# Modelling Issues in panel regression

I came across a paper that uses a panel data of US states (from 2000-2010) with the following model:

$y_{it}=b_{1}x_{it} +b_{2}x_{it}*D_{it}+other vars + \alpha_{t} + \gamma_{i}$

where, $x$ and $y$ are continuous vars and $D$ is a dummy variable that takes a value of 1 if there is a decrease in $x$ from one year to another year and zero otherwise (i.e., for an increase or no change in $x$). The paper then interprets coefficient on $x_1$ as the effect of the increase in $x$ on $y$ and $b_{1}+b_{2}$ as the effect of a decrease in $x$.I was wondering whether this is a valid interpretation.