PROBLEM TO BE SOLVED: To provide a catalyst capable of producing an alcohol compound and an olefin compound with high efficiency, and methods for producing the compounds using the catalyst.SOLUTION: There are provided a catalyst containing a predetermined amount of zirconium oxide and a predetermined amount of lanthanum for producing, from an alcohol compound, at least one kind of an alcohol compound and an olefin compound which have at least one more carbon, for producing, from an aldehyde compound and an alcohol for conversion, at least one kind of an alcohol compound and an olefin compound which have at least one more carbon than the preceding compounds, and for producing, from a ketone compound and an alcohol for conversion, at least one kind of an alcohol compound and an olefin compound which has the same number of carbons as the preceding compounds; and a method for manufacturing the compounds using the catalyst.