In this section the empirical relationship will be explained using a mathematical model and at the end the final form will be converted in to stochastic form for the econometric modeling to be applied.

3.1 Purchasing Power Parity (PPP) Model

Start with the current account interaction between countries using the Law of One price Equation

Pt = St Pt* —

Here Pt = CPI of Pakistan, St = Nominal Exchange Rate, and Pt* = CPI of USA

Pt = St + Pt* —

Converting equation (2) it into the stochastic form we get St = аю + PnPt – P12Pt* + Mt —

If the Purchasing Power Parity holds then it is expected to have parameters p11 and p12 to be statistically near to unity and for the validity of this model m ~ I (0).

3.2 Interest Parity (UIP) Model

This Uncovered Interest Parity describes the role of financial market on the exchange rate.

ASe t+1= it/it* —

Here ASe t+1= Future Expected change in Nominal Exchange Rate, it = Bond Rate of Pakistan, and it* = Bond Rate of USA.

Taking logs of equation and converting it into stochastic form

ASet+1 = а20 + P21it P22i*t + Qt—

Uncovered Interest Parity holds if the parameters p21 and p22 must be significant and near to unit. And this model will be valid if Qt ~ I

3.3 PPP Model with Capital Account (Relative PPP)

St = Pt – Pt* —

Taking first difference of equation

ASt = APt – APt* — (8)

Form UIP

AS t+1e = it – it* —

From fisher relationship rt = it – APt+1e — (10) rt* = it* – APt+1*e —

Here rt = Real Interest Rate of Pakistan, rt* = Real Interest Rate of USA, APt+1e = Future Expected Inflation in Pakistan, APt+1*e = Future Expected Inflation in USA

So using equation and in equation to form AS t+1e = (rt – rt*) + (APt+1e – APt+1e*) —-

Assuming that trade equates the real interest rate so equation becomes AS t+1e = AP t+1e – AP t+1e* —

AS t+1 – a30 + p31APt+x – P32APt+1* + nt —

qt – a40 + P41qt-1 + nt —

So for this model to hold both parameters p31 and p32 must be significant and p31=-p32=1 and nt ~ I and this model can also holds in weak form if qt is I such that a40 Ф 0 and р41 Ф 1

Hence these PPP and UIP model can be estimated jointly as follows

St+1 – Pt – Pt* + it – it* + Yt —

In this specification the equality of the real interest rate is not assumed. Here as the price level is realized at the end of the time period and interest rate difference create incentives for the future decisions hence these variables effect the Nominal Exchange Rate after one Lag.

Converting equation into stochastic form to get St= a50 + P51P t-1 – P52Pt-1* + P53U-1 – P54U-1* + Yt —

Now this final stochastic equation will be used for the estimation of the exchange rate patterns using the relevant variables that are used and described above.

The effect of all the variables to the Exchange Rate seem reasonable by the fact that the lag is very small and as domestic and foreign people see the prices and interest rate of foreign and domestic countries at the end of the time period respectively so they respond in the next time period.

In this section the empirical relationship will be explained using a mathematical model and at the end the final form will be converted in to stochastic form for the econometric modeling to be applied. 3.1 Purchasing Power Parity (PPP) Model Start with the current account interaction between countries using the Law of One price Equation Pt = St Pt* — Here Pt = CPI of Pakistan, St = Nominal Exchange Rate, and Pt* = CPI of USA Pt = St + Pt* — Converting equation (2) it into the stochastic form we get St = аю + PnPt – P12Pt* + Mt — If the Purchasing Power Parity holds then it is expected to have parameters p11 and p12 to