A three-stage: Iterative estimation approach to the permanent income model

In this paper, the minimum-variance (MV) method, originally proposed by Singh and Drost (1971) and Willassen (1975) to estimate the permanent income model (PIM), is revised in accordance with Friedman’s (1957) assumptions. It is shown that the revised MV estimator of the marginal propensity to consume permanent income (mpc) of the PIM is just the maximum-likelihood (ML) estimator of Kendall and Stuart (1901). Treating the PIM as a restricted factor-analysis model (RFAM) of two indicators and one single common factor and incorporating with Tuekey’s (1951) grouping approach, the three-stage iterative estimation method developed by Lin (1978) is suggested as an alternative approach to estimate the PIM. For illustration, estimates of mpc are computed for the data used by Haavelmo (1953). The sensitivity of estimation of mpc to the prior specification of the ratio of the variance of transitory income (error in observable income) to that of transitory consumption (error in observable consumption) ia conducted. Then, the estimates of mpc are compared to those obtained according to the original MV method and the ML or Tevised MV method. The estimate of mpc based on the ML or revised MV method is found to be remarkably close to the three-stage iterative estimate and confirms Mayer’s (1972) findings. Thus, it is pointed out that the substantially high estimates of mpc obtained from the original MV method may be misleading.