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When solving a model à la Aiyagari, why is it needed to have more points close to zero?

I would be grateful if you could point me out some reference on how to implement the sparse grid. In particular, how should the fineness of the grid decrease as we move away from zero? I tried different grids and the wealth distribution I get changes quite a bit.

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    $\begingroup$ Because, in an equilibrium stationary distribution, there may be non-zero mass of agents at the zero-wealth borrowing constraint. To reflect that numerically, one needs a fine grid close to zero. (Question sparsely formulated, not very informative.) $\endgroup$
    – Michael
    Mar 15, 2020 at 17:30
  • $\begingroup$ Sorry, I don't understand. Even without a sparse grid I still get a non-zero mass of agents at zero. $\endgroup$
    – Tecon
    Mar 15, 2020 at 18:04
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    $\begingroup$ The issue is numerical stability. In the computer there's no "continuum". Numerically, by construction you will get only non-zero mass at discrete grid points, zero or not zero. The question is how does this reflect what actually occurs in the model mathematically. The equilibrium stationary distribution is mixture of a Dirac mass at zero and a non-discrete distribution on $(0, \infty)$. To capture that numerically within reasonable tolerance, you need a fine grid close to zero. There should be a small neighborhood of 0 within which the probability mass is stable, in numerical calculation. $\endgroup$
    – Michael
    Mar 15, 2020 at 19:26

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