Catalyst and method for producing diene compound

A catalyst comprising:

• at least one element X selected from the group consisting of Hf, Zr, and Nb;
• and
• at least one element Z selected from the group consisting of Group 14 elements, wherein
• at least one diffraction peak is observed in a low angle range of θ=6° or less in an X-ray diffraction profile observed using X-ray diffraction,
• the at least one diffraction peak has a ratio (I/H) of a peak intensity I to a half width at half maximum H of the diffraction peak of 5000 or more,
• no diffraction peak due to a single oxide of the element X is observed in a high-angle range of θ=10° to 40° in the X-ray diffraction profile observed using X-ray diffraction, and
• a molar content (X/(X+Z)×100) of the element X with respect to the total amount (mole) of the element X and the element Z is 0.5 to 6 mol %.