Midterm 1 Flashcards
Fed’s preferred inflation measure method
PCE deflator
Gresham’s Law
If two forms of money are both legal tender, at a mint ratio that differs from the price ratio on the world market, the overvalued money will tend to drive the undervalued money out of circulation.
Money demand & relations to y,i, other factors
m^D = M^S/P*
Change in income y0 →y1, shift the m^D curve
Change in interest rate i0→i1, move along the m^D curve
m^D (up) if Volume of real transactions (up) or avg time held between transactions (up)
ABT Model
M^D = sqrt(BY/2i)
b=B/P
y = Y/P
m^D=sqrt(by/2i) (in real terms)
B= brokerage fees
m^D increases with sqrt of y, decreases with sqrt of i
Quantity Theory of Money
yt=Yt * P0/Pt=real income in year t0
Yt = Nominal income
P0=base year price level
Qtom: P=Ms/mD,
P->P in LR
Real money demand mD is determined by vol of real transactions conducted with M, and avg length of time M is held between receipt and expenditure. Both are positively related to mD
Walras’s Law
Aggregate Demand = Aggregate Supply
Aggregate Demand = D goods +m^D
Aggregate Supply = S good + m^S
D good + m^D = S good + m^S = Sgood + (M^s)/P
(M^s)/P - m^D = D good - S good
XS S of M = XS D for Goods
Relationship between PV and i
PV=FV/(1+i)^m
i=(FV/PV)^(1/m)-1
Bonds
PV=FV/(1+i)^m
PV=present value.
FV=future value.
i=nominal interest rate.
m =maturity.
Rise in bond yields=bond prices fall=longer maturity
ΔPV/PV ≈ -Δi * D
Consols
also known as perpetuities
PVc=C/i
Dc=1/i
Maturity and duration
For bond w/o coupon payment: ΔPV/PV ≈ -Δi * m
For bond w/ coupon payment: ΔPV/PV ≈ -Δi * D
Maturity and duration can serve to understand the sensitivity of bond price change to the change in interest rate
Duration coupon bond > duration amortized loan
GDP Calculation
Real gdp 2030 = gross gdp 2030 * (P level 2020/P level 2030)
CPI-U vs. PCE Deflator
CPI U 0.4% than pce deflator since 1983
PCE Deflator is closer to what CPI-U
measures than is GDP Deflator
Most different from PCE Deflator
PPI
Fisher Equation
i = r + π^e
Given r and π^e, we calculate nominal i by Fisher equation
Breakeven inflation rate π^e = i - r
Core CPI U and PCE Deflator excludes:
food and energy
TIPS
Provide direct observation of real rate r (indexed to CPI-U)
Treasury inflation-protected securities
Adaptive Learning
Inferred real rate r
Estimated π^e using adaptive learning (Recursive least squares, weighted avg of past inflation)
Inferred real rate r = i - π^e
Inferred real rate becomes similar to TIPS breakeven rate 2003-21
3 transfers from inflation
debt creditor redistribution
ripple effect
inflationary finance
debt creditor redistribution
Nominal Debt paying i = r + π^e
No transfer when π^e=π
Creditor hurt when π > π^e, purchasing power creditor–> debtor
Debtor hurt when π < π^e, purchasing power debtor–> creditor
Inflationary finance
Nominal Seigniorage: S = ΔM=change in money balance
s=ΔM/P = ΔM/M * M/P = μ*m
μ=money growth rate
m= real money balance
Inflation acts as a tax on m =M/P
Owners of m lose π*m
Govt. gains μ*m
purchasing power –>govt.
Ripple effect
Purchasing power: price (up) LAST → price (up) FIRST
Transfer purchasing power from those who sell goods and services whose prices go up last to those who sell goods and services whose prices go up first
Income velocity
V=Y/M = nominal income/nominal money balance
=inverse of avg time each $ is held
Why does V change: i = opportunity cost of holding M
i (up) → m^D (down), V (up)
m^D =m
Velocity rose 1950-1980. Fell 1985-present
Dynamic form of Quantity Equation
μ + ΔV/V ≈ π + g
g=real income growth
Self generating inflation
positive money supply shock results in μ (up)
→π(up) through π = μ + ΔV/V - g →π^e (up) through adaptive learning →i (up) through fisher equation →m^D (down) through m^D=sqrt(by/2i) →V (up) through V=y divided by m →ΔV/V > 0 b/c V (up) π(UP)
Tilt effect
High inflation reduces affordability of homes
self generating inflation cycle
P(up) ––> π^e (up) ––> i(up) ––> m^d (down), V (up) ––> P(up), etc.
But P is stable when π^e responds slowly to π. And when m^D responds weakly to i, π^e. Interrupting transition to expected inflation up, and to m^D (down), V(up), respectively.
Target Seigniorage and LR Monetary Laffer Curve
s = ΔM/P = ΔM/M * M/P = μ*m
m = m^D (i), i=r +μ + ΔV/V - g ≈ μ
→m^D (μ), μ = π^e -ΔV/V +g ≈ π^e
→m =m^D(μ) = m^D (π^e)
→s = μ * m^D
s* less than s max: unique and steady inf on LR laffer curve
s* more than s max: then unbounded runaway inf
Inflation induced taxation of capital equation
r AT = r(1-τ)-π τ
Bracket creep
inflation results in same real income taxed by a higher rate; income taxes increases proportional to nominal income. So since 1981, Fed brackets indexed to CPI-U (indexed for inflation rate) since 1981
Loanable funds model of r
Credit Market equilibrium (non monetary economy)
A decrease in savings behavior by household will tend to shift the supply of credit to the left and increase real interest rates.
An increase in borrowing behavior by households will tend to shift the demand for credit to the right and increase real interest rates
(1+r)^m is price of present goods in terms of future goods: 1 present good costs (1+r)^m future goods (on average)
r (up) → present goods more costly (rel. to future goods)
r (down) → present goods less costly
r=real interest rates
3 motives for μ, π
inflationary finance.
stimulate y, reduce U.
Reduce i, r
Yield to maturity..
PV=F (face value), bond is at par, YTM=C/F
PV less than F: bond is below par, YTM greater than C/F
PV>F, bond is above par, YTM less than C/F
Maturity and duration properties..
D=m if C =0 or m=1
D less than m if C more than 0 and m>1
D increases with m
D decreases with C/F
Price floor..
Pmin > P eq
Q^S > Q^D
Price ceiling..
Pmax<p></p>
