In the previous post of This sequence presents the two main approaches to analysis of distributional impact in the context of a consumption tax (per case, VAT) and showed how under a single specification (or "naive") the results back from a point significantly attenuates intertemporal approach when we rehearse. In this note we repeat the exercise by slightly altering the structure of demand. In this case, a certain foundation dotaremos micro analysis by introducing agents to making consumption and savings in a context of life cycle, subject to dissimilar conditions of access to credit. Specifically, we are interested in evaluating the effect of any "credit crunch" on the distributional impact of VAT.
Exercise not-that-naive
begin characterizing the income profiles of individuals. Without loss of generality, we take the distribution of income per capita levels of initial family (in dollars) the previous year and assume a profile for each income decile shaped or inverted, it is increasing in the first part of the cycle and then decreasing (and concave), so that the momentum for revenue growth is equivalent between deciles. This structure does not seem so trite, in light of what is observed empirically. For illustrative purposes, Figure 1 shows the profiles of some deciles.
Then we establish the behavior patterns of agents. The decision rule of consumers arises to solve the optimization program given by equation 1, which by now is a standard specification. For simplicity, equation 2 provides equal subjective discount factors (preferences) and the discount means the "market."
Restrictions credit are defined by Equation 3, and indicate that at any point in time agents can not consume beyond the possibilities that disposable income in that period. Naturally, candidates for imposing this condition are the individuals of the lowest deciles. With this scheme in mind, we evaluated the impact of a value added tax (consumption) with an average of 21% tax rate, imposing credit restrictions (3) over the first six deciles of the distribution, allowing the remaining categories make debt at will.
Note that the restriction amounts to failure to borrow, not save. Therefore, given the income profile of each category, which is noted for individuals "restricted" is a smooth consumption path at a certain period than the original. The following figures show the consumption and income profile of the first decile of the distribution (for which the restriction operates) and the lowest decile (which has perfect access to credit markets).
Figure 2, we see how the restriction operates in the first part of the life cycle, then after a certain period, and because the structure of the agent preferences and their profile income-these deciles save part of their income to finance in the twilight of their lives and ensure a stable consumption level. In particular, from the fourth period, the agent begins to shift consumption towards the future (the dotted line is below the income earned online blue-). The "savings" of each period (purple line) includes the capitalization that are made in each period, so take that. To see the surplus or deficit on the income earned in each period, net of capitalization, just look at the parable of the difference between blue and dotted line consumer.
Moreover, Figure 3 shows a process of smoothing Consumption typical: there is a significant deficit on both ends of the life cycle, which is funded with a lower level of consumption in most productive stage of the agent. Since the ability to bring future consumption at present is available only to the richest deciles, from a VAT point here is progressive, as shown in Figure 4, in conjunction with cumulative incidence analysis and tested in the previous post (for those who have not read, the curves show how much the present value of income represents the present value of taxes paid by consuming, considering up to time t).
Again, which will result in asymptotic neutrality of VAT. And bottomline mode, we noticed that for this specification simple demand heterogeneity in terms of access to credit markets (in the context of preference for stable consumption paths over time) does not introduce regressive VAT.
Discussion
Notwithstanding the above, it should draw attention to some important issues. First, this specification has several aspects to refine, and several assumptions that it is worth to rest in a future post. On the one hand, deliberately avoided modeling explicit credit market (ie not specify who offers credit to these agents or under what conditions, among other things). A quick exit this simplification might be thinking of a small open economy, but it is obvious that the formal determination of the credit market does not affect the outcome in question.
One paragraph deserves the equation (2), which oversimplifies the structure of intertemporal preferences of actors collapsing to a single parameter.
Finally, this result could reversed if in conjunction with restrictions on access to credit inflation is incorporated. These extensions will be addressed in a future post.
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