how to model this multivariate time series? Say I have a dataset as follows.
|Time     | Unemployment_rate | GDP_growth | Customer_defaults |
-------------------------------------------------------------
| 2000 Q1 |               4% |         2% |         5%         |

| 2000 Q2 |               6% |         2% |         6%         |

forecasting the defaults rate (but I already have the forecasts for the factors) 
| 2000 Q3 |              5% |          3% |               ??? |

I have timeseries data for some macroeconomic factors which drives the customer defaults for home loans. The important point here is that I ALREADY HAVE the forecasts for the factors and want to use those to forecast the defaults. 
I know this is like a multivariate time series modelling problem. But from what I have read those models would forecast my factors as well which I don't want (as I already have forecasts received from experts).
So my question is what kind of techniques I could use to solve this?
 A: VAR models predict ALL variables . A SARIMAX model https://autobox.com/pdfs/SARMAX.pdf only predicts 1 series i.e. customer default rates . Future values of all known X's can either be pre-specified or user-specified. If you have future values pre-specified then simply use them . If your software of choice doesn't allow pre-specification of the future values for your causals find one that that does.
Now the "cheat" that is normally in play is to assume that you have perfect knowledge (no uncertainty ) of the predictors . Optionally I would want to have a probability distribution of future values for each of the pre-specified exogenous predictors for each forecast period and incorporate these uncertainties via monte-carlo methods thus in my opinion providing a more honest assessment of the prediction intervals for the output series.
FYI take a look at the following question Forecasting a time series $(x_t,{\bf Y_t})$ where all we care about is forecasting $x_t$ as to how to convolute the uncertainties when your predictor variables have to be incorporated i.e. self-predicted (not your stated problem BUT a more common problem ).
