These results are produced that makes [S, P, P*, i, i*] ~ I and calculates any deviations from this long run path through the response given by following [AS, AP, AP*, Ai, Ai*] vector of variables in short run.
A valid vector error correction model (confirmed by Lagrange Multiplier test on residuals) results revealed, the domestic prices and interest rate affect the exchange rate positively in long run and the foreign prices and interest rate affect the future exchange rate negatively. Hence this hints the presence of PPP and UIP in long run equilibrium.
St= -25.1 + 2.72 Pt-1 – 6.87 PM* + 0.073 iM – 1.33 iM* + yt —
As the variables used in the model are in logarithmic form so the parameters estimated will be representing the elasticities of that particular independent variable with respect to the nominal Exchange Rate (dependent variable). Analyzing the long run relationship reveals a 1% increase in the domestic prices of Pakistan increase the Exchange rate in next time period by 2.72% on average; this more than one percent respond can be due to the ease with which the consumer can shift between local and foreign goods and services due to trade.
A 1% increase in the foreign (USA) prices will significantly decrease the exchange rate by 6.8% on average; this highly elastic response is mainly due to of some reasons like USA being a large economy and any change in the price level of USA effects the price level of the world, secondly Pakistan had pegged his Rupee with USA Dollar in the past and thirdly the amount of trade between USA and Pakistan is large enough that change in prices can alter consumers buying decisions and hence effect the exchange rate. As both domestic and foreign prices affect the exchange rate significantly, so the Purchasing Power Parity holds in long run for the case of Pakistan.
A 1% increase in the long term bond rate of Pakistan will increase the exchange rate of Pakistan by only 0.07% on average; this effect is very inelastic and statistically insignificant too. Its slight positive effect might be only due to the recent development of this industry that made bond rate more fluctuating to changes in the economy.
And a 1% increase in the long term bond rate of USA will significantly decrease the exchange rate of Pakistan by 1.33% on average: hence changes in the financial outlook of USA affect the Pakistan economy by the Exchange rate.
In any economy, any deviations from the long run path cause short run movement in these economic variables to bring back the equilibrium. A 1% deviation from the linear equilibrium path causes decrease in change of exchange rate by 0.022% on average; hence a unit deviation will be recovered in 3 years and 8 months. This slow convergence result comply with (Qayyum, Khan, & Kair-u-Zaman, 2004). This significant covergence also imply that first Hypothesis is statistically accepted and this CHEERS Model is resonable to explain the Exchange Rate deviations in Long Run.
Table 11. Vector error correction model
Short Run Parameters | Long Run Parameters | |||||||||
Series | ДLn(S)t-1 | ДLn(P)t-2 | ДLn(P*)_{t}-2 | Д Ln(i)t-2 | ДLn(i*)_{t}-2 | EC t-1 | Ln(P)t-1 | Ln(P*)t-1 | Ln(i)t-1 | Ln(i*)t-1 |
Д Ln(S)t | 0.016(0.071) | 0.413(0.203) | 0.780(0.527) | 0.007(0.009) | 0.051(0.031) | -0.022(0.008) | 2.72(0.461) | -6.87(1.364) | 0.074(0.071) | -1.33(0.258) |
ДLn(P)t-1 | 0.016(0.025) | 0.219(0.071) | 0.324(0.185) | -0.004(0.003) | 0.016(0.011) | -0.0003(0.003) | ||||
ДLn(P*)_{t}-1 | 0.011(0.010) | -0.046(0.029) | 0.493(0.075) | -0.0001(0.001) | 0.010(0.004) | -0.0001(0.001) | ||||
Д Ln(i)t-1 | 0.412(0.532) | 2.269(1.518) | 0.029(3.940) | -0.249(0.072) | 0.117(0.233) | 0.169(0.063) | ||||
ДLn(i*)t-1 | -0.014(0.159) | -0.137(0.454) | 3.633(1.179) | 0.015(0.021) | 0.302(0.069) | -0.076(0.019) | ||||
These results are produced that makes [S, P, P*, i, i*] ~ I and calculates any deviations from this long run path through the response given by following [AS, AP, AP*, Ai, Ai*] vector of variables in short run. A valid vector error correction model (confirmed by Lagrange Multiplier test on residuals) results revealed, the domestic prices and interest rate affect the exchange rate positively in long run and the foreign prices and interest rate affect the future exchange rate negatively. Hence this hints the presence of PPP and UIP in long run equilibrium. St= -25.1 + 2.72 Pt-1 – 6.87 PM* + 0.073 iM – 1.33 iM* + yt — As the variables used in the model are in