Alan the Egg Farmer consistently sells all of his fresh eggs on his island in the South Pacific. Since Alan is the only egg farmer on his island, he has no direct competition, and people seem to buy his eggs no matter what price he sets. Due to his great sales and lack of competition, Alan is considering greatly increasing the prices of his eggs. But how much do egg sales really vary when prices change? Alan wants to find out.
Luckily, he has a lot of down time and an interest in data science. He knows there are a lot of different factors involved in the production of eggs and in the sales of eggs, from chicken health to transportation costs to popular food trends, and he wants to find a single variable that can help him cut through the many possible confounding factors. So he comes up with an idea for doing an instrumental variable analysis: Alan knows that chickens produce fewer eggs in years with less rain, and he knows that farmers consistently increase their egg prices on years when they have low egg yields. Therefore, with a big dataset on egg sales and the weather history of nearby islands, Alan believes that he could study weather patterns as an instrument for egg prices, and he can use that instrument to find the impact of egg prices on egg sales. Which of the following assumptions does Alan's model depend on?