Some farmers were interested in predicting inches of growth of corn as a function of rainfall on a monthly basis, so they collected data from the growing season and estimated an equation of the following form:

G_t = β₀ + β₁R_t + β₂G_t-1 + ε_t

Where:

G_t = inches of growth of corn in month t

R_t = inches of rain in month t

ε_t = a normally distributed classical error term

The farmers expected a negative sign for β₂ (they felt that since corn can only grow so much, if it grows a lot in one month, it won’t grow much in the next month), but they got a positive estimate instead. What suggestions would you have for this problem?