TERM 1: K market integration

Question 1

Assumption of free K mobility for small open economy implies

Answer 1

r1=r*

No arbitrage opportunities between domestic and international K markets.

Question 2

In a closed economy, S and I correlations are…

Answer 2

S = I in a closed economy CA=0
Therefore correlation(S, I) = 1

Question 3

Why are S-I correlations near 1 NOT evidence of low K mobility?

Answer 3

Because S and I can be shocked simultaneously which causes them to move in the same direction, but economy is open.

Question 4

2 examples of shocks to show S-I correlations near 1 do NOT evidence low K mobility

Answer 4

1. 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

Question 5

Direct measure of K integration

Answer 5

= IR differentials

Question 6

Free K mobility means

Answer 6

There is no cost of moving capital abroad. Can choose freely between domestic and foreign assets.

Question 7

Spot ER measures

Answer 7

The today domestic price of 1 unit of foreign currency

Question 8

Forward ER =

Answer 8

the today determined domestic price of 1 unit of foreign currency, to be used for future transactions.

Question 9

CIRP formula

Answer 9

(1+i) = (1+i*) . F1/S1

Question 10

What does CIRP imply about K mobility?

Answer 10

CIRP must hold under free K mobility

Question 11

forward discount =

Answer 11

fd = (F - S) / S

Question 12

Covered IR differential =

Answer 12

(1+i) - (1+i*)(F1/S1)

Approx = i - i* - fd

Question 13

UIRP formula

Answer 13

(1+i) = (1+i*) E(S2)/S1

Question 14

Difference between CIRP and UIRP

Answer 14

CIRP = use forward ER - covers risk
UIRP = use expected future spot ER - does NOT cover risk

Question 15

Probability of good state =

Answer 15

Pi

Question 16

Probability of bad state =

Answer 16

(1 - Pi)

Question 17

For which variables is there risk in?

Answer 17

Nominal endowment: Q2g & Q2b
Consumption: C2g & C2b
Prices: P2g & P2b
Spot ER: S2g & S2b

Question 18

3 types of bonds households can buy

Answer 18

1. B1 = domestic currency, pay i
2. B1* = foreign, pay i*, forward cover
3. B1* tilda = foreign, pay i, no forward cover

Question 19

Expected utility function in terms of consumption

Answer 19

U = U(C1) + Pi U(C2g) + (1-Pi) U(C2b)

Question 20

HH BC P1 (assume B0=0)

Answer 20

Q1 = P1C1 + B1 + S1B1* + S1B1*tilda

Question 21

Households use their period 1 endowment for (2)

Answer 21

1. consumption (C1)

2. buying bonds (B1/B1/B1tilda)

Question 22

HH BC P2 good

Answer 22

Q2g + (1+i)B1 + (1+i)F1B1 + (1+i)S2gB1tilda

= P2g C2g

Question 23

HH BC P2 bad

Answer 23

Q2b + (1+i)B1 + (1+i)F1B1 + (1+i)S2bB1tilda

= P2b C2b

Question 24

What about price of bonds?

Answer 24

We normalise the price to 1.

All in terms of domestic currency.

Question 25

What do HH do in p1 and p2?

Answer 25

In period 1, HH buy bonds.

In period 2, HH get returns from their bonds.

Question 26

6 choice variables for HH

Answer 26

C1, C2g, C2b, B1, B1, B1 tilda

Question 27

Objective of HH

Answer 27

Max U=U(C1) + PiU(C2g) + (1-Pi)U(C2b)

Question 28

Constraints of HH (just name)

Answer 28

1. P1 BC
2. P2 good BC
3. P2 bad BC

Question 29

How do we eliminate consumption from utility function?

Answer 29

1. solve P1 BC for C1
2. solve P2 good BC for C2g
3. solve P2 bad BC for C2b
   and sub all into utility function

Question 30

3 FOCs

Answer 30

1. dU/dB1 = 0
2. dU/dB1*=0
3. dU/dB1*tilda=0

Question 31

for dU/dB1 what asset pricing condition do we get?

Answer 31

1 = (1+i)E1(M2)

where M2 = [U’(C2)/U’(C1) x P1/P2)]

Question 32

What is the pricing kernel?

Answer 32

M2 = (U’(C2)/U’(C1) x P1/P2)

It gives the nominal MRS between period 2 and 1 consumption.

Question 33

for dU/dB1* what asset pricing condition do we get?

Answer 33

1 = (1+i*)F1/S1 E1(M2)

Question 34

How to we get the CIRP formula?

Answer 34

Combine conditions obtained from dU/dB1 and dU/dB1*.

E1(M2) s cancel out.

Question 35

CIRP holding implies

Answer 35

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.

Question 36

What about UIRP under free K mobility?

Answer 36

UIRP FAILS under free K mobility

Question 37

What is required for UIRP to hold?

Answer 37

F1 = E1(S2)

Question 38

for dU/dB1*tilda what asset pricing condition do we get?

Answer 38

1 = (1+i*)E1[(S2/S1) M2]

Question 39

combining dU/dB1* and dU/dB1*tilda conditions? Does this imply that UIRP holds?

Answer 39

F1 E1(M2) = E1(S2M2)
This does NOT imply that F1=E1(S2)
Therefore UIRP fails

Question 40

Remember: COV(a, b) =

Answer 40

COV(a, b) = E(ab) - E(a).E(b)

Question 41

rewrite dU/dB1*tilda condition using formula for E(ab)

Answer 41

1 = (1+i*)[COV(S2/S1, M2) + E(S2/S1) E(M2)

Question 42

What do we assume about the relationship between M2 and S2/S1?

Answer 42

We assume that COV(S2/S1, M2)=0

i.e. the depreciation rate and pricing kernel are UNCORRELATED.

Question 43

Therefore, our dU/dB1*tilda condition becomes

Answer 43

1=(1+i*)E1(s2/s1)E1(M2)

Question 44

Proof that UIRP holds

Answer 44

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

Question 45

So what does UIRP mean for free K mobility?

Answer 45

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.

Question 46

Before 1920, before forward ER prevalent, what was used?

Answer 46

Long bills: bt = dollar price in NY of £1 deliverable in London after 90 days

Question 47

what is long bill IR differential formula?

Answer 47

LBIRD = 1/(1+it*) x St - bt

should be zero for perfect K mobility.