So the polar vortex is gone (for now). And to answer the question for anyone not going through it, yes it really was that cold. It was brutal on even short jaunts to the mailbox. However I did go out to the store at one point and there I made some interesting observations.
There are likely to be some real economic effects on the local economy from the extreme cold. Some are likely transitory though some may be less likely to be made up.
Lots of businesses closed as a result of the cold. Some of it was due to the cold, some because of people needing to miss work to care for children because of school closures. Depending on the importance of specific workers, and their ability to work remotely, this at least delays some work getting completed. The permanence of any output loss will depend of firm specific production factors and the nature of the work.
Here are some examples. I went to the grocery side of Target. There were entire banks of shelves empty and few people restocking the items. There was only one lane open for checkout with a live person. It seems likely that some people bought extra items or moved shopping earlier in the week based on the impending weather so that some items were purchased above store expectations.
Other shelves were stocked full though and almost overflowing. While it might be the case that people did not buy the items because they did not come out to shop I expect that any reduced purchases will be made up. It seems likely that grocery stores would, for the most part, see a changed timing pattern to the purchases as a result of weather, much like the research on hurricanes and spending shows. People move forward or move back much of this spending and while there may be some spending that never happens as a result of the delay it seems likely more than made up for by precautionary excess spending ahead of time.
There are other examples where I expect there will not be a catch-up effect. When I was out I saw that several restaurants closed during the weather. I suspect this was for workforce reasons or perhaps supply chain reasons. It would not surprise me that weather kept trucks from coming in, either because there would be no workers to unload goods or for fear that trucks would have problems in the weather.
A restaurant closed for the weather probably does not make up the lost sales for that time. People either sought out alternative suppliers, for example a different pizza place, or just made do without. Some may decide to get pizza later because of missing that day, but I doubt a complete offset happened. These potential losses are the real effects from the weather.
There are some public finance implications too. Obviously there will be some tax losses as a result of reduced sales. In addition lost wages and tips likely occur as well for the restaurant workers. The result her may be less spending by these employees with some further effects as a result. The fact that it was only 2 days moderates the magnitude of the impacts for sure, but it could be a difference for some businesses and employees. It will be a few months before we get a really good look at the data but it will be important to watch. Also if this occurred at multiple other locations the combined effects certainly get larger and more important.