The relationship between growth rate of money supply and inflation rate is frequently examined by economists. An economist suggested that inflation rate and growth rate of money has linear relationship and this relation is subject to seasonality. The parameters of the relationship are thought to vary between quarters and a researcher defined to following model: It=0+2S2t+3S3t+4S4t+4Mt+5T+t where Mt,It and T are the growth rate of money, inflation rate and time trend respectively. The seasonal dummies are defined as S2t takes the value of 1 for the second-quarter observations and 0 otherwise; S3t takes the value of 1 for the third-quarter observations and 0 otherwise; Sartakes the value of 1 for the fourthquarter observations and 0 otherwise. Using quarterly data for 20 years, a researcher obtains 80 observations and estimated multiple models. The estimation results are given below: Model 1:I =1.356.81.32.18S2+0.88S3+2.35S4+1.25M SSR =22.58 Model 2:I=4.551.12S2+0.67S3+1.94S4+1.03M+3.8T SSR =12.22 Model 3:I=7.56+2.74M SSR =43.71 Model 4:M=5.911.42S2.27+1.74S4+2.42T SSR =32.22 Model 5:e^=i.28.99+3.84S2+2.96M4.7311 SSR =52.44 Model 6:I=9.63+5.74T SSR =48.53 a) What does economic theory suggest about the sign of money growth coefficient in the model? Are these results consistent with theory? b) Is there a time trend in inflation rate? Explain your reasoning by providing statistical evidence. c) Is there a time trend in money growth rate? Explain your reasoning by providing statistical evidence. d) Test the hypothesis that there is no statistical difference between the first quarter and second quarter inflation equations. e) Can you test the hypothesis that there is no statistical difference between the second quarter and third quarter inflation equations? If yes, provide the test result. If no, explain your reasoning. f) Discuss whether seasons jointly affect the relationship between growth rate of money and inflation. Explain your reasoning by providing statistical evidence. g) Choose the best model to explain relationship between money and inflation. In addition to statistical tests, employ model selection criteria. h) Calculate the estimated equations for Inflation in the third and first quarter by using the above results