Question

Imagine that everyone in the world pays a tax of t percent on interest earnings from dollar investments. How would such a tax alter the analysis of the interest parity condition? Explain. HINT: A tax of t percent changes the return to a dollar investment to (1-t) Rs

Answer 1

As per Uncovered interest rate parity theory, the difference in interest rates between foriegn country and domestic country will equal the relative change in currency foreign exchange rates over the same period.

S(f)/S(d) = i(f) - i(d).

Where s(f) is expected future spot price of foreign currency

s(d) is expected future spot price of domestic currency

i(f) is foreign interest rate

i(d) is domestic interest rate

As tax rate on interest rate earnings in domestic economy is t and in foreign economy is t*

So after tax effect, interest rate earnings will be i(d) X (1-t) and i(f) X (1-t*) for domestic and foreign economy

So applyin actual interest rate earning uncovered interest rate parity equation will be:

S(f)/S(d) = i(f) *(1-t) - i(d)*(1-t*).

Condition 1: If t and t* are equal, let it be equal to t

then S(f)/S(d) =(1-t) i(f)- i(d)

As tax rate will be positive, change in exchange rate will be lesser in this case

Condition 2: If t is greater than t* , then t = t* + x

Then S(f)/S(d)= i(f)- t *i(f)- i(d) + t* i(d) = i(f)- i(d) - t*i(f) + t i(d) = i(f)- i(d)- t*i(f)+ t*i(d)+ x*i(d)= i(f)-i(d) -t*(i(f)-i(d) + x*i(d)

S(f)/S(d) = (1-t*)(i(f)-i(d))+ x* i(d)

this states that higher the difference between domestic tax rate and foreign tax rate, higher will be change in exchange rate.

Condition 2: If t is greater than t* , then t = t* - x

Then S(f)/S(d)= i(f)- t *i(f)- i(d) + t i(d) = i(f)- i(d) - t*i(f) + t i(d) = i(f)- i(d)- t*i(f)+ t*i(d) - x*i(d)= i(f)-i(d) -t*(i(f)-i(d) - x*i(d)

S(f)/S(d) = (1-t*)(i(f)-i(d)) - x* i(d)

this states that lesser the difference between domestic tax rate and foreign tax rate, higher will be change in exchange rate.