It may not have an effect at all. The county assessor's office has to assess the value of the property for taxes to be calculated. The higher the value, the more taxes you pay. I bought my house on the Oregon coast for $79,000 12 years ago, but I pay a lower tax rate because the assessed value is $55,000. When a private or bank assessor determines the market value of a house, that does not mean your taxes go up (or down), it just means that you could sell it for that if you put it on the market.
Many people are now buying houses at an incredibly reduced price. But be warned, the taxes are based on whatever the value was when the county assessors office last did assessments. If you have purchased a home recently, you could get stuck with higher taxes than the current market value of the home. In some cases, people are buying homes for $250,000 less than the homes value a year ago. Regardless of what they paid, they still have to pay whatever the assessors office has assessed the house at.