The General Theory of Employment Interest and Money - Research Paper Example

 The General Theory of Employment Interest and Money Abstract This paper is meant to work upon the relationship between the systematic money supply actions and the inflation rate in the context of the United States. For that purpose a simple linear model has been chosen with the CPI Inflation being the dependent variable and both the current and the lagged money supplies (represented by M1) being the independent variables. The result of this study reinforces two major findings of Friedman (1971) and his successors: firstly, the effect of any systematic monetary policy changes on the inflation rate is not instantaneous and it would take at least a year to have any effect on the inflation and secondly, the postulated lagged relationship between the money supply and the inflation rate is a more prominent component of the inflation persistence than the inflation inertia itself. Chapter 1 – Introduction & Theoretical Background 1.1 Introduction Background After the Great Depression, 1929 the idea of Classical Dichotomy which states that the real and the nominal macroeconomic variables are determined in the separate markets, i.e. none of them can affect each other, got a severe jolt. In 1933, John Maynard Keynes in his revolutionary book, The General Theory of Employment Interest and Money, claimed that the Classical Dichotomy does not hold in the short run, i.e. the nominal variables can influence the real variables in the short run and vice versa—the economy is no more dichotomized between the real and the nominal sectors. Later on, in 1960s Prof Milton Friedman postulated his famous ‘Quantity Theory of Money’, in a simple form which says that: MV= PY. M=Money supply, P=Price index, Y=Gross Output and V=Velocity of money (how frequently money changes hands). From this equation we may write: % change in M= % change in P, for a given output and velocity of money. Thus for a given output and velocity of money (which usually remains constant for a long period of time) the rate of change of money supply exactly matches the rate of inflation. Prof Friedman proved this more empirically than theoretically in the U.S. context. According to him, “Inflation is always and everywhere a monetary phenomenon”. Though, the link between the money supply and changes in inflation is not instantaneous. In Dec, 1971 Milton Friedman presented a work at American Economic Association meetings, regarding the lagged effect of money supply on the inflation rate. His estimates showed the highest correlation with 20 months’ lagged money supply (M1). Since then for many countries that have been able to arrest inflation to a moderate level, Friedman’s findings have been a ‘Rule of Thumb’ for controlling inflation—which is why this study of ‘Inflation and Money Supply’ is so important. Purpose of the Study The purpose of our article is to find a relation between the inflation rate and the money supply in the context of the U.S. economy and in this case we have chosen the money supply index M1 (which equals currency in circulation + demand deposits + travelers’ checks) and we have done the statistical analysis on the basis of weekly data on CPI Inflation and M1, for the period of February, 2001 to January 2005. This paper intends to find whether Friedman’s postulates still hold in the recent years for the U.S. economy. The choice of the lag length between the inflation and money supply is very crucial since they provide important information for the appropriate policy formulations. Policy makers should keep these in mind while developing policy mechanisms for controlling inflation, especially for the countries which pursue the policy of ‘Inflation Targeting’, i.e. the policy of pegging the money supply at a level such that the inflation cannot exceed beyond a predetermined rate. For that purpose policy makers should know exactly what level of liquid money should be allowed to circulate by the central bank in order to fix the inflation rate at a pegged level. In this study we have selected a period of political and economic stability in the U.S. and deliberately kept the turbulent years of 2006-08, out of the analysis. Fed’s monetary policy for this period has confronted severe criticisms from many noted economists of recent time and it has been convicted for its monetary measures, which is supposed to have laid the foundation of the ongoing financial crisis that actually originated from the U.S. real estate sector (Taylor’s 2007). Research Questions and Importance Our study of money supply and the inflation rate, also provides us the timing of effective monetary control, e.g. if we have to regulate inflation to a specified value and at a certain period, we could know at which period the money supply should be controlled. Generally in order to lower the rate of inflation a contractionary monetary policy (policy of reducing money supply) is taken up, but according to Keynesian theory, this would reduce output and employment in the short run. Thus the output loss in the short run should be assessed vis-à-vis the moderation of inflation in the long run, before any contractionary policy is formulated—hence reducing inflation through the ‘monetary tightening’ comes at the cost of short run output losses. The following diagram plots the growth rate of money supply (M1) and the corresponding CPI inflation rate. From the scatter plot it is quite evident that the years of high money growth are in general associated with high inflation rate which is the main plank of our theory. Figure: 1 (Source: Federal Reserve) Chapter 2 – Literature Review The literature of Quantity Theory of Money and the lagged response of the inflation to the money supply growth are dated back to Friedman’s paper presented at American Economic Association in 1971. Bernanke, Laubach, Mishkin and Posen (1999) found a two years’ lag between the monetary policy change and its effect on inflation. Gerlach and Svensson (2001), in a study under the European Central Bank reported an 18 month lag between the policy changes and the response, in the Euro area. The studies of Sbordone (1998) and Gali & Gertler (1999) are based on the New Keynesian Phillips Curve and they have modeled the path of inflation with dynamic general equilibrium models. According to their study, there is no inherent persistence of inflation in the context of U.S. economy, i.e. there is no intrinsic inertia in inflation which has also been backed by the findings of Erceg and Levin(2001). Hence all these findings assert that the non-systematic components do not govern the inflation behavior, rather the systematic monetary policy changes have crucial effects on the behavior of inflation albeit with time lags. Nicoletta Batini and Edward Nelson (January 2002) in an article named The Lag from Monetary Policy to Inflation: Friedman Revisited (External MPC Unit, Bank of England), have reaffirmed the findings of Friedman (1971) that any systematic monetary policy changes take at least a year to impart any effect on the inflation both in the context of US and UK. Keith M. Carlson has estimated a simple econometric model of inflation rate (based on GNP Deflator) and lagged changes in the money supply in his paper: ‘The Lag from Money to Prices’ (October, 1980; Federal Reserve Bank of St. Louis). Using quarterly data for U.S. and incorporating lags up to 20 quarters, Carlson showed that a 1% change in money supply results in 1% change in inflation in the long run. Our simple analysis seeks to find the postulated lagged relationship between money supply and inflation on the basis of recent data in the context of U.S. economy and ends up at the conclusion that the systematic monetary policy changes can not significantly influence the inflation path, within less than a year time period. Chapter 3 - Methodology 3.1 The Sample Regression Function The purpose of the paper is to judge the empirical validity of the classical model whether inflation is a result of a change in money supply or not. However, the change in the present flow of money supply is not the only variable that affects present inflation. It also depends upon previous money supply flows as has been explained in the introduction to this paper. In order to incorporate the previous periods’ flows, we have considered lagged values of money supply, viz, Mt-4, Mt-8, Mt-12 besides the present period’s money supply, i.e., Mt where t indicates the current period. However, despite the availability, the immediate lag is not been considered to avoid Inflation in our model has been calculated by taking the difference between the current period’s and the previous period’s consumer price indices. So, we want to test the model, CPI Inflation* = a* + b1* Mt + b2* Mt-4 + b3*Mt-8 + b4*Mt-12 where CPI Inflation* = CPI inflation estimated by sample regression function. a* = the estimated sample coefficient of constant term. b1* = the estimated sample correlation coefficient of present flow of money supply, i.e., Mt. b2* = the estimated sample correlation coefficient of money supply lagged by four periods, i.e., Mt-4. b3* = the estimated sample correlation coefficient of money supply lagged by eight periods, i.e., Mt-8. b4* = the estimated sample correlation coefficient of money supply lagged by twelve periods, i.e., Mt-12. 3.2 Hypothesis Testing In order to check the validity of the model specified above, we need to test some null hypotheses which are, 1. H01 : the coefficient of current flow of money supply, Mt is 0, i.e., b1* = 0 against the alternative hypothesis H11: b1* ≠ 0 2. H02 : the coefficient of first quarter lagged money supply Mt-4 is 0, i.e., b2* = 0 against H12 : b2* ≠ 0 3. H03 : the coefficient of second quarter lagged money supply Mt-8 is 0, i.e., b3* = 0 against H13 : b3* ≠ 0 4. H04 : the coefficient of third quarter lagged money supply Mt-12 is 0, i.e., b4* = 0 against H14 : b4* ≠ 0 5. H05 : the coefficients of all explanatory variables are 0, i.e., b1* = b2* = b3* = b4* = 0 against H13 : b1* ≠ b2* ≠ b3* ≠ b4* ≠ 0. The first four null hypotheses assume that the respective variable cannot significantly explain variations in the dependent variable. Their validity is checked with the help of Student’s t-test. On the other hand, that of the fifth one (H05) assumes that all the variables taken together cannot explain variations in the dependent variable CPI Inflation significantly and we test its validity through F-test. 3.3 Selection of Secondary data The data used in this paper are those of the Monetary Stock measures and CPI inflation. The monetary stock measures data are those for M1, obtained from the historical data on money stock in USA as is released on a monthly basis by the Federal Reserve. The data on CPI inflation is referred from the historical data on CPI-U inflation compiled by the Bureau of Labor Statistics, USA with the base year 1982. 3.4 Data Processing From the population data so obtained, a random sample of 48 observations has been drawn from February 2001 to January 2005. This data had been copied to an Excel sheet and then to an SPSS worksheet. The necessary commands had been followed to obtain the relevant statistical results. Chapter 4 – Analysis of Results However before progressing with the analysis of the results obtained from sample regression, it is necessary to check the reliability of the dataset first. Here reliability implies a check whether the explanatory variables or the independent variables are describing the same feature of a variable or not in an unidimensional way, i.e., if the present period money supply and its lagged values can reliably and consistently describe a single underlying feature of CPI inflation or not. Cronbach’s Alpha is an effective way of testing the reliability of a model. It was introduced in 1951 by Lee Cronbach and is an extension of the Kuder-Richardson Formula. 4.1 – Reliability Check using Cronbach’s Alpha The test statistic of Cronbach’s Alpha is, Where N = number of items or components. c-bar = average inter-item covariance between all the explanatory variables v-bar = average variance of the predicted output. Now, the higher the value of alpha, the more reliable is the model said to be. From the test statistic it is clear that the value of α rises as the number of components and the inter-item covariance rises or the average variance falls. This makes sense because, 1. the higher the inter item covariance, the higher would be the inter-item correlation, thus indicating that the better can the components describe a single underlying feature of the dependent variable. (Introduction to SAS,) 2. Again, higher the number of components, the higher will be the effectiveness of the test and so alpha would be higher. 3. A low average variance of the test results will imply a better test prediction and thus a higher reliability of the model. Generally a rule of thumb is that, an alpha value greater than 0.7 for a model is granted to be one with a high reliability. In the present study, we have considered five components in all and it is found that the value of alpha is 0.9209, which is a clear indicator of the reliability of the model. The detail of the test is being presented in the appendix to the paper. 4.2 – Data Analysis and Interpretation The sample regression function when estimated considering a sample of 48 monthly observations ranging from February 2001 to January 2005, out of a population of 1000 observations, yielded the following model CPI Inflation* = -9.540 + 0.015Mt – 0.019Mt-4 + 0.003Mt-8 + 0.013Mt-12 (-7.651) (2.859) (-3.361) (0.664) (3.028) Here the t-statistics are given in parentheses. 4.2.1 – Sign of the estimated correlation coefficients It is a common knowledge that a higher money supply in the present and more importantly in the previous periods leads to a higher inflation. The reasons behind this statement have been already discussed in the theoretical background and literature of this paper. However, it is found that the sign of the first quarter lag, i.e., Mt-4 is negative although those of the others are positive. The sign of the coefficients must normally be positive as per the theory goes. Hence, this anomaly must be attributed to sampling fluctuations. 4.2.2 – Statistical Significance of the explanatory variables The statistical significance of a variable implies the significance with which the variable can explain the variations in another variable which is the dependent variable. Now the null hypothesis assumes that the predicted value of a coefficient is 0, indicating the assumption that the variable cannot significantly affect the variations in the dependent variable. So, if a variable is statistically significant, then the null hypothesis corresponding to that variable must be rejected. Now, this significance test can be conducted in two ways – (i) By checking the confidence interval for a given level of significance, i.e., checking if the unstandardized estimate of the coefficient falls within the acceptance region. (ii) Through conducting statistical tests. In case of Classical Linear Regression Models using Ordinary Least Squares, the statistical test conducted to test the significance of a particular correlation coefficient is the Student’s t-test. (iii) Apart from the t-test to check the individual significances, it is also important to find if the variables can together explain any variation in the dependent variable. This is tested by conducting an F-test. 4.2.2(a) – Confidence Interval In Student’s t-tests, the confidence interval is given by Pr [-ta/2 * se(b*) + b0 ≤ b* ≤ ta/2 * se(b*) + b0] = 1 - a Where a = level of significance b* = estimated value of the correlation coefficient se(b*) = standard error of the estimated correlation coefficient b0 = value of the correlation coefficient according to the null hypothesis. The confidence interval denotes the region of acceptance, i.e., the true population parameter must lie within the given range. If the estimated sample coefficient falls within this interval, then it will be accepted as a good estimator of the true population parameter. In the present case, it is found that the estimated coefficients of all the explanatory variables fall within their respective confidence intervals suggesting a good estimate of the population parameter. 4.2.2(b) – Student’s t-test The Student’s t-test statistic is defined as, | t | = b* / se(b*) where b* = estimated sample parameter and se(b*) = standard error of the estimated sample parameter b* Looking at the value of estimated t, we may arrive at two different conclusions accordingly, (i) If the estimated | t | > tabulated t, we reject the null hypothesis at the given degrees of freedom and level of significance. (ii) If the estimated | t | < tabulated t, we do not reject the null hypothesis at the given degrees of freedom and level of significance. In this case, the degrees of freedom = 47 and considering the level of significance = 5% = 0.05, tabulated t = 2.028. Let us now look at the estimated | t | for all the variables. For Mt, estimated | t | = 2.859 > 2.028 For Mt-4, estimated | t | = 3.361 > 2.028 For Mt-8, estimated | t | = 0.664 < 2.028 For Mt-12, estimated | t | = 3.028 > 2.028 In any test, significance can also be tested by comparing the p-value with the given level of significance which is usually standardized at 5%. P-value or probability value is defined as the probability of committing a Type-I error, i.e., the probability of rejecting the null hypothesis when it is true. Speaking more technically, the probability value gives the lowest level of significance at which a null hypothesis could be rejected. The statistical findings in this study have depicted that the p-values of all the explanatory variables except that of the second quarter lagged money supply (Mt-8), and the constant term is sufficiently low, viz., lower than 5% level of significance. Hence, from both the examinations, it can be said that all the individual variables except Mt-8 can significantly explain the variations in the dependent variable, i.e., CPI inflation. 4.2.2(b) – F-test The F-test is defined as, F = (ESS/df)/ (RSS/df) Where ESS = Explained Sum of Squares RSS = Residual Sum of Squares df = Degrees of Freedom for each. Again, looking at the value of estimated F, we may arrive at two different conclusions accordingly, (iii) If the estimated | t | > tabulated t, we reject the null hypothesis at the given degrees of freedom and level of significance. (iv) If the estimated | t | < tabulated t, we do not reject the null hypothesis at the given degrees of freedom and level of significance. In this case, the degrees of freedom = 4, 43 and considering the level of significance = 5% = 0.05, tabulated F = 2.62. However, the estimated F = 36.279 Like in the previous case, here also we will take the support of the p-value of the estimated statistic. It is found from the ANOVA table, that the corresponding p-value is very low, viz., 0.000. Hence, it can be interpreted that the coefficients taken together can indeed significantly explain the variations in the dependent variable, CPI inflation. 4.2.3 – Interpretation of Coefficient of Determination From the model summary it is found that the coefficient of determination, i.e., R is quite high viz., 0.878. A high R implies a good fit, i.e., the estimated sample regression equation can well explain the actual population regression function. A rule of thumb is that, an R greater than 0.6 is sufficient enough to brand a model as a good fit. So, it can be said that the model being fitted in this paper is a good one. However, the Coefficient of Determination keeps on getting higher as we go on adding more and more explanatory variables. But, this will go on reducing the degrees of freedom of the model and hence, might not give a correct prediction after a certain point of time. So, a better prediction is offered by the Adjusted R square which adjusts even for the degrees of freedom. The Adjusted R square in this case is 0.771, which too implies a good fit. So, we may say that the model being considered is a good fit of the population regression function. 4.2.4 – Residual Plots The residual plot shows the presence of any autocorrelation in the random error terms of the sample. The more scattered the residuals are, the lower is the presence of autocorrelation in the sample, and hence, better are the variables able to predict variations in the dependent variable. This is because, if the random error terms are autocorrelated and yet the model obtained is a good fit of the population regression function, then it is accepted that they too play an important role in the prediction of the dependent variable. The model under study however is free of severe autocorrelation problems, because although the unstandardized residual plots show an upward trend, the points are highly scattered. The autocorrelation content is also found from the Durbin-Watson test statistic which in this case is nearer to 2, indicating that the random error terms do not suffer from severe autocorrelation problem. 4.2.5 – Multicollinearity The presence of multicollinearity is commonly checked by looking at the VIF (Variance Inflating Factor) of the test, where VIF is defined as, VIFj = 1/ (1 – Rj2) Where, Rj2 is the multiple correlation co-efficient, when the jth variable is regressed over the remaining explanatory variables in the model. The higher the Rj2 higher will be the VIFj and so, higher is the collinearity between the variables indicating the presence of multicollinearity. A rule of thumb is that if VIF is greater than 10, we can say that the model suffers from a multicollinearity problem. In the present study, it is found that the VIF of each and every variable is greater than 10, implying the presence of multicollinearity in the model. 4.2.6 – Internal validity Check The Internal Validity Check is conducted by taking a sample out of the sample consisting of 60% of the observations of the latter. The same statistical tests are conducted on this smaller sample as in the larger one to find whether the results so obtained are valid for within sample observations or not. We will just briefly show how our findings are in line with those for the larger sample We have considered a sample of 29 data points out of the larger sample consisting of 48 observations. All the estimated coefficients lie within their respective confidence interval. With degrees of freedom = 28 and level of significance = 0.05, tabulated t = 2.048. The estimated | t | for all variables except Mt-8 is greater than the tabulated value. The p-values of the Student’s t-statistic are also significant for all variables except Mt-8. With degrees of freedom = 4, 24 and level of significance = 0.05, tabulated F = 2.78. The estimated F = 9.250 which is greater than the tabulated value. The p-value of the F-test is also significant. The coefficient of determination is 0.779 and Adjusted R Square is 0.607, both of which are quite high suggestive of a good fit. The residual plot is scattered as well, although exhibiting an upward trend suggesting that autocorrelation although is present in the model, is not severe. The Durbin Watson statistic is also 1.491, which is indicative of almost no autocorrelation. The VIF readings show that each of the explanatory variables is highly correlated with the remaining of their counterparts, indicating the presence of multicollinearity. So, it is found that all the conclusions of the Internal Validity Check match those drawn from the larger sample, indicating that the results are indeed valid for within sample observations as well. 4.3 – Limitations and assumptions of the tests performed Two tests have mainly been performed in the paper, namely – Student’s t-test and the F-test. The limitations and assumptions made in these tests are those for this study 1) Student’s t-test Assumptions: 1. The sample must be random. 2. The data used must be quantitative or measurable 3. The data should follow normal distribution 4. The size of sample should ideally be 30. Limitation The student’s t-test assumes that the population under consideration is a normal one. But once it is hampered, the power of the test might fall, i.e., the probability of a Type-I error falls and the results might be showing completely different and unexpected results. 2) F-test Assumptions 1. The larger of the variances should always be the numerator. 2. The standard deviations must be squared to get the variances. 3. The samples must be drawn from normal populations. 4. The samples must be independent of one another. 5. The samples must have equal number of observations. Chapter 5 – Conclusion and Recommendations From the regression result, the significance of the positive coefficient of the 12 month lagged money supply is evident which is indicative of the fact that a systematic change money supply would take at least a year to have any effect on the behavior of inflation. So our finding based on the recent U.S. data, is at par with the finding of Prof. Milton Friedman and other subsequent researchers belonging to the ‘Monetarist’ school. Hence, indeed there are reasons to believe that at least a single type of persistence is present in the inflation path, even across different policy regimes in different time periods. And evidently, this persistence is the delayed response of the inflation rate to the systematic monetary policy changes. Again once the significant relationship between the inflation and the lagged monetary policy changes are in picture, we may conclude that monetary aggregates (M1, M2 etc.) will continue to be useful instruments for regulating inflation in the long run. On the basis of our study, it might be tempting to assert that the central banks can indeed safeguard the national macro economy from ‘corrosive’ inflation through effective monetary tightening. But one should also keep in mind that any monetary contraction aimed at arresting inflation or to pursue a policy of ‘inflation targeting’, would also lead to a short run loss of output and employment, i.e. the whole macro economy would have to go through the periods of lower income and higher unemployment for at least one year or more. Hence an wise policy make should strike a balance between these short run losses in terms of output and long run benefits in terms of lower rate of inflation while formulating monetary policies. There are still some additional areas of research left for the future studies. This paper simply revokes Friedman’s claim and proves it statistically; the model used here is a linear one and the regression method being OLS. But there could be a non linear response of the inflation to the lagged money supply as well. This can be taken care of in the subsequent studies. Moreover one could also include many other variables, known to have influence on the inflation path into the current linear model, e.g. exchange rate, Fed rate, future price of gold etc in order to make the model stronger and more realistic. References Federal Reserve Statistical Release, H.6 Money Stock Measures, July 30, 2009, retrieved on August 2, 2009, from http://www.federalreserve.gov/releases/h6/hist/ Introduction to SAS. UCLA: Academic Technology Services, Statistical Consulting Group. Retrieved on August 2, 2009 from http://www.ats.ucla.edu/stat/sas/notes2/ The Consumer Price Index, Bureau of Labor Statistics, USA, retrieved on August 2, 2009 from http://www.inflationdata.com/Inflation/Consumer_Price_Index/HistoricalCPI.aspx Bibliographies Batini Nicoletta and Nelson Edward. (January, 2002) The lag from Monetary Policy Actions to Inflation: Friedman Revisited, Discussion Paper No. 6 Bernanke, Ben S., Thomas laubach, Frederic S. Mishkin and Adam Posen (1999), Inflation targeting: Lessons from the International Experience Friedman Milton (1961), The Lag in Effect of Monetary Policy, Journal of Political Economy, 69. Friedman Milton (1972), have Monetary Policies Failed?, American Journal Review (Papers and proceedings), 62 Friedman Milton (1978), Inflationary Recession, Newsweek Lucas Robert E. Jr., (1972), Expectations and neutrality of Money, Journal of Economic Theory Taylor John B., (2000). Low Inflation, Pass-Through, and the Pricing Power of Firms, European Economic Review, 44. Appendix Sample Data Month_year Cpi_inflation Mt Mt-4 Mt-8 Mt-12 Feb_01 3.53 873 857.5 863.2 867 Mar_01 2.92 881.7 852.6 864.2 866.4 Apr_01 3.27 893.3 849.4 860.1 869.2 May_01 3.62 947.3 857.6 859.7 863.9 Jun_01 3.25 914.2 860 857.5 863.2 Jul_01 2.72 917.7 864.6 852.6 864.2 Aug_01 2.72 924.8 866.1 849.4 860.1 Sep_01 2.65 931.2 870.7 857.6 859.7 Oct_01 2.13 931.3 873 860 857.5 Nov_01 1.90 933.3 881.7 864.6 852.6 Dec_01 1.55 924 893.3 866.1 849.4 Jan_02 1.14 925.8 947.3 870.7 857.6 Feb_02 1.14 929.2 914.2 873 860 Mar_02 1.48 933.8 917.7 881.7 864.6 Apr_02 1.64 919.9 924.8 893.3 866.1 May_02 1.18 925.1 931.2 947.3 870.7 Jun_02 1.07 929.9 931.3 914.2 873 Jul_02 1.46 932.1 933.3 917.7 881.7 Aug_02 1.80 940.9 924 924.8 893.3 Sep_02 1.51 946.7 925.8 931.2 947.3 Oct_02 2.03 955.5 929.2 931.3 914.2 Nov_02 2.20 955.7 933.8 933.3 917.7 Dec_02 2.38 964.1 919.9 924 924.8 Jan_03 2.60 980.2 925.1 925.8 931.2 Feb_03 2.98 988.4 929.9 929.2 931.3 Mar_03 3.02 990.3 932.1 933.8 933.3 Apr_03 2.22 993.4 940.9 919.9 924 May_03 2.06 990.4 946.7 925.1 925.8 Jun_03 2.11 991.5 955.5 929.9 929.2 Jul_03 2.11 992 955.7 932.1 933.8 Aug_03 2.16 996.6 964.1 940.9 919.9 Sep_03 2.32 992.3 980.2 946.7 925.1 Oct_03 2.04 1003 988.4 955.5 929.9 Nov_03 1.77 1009.2 990.3 955.7 932.1 Dec_03 1.88 1011.3 993.4 964.1 940.9 Jan_04 1.93 1011.6 990.4 980.2 946.7 Feb_04 1.69 1017.1 991.5 988.4 955.5 Mar_04 1.74 1014 992 990.3 955.7 Apr_04 2.29 1025 996.6 993.4 964.1 May_04 3.05 1036.1 992.3 990.4 980.2 Jun_04 3.27 1033.9 1003 991.5 988.4 Jul_04 2.99 1045.2 1009.2 992 990.3 Aug_04 2.65 1048.2 1011.3 996.6 993.4 Sep_04 2.54 1042.8 1011.6 992.3 990.4 Oct_04 3.19 1049.9 1017.1 1003 991.5 Nov_04 3.52 1051.1 1014 1009.2 992 Dec_04 3.26 1035.9 1025 1011.3 996.6 Jan_05 2.97 1043.4 1036.1 1011.6 992.3 Reliability R E L I A B I L I T Y A N A L Y S I S - S C A L E (A L P H A) Mean Std Dev Cases 1. CPI_INFL 2.3519 .7060 48.0 2. M 942.7375 53.7304 48.0 3. M4 929.3000 52.0119 48.0 4. M8 917.4542 48.5589 48.0 5. M12 917.4542 48.5589 48.0 Correlation Matrix CPI_INFL M M4 M8 M12 CPI_INFL 1.0000 M .0202 1.0000 M4 .1621 .9503 1.0000 M8 .3593 .8848 .9424 1.0000 M12 .3593 .8848 .9424 1.0000 1.0000 * * * Warning * * * Determinant of matrix is zero Statistics based on inverse matrix for scale ALPHA are meaningless and printed as . N of Cases = 48.0 N of Statistics for Mean Variance Std Dev Variables Scale 3709.2977 39152.9837 197.8711 5 Item-total Statistics Scale Scale Corrected Mean Variance Item- Squared Alpha if Item if Item Total Multiple if Item Deleted Deleted Correlation Correlation Deleted CPI_INFL 3706.9458 39089.7808 .2246 . .9817 M 2766.5602 21719.2238 .9185 . .8777 M4 2779.9977 21604.0574 .9708 . .8641 M8 2791.8435 22677.2620 .9653 . .8659 M12 2791.8435 22677.2620 .9653 . .8659 _ R E L I A B I L I T Y A N A L Y S I S - S C A L E (A L P H A) Reliability Coefficients 5 items Alpha = .9209 Standardized item alpha = .9030 Regression Variables Entered/Removed(b) Model Variables Entered Variables Removed Method 1 M12, M4, M, M8(a) . Enter a All requested variables entered. b Dependent Variable: CPI Model Summary(b) Model R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson 1 .878(a) .771 .750 .41171 1.144 a Predictors: (Constant), M12, M4, M, M8 b Dependent Variable: CPI ANOVA(b) Model Sum of Squares df Mean Square F Sig. 1 Regression 24.598 4 6.150 36.279 .000(a) Residual 7.289 43 .170 Total 31.887 47 a Predictors: (Constant), M12, M4, M, M8 b Dependent Variable: CPI Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -9.540 1.247 -7.651 .000 M .015 .005 .880 2.859 .007 M4 -.019 .006 -1.165 -3.361 .002 M8 .003 .005 .224 .664 .510 M12 .013 .004 .870 3.028 .004 a Dependent Variable: CPI 95% Confidence Interval for B Collinearity Statistics Lower Bound Upper Bound Tolerance VIF -12.055 -7.026 .004 .026 .056 17.842 -.031 -.008 .044 22.610 -.007 .014 .047 21.335 .004 .022 .064 15.527 Collinearity Diagnostics(a) Model Dimension Eigenvalue Condition Index Variance Proportions (Constant) M M4 M8 M12 1 1 4.997 1.000 .00 .00 .00 .00 .00 2 .002 48.142 .82 .00 .00 .01 .01 3 .000 136.385 .14 .11 .13 .03 .31 4 .000 175.114 .02 .25 .06 .37 .23 5 5.401E-05 304.178 .02 .65 .81 .59 .46 a Dependent Variable: CPI Residuals Statistics(a) Minimum Maximum Mean Std. Deviation N Predicted Value .6527 3.6698 2.4177 .72344 48 Residual -.8708 1.0353 .0000 .39380 48 Std. Predicted Value -2.440 1.731 .000 1.000 48 Std. Residual -2.115 2.515 .000 .957 48 a Dependent Variable: CPI Graph For Internal Reliability Regression Variables Entered/Removed(b) Model Variables Entered Variables Removed Method 1 M12, M4, M, M8(a) . Enter a All requested variables entered. b Dependent Variable: CPI Model Summary(b) Model R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson 1 .779(a) .607 .541 .33710 1.491 a Predictors: (Constant), M12, M4, M, M8 b Dependent Variable: CPI ANOVA(b) Model Sum of Squares df Mean Square F Sig. 1 Regression 4.205 4 1.051 9.250 .000(a) Residual 2.727 24 .114 Total 6.932 28 a Predictors: (Constant), M12, M4, M, M8 b Dependent Variable: CPI Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -3.382 2.040 -1.657 .110 M .011 .005 .660 2.121 .044 M4 -.016 .006 -1.044 -2.882 .008 M8 -.001 .005 -.092 -.270 .790 M12 .013 .004 .871 3.067 .005 95% Confidence Interval for B Collinearity Statistics Lower Bound Upper Bound Tolerance VIF -7.593 .829 .000 .021 .170 5.897 -.028 -.005 .125 8.006 -.012 .009 .140 7.118 .004 .021 .203 4.924 a Dependent Variable: CPI Collinearity Diagnostics(a) Model Dimension Eigenvalue Condition Index Variance Proportions (Constant) M M4 M8 M12 1 1 4.998 1.000 .00 .00 .00 .00 .00 2 .001 77.440 .83 .00 .00 .03 .04 3 .000 107.779 .12 .08 .11 .02 .24 4 .000 142.890 .04 .22 .04 .31 .21 5 6.366E-05 280.199 .01 .70 .85 .65 .51 a Dependent Variable: CPI Residuals Statistics(a) Minimum Maximum Mean Std. Deviation N Predicted Value 1.0059 2.4056 1.9128 .38751 29 Residual -.8344 .6288 .0000 .31209 29 Std. Predicted Value -2.340 1.272 .000 1.000 29 Std. Residual -2.475 1.865 .000 .926 29 a Dependent Variable: CPI Graph Read More