Economic Reasoning for Structural change vs Cyclical change Often when there is an episode of low output growth, a debate takes place: Whether the downturn/recession is due to structural factors or is it cyclical. 

I understand that the analysis is largely based on statistical estimation wherein it is checked whether there is decline in trend growth or it's the beginning of trough in business cycles. 

How do I understand this in terms of pure economics? Broadly I think answer lies in understanding causes of business cycles. But without statistical estimation, how can one argue that a recession is cyclical or due to structural changes?
It is not possible ex-ante, it's all about:


economic interpretations, i.e., economic schools of thought
expectations on central banks' next moves,
political/ideological views,
the (hidden and/or unconscious) emerging willingnesses to induce self-fulfilling prophecies


... hence the debates that take place here and there.

Whether a recession is cyclical or due to structural changes can only be assessed ex-post, i.e. with data and (well driven) studies.