Solution
= Solution
Repeated measurements from one person can share persistent unobserved spending tendencies, violating model1's independent-error assumption and shifting that person's baseline. Model2 represents this <clustered data> through a common random intercept $b_i$, which induces within-person covariance $\operatorname{Cov}(Y_{ij},Y_{ik}\mid X)=\sigma^2$ for $j\ne k$.