The paper aims to estimate the Fisher index during the period 1994-1997 to explore how well the Laspeyres index can serve as the cost of living index. It is shown that the Laspeyres results in an upward substitution bias, and the bias appears to be higher for the ultra-poor and the poor. It means that for the very poor group the Laspeyres index overestimates their cost of living. With a limited budget the poor tends to have substitution to ensure a certain level of living standard. This suggests a remarkable point that if the basket weights are not revised frequently the Laspeyres index can present a significant bias from the cost of living, and this bias tends to be higher for the poor group. Since there is not a significant difference in the CPI between the poor and the non-poor and the whole population, CPI can be used as an approximate index of living cost of the poor as well as the non-poor for a period from one to three years.