Does Imperfect Capital Market Dynamically Stabilize Households' Asset Holding?

In an economy with infinitely-lived homogeneous and perfect capital market, gross interest rate is determined in equiliibrium as a reciprocal number of households' subjective discount factor as well known. They consume a constant fraction of their own total human and nonhuman wealth, and their nonhuman wealth does not change. On the other hand if households are heterogeneous, gross interest rate cannot be the same as a reciprocal number of their subjective discount factors any more for most of the households. Then majorities of the households are divided into two types. Those whose subject discount factors are higher than a reciprocal nunmber of gross interest rate, consume more and borrow the possible biggest amount to pay its interests in the long run, while those whose subjective discount factors are lower, consume less, save more for ever and their nonhuman wealth explodes in the long run. But most of households are not like either of them. This paper analyzes how imperfect capital market or liquidity constraints limit this sensitivity and dynamically stabilize asset or debt holding or debt holding of each household. Under imperfect capital market all types of heterogeneous households consume so that their absolute value of assets decreases up to zero according to Euler equation and they consume the same amount as their income after their net asset becomes zero. Equiliburium is proved to exist, where interest rate is determined to clear the capital market. Other findings are as follows. The Ricardian Equivalence may only be applicable for households who hold large assets or debts when tax cut or increase is Implemented so that it is financed while they have still assets or debts and are on their Euler equations. The larger the agency cost is, the more rapidly households decrease their absolute value of assets because of lower saving interest rate and higher borrowing interest rate. In equilibrium interest rate is determined to clear the capital market. Then it depends on the distribution of net asset holdings among households. The result depends on the assumption that income does not fluctuate a lot enough to make Euler equation valid for households without any assets. The sufficient conditions of the solution when income fluctuates are derived, then it is checked if there were any chances of consumption smoothing in Japan for rational households without any assets and found that under reasonable parameter values there had not been many chances in these ten years.