Using the annual data on gold prices, the Consumer Price Index (CPI), and the Ne

Question

Using the annual data on gold prices, the Consumer Price Index (CPI), and the New York Stock Exchange (NYSE) Index for the United States over the period 1977-1991, e have test two regressions suggesting whether gold and stocks are a good hedge against inflation, and the results are given below: 5+10 Regression 1: Gold price Bi+B2CPltu Regression 2: NYSE Indext-pl+2CPIctut a. Explain economic theory underlying the regression equations. b. The relationship between gold prices and consumer prices as well NYSE and consumer prices, as represented by the equations above, is tested by using regression analysis and the results obtained are given below. Interpret these regression results and explain whether gold or stock is better hedge against inflation. P-101.90+2.13 pe 186.18+1.84 Pe se (23.78) (0.230) R2=0.87 F= 85.32 N=15 R2=0.15 F= 2.30 N=15 se (125.40) (1.22)

Explanation / Answer

ans.

a. The economic theory behind the above regression equations is whether CPI which acts as a proxy for inflation rate can predict the dependent variables Gold price or the performance of NYSE index. At times of crisis can gold be used as a inflationary hedge. How does the NYSE Index perform when inflation fluctuates in the economy. What the relationship between the variables Gold Prices, Inflation(CPI) and Inflation(CPI) with NYSE Index. Does increase in one cause the decrease in other?

b. There is a postive relationship between Inflation (CPI) and NYSE Index as the sign of the coefficient of CPI in the regression equation between CPI and NYSE Index is positive. However, the intercept (-101.90) is negative suggesting that when CPI is zero, NYSE Index takes the value of - 101.90. This scenario is not possible in the real world as CPI can never be zero. Hence while modeling one should consider a change of the regression equatioin. Since intercept is the expected mean we could change the equation to Y = m(X - mean(X) ) + C for a more realistic scenario.

The Standard Error and R^2 are (0.230) and 0.87 respectively for the regression equation between CPI and NYSE Index whereas it is (1.22) and (0.15) for the equation between CPI and Gold respectively. The standard error and R^2 and the two measures of goodness of fit. The SE indicates how far the data points are from the regression line on an average. We want the distance between fitted values and data points to be small so that the fit is better. The standard error is greater in the second regression equation between Gold and CPI means that the there is a lot of error when CPI is used to predict Gold prices as compared to when CPI is used to predict NYSE Index price.

R^2 is also higher(0.87) in the first equation between NYSE and CPI meaning that 87% of the variation in the dependent variable can be explained by the model. A higher R^2 indicates a better fit than a lower R^2 which is the case in the second equation between CPI and Gold where R^2 = 0.15 i.e. 15% of the variation in the dependent variable can be explained by the data points. R^2 also indicates how close the data points are to the fitted values. In the first equation the higher R^2 validates the smaller SE (standard error) as compared to the second equation suggesting that the data points of CPI are a better fit to predict the NYSE Index than Gold Prices.

An F-test tests whether including the coefficients in the model improves the model fit or not. The F is 85.32 in the first equation between CPI and NYSE Index means the model where we use CPI as an independent variable to predict the dependent variable NYSE Index is a better model where the data points of CPI are a better fit than when we use CPI to predict Gold where the F is only 2.30.

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