The quantity theory of money says that there is a direct relationship between the quantity of money in the economy and the aggregate price level. Put simply, if the quantity of money doubles, then the price level should also double. Figure 13.6 shows the percentage change in a measure of the quantity of money \((M)\) and the percentage change in a measure of aggregate prices \((P)\) for the United States between 1961Q1 and 2005Q4 (data file qtm). A VEC model was estimated as follows:

a. Identify the cointegrating relationship between \(P\) and \(M\). Is the quantity theory of money supported?

b. Identify the error-correction coefficients. Is the system stable?

c. The above results were estimated using a system approach. Compute the cointegrating residuals and confirm that the series is indeed an \(\mathrm{I}(0)\) variable.

d. Estimate a VEC model using the cointegrating residuals. (Your results should be the same as above.)

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AP = -0.016(P-1.004M, +0.039) + 0.514AP1-0.005AM,-1 (t) (-2.127) (-3.696) (1.714) (7.999) (-0.215) 0.067 (P-1.004M1 +0.039) - 0.336AP-1 -0.340AM-1 , = (1) (3.017) (-3.696) (1.714) (-1.796) (-4.802)