Martha Starr looked to see whether there was an effect between weather and sales:
unusual weather has a modest but significant role in explaining monthly sales fluctuations. However, lagged effects often offset original effects, so that weather's influence tends to wash out at a quarterly frequency.
i.e. while weather may have a small affect on sales, it only changed when people spent their money - not how much people spent in a month.
Unfortunately, I don't have access to the paper to confirm the following:
- whether the effect was to increase the business during rain.
- whether the overall effect also applied to malls.
- whether rain was considered "unusual" or whether she was only looking at blizzards and the like.
Reference: Starr, Martha, The Effects of Weather on Retail Sales (January 12, 2000). FEDS Working Paper No. 2000-08. Available at SSRN: http://ssrn.com/abstract=221728 or doi:10.2139/ssrn.221728,
Anecdotally, I have spoken to parents who find that children cooped up in their homes during long periods of rain become restless. Whether that is true or not, the parents would arrange trips to malls to try to relieve the boredom.