Results from a genome-wide association study (GWAS) can be used to generate a polygenic score (PGS), an individual-level measure summarizing identified genetic influence on a trait dispersed across the genome. For complex, behavioral traits, the association between an individual's PGS and their phenotype may contain bias (from geographic, ancestral, and/or socioeconomic confounding) alongside the causal effect of the individual's genes. We formalize the introduction of a different source of bias in regression models using PGSs: the effects of parental genes on offspring outcomes, known as genetic nurture. GWAS do not discriminate between the various pathways through which genes become associated with outcomes, meaning existing PGSs capture both direct genetic effects and genetic nurture effects. We construct a theoretical model for genetic effects and show that the presence of genetic nurture biases PGS coefficients from both naïve OLS (between-family) and family fixed effects (within-family) regressions. This bias is in opposite directions; while naïve OLS estimates are biased away from zero, family fixed effects estimates are biased toward zero. We quantify this bias using two novel parameters: (1) the genetic correlation between the direct and nurture effects and (2) the ratio of the SNP heritabilities for the direct and nurture effects.