Parental goal promotion and college students’ self-esteem level and contingency: The mediating role of need satisfaction

•We aimed to predict college students’ self-esteem level and contingency.•We focused on two antecedents: intrinsic and extrinsic parental goal promotion.•Intrinsic goal promotion had a direct effect on self-esteem level intercept.•Extrinsic goal promotion had a direct effect on self-esteem contingency intercept.•Indirect intrinsic goal effects on self-esteem intercepts ran via need satisfaction.