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Summary statistics from a genome-wide association study (GWAS) can be used to generate a polygenic score (PGS). For complex, behavioral traits, the correlation between individual PGS and phenotype may contain bias alongside the causal effect of the individual's genes (due to geographic, ancestral, and/or socioeconomic confounding). We formalize the recent introduction of a different source of bias in regression models using PGSs: the effects of parental genes on offspring outcomes (i.e. genetic nurture). GWAS do not discriminate between the various pathways through which genes influence outcomes, meaning existing PGSs capture both direct genetic effects and genetic nurture effects. We construct a structural model for genetic effects and show that, unlike other sources of bias in PGSs, the presence of genetic nurture biases PGS coefficients from both naive OLS (between-family) and family fixed effects (within-family) regressions. This bias is in opposite directions; while naive OLS estimates are biased upwards, family fixed effects estimates are biased downwards. We quantify this bias for a given trait using two novel parameters that we identify and discuss: (1) the genetic correlation between the direct and nurture effects and (2) the ratio of the SNP heritabilities for the direct and nurture effects.