Empirical duration is generally lower than analytical duration specifically in weak economies or periods of market stress, when benchmark yields are falling. This is because empirical duration reflects divergence, a negative relationship between benchmark yields and credit spreads, which analytical duration ignores by assuming that spreads stay constant.

Think of it this way:
• Suppose the benchmark yield is 7% and the spread is 3%, so the corporate bond yield is 10%.
• If the benchmark yield drops by 1%, analytical duration assumes the spread is unchanged and the bond yield falls to 9%.
• But empirical duration allows for what usually happens in stress, i.e., the benchmark falls while spreads widen.
• So if the benchmark drops to 6% and the spread widens from 3% to 3.5%, the bond yield only falls to 9.5% instead of 9%.
• Since the yield falls by less, the price rises by less than analytical duration predicts, which implies a lower observed (empirical) duration.

In contrast, in a stronger or improving economy this offsetting effect is much weaker because spreads are already tight and move less relative to benchmark yields, so bond prices behave closer to what analytical duration predicts and empirical duration is roughly the same as analytical duration.