Abstract
This paper introduces durables into a dynamic general equilibrium overlapping generation model with idiosyncratic income shocks and endogenous borrowing constraints, which depend on durables. The aim of this paper is to evaluate the welfare effects of consumption tax reforms in a richer model that captures the difference between nondurable and durable consumption. When durables are considered, the standard results that a shift to consumption taxes is welfare improving are overturned. The mechanism of this opposing result is that consumption tax makes durable consumption more expensive without relaxing the borrowing constraint. The inability of borrowing to insure against income risk deviates the economy further away from market completeness and particularly hurts young and poor households. As a result, welfare decreases, coupled with negative redistribution.
A Definition of welfare gain
A.1 Welfare gain without durables
The welfare gain and the decomposition of the welfare gain are defined in the same way as Domeij and Heathcote (2004), except that we have overlapping generations and that the long-run and short-run welfare gain take different forms.
Specifically, the long run average welfare gain is defined as how much consumption need to be given to newborns in the future in order for them to be indifferent about the reform. Let
where
The short-run welfare gain are in term of the consumption equivalent of the current population. Let
Define
At last, the redistribution component
A.2 Welfare gain with durables
Here the consumption equivalent is defined as how much more consumption bundle of durables and nondurable
where cNR and cR are household nondurable consumption over time if there is no reform and if there is a reform. Other variables are interpreted in the same way.
Similar to the long run welfare gain, here the consumption equivalent is defined as how much more consumption bundle of durables and nondurable
because
We also define the aggregate component of the welfare gain in a similar way. Define
Denote the short run aggregate component by
Lastly, the short run redistribution component
B FOC for model with durables
The maximization problem of the benchmark economy is
subject to
Let
Taking derivatives with respective the arguments:
Rearranging and we get the following intratemporal and intertemporal conditions:
Because our conclusion rests on the relative tightness of the post-reform borrowing constraint, we write the post-reform borrowing constraint in a more general way,
In Section 4.2, when equal tax rates on nondurables and durables
With equal tax rates but a zero borrowing constraint
For the more relaxed borrowing constraint in Section 4.3.1
At last, in the section that explores the optimal tax mix, we have
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