# Universal Basic Income (UBI)#

[TODO: This section is far along but needs to be updated.]

We have included the modeling of a universal basic income (UBI) policy directly in the theory and code for [`OG-Core`

] on which dependency the `OG-USA`

is based. UBI shows up in the household budget constraint (17), and is described in the Budget Constraint section of the Households chapter of the `OG-Core`

documentation. We calculate the time series of a UBI matrix \(ubi_{j,s,t}\) representing the UBI transfer to every household with head of household age \(s\), lifetime income group \(j\), in period \(t\). We calculate the time series of this matrix from five parameters and some household composition data that we impose upon the existing demographics of `OG-USA`

.

## Calculating UBI#

We calculate the time series of UBI household transfers in model units \(ubi_{j,s,t)}\) and the time series of total UBI expenditures in model units \(UBI_t\) from five parameters described in the `ogusa_default_parameters.json`

file (`ubi_growthadj`

, `ubi_nom_017`

, `ubi_nom_1864`

, `ubi_nom_65p`

, and `ubi_nom_max`

) interfaced with the `OG-USA`

demographic dynamics over lifetime income groups \(j\) and ages \(s\), and multiplied by household composition matrices from the `Calibrate`

class of the `OG-USA/ogusa/calibrate.py`

module in the repository.

From the OG-USA repository, we have four \(S\times J\) matrices `ubi_num_017_mat`

\(_{j,s}\), `ubi_num_1864_mat`

\(_{j,s}\), and `ubi_num_65p_mat`

\(_{j,s}\) representing the number of children under age 0-17, number of adults ages 18-64, and the number of seniors age 65 and over, respectively, by lifetime ability group \(j\) and age \(s\) of head of household. Because our demographic age data match up well with head-of-household data from other datasets, we do not have to adjust the values in these matrices.[1]

Now we can solve for the dollar-valued (as opposed to model-unit-valued) UBI transfer to each household in the first period \(ubi^{\$}_{j,s,t=0}\) in the following way. Let the parameter `ubi_nom_017`

be the dollar value of the UBI transfer to each household per dependent child age 17 and under. Let the parameter `ubi_nom_1864`

be the dollar value of the UBI transfer to each household per adult between the ages of 18 and 64. Let `ubi_nom_65p`

be the dollar value of UBI transfer to each household per senior 65 and over. And let `ubi_nom_max`

be the maximum UBI benefit per household.

The rest of the time periods of the household UBI transfer and the respective steady-states are determined by whether the UBI is growth adjusted or not as given in the `ubi_growthadj`

Boolean parameter. The following two sections cover these two cases.

## UBI specification not adjusted for economic growth#

A non-growth adjusted UBI (`ubi_growthadj = False`

) is one in which the initial nonstationary dollar-valued \(t=0\) UBI matrix \(ubi^{\$}_{j,s,t=0}\) does not grow, while the economy’s long-run growth rate is \(g_y\) for the most common parameterization where the long-run growth rate is positive \(g_y>0\).

As described in the OG-Core chapter on stationarization, the stationarized UBI transfer to each household \(\hat{ubi}_{j,s,t}\) is the nonstationary transfer divided by the growth rate since the initial period. When the long-run economic growth rate is positive \(g_y>0\) and the UBI specification is not growth-adjusted the steady-state stationary UBI household transfer is zero \(\overline{ubi}_{j,s}=0\) for all lifetime income groups \(j\) and ages \(s\) as time periods \(t\) go to infinity. However, to simplify, we assume in this case that the stationarized steady-state UBI transfer matrix to households is the stationarized value of that matrix in period \(T\).

Note that in non-growth-adjusted case, if \(g_y<0\), then the stationary value of \(\hat{ubi}_{j,s,t}\) is going to infinity as \(t\) goes to infinity. Therefore, a UBI specification must be growth adjusted for any assumed negative long run growth \(g_y<0\).[2]

## UBI specification adjusted for economic growth#

Put description of growth-adjusted specification here.