A coating agent, comprising a modified vinyl alcohol polymer, the modified vinyl alcohol polymer comprising a structural unit derived from a derivative (a) of an ethylenically unsaturated dicarboxylic acid in a content of 0.05 mol% or more and 10 mol% or less, having a degree of saponification of 80.0 mol% or more and 99.9 mol% or less, having a methanol content of less than 3.0 mass% as measured by headspace gas chromatography, and having an amount of 0.1 ppm or more and less than 2,000 ppm of a component insoluble in a 90°C, 5 mass% aqueous solution, wherein at least a part of the structural unit derived from the derivative (a) of an ethylenically unsaturated dicarboxylic acid is a structural unit represented by the following formula, wherein R 1 is a hydrogen atom or a linear or branched alkyl group having 1 to 8 carbon atoms, and R 2 is a metal atom, a hydrogen atom, or a linear or branched alkyl group having 1 to 8 carbon atoms, and the following formula is satisfied, 0.05 ≤ Y / X < 0.98 wherein X is the content of the structural unit derived from the derivative (a) of an ethylenically unsaturated dicarboxylic acid, and Y is the content of the structural unit represented by the formula, and wherein the amount of a component insoluble in a 90°C, 5 mass% aqueous solution is determined as follows: a 500-mL flask fitted with an agitator and a reflux condenser is placed in a 20°C water bath; 285 g of distilled water is charged into the flask, followed by stirring at 300 rpm; 15 g of the modified vinyl alcohol polymer is weighed out and is gradually charged into the flask; as soon as all the modified vinyl alcohol polymer is charged into the flask, the water bath temperature is increased to 90°C over a time period of about 30 minutes; after the temperature reaches 90°C, the modified vinyl alcohol polymer is further dissolved while stirring the mixture for 60 minutes at 300 rpm; the mixture is then filtered through a metal filter with 63-μm openings to trap undissolved, remaining particles; the filter is thoroughly washed with 90°C hot water to remove the solution on the filter; the filter is then dried for 1 hour with a heating drier at 120°C; and the mass of the undissolved particles thus collected is determined as the amount of a component insoluble in a 90°C, 5 mass% aqueous solution. the modified vinyl alcohol polymer comprising a structural unit derived from a derivative (a) of an ethylenically unsaturated dicarboxylic acid in a content of 0.05 mol% or more and 10 mol% or less, having a degree of saponification of 80.0 mol% or more and 99.9 mol% or less, having a methanol content of less than 3.0 mass% as measured by headspace gas chromatography, and having an amount of 0.1 ppm or more and less than 2,000 ppm of a component insoluble in a 90°C, 5 mass% aqueous solution, wherein at least a part of the structural unit derived from the derivative (a) of an ethylenically unsaturated dicarboxylic acid is a structural unit represented by the following formula, wherein R 1 is a hydrogen atom or a linear or branched alkyl group having 1 to 8 carbon atoms, and R 2 is a metal atom, a hydrogen atom, or a linear or branched alkyl group having 1 to 8 carbon atoms, and the following formula is satisfied, 0.05 ≤ Y / X < 0.98 wherein X is the content of the structural unit derived from the derivative (a) of an ethylenically unsaturated dicarboxylic acid, and Y is the content of the structural unit represented by the formula, and wherein the amount of a component insoluble in a 90°C, 5 mass% aqueous solution is determined as follows: a 500-mL flask fitted with an agitator and a reflux condenser is placed in a 20°C water bath; 285 g of distilled water is charged into the flask, followed by stirring at 300 rpm; 15 g of the modified vinyl alcohol polymer is weighed out and is gradually charged into the flask; as soon as all the modified vinyl alcohol polymer is charged into the flask, the water bath temperature is increased to 90°C over a time period of about 30 minutes; after the temperature reaches 90°C, the modified vinyl alcohol polymer is further dissolved while stirring the mixture for 60 minutes at 300 rpm; the mixture is then filtered through a metal filter with 63-μm openings to trap undissolved, remaining particles; the filter is thoroughly washed with 90°C hot water to remove the solution on the filter; the filter is then dried for 1 hour with a heating drier at 120°C; and the mass of the undissolved particles thus collected is determined as the amount of a component insoluble in a 90°C, 5 mass% aqueous solution.