More defensible values with statistics
Source: www.spss.com
Copyright SPSS, Inc. 2004


Assessors use mass appraisal techniques to estimate the current market value of property in their jurisdictions for property tax purposes. This article describes how they - and others concerned with mass appraisal - can use statistics to enhance analysis and improve the accuracy and credibility of value estimates. It focuses on basic statistical analyses found in "ratio studies."

Just as assessors' estimates of property value govern the distribution of property taxes, a major source of local government revenue, state governments use ratio studies in the distribution of important school and other state-level aid payments. Billions of dollars are at stake.

Property owners, legislators and the courts increasingly demand accuracy and fairness in property assessments. They use professional standards such as the Uniform Standards of Professional Appraisal Practice and the assessment standards issued by the International Association of Assessing Officers to reinforce their demands.

In particular, property owners expect assessors to use the best available mass appraisal method and to be able to prove equity with supporting data and analyses. Further, in today's highly automated environment, analyses must be quick, accurate and clear.

Statistics make achieving such expectations possible. Today's statistical tools make effective use of statistics accessible to everyone. Indeed, assessors can use these tools to achieve more accurate and equitable values, at a fraction of the cost, of manual appraisals. They can also use statistics to prove the accuracy of the results.

Users of mass valuation statistics include:
¨ Assessors responsible for mass appraisal
¨ Oversight agencies charged with ensuring the achievement of legal requirements and equity among jurisdictions and property classes
¨ Appeal boards hearing complaints about property assessments
¨ Mass appraisal vendors who help assessors on a contract basis
¨ Property owners and organizations concerned with the fairness of property assessments


Statistics in mass appraisal
Major uses of statistics include:

1. Data profiles. Successful mass appraisal, like any other form of applied statistics, begins with data analysis. What is the current inventory of properties by type and location? What is the rate of growth? The age distribution? What is the average sale price, both by property type and on a per-unit basis, such as per square foot or per apartment unit? How do prices vary with size, location and other amenities? Statistics can answer these and related questions. For example, frequency distributions provide counts of properties in each category. Measures of central tendency suggest what is typical. Measures of dispersion provide a picture of the uniformity. Graphs, produced by all statistical software, help visualize patterns.

2. Time trend analyses. Accuracy in property valuation means keeping abreast of the market. Property values in strong markets must be adjusted upward. Values in declining markets should be reduced. Statistics offer a toolbox of techniques for tracking price trends and targeting adjustments. Values in this area should be adjusted upward. What should the adjustment be? There are four accepted methods of adjusting sales prices for time. All involve estimating the typical rate of change over the time interval in question. Calculating the median percentage change is a good beginning.

3. Refining cost models. Many assessors use the cost model to appraise properties. The method starts with per-unit construction costs (often obtained from published sources), makes adjustments for depreciation and other factors, and adds land
value. Statistics can be used to fine-tune cost models to the market. For example, depreciation schedules can be derived or validated by correlating sales prices (less land values) with building age. Values produced by cost models can be compared with sales prices to decide whether the results are accurate and consistent. Often such analyses will suggest market-based neighborhood or other adjustments.

4. Market modeling. Frequently, assessors are using multiple regression analysis (MRA) to derive valuation models directly from sales data. These models relate recent sales to key property characteristics, for example:

PRICE = 25,000 + 68.87*SQFT + 5674*QUAL - 790*AGE . . . ,
where PRICE is estimated sale price, SQFT is square feet of living area, QUAL is an index of construction quality and AGE is building age. Based on experience and judgement, assessors can determine which variables to include in MRA models (15 to 20 are often sufficient). The technique determines the corresponding prices or "coefficients" (e.g., $68.87 per square foot of living area in the above example) so as to minimize differences between actual and predicted prices. In fact, the average error in such models is always zero. (This means the models fully reflect current value levels.) Statistical packages can calibrate such models using hundreds of sales in a matter of seconds.

5. Income and expense analysis. Statistical and spreadsheet software can be used to assemble and analyze rent and expense data used in the income approach to value. Appraisers can extract typical rents and expense ratios by property type and location
using measure of central tendency. Further, income data can be correlated with sales prices to develop capitalization rates. Some assessors use MRA to build income models from data gathered from property owners.

6. Sales ratio studies. Quality control is paramount in any industry - and mass appraisal is no exception. The assessor's mainstay quality control technique is the sales ratio study, in which appraised values are matched with recent sales. If appraisal quality is good, the "average" appraisal-sales ratio should be close to 100 percent. More importantly, ratios should be consistent (low dispersion), both among and within property groups. For example, each of two neighborhoods should be appraised at the same level of value and, within each, values should be equitable.

Sales ratio studies
Assessors can use various sales ratio statistics to evaluate appraisal performance and pinpoint needed improvements. The following describes some of the popular basic and advanced ratio study techniques and gives rules of thumb for interpreting the results.
¨ Three measures of central tendency: median, mean and weighted (aggregate) mean. The mean is the common average obtained by adding all the ratios (or other variable) and dividing by the number of variables. The median is the middle ratio when they are arrayed from highest to lowest. The weighted mean is the sum of the assessments divided by the sum of the sales prices. It is so called because it weights each ratio by its sale price. Although the median is the generally preferred measure of central tendency when evaluating assessment performance, good practice dictates that all three measures of central tendency be calculated for each group of properties of interest. When measures of central tendency deviate from the legal level of assessment by 10 percent or so, the value estimates being studied need to be updated.

¨ Measures of dispersion: coefficient of dispersion (COD), coefficient of variation (COV), price-related differential (PRD), standard deviation, average absolute deviation, minimum, maximum and range. The COD, the most common measure of equity in mass appraisal, expresses the average absolute of individual ratios deviation from the median ratio as a percentage. A COD of 14.5, for example, means that properties are, on average, appraised within 14.5 percent of the median assessment level. Similarly, the COV expresses the standard deviation as a percentage of the mean. CODs greater than 15 or 20 percent are a cause of concern. A property under-valued by 20 percent pays only 50 percent of the property taxes paid by a property over-valued by 20 percent.

The price-related differential (PRD) provides an index of price-related bias, indicating whether low- and high-value properties are assessed at the same level. It is the ratio of the mean ratio to the weighted mean ratio. PRDs that exceed 103 suggest that high-value properties are relatively under-valued. PRDs under 98 suggest low-value properties are under-valued.

¨ Confidence intervals. Confidence intervals help assessment administrators conclude whether required assessment level standards have been violated. The assessor may specify a 95 percent confidence interval about any of the three measures of central tendency. A median confidence interval of 0.856 to 0.974 would suggest, for example, that one can be 95 percent confident that the true median assessment level is between 0.856 and 0.974. As the interval widens, the measure of central tendency becomes less reliable.

¨ Concentration index. The concentration index shows the percentage of ratios that lie between specified bounds, or the percentage that fall within specified percentages of the median ratio. For example, a large majority of ratios within 15 percent of the median indicates good performance.

¨ Percentile values. Quartiles divide the ratios into four equal parts. The closer the first and third quartile, the better.

¨ Distribution statistics. Includes kurtosis and normality; binomial and chi-square normality tests can also be conducted. As a rule, the former is appropriate for small samples (100 or less) and the later is better for larger samples. They indicate whether assessment ratios can be considered normally distributed. If not, nonparametric statistics (such as the COD) and tests are preferred.