The Relevance of Inflation, Unemployment and Interest Rates in Predicting the UK Gross Domestic Product - Statistics Project Example

1. Introduction This analysis aimed at the development of an econometric model that would predict the dependant variable the annual real gross domestic product (GDP) of the United Kingdom (UK) using the independent variables; the real interest rate and the rate of unemployment in the UK. The data used to build and refine the econometric model was extracted from the Economic Trend Annual Supplement (ETAS) presented by the British Office for National Statistics (ONS). This was accomplished by applying fundamental econometric methods such as linear regression, misspecification testing, and hypothesis testing using the computer package E-Views. 2. The dependent Variable: Gross Domestic Product (GDP): 2.1 Importance of GDP: The dependent variable used for this study is the Gross domestic product (GDP) of the United Kingdom (UK). GDP is an important measure for any country because it represents the healthiness of its economy. It is calculated by summing the market value of all goods and services produced within this economy. The percent change in GDP is used to measure the growth in the economy during the specified period. GDP is measured in real prices in order to remove the effect of inflation. 2.2 Source of Data: The data for the GDP for the UK is extracted from the Economic Trend Annual Supplement (ETAS) database. ETAS is released annually from British office of national statistics (ONS). It contains a summary of the United Kingdom (UK) economic accounts. Field number 2.1A is selected from the database which contains the time series of GDP chained volume measures which is referenced by the variable ABMI. These values are seasonally adjusted to represent the period from 1948 to 2005. Annually linked and weighted chain volume measures better highlight changes in GDP than constant price values. This is because take account of year-to-year changes (Aspden & Person 2000). 2.3 Time Series Data of British GDP: The time series of the British GDP (appendix A) is presented in the following graph: Figure 1: Chained volume and seasonally adjusted UK GDP from 1948 to 2005 Figure 1 shows little change from year to year in UK GDP. Therefore the percent change from year-to-year is computed and replaces by the real values of annual GDP. The percent change in the British GDP (appendix B) is shown in the following figure: Figure 2: Percent Change in UK GDP from 1948 to 2005 Figure 2 amplifies the changes and highlights that occurred during the period of the study. It shows periods when GDP positively increased or negatively decreased which were not visible in figure 1. From the above graph the following years experienced major increase in the British GDP: 1973 (7.1%), 1964 (5.5%), 1960 (5.3%), 1988 (5%). The following years also experienced the most decrease in GDP values: 1980 (-2.1%), 1981 (-1.5%), 1991 (-1.4%), 1974 (-1.4). 3. Econometric Model: Regression is considered as a special case of econometric modeling (Wang & Jain 2003). Theory suggests that GDP growth is positively related to inflation and negatively related to unemployment and real interest rates (RIT). The following relevances of these three variables are explored in the following sections. 3.1 The relevance of Inflation in predicting GDP: The relationship between inflation and GDP is a very delicate relationship and still causes much controversy in both theory and empirical findings (Hossain & Chowdhury 1996). Mallik & Chowdhury (2001) examined the long-run and short-run dynamics of the relationship between GDP and inflation. They found that inflation and economic growth are positively related on the long run. They also found that inflation is more sensitive to changes in growth rates than that of growth rates to changes in inflation. Thus moderate inflation is good for growth but fast economic growth feeds back into inflation. Thus too much GDP growth would accelerate inflation rates, which would decrease the value of money more than the value gained by GDP and even more taking the economy downhill as verified by Bruno and Easterly (1998). 3.2 The relevance of Unemployment in predicting GDP: Macroeconomist Arthur Okun was the first to quantify the relationship between the rate of unemployment and GDP. Okun stated that "for every one percent point by which actual unemployment rate exceeds the natural rate, a negative GDP gap of about two percent occurs" (McConnell & Brue 2005).. Slow or decreasing rates in real GDP causes unemployment rates to increase. On the contrary, during periods of rapid growth in real GDP, businesses seek workers to produce higher output and thus cause unemployment to decrease. However, too much growth in real GDP would cause faster rates of increase in inflation, causing unemployment to increase again. 3.3 The relevance of Interest Rates in predicting GDP: Oosterbaan, Steveninck, & Windt (2000) mention the existence of the significant positive relationship between interest rates and the average rates of growth in GDP. They present empirical results that suggest that a one percentage point increase in real interest rate toward its competitive free-market equilibrium level is associated with one half percentage point in the rate of economic growth in Asia. 3.4 Econometric Model: A regression model was estimated to predict the annual percent change in British GDP as a dependent variable which is referred to by DGDP by using the following independent variables; annual rate of inflation (INF), annual rate of unemployment (UNEMP), and annual average of interest rates (INT). The following econometric model equation is suggested: DGDPt = 1 + 2INFt + 3UNEMPt + 4INTt + ut 4. Independent Variables Data: 4.1. Data Series for Annual Rate of Inflation: Time series data for the annual rate of inflation was not available. Since inflation represents change in price levels compared to a benchmark, inflation will be replaced by consumer price indices (CPI) which time series data is available. CPI is used in the U.S. as the standard measure of inflation. The computation of CPI excludes the food and energy prices as they show more volatility than other goods. The annual time series data for CPI in the UK is extracted from ETAS which is released from ONS. CPI time series data is referenced in the database by CZBH. It is computed as the retail price index (RPI) percent change over the last twelve months. The index is measured relatively on the basis that it is equal to hundred in the year 1987 (January 1987=100). The data is collected for the period from 1949 to 2005 (appendix C) as presented in the following graph: Figure 4: CPI Percent Change over 12 months from 1949 to 2005 Figure 4 exhibits adequate change in annual CPI from year to year during the period of the study pressing no need to further transform the data. The above graph displays major increase in CPI during the years: 1975, 1951, and 1980. It also shows major decreases in CPI during the years: 1976, 1981, 1953, and 1983. 4.2. Data Series for Annual Rate of Unemployment: Unemployment rates were surveyed by the Labor Force (LF). The data was obtained from ETAS release of ONS which was updated in 10 October 2006. The variable is referred to in the database by the symbol MGSX. The data measures the unemployment rates in the UK for all aged 16 and over. The data is collected for the period from 1971 to 2005. The data is seasonally adjusted as shown in appendix D. The data is shown in the following graph: Figure 5: Unemployment in the UK for all ages above 16 from 1971 to 2005 Figure 5 exhibits little change from year to year in unemployment rates in the UK during the period of the study. The data is transformed in percent change per year as tabulated in appendix E and show in the following graph: Figure 6: Percent Change in Unemployment in the UK for all ages above 16 from 1972 to 2005 Figure 6 shows adequate change in percent change in unemployment in the UK for all ages above 16 from 1972 to 2005. 4.3. Data Series for Annual Interest Rates: Annual averages on interest on US dollar deposits in London for 3 months were extracted form ETAS release of ONS which was updated in 10 October 2006. The variable is referred to in the database by the symbol AJIB. The data is collected for the period from 1963 to 2005 as shown in appendix F. The data is graphically presented in the following graph: Figure 7: Annual averages on interest on US dollar deposits in London for 3 months from 1963 to 2005 Figure 7 exhibits adequate change in annual averages on interest on US dollar deposits in London for 3 months. This shows no need to further transform the data. 5. Estimating Regression Model using Eviews: Regression analysis using Ordinary Least Squares (OLS) estimation method is utilized to estimate the econometric model to predict percentage change GDP of the UK. OLS is the most commonly used estimation method but it requires the satisfaction of a number of assumptions. Assumptions that must be met to ensure that the model is unbiased are data are a random sample of the population where the errors are normally distributed and statistically independent of each others, expected value of errors are always zero, and independent variables are not strongly collinear. It is also assumed that residuals have constant variance to ensure model has minimum variance of all unbiased estimators. An alpha level of .05 is suggested to determine whether to accept or reject the null hypothesis during this analysis. 5.1 Testing for Assumptions of OLS Model 5.1.1 Zero mean assumption: A constant term is added in the regression equation to ensure that the average value of the constant term is zero. 5.1.2 Homoscedasticity assumption: Residuals are plotted against the predicted values to observe whether the variance of the error changes systematically with the predicted variable to give us an indication of heteroscedasticity. White test statistic is observed in eviews to reject the null hypothesis of no heteroskedasticity. 5.1.3 MultiColinearity: Correlation between independent variables were tested to detect signs of multicolinearity as shown in appendix 5.2 First Estimation of the OLS Regression Model: The data of independent variable percent change in GDP in the UK (DGDP) from 1948 to 2005 is entered in the workfile of Eviews (4.0). The data of the chosen dependent variables are also entered in the same workfile in Eviews. The first dependent variable entered was consumer price index (CPI) from 1949 to 2005. The second dependent variable entered was percent change in unemployment in the UK from 1972 to 2005. The third dependent variable entered was interest rates (INT) from 1963 to 2005. The output of the first estimation of the regression model is show in appendix G. The adjusted R squared value was 39.9% giving an acceptable level of predicting DGDP. The Akaike info criterion (AIC) and the Schwarz Criterion (SC) generated a fit value of the model of 3.98 and 4.17 respectively. The probability of the F statistic for the model was less than .05 and thus the null hypothesis that the three coefficients of the suggested model are zero is rejected. The following graph demonstrates the closeness of the regression model to the actual data: Figure 8: Comparison of actual to fitted graphs and residual error in the first estimation of the regression model. The probabilities of the all coefficient were T statistic was less than the suggested alpha level of .05 except for the interest rates variable, which was 0.96. It was decided to transform the INT variable and introduce a log of one year in its data in the second estimation of the model. 5.3 Second Estimation of the OLS Regression Model: The output of the second estimation presented in appendix H demonstrates the probability of the INT variable as still larger than .05. The log of INT was also tried but it still produced a high probability. It was decided to remove the INT variable from the model. 5.4 Third Estimation of the OLS Regression Model: The output of the third estimation is presented in the appendix I. The model was accepted after the probability of F statistic was less than .05 and the probability of the T statistics of the three coefficients of the model were less than .05, thus rejecting the null hypothesis and accepting the model. AIC and SC showed better fit of the selected model and adjusted R-squared proved that the model can predict 42.3% of DGDP in the UK. The fit of the predicted model is compared to the actual model in the following graph: Figure 9: Comparison of actual to fitted graphs and residual error in the Selected Model 5.5 Final Model: DGDP = 3.431755482 - 0.1211716857*CPI - 0.06610682776*DUNEMP 6. Forecasting Performance of the Selected Model: Eviews forecast function was used to forecasting DGDP using the selected model generated the following graph: Figure 10: Forecasted DGDP from 2001 to 2005 The chow forecast test of Eviews is conducted and presented in appendix K. The value of the probability of F statistic is higher than .05 and thus the null hypothesis is not rejected. By comparing actual versus forecasted DGDP values, the selected model has an average ability to predict the values of DGDP. The following table shows both the actual and the forecasted values of DGDP in the UK: Table 1: Actual vs. Forecasted values of DGDP using selected Model Actual DGDP Forecasted DGDP 4.039982 2.400000 2.822512 2.100000 3.331564 2.700000 3.332668 3.300000 3.231299 1.900000 The selected model can be further improved by adding more independent variables which are more or as equal predictive in the value of GDP of the UK. Data should be collected for the full spectrum from 1948 to 2005 for all selected variables. 7. Critical Evaluation of the Econometric Approach: There is no clear distinction between regression and econometric models. Both are cause and effect models. The econometric approach uses regression analysis to build a model to predict and simulate the values of some dependent variable is not easy and straight forward. The more knowledge that is acquired of the different regression and statistical test techniques, the better the results and the guidance to build the best econometric model. Deep and sound knowledge of the process would shorten and sharpen the road to achieve the best possible model. The process is iterative and requires the addition or deletion of different variables until statistically relevant independent variables are found. Variables can be further transformed to achieve better results and to avoid different problems that would bias the result of the model. Computerized statistical packages are a great tool to help guide the search for the best econometric model. References Aspden, C. & Person R. (2000). Introduction of Chain Volume and Price Measures - The Australian Approach. United Nations: Economic and Social Commission for Asia and the Pacific, Bangkok, Thailand. Bruno, M. and W. Easterly, 1998. Inflation crises and long-run growth, Journal of Monetary Economics, vol. 41, pp. 3-26. Hicks, J. & Allen, G. (1999). A Century of Change: Trends in UK Statistics since 1900. Social and General Statistics Section, House of Commons, United Kingdom. Hossain, A. and A. Chowdhury, 1996. Monetary and Financial Policies in Developing Countries, London: Routledge McConnell, C.R. & Brue, S.L. (2005). Economics: Principles, Problems, and Policies McGraw-Hill Professional. Mallik, G. & Chowdhury, A. (2001).Inflation and Economic Growth: Evidence from Four South Asian Countries. Asia-Pacific Development Journal, Vol. 8, No. 1, June 2001. Office for National Statistics. Accessed on April 19, 2008 from http://www.statistics.gov.uk/statbase/tsdintro.asp. Oosterbaan, M.S., Steveninck, T.R., & Windt, N.D. (2000). The Determinants of Economic Growth. Springer. Wang G.C.S & Jain C.L., (2003). Regression Analysis: Modelling and Forecasting. Institute of business forecasting. Appendix A Year UK GDP Chained Volume, Seasonally adjusted 1948 286,763 1949 295,781 1950 304,221 1951 312,845 1952 313,186 1953 324,581 1954 337,545 1955 349,062 1956 352,199 1957 357,968 1958 359,013 1959 374,365 1960 394,292 1961 403,406 1962 407,616 1963 425,077 1964 448,359 1965 458,368 1966 467,207 1967 478,737 1968 498,789 1969 509,158 1970 520,568 1971 531,049 1972 550,002 1973 589,158 1974 581,111 1975 577,489 1976 592,659 1977 606,780 1978 626,382 1979 643,043 1980 629,559 1981 620,332 1982 632,052 1983 654,267 1984 670,995 1985 694,661 1986 721,977 1987 754,678 1988 792,176 1989 809,214 1990 814,956 1991 803,892 1992 805,699 1993 824,085 1994 859,566 1995 884,748 1996 909,102 1997 936,717 1998 968,040 1999 997,295 2000 1,035,295 2001 1,059,648 2002 1,081,469 2003 1,110,296 2004 1,146,523 2005 1,167,792 Appendix B Year UK GDP Chained Volume, Seasonally adjusted Percent Change from year-to-year 1948 1949 3.1 1950 2.9 1951 2.8 1952 0.1 1953 3.6 1954 4 1955 3.4 1956 0.9 1957 1.6 1958 0.3 1959 4.3 1960 5.3 1961 2.3 1962 1 1963 4.3 1964 5.5 1965 2.2 1966 1.9 1967 2.5 1968 4.2 1969 2.1 1970 2.2 1971 2 1972 3.6 1973 7.1 1974 -1.4 1975 -0.6 1976 2.6 1977 2.4 1978 3.2 1979 2.7 1980 -2.1 1981 -1.5 1982 1.9 1983 3.5 1984 2.6 1985 3.5 1986 3.9 1987 4.5 1988 5 1989 2.2 1990 0.7 1991 -1.4 1992 0.2 1993 2.3 1994 4.3 1995 2.9 1996 2.8 1997 3 1998 3.3 1999 3 2000 3.8 2001 2.4 2002 2.1 2003 2.7 2004 3.3 2005 1.9 Appendix C Year CPI Percent Change over 12 months from 1949 to 2005 1948 1949 2.8 1950 3.1 1951 9.1 1952 9.2 1953 3.1 1954 1.8 1955 4.5 1956 4.9 1957 3.7 1958 3 1959 0.6 1960 1 1961 3.4 1962 4.3 1963 2 1964 3.3 1965 4.8 1966 3.9 1967 2.5 1968 4.7 1969 5.4 1970 6.4 1971 9.4 1972 7.1 1973 9.2 1974 16 1975 24.2 1976 16.5 1977 15.8 1978 8.3 1979 13.4 1980 18 1981 11.9 1982 8.6 1983 4.6 1984 5 1985 6.1 1986 3.4 1987 4.2 1988 4.9 1989 7.8 1990 9.5 1991 5.9 1992 3.7 1993 1.6 1994 2.4 1995 3.5 1996 2.4 1997 3.1 1998 3.4 1999 1.5 2000 3 2001 1.8 2002 1.7 2003 2.9 2004 3 2005 2.8 Appendix D Year Unemployment in the UK for all ages above 16 from 1971 to 2005 1971 4 1972 4.5 1973 3.8 1974 3.6 1975 4.2 1976 5.4 1977 5.5 1978 5.6 1979 5.3 1980 6.1 1981 9.4 1982 10.5 1983 11.3 1984 11.9 1985 11.4 1986 11.3 1987 10.9 1988 8.9 1989 7.3 1990 6.9 1991 8.5 1992 9.8 1993 10.5 1994 9.8 1995 8.8 1996 8.3 1997 7.2 1998 6.3 1999 6.1 2000 5.6 2001 4.9 2002 5.2 2003 5 2004 4.8 2005 4.7 Appendix E Year Percent Change in Unemployment in the UK for all ages above 16 from 1971 to 2005 1971 1972 12.5 1973 -15.6 1974 -5.3 1975 16.7 1976 28.6 1977 1.9 1978 1.8 1979 -5.4 1980 15.1 1981 54.1 1982 11.7 1983 7.6 1984 5.3 1985 -4.2 1986 -0.9 1987 -3.5 1988 -18.3 1989 -18 1990 -5.5 1991 23.2 1992 15.3 1993 7.1 1994 -6.7 1995 -10.2 1996 -5.7 1997 -13.3 1998 -12.5 1999 -3.2 2000 -8.2 2001 -12.5 2002 6.1 2003 -3.8 2004 -4 2005 -2.1 Appendix F Year Annual averages on interest on US dollar deposits in London for 3 months 1963 4.25 1964 4.56 1965 5.31 1966 6.56 1967 6.31 1968 7.13 1969 10.06 1970 6.56 1971 5.75 1972 5.91 1973 10.19 1974 10.06 1975 5.87 1976 5.06 1977 7.19 1978 11.69 1979 14.5 1980 17.75 1981 13.63 1982 9.25 1983 9.94 1984 8.69 1985 7.94 1986 6.31 1987 7.38 1988 9.25 1989 8.34 1990 7.53 1991 4.22 1992 3.37 1993 3.31 1994 6.44 1995 5.54 1996 5.5 1997 5.69 1998 5 1999 5.98 2000 6.35 2001 1.83 2002 1.35 2003 1.1 2004 2.56 2005 4.51 Appendix G Dependent Variable: DGDP Method: Least Squares Date: 04/25/08 Time: 15:56 Sample(adjusted): 1972 2000 Included observations: 29 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 3.401035 0.811470 4.191203 0.0003 CPI -0.122632 0.065654 -1.867853 0.0735 DUNEMP -0.066050 0.021699 -3.043916 0.0054 INT 0.005336 0.105444 0.050601 0.9600 R-squared 0.464085 Mean dependent var 2.344828 Adjusted R-squared 0.399775 S.D. dependent var 2.146190 S.E. of regression 1.662744 Akaike info criterion 3.982258 Sum squared resid 69.11794 Schwarz criterion 4.170850 Log likelihood -53.74274 F-statistic 7.216383 Durbin-Watson stat 1.542969 Prob(F-statistic) 0.001197 Appendix H Dependent Variable: DGDP Method: Least Squares Date: 04/25/08 Time: 15:58 Sample(adjusted): 1972 2000 Included observations: 29 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 4.279056 0.848008 5.046010 0.0000 CPI -0.089143 0.062497 -1.426356 0.1661 DUNEMP -0.056283 0.022390 -2.513685 0.0188 INT(-1) -0.142603 0.112487 -1.267731 0.2166 R-squared 0.496404 Mean dependent var 2.344828 Adjusted R-squared 0.435972 S.D. dependent var 2.146190 S.E. of regression 1.611827 Akaike info criterion 3.920056 Sum squared resid 64.94968 Schwarz criterion 4.108649 Log likelihood -52.84081 F-statistic 8.214313 Durbin-Watson stat 1.481707 Prob(F-statistic) 0.000566 Appendix I Dependent Variable: DGDP Method: Least Squares Date: 04/25/08 Time: 16:20 Sample(adjusted): 1972 2000 Included observations: 29 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 3.431755 0.527991 6.499653 0.0000 CPI -0.121172 0.057827 -2.095426 0.0460 DUNEMP -0.066107 0.021251 -3.110836 0.0045 R-squared 0.464030 Mean dependent var 2.344828 Adjusted R-squared 0.422801 S.D. dependent var 2.146190 S.E. of regression 1.630538 Akaike info criterion 3.913395 Sum squared resid 69.12502 Schwarz criterion 4.054839 Log likelihood -53.74422 F-statistic 11.25507 Durbin-Watson stat 1.542663 Prob(F-statistic) 0.000301 Appendix J Correlation between dependent variables CPI DGDP DUNEMP INT CPI 1.000000 -0.514334 0.387832 0.453366 DGDP -0.514334 1.000000 -0.611160 -0.206063 DUNEMP 0.387832 -0.611160 1.000000 0.133475 INT 0.453366 -0.206063 0.133475 1.000000 Appendix K Chow Forecast Test: Forecast from 1990 to 2000 F-statistic 0.838916 Probability 0.608812 Log likelihood ratio 13.90440 Probability 0.238329 Test Equation: Dependent Variable: DGDP Method: Least Squares Date: 04/25/08 Time: 17:20 Sample: 1972 1989 Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. C 4.870921 0.839527 5.801985 0.0000 CPI -0.217158 0.075375 -2.881046 0.0114 DUNEMP -0.052347 0.025146 -2.081685 0.0549 R-squared 0.569320 Mean dependent var 2.394444 Adjusted R-squared 0.511896 S.D. dependent var 2.417698 S.E. of regression 1.689111 Akaike info criterion 4.037293 Sum squared resid 42.79643 Schwarz criterion 4.185689 Log likelihood -33.33564 F-statistic 9.914321 Durbin-Watson stat 2.023327 Prob(F-statistic) 0.001804 Read More