Predictability of Exchange Rate: USD and Yen - Statistics Project Example

Statistics TOPIC PAPER: Statistics – predictability of exchange rate (USD/Yen) PURPOSE MENT AND MODEL The platform of social science in the modern world has encountered an immense usefulness with the application of statistics and their useful tools in developing certain assumptions and inferences. They help us in directing towards the establishment of policy formulations whose successful implementation generates positive results and foundations of new theories in application. These results have been the precursor of diverse types of inferences which develop a new dynamic view towards analysis paradigm. In the economic forefront there have been various implications of statistics. In this world of global competition and free international trade, the currency is one parameter which is highly useful in the measurement of the economic strength of a country. The strength of the currency is evaluated on the basis of the ratio of the home currency to that of the international currency of the country in question. If the currency of United States of America is denoted as USD and that the currency of Japan is denoted as Yen, then the ratio of both the currencies will be written as which is defined as the dependent variable in the paper which will be defined later . Now the ratio of the currencies depend on various economic variables like Gross Domestic Product (GDP), Unemployment rate, stock index, trade balance and so on as in these variables have effects on the ratio. The variables stated above can be represented as determinants of the exchange rate. A suitable method for analyzing is to see the change in the ratio of the currency of USA with respect to Japan and how much it is explained by the variables like GDP, unemployment, inflation and that of the trade balance can be best explained by a multiple regression analysis. The regression model can be written as follows: RESEARCH PAPER Introduction The platform of social science in the modern world has encountered an immense usefulness with the application of statistics and their useful tools in developing certain assumptions and inferences (Haferkamp & Smelser, 1992, p. 2). They help us in directing towards the establishment of policy formulations whose successful implementation generates positive results and foundations of new theories in application. These results have been the precursor of diverse types of inferences which develop a new dynamic view towards analysis paradigm. In the economic forefront there have been various implications of statistics. In this world of global competition and free international trade, the currency is one parameter which is highly useful in the measurement of the economic strength of a country. The strength of the currency is evaluated on the basis of the ratio of the home currency to that of the international currency of the country in question. If the currency of United States of America is denoted as USD and that the currency of Japan is denoted as Yen, then the ratio of both the currencies will be written as which is defined as the dependent variable in the paper which will be defined later . Now the ratio of the currencies depend on various economic variables like Gross Domestic Product (GDP), Unemployment rate, stock index, trade balance and so on as in these variables have effects on the ratio. The variables stated above can be represented as determinants of the exchange rate. Methodology A suitable method for analyzing is to see the change in the ratio of the currency of USA with respect to Japan and how much it is explained by the variables like GDP, unemployment, inflation and that of the trade balance can be best explained by a multiple regression analysis. The regression model can be written as follows: Definition of Variables In the above equation, the Y can be defined as the ratio of USD to Yen () which is a dependent variable and that independent variables affecting the dependent variable are GDP ($ billion nominal) =GDPUS, Unemployment rate= UNRUS, Inflation rate= INRUS, Trade Balance of goods ($ billion nominal) of USA with respect to that of Japan =TBGUSJ and (BOPUST-TBJUSG) representing the deviation between the total balance of payments of the United States with all the countries and total trade balance of US in goods with Japan. Here a2, a3, a4 and a5 and a6 are the slope coefficients of gross domestic product, unemployment, inflation and that of the trade balance and the deviation between the total balance of payment and that of the trade balance of US with Japan and a1 is the intercept term. The purpose of the paper is in identifying the effect of the independent variables on the dependent variable that is the exchange rate (USD/Yen). The ratio of the currencies can be also defined as exchange rate which is defined as the ratio of USD to that of Yen where Yen is the quoted currency and that USD is of the base currency and it is taken as the prime dependent variable. The rate of exchange play a predominant part in the level of trade of a country which can be said to be of high significance and as it is highly critical within majority of the free economies of the world. The exchange rate acts as a key performance indicator of a country and they are most popularly watched and are subjected to analysis and also that of manipulation within the governmental system canalizing the economic resources. The exchange rate or the ratio between the quoted and base currency with that of GDP is also of high importance. There has been rapid growth in several countries of the economy in the present world. The intensity of the economic growth is highly associated with the increase in GDP. The increase in GDP and that of the exchange rate can be said to bear a positive relation with each other. It can be said that the rise in the GDP of a country will lead to higher output generation in the economy and that it leads to the rise in the revenue generation of the country as well. Now as the GDP rises the economy becomes stronger and the value of currency also rises. In this case the exchange rate ratio has been taken as USD to that of Japanese Yen for thirty years. Now it can be stated that previously in order to purchase 1 US dollar now it will require more Yen for purchasing 1 US dollar and the ratio will fall down with the rise in GDP and as a result the sign of the coefficient is negative. Inflation is generally the rise of the price level in the economy of a country. It can be said that the rising value of inflation is bad for the economy (although various exceptions like that of Philips curve which declares a negative relation between the unemployment and the inflation which states that if unemployment rises then the inflation falls). Now the inflation and expanding unemployment is bad for the economy. But it is assumed here that inflation that any such exceptions will be violated and it will be generally held that the high rate of inflation affects the economy adversely (Unfounded Fear of Inflation, 2012). Now, as general rule, a country with a consistently lower inflation rate exhibits a rising currency value, as its purchasing power increases relative to other currencies. During the last half of the twentieth century, the countries with low inflation included Japan, Germany and Switzerland, while the U.S. and Canada achieved low inflation only later. Those countries with higher inflation typically see depreciation in their currency in relation to the currencies of their trading partners. This is also usually accompanied by higher interest rates. Thus it can be said that the inflation rate and the exchange rates bear an indirect relation and hence as a result there is a negative sign attached in the model before its coefficient. The relation between the unemployment in general with that of the ratio of base currency to that of the quoted currency is also negative in the sense as unemployment rises then the value of the economy becomes less stronger and the currency becomes cheaper and that the ratio will rise and so with the rise in unemployment the ratio of the USD to that of Yen also rises and so there is a positive relation between them. The TBGUSG is trade balance of goods of United States and it can be said that as trade balance falls the ratio will raise bearing a negative relation with the ratio of the US dollar to that of the Japanese Yen. The last variable is the deviation between the balance of payments which includes that of the goods and services and it is subtracted from the Trade balance of goods for obtaining the trade balance in services and it bears also positive relation with the ratio of the USD to that of Yen likewise the explanation of the previous one. Data Description The data considered for the purpose of running regression is focused on the time series data of 30 years starting from that of 1982 to 2011. The database has been extracted from different sources which includes majorly from the US census government sites. The GDP have been extracted from calculating them at nominal prices. The unemployment rate has been taken as percentage term fetched from various authentic sources from the internet. Inflation rate have been also taken as the percentage form concerning various internet sources. The trade balance data have been deflated in terms of billions of dollars extracted from the census sites of the US government department. The last variable is calculated as the difference of the total BOP of the United States with that of the total trade balance with Japan with respect to goods. The limitations in the collection of the data sources which were encountered were that all the available data cannot be collected from the government sites and different websites were considered for the data collection procedure. The main purpose is to see the variation of the independent variables on the dependent variable. The following is the data for thirty years with all the variables defined. Years (USD/Yen)=Y GDP ($ billion nominal)=GDP Unemployment(%) rate= UN Inflation (%)rate= IN Trade balance($ billion nominal)=TB BOP (BUSD) -TBJ(BUSD)=IJ 2011 76.98 15094.5 8.5 3.16 -63.2 -559.88 2010 81.67 14526.5 9.4 1.64 -60.1 -494.74 2009 93.08 13939 9.9 -0.34 -44.7 -379.15 2008 90.79 14369.1 7.3 3.85 -74.1 -698.34 2007 111.7 14028.7 5 2.85 -84.3 -696.73 2006 119 13377.2 4.5 3.24 -89.7 -753.29 2005 117.9 12623 4.9 3.39 -83.3 -708.62 2004 102.7 11853.3 5.4 2.68 -76.3 -605.36 2003 107.1 11142.2 5.7 2.27 -66 -490.98 2002 118.4 10642.3 6 1.59 -70 -417.43 2001 121.5 10286.2 5.7 2.83 -69 -361.77 2000 107.8 9951.5 3.9 3.38 -81.6 -376.75 1999 113.8 9353.5 4 2.19 -73.4 -263.16 1998 130.8 8793.5 4.4 1.55 -64 -166.14 1997 121 8332.4 4.7 2.34 -56.1 -108.27 1996 108.8 7838.5 5.4 2.93 -47.6 -104.07 1995 94.05 7414.7 5.6 2.81 -59.1 -96.38 1994 102.2 7085.2 5.5 2.61 -65.7 -98.49 1993 111.1 6667.4 6.5 2.96 -59.4 -70.31 1992 126.7 6342.3 7.4 3.03 -49.6 -39.21 1991 134.5 5992.1 7.1 4.25 -43.4 -31.14 1990 144.8 5800.5 6.3 5.39 -41.1 -80.86 1989 138 5482.1 5.4 4.83 -49.1 -93.14 1988 128.1 5100.4 5.3 4.08 -51.8 -114.57 1987 144.6 4736.4 5.8 3.66 -56.3 -151.68 1986 168.5 4460.1 6.6 1.91 -55 -138.54 1985 238.3 4217.5 7.5 3.55 -46.2 -121.88 1984 237.4 3930.9 7.3 4.3 -33.1 -109.07 1983 237.4 3534.6 8.3 3.22 -18.2 -57.77 1982 248.8 3253.2 10.8 6.16 -12.2 -24.16 Table 1. [US Gross Domestic Product History, (2012), Historical Exchange rate (2012), Unemployment rate, seasonally adjusted, (2012), Trade in Goods with Japan, (2012), Historical Inflation Rate, (2012)] Analysis The process of multiple regressions has been adapted for finding our results. The process of multiple regressions is a statistical tool which allows in the prediction of the values of one variable on the basis of the values of several other variables. In the field of social science this technique is widely used. As an example, it can be said that we are interested in analyzing how much an individual enjoys their jobs and the variables like that of salary, extent of academic qualification, age, sex, number of years in full time employment, socio economic status and so on are highly useful in the contributing towards the job satisfaction of the employees. If the data are collected on all these variables suppose with that of the process of surveying it would be useful in measuring the accurate prediction of job satisfaction (Multiple regression, 2012, p.206). Presentation and interpretation of the regression results The model of multiple regressions which is used in the paper is written as follows: Microsoft Excel 2007 is used in finding out the regression which generated the estimated equation as: Y= 333.01-0.018+0.18-4.30+1.68-0.24…..(2) DW 0.98342361 Table 2. Running the regression the estimated values of the slope coefficients of the independent variables have been determined and they are in accordance with that of the signs as interpreted by that of the above theoretical explanation. The values of the estimated slope coefficients have been taken from the table and plugged in the equation and represented as equation 2. The outcome of the regression results can be interpreted from the results of the coefficients of the independent variables also. The -0.018 coefficient of the GDP indicates that increase in every one percent or unit increase in GDP the ratio of US dollar and that of Japanese Yen decreases by the value of 0.018. The value 0.18 is the coefficient for the predictor Unemployment rate of USA given by the variable and it indicates that with the rise 1 percent change in the unemployment rate of the United States, the value of the ratio of the US dollars to that of the Japanese Yen will also rise by the amount of .18. The value -4.30 is the coefficient value of the predictor of the inflate rate of the United States. It represents that with 1 unit rise in the inflation rate the value of the dollar becomes cheaper and the ratio increases by a magnitude of 4.30. The value -1.68 is the coefficient for the predictor trade balance in goods of USA with respect to Japan. The trade balance in the dataset is negative and with the rise in 1 unit of trade balance in goods of USA with that of Japan the value of the ratio of the currency of USA and that of Japanese Yen will rise by the amount 1.68. The last variable which is taken as the difference between the balance of payment of USA with the world and that of the trade balance of USA in goods with Japan has been taken which yields the variable representing the values of services of USA with Japan and the balance of payments of USA with that of the rest of the world. The coefficient of this predictor is given by the value of the coefficient that is 0.24 and it indicates that with the rise in the variable thus constructed increases by 1 unit, the value of the ratio of the US dollar to that of the Japanese Yen. For the purpose of the measuring the presence of the autocorrelation among the residuals Durbin Watson test is calculated. The test is usually exercised for the purpose of testing the null hypothesis that the residuals of regression are not auto correlated with each other. The range of Durbin Watson generally varies from 0 to 4 with the value near to that of 2 generally indicating non autocorrelation and with that of the alternative hypothesis that the residuals do follow autocorrelation among the residuals. Here the value of the Durbin Watson test is 0.9834261 and it indicates autocorrelation among the residuals and it can be stated that the variables are biased to an unknown extent and generally cannot be very much reliably applicable in scholarly paper, publication or journals and so on (Durbin-Watson Significance Tables, 2012, pp. 1-2). In statistics the coefficient of R2 is the coefficient of determination which generally indicates the proportion or the degree of variability within a data set which is accounted for by a statistical model. The value of R2 lies between -1 and +1. More the value is close to 1, more is the association between the variables. A small value of the R2 also implies that the error variance is large as compared to that of the variance of the dependant variable and it will become hard in estimating the coefficients of the independent variables and this error can be avoided by the inclusion of large samples. In large samples the addition of large samples the R2 does not give proper results and in this case another statistic known as the adjusted R squared whose value takes into account the number of the independent variables in the model but the value of ordinary R squared does not take that in account and thus gives biased results. However in the model, the variables in consideration are not much in number and that the dataset is also not so large. The values of the regression statistics is provided below: Regression Statistics Multiple R 0.920959799 R Square 0.848166951 Adjusted R Square 0.816535066 Standard Error 20.21059879 Observations 30 Table 3. In the above table, the value of R square is 84.8% which suggests that the independent variables used in the model generally accounts for around 84.8% of the variation of the outcome and it is highly predominant in case of time series regressions in which one of the observation generally associates with each other. For the valuation of the adjusted R squared it is generally desirable to be of more than that of 50% or of greater percentage. For the adjusted R squared also the value is usually desired about more than fifty percent. In our modeling, the value of the adjusted Adj. R2 is 0.816 which is also good in explaining the variation of the independent variables on the dependent variables although the passing of the Durbin Watson test is required to be passed. With respect to adjusted R2, the regression results indicate that the independent variables explain around 81 percent of the variance of the dependent variable. It is also a common notion that the adjusted R squared and R2 is considered often neglecting the test of autocorrelation of Durbin Watson test. But the passing of the Durbin Watson test is also highly required while executing a time series regression. Now the significance of the model will be tested with respect to the t-statistic. The thumb rule is that if the value of the t-statistic is greater than 2 at 95% confidence interval level, then that variable is significant in resulting to its variation on the dependent variable. The p-value generated from the regression result is also highly useful in the measuring the significance of variation of the independent variable on the dependent variable. The following tables shows the variables and their t-statistic and p-value at 95% confidence interval.   Intercept GDP ($ billion nominal)=GDPUS Unemployment(%) rate= UNRUS Inflation (%)rate= INRUS Trade balance($ billion (in goods only) nominal)= Table 4. Table 5. P-value 5.25E-06 1.45E-06 0.96816 0.226471 0.014366 6.63E-06 Table 6. From the above tables, it can be found that the absolute value of the is GDPUS 6.348695603 and trade balance in goods of USA with Japan, is 2.639290943 and that of is 5.730855495 which signifies that GDP ($ billion nominal)=GDPUS , Trade balance($ billion (in goods only) nominal)= and that of are the most significant variable in explaining the variation on the ratio of the US dollars to that of Japanese Yen which is the dependent variable in this paper and taken as Y. The other variables like Inflation (%) rate= INRUS and Unemployment (%) rate= UNRUS whose values of t-statistic are 0.040334239 and 1.241353444 which are less than 2 and hence insignificant. Conclusion The paper dealt with the multiple regression analysis with five independent variables and one dependent variable. The target was to show how the independent variables affect the dependent variables with the statistical analysis. The analysis has been made from a socio economic point of view as the dependent variable which is ratio of the currencies of two countries is treated as a very useful tool in indicating the economic performance of a country. From the analysis it can be found that the variables GDPUS that is the gross domestic product of United States is the most significant variable in explaining the variation of Y which is followed by and . References Historical Exchange rate, (2012), retrieved on August 31, 2012 from: Historical Inflation Rate, (2012), retrieved on August 31, 2012 from: Haferkamp, H & Smelser, N, (1992), Social Change and Modernity, The Regents of the University of California, retrieved on August 31, 2012 from: < http://www.communication-sensible.com/download/Social%20Change%20and%20Modernity.pdf Multiple regression, An introduction to multiple regression Performing a multiple regression on SPSS (2012), retrieved on August 31, 2012 from: Trade in Goods with Japan, (2012), retrieved on August 31, 2012 from: < http://www.census.gov/foreign-trade/balance/c5880.html> Unemployment rate, seasonally adjusted, (2012), retrieved on August 31, 2012 from: US Gross Domestic Product History, (2012), retrieved on August 31, 2012 from: http://www.usgovernmentspending.com/us_gdp_history#copypaste> Unfounded Fear of Inflation, (2012), retrieved on August 31, 2012 from: < http://economistsview.typepad.com/economistsview/inflation/> Read More