Here you can see the notable difference between the manufacturing PMI and industrial production. Overlaid is the annual per cent change in electricity demand from industry. The sector is reporting strong activity in the PMI survey and electricity use is confirming it. The IP seems to be referring to a different country.
Again, revenues from large industrial firms (as reported to the country's tax collector, the AEAT) do not confirm the published IP.
As to why this is taking place, the most obvious candidates would be inappropriateness of the sample data the INE bases its estimates on and/or problems with the methodology they use to extrapolate industry-wide statistics from those survey results.
A friend of the blog will, in fact, be meeting with some people fairly high up in the INE organization next week. He has promised to bring the matter up. Stay tuned.
Javier García Echegaray and Charles Butler