Figure 2: Exchange Rate Trend by Season As shown, Q1 and Q4 have similar trends beginning with fall in exchange rates and ending with a fall in exchange rates. The results also show that Q2 and Q3 trends are similar as they begin with rising exchange rates and end with rising exchange rates. Overall, each quarter shows a fluctuating trend of exchange rate for the years observed. The Evolution of Share Index in the UK Figure 3 shows the evolution of FTSE 100 share index since 1992 in the UK. As shown, there has been a general upward trend in the share index since 1992 with slumps in 2002 and 2008. There was an economic recession in 2000 – 2001 that affected the European Union but Britain was unaffected by that recession. It may seem that while it was not directly affected in terms of its impact on GDP, the share index was slightly affected as the index was lowest in 2002 after having an upward rise in the previous years. The index then rose until 2007 when it started falling to another lower level in 2008. This is attributed to the global economic crisis of 2008. The index has since improved. The trend by season graph shown in Figure 4 reveals a similar cyclical trend of FTSE 100 index for all the four seasons. Thus for all the four quarters, the index begins from a low point and ends at a higher point with two highs and two lows in between them. Figure 3: Trend of FTSE 100 Index (1992 – 2012) Figure 4: Trend of FTSE 100 Index by Season The Evolution of Real GDP in the UK The real GDP shown in Figure 5 show an upward rising real GDP from 1992 – 2012 with a slight fall in 2009 following the global financial crisis of 2008. As shown, it can also be noticed that the economic recession of 2000 – 2001 (Amadeo, 2012) that affected the European Union did not affect the UK as the GDP growth remained stable. The trend by seasons in Figure 6 show a strikingly similar performance of real GDP in all the four quarters as is upward rising at the beginning of the period and slightly falls towards the end of the quarter then rises again. Quarters 1 and 2 had the sharpest falls though towards the end of the period. Figure 5: Trend of Real GDP (1992 – 2012) Figure 6: Trend of Real GDP by Season (1992 – 2012) The Evolution of Inflation Rates in the UK The trend in Figure 7 reveals that inflation rates fell from 1992 – 2000 when they were at their lowest. From there, inflation rose slowly before shooting to the maximum point in 2008. This shows that the global financial crisis of 2008 led to the highest inflations recorded within the period of study in the UK. The inflation rate fell sharply the subsequent year before rising again until 2011 when they started falling. Thus the recent inflation rate performance has been turbulent and the recent figures of 2012 suggest a rise in inflation rates. The seasonal trends in Figure 8 show that in all the quarters, the trends begin with a fall and end with a fall in inflation rates. The last month of the each quarter records the most activities with the rise and fall of inflation rates in the UK. Figure 7: Trend of Inflation Rate in the UK (1992 – 2012) Figure 8: Trend of Inflation by Season (1992 – 2012) The Evolution of Interest Rates in the UK The results of the evolution of interest rates are shown in Figure 9 and Figure 10. As shown in Figure 9, the interest rates for the UK have been falling since 1992. This can generally be attributed to the deliberate attempts to reduce the base rates by the Monetary Policy Committee. The sharpest fall was in 2008 when they were reduced to the lowest ever of 0.5% where they have remained to date. According to BBC (2012), the MPC made a decision to maintain the base interest rates at 0.5% since 2009. The seasonal trends in Figure 10 show that interest rates behave in the same manner across all the four quarters. Further, Q2 begins with the highest levels of interest rates than any other quarter before falling in the same manner as the rest. Figure 9: Trend of Interest Rate for UK (1992 – 2012) Figure 10: Trend of Interest Rate by Season (1992 – 2012) The Evolution of Money Supply in the UK Figure 11 reveals that money supply increased from 1992 – 2008 when it fell sharply following the 2008 global financial crisis. The money supply has however started an upward rise since 2009 and this can be attributed to the deliberate attempt by the MPC to inject money directly into the economy through quantitative easing (Bank of England, 2013). The seasonal trends in Figure 12 reveal that all the four quarters behaved in a similar manner as the trends began with a low but rising money supply before hitting the highest peak towards the end of the quarter then dropping sharply at the end. Q4 shows the highest money supply while Q1 shows the fastest recovery from a lower money supply at the end of the period. Figure 11: Trend of Money Supply in UK (1992 – 2012) Figure 12: Trend of Money Supply by Season (1992 – 2012) The Evolution of Unemployment in the UK Figure 13 shows that unemployment fell from 1993 – 2005 when it began rising to date. The rates of unemployment have sharply risen since the global economic crisis of 2008 suggesting that the crisis had a negative effect on unemployment levels by increasing them. The results in Figure 14 show that there was a similar behaviour of unemployment results in all the four quarters beginning with the highest points and falling to the lowest levels then rising again. The end of each of the four quarters shows a rise in unemployment levels. Figure 13: Trend of Unemployment (1992 – 2012) Figure 14: Trend of Unemployment by Season (1992 – 2012) Unit-Root Tests This section presents the results of unit-root tests done using EVIEWS. The method used to conduct the unit-root tests were the Augmented Dickey Fuller (ADF) and Phillips-Perron (PP) unit-root statistics. The summary results are shown in Table 1 while the full results are presented in appendix 1. Using the ADF results, only FTSE100 index, money supply, and unemployment were stationary at level. All the variables were stationary at first-difference suggesting a first-difference stationarity for all the variables in the study at confidence levels of up to 5%. Further, the Philips-Perron test results show that at level, only inflation and money supply were stationary. But at first-difference, stationarity was observed for all the variables at 1% level. This means that there was a first-difference stationarity for all the variables in the study. To achieve stationarity for those variables that are not stationary, it is advisable to difference. Thus differencing at first levels achieves stationarity for all the variables using the ADF test and for the PP test. Table 1: Stationarity Test Dickey-Fuller Phillips-Perron Level 1st Diff Level 1st Diff EXHC -1.88 -8.55* -2.50 -6.86* FTSE100 -2.38** -6.48* -2.01 -6.48* GDP -0.86 -6.06* -0.51 -6.23* INFL -1.16 -7.87* -3.00** -7.12* IR -1.83 -5.30* -1.95 -5.06* M4 -3.91* 10.31* -3.74* -21.89* U -2.15** -3.25** -1.54 -11.58* *significant at 1%, **significant at 5% Correlation Tests for Inflation Appendix 2 shows the results of ACF and PACF tests on inflation. The ACF results show that the autocorrelations are significant and positive up to 14 lags. PACF results show that only lag 1 is significant and positive. Given these results, the most appropriate process is an AR (1) process. ARIMA Model Test The study has also computed the AIC and BIC information criteria for an AR(1), AR(2), AR(3), MA(1), MA(2), MA(3), ARMA(1,1), ARMA(1,2), ARMA(2,1) and ARMA(2,2) process for the inflation series (see appendix 3 for EVIEWS output). The results in Table 2 reveal that the model suggested by the two criteria is ARMA (1, 1) model as it has the smallest AIC and BIC values. The five best models are AR (1), MA (1), ARMA (1, 1), ARMA (1, 2), and ARMA (2, 2). This is because these models have the least AIC and BIC values. Table 2: ARIMA Processes for Inflation Series Model AIC BIC AR(1) 1.275727 1.334427 AR(2) 2.087987 2.147109 AR(3) 2.387698 2.447248 MA(1) 1.734011 1.792296 MA(2) 2.130487 2.188772 MA(3) 2.589657 2.647942 ARMA(1,1) 1.132226 1.220277 ARMA (1,2) 1.287406 1.375457 ARMA (2,1) 1.463875 1.552558 ARMA (2,2) 2.020886 2.109569 Inflation Forecasting The results in Figure 15 show the forecast based on the AR (1) model. The results show fairly stable inflation rates for 2010Q1 – 2012Q4. The MA (1) model shows stable inflation rates forecast (Figure 16). The ARMA (1, 1) model shows falling inflation rate forecast (Figure 17). The ARMA (1, 2) model forecasts a fairly stable inflation rates (Figure 18) while the ARMA (2, 2) model forecasts volatile inflation rates over the period (Figure 19). Figure 15: AR (1) Model Inflation Forecast (2010Q1 – 2012Q4) Figure 16: MA (1) Model Inflation Forecast (2010Q1 – 2012Q4) Figure 17: ARMA (1, 1) Model Inflation Forecast (2010Q1 – 2012Q4) Figure 18: ARMA (1, 2) Model Inflation Forecast (2010Q1 – 2012Q4) Figure 19: ARMA (2, 2) Model Inflation Forecast (2010Q1 – 2012Q4) Phillips Curve Equation Estimation A version of Philip’s Curve relating inflation to the change in unemployment was also estimated. To estimate the Phillips curve equation given, the researcher created a new variable called DU (meaning change in unemployment) using EVIEWS. This model is given as follows: 𝐼𝑁𝐹𝑡=𝛽1+𝛽2𝐷𝑈+𝜀𝑡 (1) Table 3: Change in Unemployment and Inflation Rate Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 13:01 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   C 2.201378 0.102527 21.47127 0.0000 DU 0.613935 0.284562 2.157474 0.0340 R-squared 0.054984     Mean dependent var 2.189130 Adjusted R-squared 0.043172     S.D. dependent var 0.947676 S.E. of regression 0.926994     Akaike info criterion 2.710349 Sum squared resid 68.74545     Schwarz criterion 2.769049 Log likelihood -109.1243     Hannan-Quinn criter. 2.733916 F-statistic 4.654692     Durbin-Watson stat 0.361239 Prob(F-statistic) 0.033969 The results presented in Table 3 show that the change in unemployment had a positive and significant effect on inflation (β = 0.61, p < .05). The model explained 5.49% of the variance in inflation as given by the R-squared of 0.0549). The F-statistic was significant at 5% level suggesting the model was fit. The correlogram for the least squares results are shown in appendix 4. As shown, the results revealed that ACF showed was positive and significant up to 3 lags while the PACF showed that only lag 1 was significant. The most appropriate model therefore given these results is an AR (1) model. Table 4: Breusch-Godfrey Serial Correlation LM Test Breusch-Godfrey Serial Correlation LM Test: F-statistic 51.65028     Prob. F(4,76) 0.0000 Obs*R-squared 59.94772     Prob. Chi-Square(4) 0.0000 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 04/28/13 Time: 13:04 Sample: 1992Q3 2012Q4 Included observations: 82 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob.   C -0.002758 0.054700 -0.050428 0.9599 DU -0.511200 0.187609 -2.724811 0.0080 RESID(-1) 0.912119 0.112090 8.137401 0.0000 RESID(-2) 0.026860 0.137813 0.194904 0.8460 RESID(-3) -0.223709 0.144541 -1.547723 0.1258 RESID(-4) 0.177291 0.118562 1.495344 0.1390 R-squared 0.731070     Mean dependent var 9.48E-16 Adjusted R-squared 0.713377     S.D. dependent var 0.921254 S.E. of regression 0.493214     Akaike info criterion 1.494607 Sum squared resid 18.48773     Schwarz criterion 1.670708 Log likelihood -55.27888     Hannan-Quinn criter. 1.565309 F-statistic 41.32022     Durbin-Watson stat 1.724325 Prob(F-statistic) 0.000000 A serial correlation of the least squares residuals of the Philips-Curve equation was tested for up to four lags using the Breusch-Godfrey test for autocorrelation. The results shown in Table 4 reveal that the null hypothesis of no serial correlation up to lag 4 is rejected. The Philips-Curve equation was further tested for heteroskedasticity of the residuals using the White test. The results presented in Table 5 revealed that the null hypothesis of no heteroskedasticity cannot is accepted. Table 5: White Test for Heteroskedasticity Heteroskedasticity Test: White F-statistic 1.831429     Prob. F(2,79) 0.1669 Obs*R-squared 3.633486     Prob. Chi-Square(2) 0.1626 Scaled explained SS 3.728521     Prob. Chi-Square(2) 0.1550 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 04/28/13 Time: 13:05 Sample: 1992Q3 2012Q4 Included observations: 82 Variable Coefficient Std. Error t-Statistic Prob.   C 0.747789 0.171865 4.351025 0.0000 DU 0.644219 0.377208 1.707862 0.0916 DU^2 0.796695 0.817188 0.974922 0.3326 R-squared 0.044311     Mean dependent var 0.838359 Adjusted R-squared 0.020116     S.D. dependent var 1.238625 S.E. of regression 1.226104     Akaike info criterion 3.281459 Sum squared resid 118.7631     Schwarz criterion 3.369510 Log likelihood -131.5398     Hannan-Quinn criter. 3.316810 F-statistic 1.831429     Durbin-Watson stat 0.834650 Prob(F-statistic) 0.166920 The Ramsey RESET test was used to test for misspecification and the full results of the analysis are presented in appendix 5. As shown, the null hypothesis that the coefficients on the added variables are jointly zero are accepted at the 5% level. Finally, the Philips-Curve equation was used to perform inflation forecasts over the period 2010Q1-2012Q4. The results shown in Figure 20 revealed a stable inflation forecast averaging about 2.2%. This mirrors the actual inflation rates which averaged 2.2% over the period of analysis. Figure 20: Inflation Forecast from Phillips Curve References Amadeo, K, 2012, Causes of Economic Recession, Available from http://useconomy.about.com/od/grossdomesticproduct/a/cause_recession.htm Bank of England, 2012, Monetary Policy Committee (MPC), Available from http://www.bankofengland.co.uk/monetarypolicy/Pages/overview.aspx Bank of England, 2013, Quantitative Easing - How it Works, Available from http://www.bankofengland.co.uk/education/pages/inflation/qe/video.aspx BBC, 2013, What is quantitative easing, Available from http://www.bbc.co.uk/news/business-15198789 Politics.co.uk, 2013, Monetary Policy Committee, http://www.politics.co.uk/reference/monetary-policy-committee. Appendices Appendix 1: Unit Root Tests Tables (Level and 1st Difference) Null Hypothesis: EXHC has a unit root Exogenous: Constant Lag Length: 2 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -1.884968  0.3377 Test critical values: 1% level -3.514426 5% level -2.898145 10% level -2.586351 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(EXHC) Method: Least Squares Date: 04/28/13 Time: 01:27 Sample (adjusted): 1993Q1 2012Q4 Included observations: 80 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   EXHC(-1) -0.081015 0.042980 -1.884968 0.0633 D(EXHC(-1)) 0.411337 0.088831 4.630533 0.0000 D(EXHC(-2)) -0.273529 0.091730 -2.981895 0.0038 C 0.049472 0.026466 1.869283 0.0654 R-squared 0.286771     Mean dependent var -4.33E-05 Adjusted R-squared 0.258617     S.D. dependent var 0.022620 S.E. of regression 0.019477     Akaike info criterion -4.990465 Sum squared resid 0.028831     Schwarz criterion -4.871364 Log likelihood 203.6186     Hannan-Quinn criter. -4.942714 F-statistic 10.18588     Durbin-Watson stat 1.798439 Prob(F-statistic) 0.000010 Null Hypothesis: D(EXHC) has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -8.554130  0.0000 Test critical values: 1% level -3.514426 5% level -2.898145 10% level -2.586351 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(EXHC,2) Method: Least Squares Date: 05/02/13 Time: 15:32 Sample (adjusted): 1993Q1 2012Q4 Included observations: 80 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(EXHC(-1)) -0.936486 0.109478 -8.554130 0.0000 D(EXHC(-1),2) 0.326153 0.088815 3.672266 0.0004 C -0.000245 0.002217 -0.110667 0.9122 R-squared 0.499888     Mean dependent var -0.001379 Adjusted R-squared 0.486899     S.D. dependent var 0.027638 S.E. of regression 0.019797     Akaike info criterion -4.969774 Sum squared resid 0.030179     Schwarz criterion -4.880448 Log likelihood 201.7910     Hannan-Quinn criter. -4.933961 F-statistic 38.48283     Durbin-Watson stat 1.806784 Prob(F-statistic) 0.000000 Null Hypothesis: EXHC has a unit root Exogenous: Constant Bandwidth: 1 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -2.500862  0.1190 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.000606 HAC corrected variance (Bartlett kernel)  0.000774 Phillips-Perron Test Equation Dependent Variable: D(EXHC) Method: Least Squares Date: 04/28/13 Time: 01:28 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   EXHC(-1) -0.113541 0.050140 -2.264483 0.0263 C 0.070524 0.030851 2.285946 0.0249 R-squared 0.060237     Mean dependent var 0.000941 Adjusted R-squared 0.048490     S.D. dependent var 0.025557 S.E. of regression 0.024930     Akaike info criterion -4.521435 Sum squared resid 0.049719     Schwarz criterion -4.462735 Log likelihood 187.3788     Hannan-Quinn criter. -4.497868 F-statistic 5.127883     Durbin-Watson stat 1.422418 Prob(F-statistic) 0.026251 Null Hypothesis: D(EXHC) has a unit root Exogenous: Constant Bandwidth: 7 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -6.868000  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.000604 HAC corrected variance (Bartlett kernel)  0.000510 Phillips-Perron Test Equation Dependent Variable: D(EXHC,2) Method: Least Squares Date: 05/02/13 Time: 15:26 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(EXHC(-1)) -0.755552 0.108176 -6.984449 0.0000 C 0.001059 0.002766 0.382662 0.7030 R-squared 0.381762     Mean dependent var 0.000322 Adjusted R-squared 0.373936     S.D. dependent var 0.031444 S.E. of regression 0.024880     Akaike info criterion -4.525120 Sum squared resid 0.048902     Schwarz criterion -4.465998 Log likelihood 185.2674     Hannan-Quinn criter. -4.501399 F-statistic 48.78252     Durbin-Watson stat 1.442523 Prob(F-statistic) 0.000000 Null Hypothesis: FTSE100 has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -2.377278  0.1513 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(FTSE100) Method: Least Squares Date: 04/28/13 Time: 01:29 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   FTSE100(-1) -0.065007 0.027345 -2.377278 0.0199 D(FTSE100(-1)) 0.322313 0.103664 3.109215 0.0026 C 6.750363 2.660613 2.537146 0.0132 R-squared 0.157486     Mean dependent var 0.822119 Adjusted R-squared 0.135883     S.D. dependent var 5.799965 S.E. of regression 5.391524     Akaike info criterion 6.243867 Sum squared resid 2267.346     Schwarz criterion 6.332550 Log likelihood -249.8766     Hannan-Quinn criter. 6.279448 F-statistic 7.290051     Durbin-Watson stat 1.991925 Prob(F-statistic) 0.001252 Null Hypothesis: D(FTSE100) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -6.483759  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(FTSE100,2) Method: Least Squares Date: 05/02/13 Time: 15:34 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(FTSE100(-1)) -0.690674 0.106524 -6.483759 0.0000 C 0.590514 0.621580 0.950020 0.3450 R-squared 0.347319     Mean dependent var 0.073378 Adjusted R-squared 0.339057     S.D. dependent var 6.824214 S.E. of regression 5.547978     Akaike info criterion 6.289126 Sum squared resid 2431.625     Schwarz criterion 6.348248 Log likelihood -252.7096     Hannan-Quinn criter. 6.312846 F-statistic 42.03913     Durbin-Watson stat 1.956821 Prob(F-statistic) 0.000000 Null Hypothesis: FTSE100 has a unit root Exogenous: Constant Bandwidth: 3 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -2.010976  0.2817 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  31.71941 HAC corrected variance (Bartlett kernel)  50.23576 Phillips-Perron Test Equation Dependent Variable: D(FTSE100) Method: Least Squares Date: 04/28/13 Time: 01:29 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   FTSE100(-1) -0.052558 0.028192 -1.864288 0.0659 C 5.723367 2.733962 2.093433 0.0395 R-squared 0.041636     Mean dependent var 0.763500 Adjusted R-squared 0.029656     S.D. dependent var 5.788442 S.E. of regression 5.701964     Akaike info criterion 6.343586 Sum squared resid 2600.991     Schwarz criterion 6.402287 Log likelihood -258.0870     Hannan-Quinn criter. 6.367154 F-statistic 3.475570     Durbin-Watson stat 1.359935 Prob(F-statistic) 0.065949 Null Hypothesis: D(FTSE100) has a unit root Exogenous: Constant Bandwidth: 0 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -6.483759  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  30.02006 HAC corrected variance (Bartlett kernel)  30.02006 Phillips-Perron Test Equation Dependent Variable: D(FTSE100,2) Method: Least Squares Date: 05/02/13 Time: 15:27 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(FTSE100(-1)) -0.690674 0.106524 -6.483759 0.0000 C 0.590514 0.621580 0.950020 0.3450 R-squared 0.347319     Mean dependent var 0.073378 Adjusted R-squared 0.339057     S.D. dependent var 6.824214 S.E. of regression 5.547978     Akaike info criterion 6.289126 Sum squared resid 2431.625     Schwarz criterion 6.348248 Log likelihood -252.7096     Hannan-Quinn criter. 6.312846 F-statistic 42.03913     Durbin-Watson stat 1.956821 Prob(F-statistic) 0.000000 Null Hypothesis: GDP has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -0.858275  0.7965 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 04/28/13 Time: 01:30 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   GDP(-1) -0.002994 0.003488 -0.858275 0.3934 D(GDP(-1)) 0.356467 0.106401 3.350209 0.0012 C 2.662983 1.036420 2.569406 0.0121 R-squared 0.132869     Mean dependent var 2.869617 Adjusted R-squared 0.110635     S.D. dependent var 2.429098 S.E. of regression 2.290790     Akaike info criterion 4.532004 Sum squared resid 409.3220     Schwarz criterion 4.620687 Log likelihood -180.5462     Hannan-Quinn criter. 4.567585 F-statistic 5.975892     Durbin-Watson stat 2.049691 Prob(F-statistic) 0.003849 Null Hypothesis: D(GDP) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -6.059594  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,2) Method: Least Squares Date: 05/02/13 Time: 15:35 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(GDP(-1)) -0.643673 0.106224 -6.059594 0.0000 C 1.841903 0.398036 4.627481 0.0000 R-squared 0.317310     Mean dependent var -0.014568 Adjusted R-squared 0.308668     S.D. dependent var 2.750533 S.E. of regression 2.286968     Akaike info criterion 4.516712 Sum squared resid 413.1876     Schwarz criterion 4.575835 Log likelihood -180.9269     Hannan-Quinn criter. 4.540433 F-statistic 36.71868     Durbin-Watson stat 2.036077 Prob(F-statistic) 0.000000 Null Hypothesis: D(INFL) has a unit root Exogenous: Constant Lag Length: 3 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -7.873547  0.0000 Test critical values: 1% level -3.516676 5% level -2.899115 10% level -2.586866 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(INFL,2) Method: Least Squares Date: 05/02/13 Time: 15:35 Sample (adjusted): 1993Q3 2012Q4 Included observations: 78 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(INFL(-1)) -1.547749 0.196576 -7.873547 0.0000 D(INFL(-1),2) 0.755014 0.161305 4.680649 0.0000 D(INFL(-2),2) 0.474904 0.132169 3.593161 0.0006 D(INFL(-3),2) 0.435653 0.107652 4.046872 0.0001 C 0.005474 0.045320 0.120783 0.9042 R-squared 0.531802     Mean dependent var 0.002171 Adjusted R-squared 0.506148     S.D. dependent var 0.569505 S.E. of regression 0.400217     Akaike info criterion 1.068338 Sum squared resid 11.69270     Schwarz criterion 1.219409 Log likelihood -36.66519     Hannan-Quinn criter. 1.128815 F-statistic 20.72926     Durbin-Watson stat 1.947160 Prob(F-statistic) 0.000000 Null Hypothesis: GDP has a unit root Exogenous: Constant Bandwidth: 5 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -0.508230  0.8833 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  5.842068 HAC corrected variance (Bartlett kernel)  11.47182 Phillips-Perron Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 04/28/13 Time: 01:32 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   GDP(-1) -0.002087 0.003667 -0.569081 0.5709 C 3.402490 1.036707 3.282015 0.0015 R-squared 0.004032     Mean dependent var 2.832915 Adjusted R-squared -0.008418     S.D. dependent var 2.436829 S.E. of regression 2.447064     Akaike info criterion 4.651742 Sum squared resid 479.0496     Schwarz criterion 4.710443 Log likelihood -188.7214     Hannan-Quinn criter. 4.675310 F-statistic 0.323853     Durbin-Watson stat 1.260824 Prob(F-statistic) 0.570895 Null Hypothesis: D(GDP) has a unit root Exogenous: Constant Bandwidth: 4 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -6.233517  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  5.101082 HAC corrected variance (Bartlett kernel)  5.819739 Phillips-Perron Test Equation Dependent Variable: D(GDP,2) Method: Least Squares Date: 05/02/13 Time: 15:28 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(GDP(-1)) -0.643673 0.106224 -6.059594 0.0000 C 1.841903 0.398036 4.627481 0.0000 R-squared 0.317310     Mean dependent var -0.014568 Adjusted R-squared 0.308668     S.D. dependent var 2.750533 S.E. of regression 2.286968     Akaike info criterion 4.516712 Sum squared resid 413.1876     Schwarz criterion 4.575835 Log likelihood -180.9269     Hannan-Quinn criter. 4.540433 F-statistic 36.71868     Durbin-Watson stat 2.036077 Prob(F-statistic) 0.000000 Null Hypothesis: INFL has a unit root Exogenous: Constant Lag Length: 4 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -1.164567  0.6860 Test critical values: 1% level -3.516676 5% level -2.899115 10% level -2.586866 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(INFL) Method: Least Squares Date: 04/28/13 Time: 01:32 Sample (adjusted): 1993Q3 2012Q4 Included observations: 78 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   INFL(-1) -0.064564 0.055440 -1.164567 0.2480 D(INFL(-1)) 0.241828 0.109560 2.207272 0.0305 D(INFL(-2)) -0.241158 0.113491 -2.124904 0.0370 D(INFL(-3)) -0.012302 0.110770 -0.111054 0.9119 D(INFL(-4)) -0.401998 0.111211 -3.614738 0.0006 C 0.144673 0.127793 1.132090 0.2614 R-squared 0.304632     Mean dependent var 0.002827 Adjusted R-squared 0.256343     S.D. dependent var 0.462970 S.E. of regression 0.399245     Akaike info criterion 1.075318 Sum squared resid 11.47653     Schwarz criterion 1.256603 Log likelihood -35.93741     Hannan-Quinn criter. 1.147890 F-statistic 6.308471     Durbin-Watson stat 1.928380 Prob(F-statistic) 0.000066 Null Hypothesis: D(INFL) has a unit root Exogenous: Constant Lag Length: 3 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -7.873547  0.0000 Test critical values: 1% level -3.516676 5% level -2.899115 10% level -2.586866 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(INFL,2) Method: Least Squares Date: 05/02/13 Time: 15:38 Sample (adjusted): 1993Q3 2012Q4 Included observations: 78 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(INFL(-1)) -1.547749 0.196576 -7.873547 0.0000 D(INFL(-1),2) 0.755014 0.161305 4.680649 0.0000 D(INFL(-2),2) 0.474904 0.132169 3.593161 0.0006 D(INFL(-3),2) 0.435653 0.107652 4.046872 0.0001 C 0.005474 0.045320 0.120783 0.9042 R-squared 0.531802     Mean dependent var 0.002171 Adjusted R-squared 0.506148     S.D. dependent var 0.569505 S.E. of regression 0.400217     Akaike info criterion 1.068338 Sum squared resid 11.69270     Schwarz criterion 1.219409 Log likelihood -36.66519     Hannan-Quinn criter. 1.128815 F-statistic 20.72926     Durbin-Watson stat 1.947160 Prob(F-statistic) 0.000000 Null Hypothesis: INFL has a unit root Exogenous: Constant Bandwidth: 3 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -3.003062  0.0387 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.199702 HAC corrected variance (Bartlett kernel)  0.263556 Phillips-Perron Test Equation Dependent Variable: D(INFL) Method: Least Squares Date: 04/28/13 Time: 01:32 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   INFL(-1) -0.143559 0.051609 -2.781648 0.0067 C 0.297425 0.124463 2.389667 0.0192 R-squared 0.088190     Mean dependent var -0.019668 Adjusted R-squared 0.076792     S.D. dependent var 0.470872 S.E. of regression 0.452431     Akaike info criterion 1.275727 Sum squared resid 16.37554     Schwarz criterion 1.334427 Log likelihood -50.30481     Hannan-Quinn criter. 1.299294 F-statistic 7.737565     Durbin-Watson stat 1.340784 Prob(F-statistic) 0.006743 Null Hypothesis: D(INFL) has a unit root Exogenous: Constant Bandwidth: 9 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -7.123744  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.194436 HAC corrected variance (Bartlett kernel)  0.065446 Phillips-Perron Test Equation Dependent Variable: D(INFL,2) Method: Least Squares Date: 05/02/13 Time: 15:29 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(INFL(-1)) -0.732119 0.105578 -6.934389 0.0000 C -0.001690 0.049670 -0.034028 0.9729 R-squared 0.378372     Mean dependent var 0.015161 Adjusted R-squared 0.370504     S.D. dependent var 0.562756 S.E. of regression 0.446495     Akaike info criterion 1.249605 Sum squared resid 15.74928     Schwarz criterion 1.308727 Log likelihood -48.60901     Hannan-Quinn criter. 1.273326 F-statistic 48.08575     Durbin-Watson stat 1.902394 Prob(F-statistic) 0.000000 Null Hypothesis: IR has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -1.825759  0.3657 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(IR) Method: Least Squares Date: 04/28/13 Time: 01:33 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   IR(-1) -0.042813 0.023449 -1.825759 0.0717 D(IR(-1)) 0.502524 0.094528 5.316140 0.0000 C 0.146732 0.117782 1.245791 0.2166 R-squared 0.281416     Mean dependent var -0.103395 Adjusted R-squared 0.262991     S.D. dependent var 0.530529 S.E. of regression 0.455455     Akaike info criterion 1.301294 Sum squared resid 16.18026     Schwarz criterion 1.389978 Log likelihood -49.70242     Hannan-Quinn criter. 1.336875 F-statistic 15.27342     Durbin-Watson stat 1.842813 Prob(F-statistic) 0.000003 Null Hypothesis: D(IR) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -5.303294  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(IR,2) Method: Least Squares Date: 05/02/13 Time: 15:36 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(IR(-1)) -0.507756 0.095744 -5.303294 0.0000 C -0.046422 0.052530 -0.883728 0.3795 R-squared 0.262543     Mean dependent var 0.012346 Adjusted R-squared 0.253208     S.D. dependent var 0.534770 S.E. of regression 0.462132     Akaike info criterion 1.318451 Sum squared resid 16.87174     Schwarz criterion 1.377573 Log likelihood -51.39726     Hannan-Quinn criter. 1.342171 F-statistic 28.12492     Durbin-Watson stat 1.840020 Prob(F-statistic) 0.000001 Null Hypothesis: IR has a unit root Exogenous: Constant Bandwidth: 4 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -1.953478  0.3067 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.274393 HAC corrected variance (Bartlett kernel)  0.549228 Phillips-Perron Test Equation Dependent Variable: D(IR) Method: Least Squares Date: 04/28/13 Time: 01:33 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   IR(-1) -0.044616 0.026278 -1.697861 0.0934 C 0.088654 0.133126 0.665936 0.5074 R-squared 0.034781     Mean dependent var -0.114329 Adjusted R-squared 0.022716     S.D. dependent var 0.536460 S.E. of regression 0.530332     Akaike info criterion 1.593463 Sum squared resid 22.50020     Schwarz criterion 1.652163 Log likelihood -63.33196     Hannan-Quinn criter. 1.617030 F-statistic 2.882731     Durbin-Watson stat 0.972136 Prob(F-statistic) 0.093421 Null Hypothesis: D(IR) has a unit root Exogenous: Constant Bandwidth: 5 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -5.057342  0.0001 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.208293 HAC corrected variance (Bartlett kernel)  0.163692 Phillips-Perron Test Equation Dependent Variable: D(IR,2) Method: Least Squares Date: 05/02/13 Time: 15:29 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(IR(-1)) -0.507756 0.095744 -5.303294 0.0000 C -0.046422 0.052530 -0.883728 0.3795 R-squared 0.262543     Mean dependent var 0.012346 Adjusted R-squared 0.253208     S.D. dependent var 0.534770 S.E. of regression 0.462132     Akaike info criterion 1.318451 Sum squared resid 16.87174     Schwarz criterion 1.377573 Log likelihood -51.39726     Hannan-Quinn criter. 1.342171 F-statistic 28.12492     Durbin-Watson stat 1.840020 Prob(F-statistic) 0.000001 Null Hypothesis: M4 has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -3.913700  0.0030 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(M4) Method: Least Squares Date: 04/28/13 Time: 01:33 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   M4(-1) -0.318068 0.081270 -3.913700 0.0002 C 6555.726 2232.540 2.936442 0.0043 R-squared 0.160696     Mean dependent var 115.6341 Adjusted R-squared 0.150204     S.D. dependent var 14821.15 S.E. of regression 13662.78     Akaike info criterion 21.90683 Sum squared resid 1.49E+10     Schwarz criterion 21.96553 Log likelihood -896.1799     Hannan-Quinn criter. 21.93039 F-statistic 15.31705     Durbin-Watson stat 1.984925 Prob(F-statistic) 0.000190 Null Hypothesis: D(M4) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -10.30899  0.0000 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(M4,2) Method: Least Squares Date: 05/02/13 Time: 15:39 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(M4(-1)) -1.152918 0.111836 -10.30899 0.0000 C 166.6672 1648.427 0.101107 0.9197 R-squared 0.573607     Mean dependent var -167.6790 Adjusted R-squared 0.568210     S.D. dependent var 22573.14 S.E. of regression 14832.97     Akaike info criterion 22.07147 Sum squared resid 1.74E+10     Schwarz criterion 22.13060 Log likelihood -891.8947     Hannan-Quinn criter. 22.09519 F-statistic 106.2753     Durbin-Watson stat 2.058068 Prob(F-statistic) 0.000000 Null Hypothesis: M4 has a unit root Exogenous: Constant Bandwidth: 4 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -3.744851  0.0050 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  1.82E+08 HAC corrected variance (Bartlett kernel)  1.59E+08 Phillips-Perron Test Equation Dependent Variable: D(M4) Method: Least Squares Date: 04/28/13 Time: 01:33 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   M4(-1) -0.318068 0.081270 -3.913700 0.0002 C 6555.726 2232.540 2.936442 0.0043 R-squared 0.160696     Mean dependent var 115.6341 Adjusted R-squared 0.150204     S.D. dependent var 14821.15 S.E. of regression 13662.78     Akaike info criterion 21.90683 Sum squared resid 1.49E+10     Schwarz criterion 21.96553 Log likelihood -896.1799     Hannan-Quinn criter. 21.93039 F-statistic 15.31705     Durbin-Watson stat 1.984925 Prob(F-statistic) 0.000190 Null Hypothesis: D(M4) has a unit root Exogenous: Constant Bandwidth: 58 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -21.89235  0.0001 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  2.15E+08 HAC corrected variance (Bartlett kernel)  17177117 Phillips-Perron Test Equation Dependent Variable: D(M4,2) Method: Least Squares Date: 05/02/13 Time: 15:30 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(M4(-1)) -1.152918 0.111836 -10.30899 0.0000 C 166.6672 1648.427 0.101107 0.9197 R-squared 0.573607     Mean dependent var -167.6790 Adjusted R-squared 0.568210     S.D. dependent var 22573.14 S.E. of regression 14832.97     Akaike info criterion 22.07147 Sum squared resid 1.74E+10     Schwarz criterion 22.13060 Log likelihood -891.8947     Hannan-Quinn criter. 22.09519 F-statistic 106.2753     Durbin-Watson stat 2.058068 Prob(F-statistic) 0.000000 Null Hypothesis: U has a unit root Exogenous: Constant Lag Length: 5 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -2.152618  0.2252 Test critical values: 1% level -3.517847 5% level -2.899619 10% level -2.587134 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(U) Method: Least Squares Date: 05/02/13 Time: 15:14 Sample (adjusted): 1993Q4 2012Q4 Included observations: 77 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   U(-1) -0.036620 0.017012 -2.152618 0.0348 D(U(-1)) 0.273218 0.109319 2.499264 0.0148 D(U(-2)) 0.161918 0.094842 1.707243 0.0922 D(U(-3)) -0.147097 0.094702 -1.553261 0.1249 D(U(-4)) 0.524342 0.093238 5.623716 0.0000 D(U(-5)) -0.318020 0.107988 -2.944956 0.0044 C 0.228001 0.115064 1.981518 0.0515 R-squared 0.633756     Mean dependent var -0.031635 Adjusted R-squared 0.602364     S.D. dependent var 0.361787 S.E. of regression 0.228137     Akaike info criterion -0.031230 Sum squared resid 3.643266     Schwarz criterion 0.181844 Log likelihood 8.202338     Hannan-Quinn criter. 0.053998 F-statistic 20.18823     Durbin-Watson stat 1.971226 Prob(F-statistic) 0.000000 Null Hypothesis: D(U) has a unit root Exogenous: Constant Lag Length: 4 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -3.254498  0.0206 Test critical values: 1% level -3.517847 5% level -2.899619 10% level -2.587134 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(U,2) Method: Least Squares Date: 05/02/13 Time: 15:40 Sample (adjusted): 1993Q4 2012Q4 Included observations: 77 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(U(-1)) -0.509614 0.156588 -3.254498 0.0017 D(U(-1),2) -0.177127 0.166246 -1.065450 0.2903 D(U(-2),2) -0.001109 0.146776 -0.007555 0.9940 D(U(-3),2) -0.149496 0.133437 -1.120349 0.2663 D(U(-4),2) 0.368688 0.108055 3.412036 0.0011 C -0.013098 0.027031 -0.484532 0.6295 R-squared 0.849621     Mean dependent var -0.002489 Adjusted R-squared 0.839031     S.D. dependent var 0.582993 S.E. of regression 0.233903     Akaike info criterion 0.006894 Sum squared resid 3.884438     Schwarz criterion 0.189528 Log likelihood 5.734573     Hannan-Quinn criter. 0.079946 F-statistic 80.22792     Durbin-Watson stat 1.992930 Prob(F-statistic) 0.000000 Null Hypothesis: U has a unit root Exogenous: Constant Bandwidth: 4 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -1.543624  0.5067 Test critical values: 1% level -3.512290 5% level -2.897223 10% level -2.585861 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.125809 HAC corrected variance (Bartlett kernel)  0.147595 Phillips-Perron Test Equation Dependent Variable: D(U) Method: Least Squares Date: 05/02/13 Time: 15:15 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   U(-1) -0.034027 0.022469 -1.514372 0.1339 C 0.212207 0.158349 1.340127 0.1840 R-squared 0.027868     Mean dependent var -0.019950 Adjusted R-squared 0.015716     S.D. dependent var 0.361957 S.E. of regression 0.359102     Akaike info criterion 0.813667 Sum squared resid 10.31634     Schwarz criterion 0.872367 Log likelihood -31.36034     Hannan-Quinn criter. 0.837234 F-statistic 2.293321     Durbin-Watson stat 2.552362 Prob(F-statistic) 0.133873 Null Hypothesis: D(U) has a unit root Exogenous: Constant Bandwidth: 4 (Newey-West automatic) using Bartlett kernel Adj. t-Stat   Prob.* Phillips-Perron test statistic -11.58210  0.0001 Test critical values: 1% level -3.513344 5% level -2.897678 10% level -2.586103 *MacKinnon (1996) one-sided p-values. Residual variance (no correction)  0.117611 HAC corrected variance (Bartlett kernel)  0.229106 Phillips-Perron Test Equation Dependent Variable: D(U,2) Method: Least Squares Date: 05/02/13 Time: 15:31 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   D(U(-1)) -1.292366 0.106603 -12.12315 0.0000 C -0.031069 0.038645 -0.803965 0.4238 R-squared 0.650397     Mean dependent var -0.004835 Adjusted R-squared 0.645972     S.D. dependent var 0.583626 S.E. of regression 0.347259     Akaike info criterion 0.746889 Sum squared resid 9.526506     Schwarz criterion 0.806011 Log likelihood -28.24899     Hannan-Quinn criter. 0.770609 F-statistic 146.9709     Durbin-Watson stat 1.685010 Prob(F-statistic) 0.000000 Appendix 2: Testing Autocorrelation Date: 04/28/13 Time: 01:37 Sample: 1992Q2 2012Q4 Included observations: 83 Autocorrelation Partial Correlation AC   PAC  Q-Stat  Prob       . |******|       . |******| 1 0.854 0.854 62.792 0.000       . |***** |       **| . | 2 0.674 -0.207 102.34 0.000       . |**** |       . |*. | 3 0.542 0.095 128.29 0.000       . |*** |       . |*. | 4 0.466 0.078 147.65 0.000       . |*** |       . |** | 5 0.471 0.244 167.70 0.000       . |*** |       . | . | 6 0.482 -0.005 189.03 0.000       . |*** |       .*| . | 7 0.440 -0.106 207.03 0.000       . |*** |       . | . | 8 0.362 -0.056 219.37 0.000       . |** |       . |*. | 9 0.331 0.213 229.85 0.000       . |** |       . |*. | 10 0.350 0.100 241.66 0.000       . |*** |       . | . | 11 0.393 0.049 256.77 0.000       . |*** |       .*| . | 12 0.397 -0.133 272.44 0.000       . |** |       . | . | 13 0.349 -0.017 284.73 0.000       . |** |       .*| . | 14 0.258 -0.093 291.52 0.000       . |*. |       .*| . | 15 0.165 -0.066 294.34 0.000       . |*. |       .*| . | 16 0.099 -0.141 295.37 0.000       . |*. |       . | . | 17 0.074 0.023 295.96 0.000       . | . |       .*| . | 18 0.052 -0.071 296.24 0.000       . | . |       . | . | 19 0.013 -0.020 296.26 0.000       . | . |       . | . | 20 -0.019 -0.015 296.30 0.000       . | . |       . | . | 21 -0.043 0.010 296.51 0.000       .*| . |       .*| . | 22 -0.074 -0.145 297.15 0.000       .*| . |       .*| . | 23 -0.109 -0.083 298.54 0.000       .*| . |       .*| . | 24 -0.158 -0.129 301.52 0.000       **| . |       . | . | 25 -0.212 0.016 306.97 0.000       **| . |       . | . | 26 -0.245 -0.003 314.41 0.000       **| . |       .*| . | 27 -0.283 -0.104 324.50 0.000       **| . |       . | . | 28 -0.293 0.058 335.48 0.000       **| . |       . | . | 29 -0.308 -0.038 347.83 0.000      ***| . |       .*| . | 30 -0.348 -0.102 363.95 0.000      ***| . |       . | . | 31 -0.379 -0.043 383.40 0.000      ***| . |       . | . | 32 -0.394 -0.031 404.84 0.000      ***| . |       . | . | 33 -0.403 -0.033 427.74 0.000      ***| . |       . |*. | 34 -0.384 0.084 448.93 0.000      ***| . |       . | . | 35 -0.356 0.036 467.51 0.000       **| . |       . |*. | 36 -0.327 0.149 483.61 0.000 Appendix 3: Model Specifications Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:14 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Convergence achieved after 3 iterations Variable Coefficient Std. Error t-Statistic Prob.   C 2.071798 0.351497 5.894210 0.0000 AR(1) 0.856441 0.051609 16.59474 0.0000 R-squared 0.774892     Mean dependent var 2.189130 Adjusted R-squared 0.772078     S.D. dependent var 0.947676 S.E. of regression 0.452431     Akaike info criterion 1.275727 Sum squared resid 16.37554     Schwarz criterion 1.334427 Log likelihood -50.30481     Hannan-Quinn criter. 1.299294 F-statistic 275.3852     Durbin-Watson stat 1.340784 Prob(F-statistic) 0.000000 Inverted AR Roots       .86 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:14 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Convergence achieved after 3 iterations Variable Coefficient Std. Error t-Statistic Prob.   C 2.111065 0.233754 9.031135 0.0000 AR(2) 0.675711 0.077475 8.721609 0.0000 R-squared 0.490541     Mean dependent var 2.175392 Adjusted R-squared 0.484092     S.D. dependent var 0.945329 S.E. of regression 0.678999     Akaike info criterion 2.087987 Sum squared resid 36.42213     Schwarz criterion 2.147109 Log likelihood -82.56348     Hannan-Quinn criter. 2.111708 F-statistic 76.06647     Durbin-Watson stat 0.772412 Prob(F-statistic) 0.000000 Inverted AR Roots       .82          -.82 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:15 Sample (adjusted): 1993Q1 2012Q4 Included observations: 80 after adjustments Convergence achieved after 3 iterations Variable Coefficient Std. Error t-Statistic Prob.   C 2.133890 0.194445 10.97426 0.0000 AR(3) 0.545512 0.090154 6.050896 0.0000 R-squared 0.319451     Mean dependent var 2.169760 Adjusted R-squared 0.310726     S.D. dependent var 0.949925 S.E. of regression 0.788651     Akaike info criterion 2.387698 Sum squared resid 48.51375     Schwarz criterion 2.447248 Log likelihood -93.50791     Hannan-Quinn criter. 2.411573 F-statistic 36.61334     Durbin-Watson stat 0.536266 Prob(F-statistic) 0.000000 Inverted AR Roots       .82     -.41+.71i   -.41-.71i Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 12:12 Sample: 1992Q2 2012Q4 Included observations: 83 Convergence achieved after 7 iterations MA Backcast: 1992Q1 Variable Coefficient Std. Error t-Statistic Prob.   C 2.207322 0.122636 17.99896 0.0000 MA(1) 0.963302 0.036683 26.26033 0.0000 R-squared 0.659646     Mean dependent var 2.214301 Adjusted R-squared 0.655444     S.D. dependent var 0.969394 S.E. of regression 0.569023     Akaike info criterion 1.734011 Sum squared resid 26.22679     Schwarz criterion 1.792296 Log likelihood -69.96145     Hannan-Quinn criter. 1.757427 F-statistic 156.9875     Durbin-Watson stat 1.000403 Prob(F-statistic) 0.000000 Inverted MA Roots      -.96 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 12:12 Sample: 1992Q2 2012Q4 Included observations: 83 Convergence achieved after 4 iterations MA Backcast: 1991Q4 1992Q1 Variable Coefficient Std. Error t-Statistic Prob.   C 2.182557 0.127667 17.09568 0.0000 MA(2) 0.674000 4.01E-06 168037.1 0.0000 R-squared 0.494038     Mean dependent var 2.214301 Adjusted R-squared 0.487791     S.D. dependent var 0.969394 S.E. of regression 0.693783     Akaike info criterion 2.130487 Sum squared resid 38.98814     Schwarz criterion 2.188772 Log likelihood -86.41520     Hannan-Quinn criter. 2.153903 F-statistic 79.09096     Durbin-Watson stat 0.568923 Prob(F-statistic) 0.000000 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 12:12 Sample: 1992Q2 2012Q4 Included observations: 83 Failure to improve SSR after 9 iterations MA Backcast: 1991Q3 1992Q1 Variable Coefficient Std. Error t-Statistic Prob.   C 2.219698 0.130996 16.94474 0.0000 MA(3) 0.377291 0.099195 3.803535 0.0003 R-squared 0.199183     Mean dependent var 2.214301 Adjusted R-squared 0.189296     S.D. dependent var 0.969394 S.E. of regression 0.872833     Akaike info criterion 2.589657 Sum squared resid 61.70886     Schwarz criterion 2.647942 Log likelihood -105.4708     Hannan-Quinn criter. 2.613073 F-statistic 20.14672     Durbin-Watson stat 0.433411 Prob(F-statistic) 0.000023 Inverted MA Roots  .36+.63i      .36-.63i        -.72 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:29 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Convergence achieved after 7 iterations MA Backcast: 1992Q2 Variable Coefficient Std. Error t-Statistic Prob.   C 2.133104 0.294121 7.252469 0.0000 AR(1) 0.764803 0.073038 10.47126 0.0000 MA(1) 0.494341 0.106305 4.650225 0.0000 R-squared 0.809684     Mean dependent var 2.189130 Adjusted R-squared 0.804865     S.D. dependent var 0.947676 S.E. of regression 0.418627     Akaike info criterion 1.132226 Sum squared resid 13.84463     Schwarz criterion 1.220277 Log likelihood -43.42127     Hannan-Quinn criter. 1.167577 F-statistic 168.0490     Durbin-Watson stat 2.011674 Prob(F-statistic) 0.000000 Inverted AR Roots       .76 Inverted MA Roots      -.49 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:29 Sample (adjusted): 1992Q3 2012Q4 Included observations: 82 after adjustments Convergence achieved after 47 iterations MA Backcast: 1992Q1 1992Q2 Variable Coefficient Std. Error t-Statistic Prob.   C 2.073988 0.385490 5.380130 0.0000 AR(1) 0.879841 0.049997 17.59783 0.0000 MA(2) -0.090804 0.000480 -189.2244 0.0000 R-squared 0.777735     Mean dependent var 2.189130 Adjusted R-squared 0.772109     S.D. dependent var 0.947676 S.E. of regression 0.452401     Akaike info criterion 1.287406 Sum squared resid 16.16870     Schwarz criterion 1.375457 Log likelihood -49.78364     Hannan-Quinn criter. 1.322757 F-statistic 138.2162     Durbin-Watson stat 1.335961 Prob(F-statistic) 0.000000 Inverted AR Roots       .88 Inverted MA Roots       .30          -.30 Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:30 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Convergence achieved after 51 iterations MA Backcast: OFF (Roots of MA process too large) Variable Coefficient Std. Error t-Statistic Prob.   C 2.152006 0.115159 18.68727 0.0000 AR(2) 0.032848 0.066613 0.493113 0.6233 MA(1) 1.132504 0.065244 17.35791 0.0000 R-squared 0.733721     Mean dependent var 2.175392 Adjusted R-squared 0.726893     S.D. dependent var 0.945329 S.E. of regression 0.494026     Akaike info criterion 1.463875 Sum squared resid 19.03678     Schwarz criterion 1.552558 Log likelihood -56.28693     Hannan-Quinn criter. 1.499456 F-statistic 107.4628     Durbin-Watson stat 0.829280 Prob(F-statistic) 0.000000 Inverted AR Roots       .18          -.18 Inverted MA Roots      -1.13 Estimated MA process is noninvertible Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 11:30 Sample (adjusted): 1992Q4 2012Q4 Included observations: 81 after adjustments Convergence achieved after 51 iterations MA Backcast: 1992Q2 1992Q3 Variable Coefficient Std. Error t-Statistic Prob.   C 2.153499 0.196349 10.96772 0.0000 AR(2) 0.447279 0.100540 4.448755 0.0000 MA(2) 0.489943 2.78E-05 17605.88 0.0000 R-squared 0.535223     Mean dependent var 2.175392 Adjusted R-squared 0.523306     S.D. dependent var 0.945329 S.E. of regression 0.652684     Akaike info criterion 2.020886 Sum squared resid 33.22770     Schwarz criterion 2.109569 Log likelihood -78.84588     Hannan-Quinn criter. 2.056467 F-statistic 44.91130     Durbin-Watson stat 0.892009 Prob(F-statistic) 0.000000 Inverted AR Roots       .67          -.67 Appendix 4: Autocorrelation Test in Phillips Curve Model Date: 04/28/13 Time: 13:02 Sample: 1992Q3 2012Q4 Included observations: 82 Autocorrelation Partial Correlation AC   PAC  Q-Stat  Prob       . |**** |       . |**** | 1 0.613 0.613 31.960 0.000       . |*** |       . | . | 2 0.396 0.031 45.428 0.000       . |*. |       .*| . | 3 0.206 -0.077 49.138 0.000       . |*. |       . | . | 4 0.098 -0.014 49.984 0.000       . | . |       .*| . | 5 -0.025 -0.103 50.041 0.000       . |*. |       . |** | 6 0.079 0.236 50.613 0.000       . | . |       .*| . | 7 0.018 -0.137 50.643 0.000       . | . |       . | . | 8 -0.008 -0.034 50.649 0.000       . | . |       . |*. | 9 0.032 0.114 50.747 0.000       . |*. |       . | . | 10 0.103 0.070 51.767 0.000       . |*. |       . | . | 11 0.107 0.049 52.874 0.000       . |*. |       . | . | 12 0.164 0.035 55.525 0.000       . |*. |       . | . | 13 0.141 -0.019 57.518 0.000       . | . |       .*| . | 14 -0.015 -0.186 57.540 0.000       .*| . |       .*| . | 15 -0.124 -0.081 59.127 0.000       .*| . |       . | . | 16 -0.114 0.065 60.488 0.000       .*| . |       . | . | 17 -0.089 0.054 61.334 0.000       .*| . |       . | . | 18 -0.084 -0.064 62.091 0.000       .*| . |       .*| . | 19 -0.114 -0.167 63.501 0.000       .*| . |       . | . | 20 -0.109 0.052 64.817 0.000       .*| . |       . | . | 21 -0.156 -0.063 67.561 0.000       .*| . |       .*| . | 22 -0.184 -0.131 71.429 0.000       .*| . |       . | . | 23 -0.165 -0.029 74.607 0.000       .*| . |       . | . | 24 -0.110 0.050 76.034 0.000       .*| . |       . | . | 25 -0.096 0.025 77.146 0.000       .*| . |       .*| . | 26 -0.100 -0.090 78.383 0.000       . | . |       . |*. | 27 -0.059 0.102 78.818 0.000       . | . |       . | . | 28 -0.061 -0.000 79.290 0.000       . | . |       . | . | 29 -0.034 -0.026 79.440 0.000       . | . |       . | . | 30 -0.020 -0.059 79.493 0.000       . | . |       . |*. | 31 0.042 0.164 79.728 0.000       . | . |       . | . | 32 0.020 0.059 79.784 0.000       . | . |       . | . | 33 0.065 -0.007 80.381 0.000       . |*. |       . | . | 34 0.084 0.061 81.406 0.000       . | . |       . | . | 35 0.065 -0.004 82.033 0.000       . | . |       . | . | 36 0.037 -0.003 82.238 0.000 Appendix 5: Ramsey RESET Test for Model Misspecification Ramsey RESET Test Equation: UNTITLED Specification: INFL C DU Omitted Variables: Squares of fitted values Value df Probability t-statistic  1.476660  79  0.1437 F-statistic  2.180524 (1, 79)  0.1437 Likelihood ratio  2.232656  1  0.1351 F-test summary: Sum of Sq. df Mean Squares Test SSR  1.846515  1  1.846515 Restricted SSR  68.74545  80  0.859318 Unrestricted SSR  66.89893  79  0.846822 Unrestricted SSR  66.89893  79  0.846822 LR test summary: Value df Restricted LogL -109.1243  80 Unrestricted LogL -108.0080  79 Unrestricted Test Equation: Dependent Variable: INFL Method: Least Squares Date: 04/28/13 Time: 13:05 Sample: 1992Q3 2012Q4 Included observations: 82 Variable Coefficient Std. Error t-Statistic Prob.   C -9.560003 7.965506 -1.200175 0.2337 DU -5.853305 4.388742 -1.333709 0.1861 FITTED^2 2.402849 1.627219 1.476660 0.1437 R-squared 0.080368     Mean dependent var 2.189130 Adjusted R-squared 0.057086     S.D. dependent var 0.947676 S.E. of regression 0.920229     Akaike info criterion 2.707512 Sum squared resid 66.89893     Schwarz criterion 2.795562 Log likelihood -108.0080     Hannan-Quinn criter. 2.742863 F-statistic 3.451952     Durbin-Watson stat 0.351455 Prob(F-statistic) 0.036539 Read More