TERM 1: K market integration Flashcards
Assumption of free K mobility for small open economy implies
r1=r*
No arbitrage opportunities between domestic and international K markets.
In a closed economy, S and I correlations are…
S = I in a closed economy CA=0 Therefore correlation(S, I) = 1
Why are S-I correlations near 1 NOT evidence of low K mobility?
Because S and I can be shocked simultaneously which causes them to move in the same direction, but economy is open.
2 examples of shocks to show S-I correlations near 1 do NOT evidence low K mobility
- Persistent productivity shock: S and I rise
2. Large open economy e.g. uncertainty raises S, I also rises as IR fall to ensure CA US=-CA ROW
Direct measure of K integration
= IR differentials
Free K mobility means
There is no cost of moving capital abroad. Can choose freely between domestic and foreign assets.
Spot ER measures
The today domestic price of 1 unit of foreign currency
Forward ER =
the today determined domestic price of 1 unit of foreign currency, to be used for future transactions.
CIRP formula
(1+i) = (1+i*) . F1/S1
What does CIRP imply about K mobility?
CIRP must hold under free K mobility
forward discount =
fd = (F - S) / S
Covered IR differential =
(1+i) - (1+i*)(F1/S1)
Approx = i - i* - fd
UIRP formula
(1+i) = (1+i*) E(S2)/S1
Difference between CIRP and UIRP
CIRP = use forward ER - covers risk UIRP = use expected future spot ER - does NOT cover risk
Probability of good state =
Pi
Probability of bad state =
(1 - Pi)
For which variables is there risk in?
Nominal endowment: Q2g & Q2b
Consumption: C2g & C2b
Prices: P2g & P2b
Spot ER: S2g & S2b
3 types of bonds households can buy
- B1 = domestic currency, pay i
- B1* = foreign, pay i*, forward cover
- B1* tilda = foreign, pay i, no forward cover
Expected utility function in terms of consumption
U = U(C1) + Pi U(C2g) + (1-Pi) U(C2b)
HH BC P1 (assume B0=0)
Q1 = P1C1 + B1 + S1B1* + S1B1*tilda
Households use their period 1 endowment for (2)
- consumption (C1)
2. buying bonds (B1/B1/B1tilda)
HH BC P2 good
Q2g + (1+i)B1 + (1+i)F1B1 + (1+i)S2gB1tilda
= P2g C2g
HH BC P2 bad
Q2b + (1+i)B1 + (1+i)F1B1 + (1+i)S2bB1tilda
= P2b C2b
What about price of bonds?
We normalise the price to 1.
All in terms of domestic currency.
What do HH do in p1 and p2?
In period 1, HH buy bonds.
In period 2, HH get returns from their bonds.
6 choice variables for HH
C1, C2g, C2b, B1, B1, B1 tilda
Objective of HH
Max U=U(C1) + PiU(C2g) + (1-Pi)U(C2b)
Constraints of HH (just name)
- P1 BC
- P2 good BC
- P2 bad BC
How do we eliminate consumption from utility function?
- solve P1 BC for C1
- solve P2 good BC for C2g
- solve P2 bad BC for C2b
and sub all into utility function
3 FOCs
- dU/dB1 = 0
- dU/dB1*=0
- dU/dB1*tilda=0
for dU/dB1 what asset pricing condition do we get?
1 = (1+i)E1(M2)
where M2 = [U’(C2)/U’(C1) x P1/P2)]
What is the pricing kernel?
M2 = (U’(C2)/U’(C1) x P1/P2)
It gives the nominal MRS between period 2 and 1 consumption.
for dU/dB1* what asset pricing condition do we get?
1 = (1+i*)F1/S1 E1(M2)
How to we get the CIRP formula?
Combine conditions obtained from dU/dB1 and dU/dB1*.
E1(M2) s cancel out.
CIRP holding implies
The return on domestic assets in domestic currency = the return on foreign assets also in domestic currency, when bought using forward cover. This means there are no arbitrage opportunities.
What about UIRP under free K mobility?
UIRP FAILS under free K mobility
What is required for UIRP to hold?
F1 = E1(S2)
for dU/dB1*tilda what asset pricing condition do we get?
1 = (1+i*)E1[(S2/S1) M2]
combining dU/dB1* and dU/dB1*tilda conditions? Does this imply that UIRP holds?
F1 E1(M2) = E1(S2M2) This does NOT imply that F1=E1(S2) Therefore UIRP fails
Remember: COV(a, b) =
COV(a, b) = E(ab) - E(a).E(b)
rewrite dU/dB1*tilda condition using formula for E(ab)
1 = (1+i*)[COV(S2/S1, M2) + E(S2/S1) E(M2)
What do we assume about the relationship between M2 and S2/S1?
We assume that COV(S2/S1, M2)=0
i.e. the depreciation rate and pricing kernel are UNCORRELATED.
Therefore, our dU/dB1*tilda condition becomes
1=(1+i*)E1(s2/s1)E1(M2)
Proof that UIRP holds
Combine dU/dB1* & new dU/dB1*tilda
We get F1=E1(S2)
Or if combine with dU/dB1 we get the UIRP formula as E1(M2) s cancel out
So what does UIRP mean for free K mobility?
It does NOT have to hold under free K mobility, therefore if it does NOT hold this is NOT conclusive evidence against free K mobility.
Before 1920, before forward ER prevalent, what was used?
Long bills: bt = dollar price in NY of £1 deliverable in London after 90 days
what is long bill IR differential formula?
LBIRD = 1/(1+it*) x St - bt
should be zero for perfect K mobility.
