# A problem with model setting
**URL:** https://forum.dynare.org/t/a-problem-with-model-setting/20628
**Category:** General DSGE Modeling
**Created:** [29 June 2022 13:56 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628 "2022-06-29T13:56:04Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@jamess](https://forum.dynare.org/u/jamess)
#### Post date: [29 June 2022 13:56 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628/1 "2022-06-29T13:56:04Z")
Dear Professor Pfeifer,
I read in paper Zhang(2010) [Zhang(2010).pdf](https://forum.dynare.org/uploads/short-url/tKX6iBHOOtYzlkAlABQ2UOsEjuZ.pdf) (305.2 KB) that the author set default probability of bank using a log-normal distribution written as {{\phi }\_{t}}=cdf\left( {{\Delta }\_{t}},\sigma \right) on page 11, in which {\Delta }\_{t} is an endogenous variable and represents for aggregate capital ratio. I feel very confused that why the author set a variable as the mean of this cdf instead of a parameter, and how should I write this equation in Matlab?
Thank you very much for reading this post.
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [30 June 2022 06:31 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628/2 "2022-06-30T06:31:34Z")
I am not sure what the problem is. There is a variable on the right-hand side, so it’s a variable on the left as well. In Dynare, you have a normcdf-function. See [4. The model file — Dynare 5.1 documentation](https://www.dynare.org/manual/the-model-file.html?highlight=normcdf#normcdf)
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### Author:  [@jamess](https://forum.dynare.org/u/jamess)
#### Post date: [30 June 2022 07:45 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628/3 "2022-06-30T07:45:38Z")
Dear Professor Pfeifer,
Sorry if I did not make myself clear. Generally the log-normal distribution function is written as {{\phi }\_{t}}=cdf\left( {\mu},\sigma \right). While according to the content in that paper, it seems that the author used a endogenous variable {\Delta }\_{t} as the mean of the distribution instead of a fixed parameter. That’s why I feel confused. It seems that the original independent variable is treated as given and the original mean is treated as independent variable.
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [30 June 2022 07:51 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628/4 "2022-06-30T07:51:27Z")
There is no reason why the mean of the distribution may differ across periods.
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### Author:  [@jamess](https://forum.dynare.org/u/jamess)
#### Post date: [30 June 2022 16:09 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628/5 "2022-06-30T16:09:52Z")
Dear Professor Pfeifer,
As the author says “The health of the banking sector as a whole will depend largely on the variation of aggregate capital ratio. With a higher aggregate ratio, the distribution moves to the right, and fewer banks will fall short of the 8 percent threshold and thus default, and vice versa.” If {\Delta }\_{t} is the independent variable of this function, then bank default rate {\phi }\_{t} will increase along with {\Delta }\_{t}, which seems conflict with the statement in that paper.
Another paper Funke et al.(2015) [Funke et al.(2015).pdf](https://forum.dynare.org/uploads/short-url/lMtgptjczWLx0uKyqakZDXYbwwy.pdf) (874.6 KB) displays the same setting on page 23, and they also said the capital adequacy ratio {\Delta }\_{t} is the mean of distribution.
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [30 June 2022 16:43 UTC](https://forum.dynare.org/t/a-problem-with-model-setting/20628/6 "2022-06-30T16:43:18Z")
The CDF of the log normal distribution is characterized by
1. the mean of the distribution \Delta\_t
2. the standard deviation \sigma
3. the cutoff of 8% for the CDF (\int\_{-\infty}^{8\%})
The aggregate distribution shifts its mean, causing a higher or lower share to fall below the cutoff and go bust.