Catalyst, method for preparing catalyst, and method for producing unsaturated carboxylic acid and/or unsaturated carboxylic acid ester

A method for producing an unsaturated carboxylic acid ester by reacting a carboxylic acid with formaldehyde in the presence of a catalyst

• wherein the catalyst comprises:
• (i) a compound comprising at least one first element selected from boron, magnesium, zirconium, and hafnium;
• and
• (ii) an alkali metal element,
• wherein the compound and the alkali metal element are supported on a carrier having silanol groups,
• an average particle size of the compound is 0.4 nm or more and 50 nm or less, and
• the catalyst satisfies the following formula (1):
• 0.90×10−21(g/number)≤X/(Y×Z)<10.8×10−21(g/number) formula (1),
• in which X is a molar ratio of the alkali metal element to the at least one first element in the catalyst, Y is a BET specific surface area of the catalyst (m2/g), and Z is a number of the silanol groups per unit area (number/nm2).