I want to model a high inflation setting in NK model. Given current inflation levels, the real interest rates are negative. However, this means that the Beta would be greater than 1. Is that possible? Mathematically and conceptually it seems like the correct approach, but is it possible for Beta to have a value greater than 1?

The equations of the NK model are obtained by maximizing the household’s utility function (an infinite sum) that diverges if beta>1. Therefore, this case does not make any sense.

For the first part, definitely not. Consumption discounting hasn’t changed that much. But I’m really confused as to how I can add negative interest rates in my model if the only thing representing them is the Beta. In the UK, for instance, real rates are negative. I really want to focus on that aspect and include in my model, but I’m at a loss as to how I can do that, considering that, as you said, people aren’t actually behaving like that.

The discount factor only determines the steady state real interest rate. In many models shocks can explain interest rates that are temporarily different from steady state and can therefore be negative.