Question

The table below contains the following variables, growth rates of real GDP, M1, M2, velocity of M1 and M2 (denoted V1 and V2), the federal funds rate (FFR), and the CPI inflation rate. Use the quantity equation to calculate the equilibrium inflation rate using individually M1 and M2. Next, calculate the equilibrium inflation rate assuming the quantity theory of money holds (i.e. assuming velocity is constant). According to your calculations, which is a better predictor of inflation, M1 or M2? Similarly, which is a better predictor of inflation, assuming the quantity theory holds, or not?

Table 8.3: Growth Rates

	RGDP	M1	M2	V1	V2	FFR	CPI
1990	1.9	3.6	5.5	2.0	0.2	8.10	5.4
1995	2.7	-0.2	2.0	5.1	2.8	5.84	2.8
2000	4.1	0.1	6.0	6.3	0.4	6.24	3.4
2005	3.3	2.1	4.3	4.5	2.2	3.21	3.4
2010	2.5	6.4	2.5	-2.5	1.2	0.18	1.6
2015	2.4	7.5	5.9	-3.8	-2.3	0.13	0.1

(Source: FRED II, St. Louis Federal Reserve)

Answer 1

According to Quantity Equation: Mt * Vt = Pt * Yt

taking log the two sides, we get: LogMt + Log Vt = logPt + LogYt

taking partial derivatives on the two sides w.r.t. to time, we get:

(1/Mt)(dMt/dt) + (1/Vt)(dVt/dt) = (1/Pt)(dPt/dt) + (1/Yt)(dYt/dt)

or on the other hand gm + gv= π+ gy

where g speak to development rate of individual variables, and π is the balance inflation rate. Along these lines,

π = gm + gv - gy

	RGDP	M1	M2	V1	V2	FRR	CPI	inflation rate using M1	inflation rate using M2
1990	1.9	3.6	5.5	2	0.2	8.1	5.4	3.7	3.8
1995	2.7	-0.2	2	5.1	2.8	5.84	2.8	2.2	2.1
2000	4.1	0.1	6	6.3	0.4	6.24	3.4	2.3	2.3
2005	3.3	2.1	4.3	4.5	2.2	3.21	3.4	3.3	3.2
2010	2.5	6.4	2.5	-2.5	1.2	0.18	1.6	1.4	1.2
2015	2.4	7.5	5.9	-3.8	-2.3	0.13	0.1	1.3	1.2

According to Quantity Theory of Money: Mt * V = Pt * Yt

taking log the two sides, we get: LogMt + Log V = logPt + LogYt

taking partial derivatives on the two sides w.r.t. to time, we get:

(1/Mt)(dMt/dt) + (1/Vt)(dV/dt) = (1/Pt)(dPt/dt) + (1/Yt)(dYt/dt)

or on the other hand gm + gv= π​​​​​​​+ gy, in any case, gv = 0 since speed is constant

where g speak to development rate of individual variables, and π is the balance inflation rate. Consequently,

π = gm - gy

	RGDP	M1	M2	V1	V2	FRR	CPI	inflation rate using M1	inflation rate using M2
1990	1.9	3.6	5.5	2	0.2	8.1	5.4	1.7	3.6
1995	2.7	-0.2	2	5.1	2.8	5.84	2.8	-2.9	-0.7
2000	4.1	0.1	6	6.3	0.4	6.24	3.4	-4	1.9
2005	3.3	2.1	4.3	4.5	2.2	3.21	3.4	-1.2	1
2010	2.5	6.4	2.5	-2.5	1.2	0.18	1.6	3.9	0
2015	2.4	7.5	5.9	-3.8	-2.3	0.13	0.1	5.1	3.5

According to the calculation M2 is better indicator of Inflation rate because M2 is a broader measure of cash flexibly as it contains all components of M1 along with saving stores and the momentary mutual reserve stores and time stores that can be easily changed over to fluid cash.

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