In this paper we analyze the investment patterns of Japanese households using three kinds of generalized Tobit models. We consider the following three types of investments: (1) bank deposits, (2) long-term income-gain assets, and (3) capital-gain assets. Generalized Tobit models are called for because there are households which do not possess either or both of the last two types of assets. In our data every household does possess the first type of asset, and this fact will be incorporated into our models as a priori specification. The three models we estimate are a simultaneous equations Tobit model, a Dubin-McFadden type model, and a sequential Tobit model. The first model arises from a Kuhn-Tucker solution to the maximization of a quadratic utility function subject to the constraint that the sum of the investments into the three types of assets is equal to an exogenously-determined value of the total assets of a household. The second model is based on the assumption that there are fixed costs of owning the last two types of assets. Finally, the last model is derived from the assumption that a household first determines the amount of the first type of asset it should hold and second allocates whatever left into the other two types of assets. Simpler, more obvious ways to analyze our data are available, such as ordinary least squares, probit and logit, and standard Tobit. These estimates are also reported and compared with our elaborate estimates in a later section.

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This paper elucidates the question of whether production efficiency (in the weak sense) obtains in an optimally taxed economy, which is posed by the seminal paper of Diamond and Mirrlees. This paper presents a complete conclusion and a proof for that the (desirability of) production efficiency holds, except (i) a not interesting case where private production is wholly less efficient than public production, or (ii) a case where some good(s) is exempt from tax imposition.

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