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A New Approach to the Analysis of Assessment Equity1

Claudia M. De Cesare and Les Ruddock

Claudia M. De Cesare works for the Porto Alegre city council, Brazil, and is a PhD Candidate - Centre for the Built and Human Environment - University of Salford, UK. E-mail: C.M.DeCesare@surveying.salford.ac.uk

Dr. Les Ruddock is the Director of EMEC- Centre for the Built and Human Environment - University of Salford, UK. E-mail: L.Ruddock@surveying.salford.ac.uk

Introduction

Property taxes are one of the most popular options to fund local services. Property taxes are adopted by 17 out of the 22 countries that are members of the Organisation for Economic Co-operation and Development [OECD] and they are the most important source of local revenue in 9 of these countries (Kitchen 1992). According to the International Association of Assessing Officers [IAAO], property taxes exist in about 130 countries with varying importance (IAAO 1990).

In spite of their high popularity in integrating taxation systems, property taxes are strongly criticised due to inequities present in current systems. Frequently, assessment bias is identified in the tax base estimated. Market value is adopted as the tax base in a large number of countries, including Canada, Denmark, Great Britain for domestic rates, Netherlands, Philippines, the majority of the states in the United States and Brazil. In many cases, high value properties tend to be under-appraised relative to low-value properties.

There are many excuses for the occurrence of assessment bias. Low performance in valuation for taxation purposes may be related to the need for more sophisticated valuation techniques, poor access to market information and omission of important attributes in estimating the tax base. Additionally, the use of non-representative samples on which the estimates are based, the lack of frequent revaluation and the inaccuracies present in the real estate cadastre may also cause assessment bias.

1 Assessment Journal 5-2: 57-69 (1998).

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Administrators of property taxes might argue that the high cost of reassessment services represents a strong reason for keeping current assessed values even when inequities are clearly perceptible. However, Edelstein (1979) notes that “no matter how differentials in property tax treatment are generated, … it is illegal to have non-uniform assessment practices across residential properties”.

The present study is concerned with devising a methodology for analysing the assessment performance for taxation purposes. In order to be able to eliminate or reduce assessment inequities, appraisers need to detect bias and determine the forms of inequity which are present (Sunderman et al. 1990b). The proposed methodology aims to make it possible to identify assessment bias properly and consistently.

The relevance of the analysis of assessment equity can easily be explained by the taxpayer satisfaction with the tax system and by the inherent requirement for a fair tax administration. Assessment inequities can cause taxpayers to lose confidence in the system and reduce the tax base.

The paper is subdivided into four main sections. The present section provides an overview of the study. A short literature review on the assessment equity is presented in the second section. The third section discusses some methodological aspects that should be considered when analysing assessment performance. These methodological aspects are explored empirically in the following section. The analysis is limited to the segment of the residential market represented by individual apartment units, and covers a three-year period of taxation (from 1993 to 1995). The final section presents a summary of the study.

As explained above, the present study is aimed at proposing a methodology for identifying assessment bias consistently. Therefore, courses of action for practising assessors concerning valuation methods or how to avoid assessment bias are not addressed in the study.

Assessment Equity: Fundamental Issues

The analysis of the assessment performance aims to measure two primary aspects of mass-appraisal accuracy: level and uniformity (IAAO 1990). Assessment level refers to the overall ratio at which properties are appraised in relation to true market value.

In addition to keeping the desired assessment level, a basic condition for valuations for taxation purposes is to present uniformity. Assessment uniformity is related to the fair and equitable treatment of individual properties. Each property has to be appraised at the same level, or ratio, to market value (IAAO 1990).

Assessment equity in property taxes is the degree to which assessment bears a consistent relationship to market value for all properties at the assessment date. There is perfect equity when the ratio between assessed value and market value is constant, no matter what the specific value (Paglin and Fogarty 1973).

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Assessment bias occurs when some classes of properties have a ratio of assessment to market value significantly different from the ratio of others in the same taxing jurisdiction (IAAO 1990). These assessment inequities can be divided into horizontal and vertical components. Horizontal inequities are systematic differences in assessment level between properties, being present when persons having similar properties with the same value pay different taxes due to assessment bias.

Vertical inequities are systematic differences in assessment levels for groups of properties defined by value. They can be either regressive when high-value properties are under appraised relative to low-value properties, or progressive, when the opposite occurs.

Sale prices are usually used to represent market values in ratio studies. The median and the coefficient of dispersion about the median (COD) of assessed value to sale price ratio are frequently suggested for analysing assessment performance, since they provide a meaningful measure even when the distribution of assessment ratios is not normal. The median shows how close, on average, properties are being assessed to the legal or the desired assessment level. The COD indicates the variability of the assessment levels.

A central issue of the academic controversy on assessment equity concerns how to identify vertical assessment inequity. The extensive series of articles by scholars on the measurement of vertical assessment bias have in common the desire to find a way of testing the degree to which residential real property is uniformly assessed for taxation purposes (Bell 1984).

Basically, regression models between assessed values and sale prices are suggested as a way to verify whether differences in assessment levels are defined by value. The different methodologies for measuring the vertical assessment bias yield mixed conclusions about the existence of assessment progressivity or regressivity in property tax systems.

The possibility of inconsistent results, when different measures and tests are used to indicate vertical inequities, is demonstrated empirically in Cannaday et al. (1987) and Sirmans et al. (1995). Some evidence of inconsistent results is also provided by Kochin and Parks (1982a,b) and Clapp (1990). As noted by Sunderman et al. (1990a), “no measure of vertical inequity is widely accepted”.

There are two basic differences among the many models established. The first is concerned with which variable should be used as the independent one, and the second concerns the form of the relationship assumed between the key-variables considered, i. e. assessed value and sale price.

The traditional approach for identifying vertical assessment bias assumes that arm length sale prices are able to reflect the true market values on average. In the context of the traditional approach, market values can be represented by sale prices. There is a general agreement that assessed value depends, or should depend, upon sale prices (Bell 1984).

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Different regression models for indicating vertical inequities based on the traditional approach are proposed by Paglin and Fogarty 1972; Cheng 1974; IAAO 1978; Bell 1984; Sunderman et al. 1990a. These models are summarised in Table 1.

////Insert table 1 # here////

In order to estimate the model proposed by Sunderman et al. (1990a), points at which the regression line changes slope, i.e. knots, must be calculated. The tests described in Table 1 are related to the null hypothesis that there is no vertical inequity.

Kochin and Parks (1982a,b) propose an alternative model that inverts the traditional structure of the tests for vertical inequity. Assessed value is used as the independent variable to determine sale prices (See Table 1). Many criticisms have been addressed at the Kochin and Parks’ contribution by the authors who support the traditional approach. According to Kennedy (1984) and Bell (1984), the results achieved by Kochin and Parks are just attributable to their implicit assumption that assessment errors do not exist.

Clapp (1990) recommends another alternative approach for analysing vertical assessment equity. A simultaneous model composed of two equations is proposed (See Table 1). The author introduces the use of an instrumental variable that is highly correlated with market value and, therefore, with assessed value and sale price. According to Clapp (1990), the instrumental variable has the advantage of being uncorrelated with market or assessment errors. In the model proposed, sale price is used as the dependent variable to be determined by assessed value estimates. These estimates are the predicted values established by a regression of assessed values against the instrumental variable “Z”.

In general, models are likely to indicate regressivity when assessed values are used as the dependent variable (traditional approach). In contrast, they are likely to indicate progressivity when assessed values are used as the independent variable (alternative approaches).

Additionally, a simple measure for identifying vertical assessment bias, the price-related differential (PRD), is recommended by the IAAO. The statistic is calculated by dividing the mean by the weighted mean of assessed values to sale prices ratios. The weighted mean of assessed values to sale prices ratios results from the sum of assessed values divided by the sum of sale prices for the entire data sample.

According to the IAAO (1990), a PRD greater (less) than “1” would suggest vertical assessment regressivity (progressivity). It shows that the mean (weighted mean) exceeds the weighted mean (mean) of assessed values to sale prices ratios. The weighted mean weights the assessment ratios proportionally to their sale prices.

In spite of the measure being considered as a standard for identifying vertical assessment bias in the United States, the IAAO (1990) highlights that PRD “provides only an indication, not a proof, of appraisal bias”.

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Nature of the Problem: The Need for Understanding the Analysis

An unobservable key-variable: The market value

The difficulty in analysing assessment performance and, principally, the existence of vertical assessment equity emerges from the fact that assessed values, i.e. the actual basis on which property tax is allocated, must be compared to market values.

The usual concepts adopted for defining market value present slight variations. However, the usual definitions involve the idea of the most probable price in terms of money that a property will bring in a competitive and open market, assuming that seller and buyer are acting prudently and knowledgeably, without any special stimulus.

As noted by Clapp (1990), market value is essentially unobservable and associated with ideal conditions, such as the parties involved acting prudently and with knowledge. Therefore, a primary issue is how to develop estimates of market value (Cannaday et al. 1987).

On the other hand, information about sale prices and assessed values is observable and available. In most cases, recent property sale prices are used as proxies of market value. Part of the academic community believes that the use of current sale prices for representing market value in ratio studies may cause a false indication of assessment bias.

The supposed inefficiency of the real estate market

Part of the difficulty in assessing residential property can be attributed to the characteristics of the real estate market. Evans (1995) argues that neither skilled assessors nor sophisticated statistical methods can predict sale prices of properties with any degree of precision, and assumes that the error in predicting market price is likely to be, “at best”, around 10%. The author explains that it is a consequence of the property market being actually inefficient. In other words, , “there is no true market value of the property, only a range of prices” (Evans 1995).

According to the author, the distribution of prices for similar properties is caused by market errors, which are related to the inefficiency of the real estate market. Properties will always be heterogeneous and attached to a particular location. Each transaction is also prone to be influenced by the particular buyer and seller characteristics. In summary, nothing can be done for actually eliminating market errors.

On the other hand, assessed values also contain errors caused by the subjectivity of the valuation process, inaccuracies of the real estate cadastre, omission of important variables, and political decisions intentionally overriding market value estimates. Current assessed values are also influenced by time lags between valuations.

Realistically, both sale prices and assessed values are subject to errors. However, errors in sale price can be considered smaller than the assessment errors, providing that price information is from a good sale and it is adjusted as appropriate (Cheng 1974; Gaston 1984; Bell 1984).

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Models for analysing vertical assessment equity

The use of regression models for analysing vertical assessment equity is widely accepted. The focus of the controversy is which variable, i. e. sale price or assessed value, should be used as the dependent variable in the regression models generated to indicate vertical assessment equity.

In practical terms, market value is determined by (or is a function of) the observable sale prices. Additionally, by definition, market value is the most probable price of an arm-length transaction. It means, sale prices, on average, are supposed to represent market values. Even admitting that market errors exist and some bias may result from using sale prices to represent market values, they seem to be the closest measure available to represent market values.

Clearly, sale price is the independent variable in any model that explains the relationship between sale price and assessed value. Therefore, the traditional models for analysing vertical assessment equity are able to better reflect economic behaviour than do the alternative approaches.

Benson and Schwartz (1997) resume the question expressing their support for the traditional approach based upon the fact that sale prices are the best proxy of the true market value and “in a well-functioning environment, assessed value should be a function of (or be determined by) sale prices”.

Concerning the form of the relationship between the variables, some of the models proposed for indicating vertical assessment inequity alert for the possibility of a non-linear relationship between assessed value and sale price. A graphical analysis may be useful to identify the form of the relationship between assessed values and sales prices in order to define the appropriate model for analysing vertical inequity.

Assuming that more consistency is still achieved by adopting the models based upon the traditional approach, an important issue would be to discuss the validity of the models considering only two variables, i.e. assessed value and sale price.

A reviewer of the paper written by Sirmans et al. (1995) suggests the possibility of objecting all models designed to measure vertical inequity. The comment is based upon the existence of variables other than market value that would influence the analysis, such as housing attributes, political, economic and social factors. According to the reviewer, these variables may have different effects on sale price and assessed value, even though influencing both.

Indeed, the use of a bivariate model to explain assessed value in terms of sale price may bias the interpretation of the vertical inequity, since assessment levels are influenced by a large group of other variables.

Issues of time

A false indication of assessment bias might emerge from ignoring the fact that assessed values and sale prices are not related to the same date. The need for adjusting

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sale prices to the date for which assessed values are estimated is recognised in the majority of the studies on assessment equity.

Kochin and Parks (1982a) inflate or deflate the actual sale prices to the assessment date according to a time trend. It is considered a quite subjective and arbitrary approach, being able to cause bias in the analysis toward regressivity or progressivity. Kochin and Parks (1982b) also examine the use of dichotomous variables for representing the date of the sales.

The use of a price index is often suggested as an alternative for the adjustment of sale price for the date of sales (Cannaday et al. 1987; Sunderman et al. 1990a; Benson and Schwartz; 1997). Clapp (1990) introduces the use of a time variable, in that assessed value is associated at an initial time (assumed as “time = 0”) and sale prices is related to the subsequent time period in months. Sirmans et al. (1995) also add a time trend variable to the equations, where sale price is the dependent variable.

In addition to adjusting sale prices to the assessment date, incorrect designs of the empirical analyses undertaken for assessment performance may also cause a false indication of assessment bias. There are studies in which assessed values, estimated to the middle of the period in which sales occurred, are compared with sale prices. Some studies compare assessed values with future sale prices. Others compare assessed values with sale prices that occurred before the assessment date. Finally, there are studies that compare assessed values and sale prices during a single year.

“The fact that, in many studies, valuations are compared with future sales prices data merely indicates how well current assessments predict future sale prices” (Benson and Schwartz 1997). In this context, valuers are required to anticipate shifts in sectoral values instead of interpreting market and property information properly.

Valuers do not have any instruments to predict the market. They do not have any control over inflation shocks, sellers/buyers behaviour, or any social or economic changes. They are realistically supposed to interpret the market at some point in time.

Therefore, the next important point for analysing properly assessment bias is to recognise that, by definition, assessment equity is the degree to which assessment bears a consistent relationship to market value “at the assessment date”.

Valuations for taxation purposes are carried out some time after the sales and they are inherently based on the existing information about prices. Ideally, tests should be performed comparing current sale prices used to estimate assessed values with assessed values. Of course, information on sale prices should be divided into two subsets: one for estimating assessed values and another for testing assessment inequity. The procedure aims at consistently evaluating the assessment performance for a taxing jurisdiction, instead of limiting the analysis to the data sample.

The reasons for comparing assessed values with future sales prices are only based upon achieving a more operational way to analyse assessment performance. However,

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the procedure might bias the analysis. Moreover, assessment equity is not what is being analysed when valuations are compared with future prices.

Additional considerations

As pointed out by IAAO (1978), measures of assessment performance are affected by the degree of sales editing, in that a good sales edit increases the accuracy of sales information. Consequently, lack of good sales analysis procedures affects adversely the measures of assessment performance.

Exploring Methodological Aspects for Analysing Assessment Equity: An Empirical Analysis

Data sample

A sample containing information about approximately 1700 sales of residential apartments units that took place in the city of Porto Alegre, Brazil, from January 1993 to December 1995, was used in the empirical analysis carried out.

Porto Alegre is the capital of the state of Rio Grande do Sul, which is the southernmost state of Brazil. The city covers 500 km2 in area and had approximately 1.5 million inhabitants in 1994, being the largest city in the South Region. Residential properties represent more than 81% of the total number of properties, but they contribute only 39% in terms of revenue from the property tax. Additionally, residential apartments represent more than 55% of all the properties.

Market value is the property tax base and the cost approach is the method traditionally employed for assessing real estate property for taxation purposes. In Porto Alegre, assessed values are estimated at a fixed date (December of each year). No legal requirement exists concerning intervals between general valuations. For years without valuations, the tax base has been readjusted generically according to prevailing inflation rates.

The data sample includes information about sale prices and conditions, assessed values, and the main physical and locational attributes of the properties. Additionally, some economic attributes related to the date on which sales took place and the neighbourhoods, in which the apartments are located, were also recorded.

Since the assessment performance is being analysed for the property class formed by individual apartments units, the data collected is not limited to some specific neighbourhoods or districts in the city of Porto Alegre. The data collection was designed to represent the actual distribution of residential apartments in the city.

Therefore, all types of residential apartments are represented in the data sample. It explains the large variability of the attributes that compose the database. Sale prices vary approximately from USA$ 3,800.00 to 360,000.00 and the mean of sale prices is USA$ 39,300.00; while assessed values are approximately between 1,900.00 and

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122,000.00 with a mean of USA$ 15,600.00. The building floor area of properties selected is between 24 and 561square metres (m2) and their year of construction lies between 1936 and 1995, representing properties as old as 59 years as well as new properties.

Analysis of the results

The analysis of the assessment performance involved a comparison of assessed values and sale prices. As the last general valuation took place in 1991, assessed values estimated in 1991 were adjusted according to the annual inflation rates for 1993, 1994, and 1995.

The assessed value considered for each individual property was the actual basis on which the property tax was levied in the year in which its sale took place. For instance, for a property that sold in 1993, the assessed value considered was the actual property tax base estimated in December 1993. When the last valuation took place, the level of valuations in Porto Alegre aimed at 60% of the market value of the properties. However, the statutory level of assessments is 100% of market value.

Adjusting sale prices

For each single year, sales took place from January to December, while assessed values are estimated at a fixed date (December). Both sale prices and assessed values were transformed into American dollars. It is supposed to absorb the effects of the inflation during the period of the analysis. However, inflation may not reflect the real estate market movements.

Additionally, almost 20% of the properties included in the data sample sold with a mortgage. Due to bargaining power, prices of properties that sold without a mortgage may be less than the ones of the properties sold with a mortgage.

Models were established using multiple regression analysis to adjust sale prices to the date for which assessed values are estimated and also for expressing the full cash value, i.e. to reflect the price that would have been paid without mortgage.

The data sample was divided into four groups according to geographical region of the city, viz.: Centre, Heart, North and South. A model was generated for each geographical region. This procedure tests the hypothesis about the existence of housing sub-markets. In other words, relative market values in various geographic sub-areas may change at differential rates over time. However, in order to simplify the analysis, a general index has been preferred in the majority of the empirical studies undertaken.

Sale price per unit of floor area (Spu) was used as the dependent variable and a large group of housing attributes were used as the independent variables. These attributes include the physical characteristics of the flats (such as age, floor area, building quality, car parking spaces, etc), neighbourhood conditions, etc. In total, more than 40 attributes were tested. Only the variables that were statistically significant in explaining the sale prices per unit floor area at the 5% level, at least, were integrated into the final models (See Table 2).

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////Insert table 2 # here////

The models with better explanatory power are described below. The adjusted coefficients of determination ( )2R are also presented. The models explain approximately 92%, 89%, 79%, and 87% of the variation in sale prices per unit of floor area for the region Heart, North, Centre and South respectively.

A time variable “sales date” was used for representing the date on which the sales took place. Properties that sold in Jan.1993 were associated to an initial time, assumed as “sales date=1”, and other properties were related to a subsequent time period in months. A variable, “% mortgage”, that identifies the percentage of the sale price paid with a mortgage was also tested.

Both variables, i.e. “sales date” and “% mortgage”, were statistically significant in all models generated for the different housing sub-markets. It confirms the need to adjust sale prices to the assessment date and to represent the price with a mortgage equal to zero.

The coefficient of the variables in the various models are, indeed, different. It confirms the existence of different housing sub-markets with distinct rates of growth. The coefficient of the variable “sales date” is positive in all models, suggesting that the growth rate of the sale prices was higher than the inflation rate during the period of the analysis. The coefficient of the variable “% mortgage” is also positive. It indicates that properties that sold with a mortgage were transacted at higher prices than the other properties.

Therefore, sale prices were adjusted to the assessment date and also for expressing the full cash value using the coefficients provided by models.

All other variables in the models established present the expected signal. For instance, the models adjust higher prices for newer properties and properties situated in high quality districts. Additionally, the presence of a lift and number of car parking spaces also adds a contribution in the formation of sale prices. Besides the variable “sales date” and “% mortgage, the building year is the only variable that contributes to explain the variation of sale prices per unit of floor area in all models produced.

An analysis of the residuals of the models was used to select the sales to be considered for the analysis of assessment performance presented in the next section. Up to 5% of the information about sale prices was excluded in each model, when necessary. It involved the removal from the analysis of the smallest and the largest 2.5% of the residuals of the models that explain sale price per unit of floor area. The procedure was aimed at including only reliable information about sale prices for representing the most probable price resulting from an arm-length transaction.

Assessment level and horizontal inequity

Properties were assessed on the median at only 34% of their sale prices. Therefore, the actual assessment level is much less than the desired level (60%) or the legal level (100%).The coefficient of dispersion of the median (COD) of assessed value to sale price ratio is almost 32%, indicating a low degree of assessment uniformity. In Brazil,

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there are neither local nor national standards for evaluating ratio studies. In the United States, the IAAO (1990) recommends some general standards for this purpose. However, standards for acceptable CODs are not designed for residential individual apartment units. For single-family residential property, an acceptable degree of uniformity could be indicated for a coefficient up to between 10 and 15% (IAAO 1990). Additionally, for income-producing property, the Institute recommends CODs should not exceed 20%. In any case, the coefficient computed for the data sample is higher than the standard measures recommended by the IAAO.

When measures were computed for the same data sample without adjusting sale prices (See De Cesare and Ruddock 1997), the assessment ratios achieved a median of 40% and a COD of 38% . The difference between the results of the two analyses undertaken (with and without adjusting sale prices) confirms the need for the adjusting procedures.

In order better to understand eventual assessment bias, some subsets of the data sample were analysed.

Assessment Year

Sets of the data classified according to the year in which sales took place were analysed. As demonstrated in Figure 1, the median of assessed value to sale price ratios is being reduced on an annual basis, principally in 1995. Properties were assessed on median at 40% of their sale prices in 1993, 37% of their sale prices in 1994, and only 27% of their sale prices in 1995. The last real valuation was undertaken in 1991. Thus, the investigation confirms that a lack of frequent valuations can significantly reduce the tax base. The coefficients of dispersion (CODs) computed for the sets of data analysed are quite similar, at around 28%.

////Insert figure 1 # here////

Range of Price

Concerning the range of price, low-price properties were assessed at approximately 42% of sale prices on the median; while high-price properties were assessed at approximately only 33% as observed in Figure 2. It suggests that low-price properties were over-assessed in relation to high-price properties.

////Insert figure 2 # here////

Considering the three ranges of price adopted previously but for groups of properties classified according to the assessment year (See Figure 3), no major differences in terms of assessment level between the properties assessed in 1993 and 1994 are observed. Low-price properties seem to be over-assessed in relation to other properties. However, for the assessment year 1995, the tax seems to be slightly progressive, with high-price properties over-assessed compared to other properties. The coefficients of dispersion computed vary from 25 to 32%, again indicating a low degree of assessment uniformity.

////Insert figure 3 # here////

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All the coefficients of dispersion computed for the several subsets of data are greater than any of the standards recommended by the IAAO (1990) as indicators of an acceptable degree of uniformity.

Vertical assessment equity

Price-related differential [PRD]

As discussed previously, according to the IAAO (1990), the price-related differential [PRD] provides an indication of vertical assessment bias. Price-related differentials are established for the entire data sample and subsets of properties classified according to the assessment year in Table 3.

////Insert table 3 # here////

No vertical assessment bias would be indicated when PRD is equal to “1”. Otherwise, assessment regressivity or progressivity would be indicated. However, assuming the existence of measurement errors, the IAAO establishes a margin for sampling error in the interpretation of PRD. Standards for PRD are recommended in that PRD greater (less) than “1.03” (“0.98”) would suggest vertical assessment regressivity (progressivity).

Considering the described rule suggested by IAAO (1990), the test would indicate assessment regressivity for the entire data sample and assessment year 1993. A slight assessment progressivity would be indicated for the assessment year 1995. And, finally, no vertical assessment bias would be indicated for the assessment year 1994 with a PRD approximately equal to the inferior limit for no vertical bias. It might also be indicating a slight assessment regressivity.

Bivariate Models: The Traditional Approach

As discussed initially, there are different methodologies for identifying vertical assessment inequity. In the present study, only models that use assessed value as the dependent variable and sale prices as the independent variable were tested, as justified in the previous section.

The model that fitted better to the data sample employed both assessed values and sale prices transformed as natural logarithmic functions. The test for indicating vertical assessment bias involves the analysis of the coefficient of the slope. If it is equal to 1, there is no vertical assessment regressivity.

The models generated are presented in Table 4. For the assessment years 1993 and 1994, the test indicates assessment regressivity since the coefficient of the slope is less than 1. In contrast, for assessment year 1995, the test indicates assessment progressivity. The tax seems to be more regressive in the assessment year 1993. Considering all cases together, the test indicates assessment regressivity.

////Insert table 4 # here////

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In general terms, the results achieved using the bivariate models confirm the indications provided by computing price-related differentials for the data sample.

Multivariate Models

Another analysis was performed to identify vertical assessment inequity. The methodology consists of inserting housing attributes into the model, instead of using only sale prices to explain assessed value. As discussed previously, assessment ratios vary significantly between different groups of properties. When only two variables, i.e. assessed value and sale price, are considered in the analysis, the variability of the assessment levels that are not caused by groups of properties defined by value might be incorrectly interpreted as regressivity or progressivity.

In summary, systematic differences in assessment levels for group of properties defined by value can be isolated and can, therefore, be properly identified when other attributes that influence this relationship are clearly represented in the model.

Multiple regression analysis was used to generate these models (See Table5). The models presented are the ones with better explanatory power. Additionally, all variables included in the models are statistically significant in explaining assessed values at the 5% level, at least. And, finally, the multiple regression assumptions are respected.

////Insert table 5# here////

The test for indicating vertical assessment bias also involves the analysis of the coefficient of the slope. The model generated for the entire data sample indicates that the tax is regressive in terms of assessment. Models were also generated for sets of data classified according to the assessment year. For the assessment years 1993 and 1994, the test indicates assessment regressivity. And, for the assessment year 1995, the test now with the introduction of new variables indicates assessment regressivity as well. But using a t-test, the coefficient is not statistically significant different from 1. It indicates that the tax would be neutral for the assessment year 1995. The tax seems to be more regressive in the assessment year 1993, confirming the previous results.

In comparative terms (See Table 6), the models containing the housing attributes present better explanatory power independently of the number of variables and cases since the adjusted coefficient of determination is being compared between the models. A greater proportion of the variation in assessed values is explained by the multivariate models.

They also consider differences between assessment levels defined not only by price but also by other housing attributes, such as geographical region, building year, apartment quality, presence of lift, etc (See Table 5).

This methodology may make it possible to isolate, in fact, vertical assessment equity. The coefficients estimated using those models are different from those using only two variables. Further investigation is required and models including housing attributes should be tested with other data samples. When adopting this type of model, it is important to examine the multicollinearity between the independent variables.

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////Insert table 6 # here////

Summary and Conclusion

The study aims to devise a methodology for properly analysing the assessment performance. Methodological aspects related to the analysis of assessment performance are discussed.

As discussed initially, efforts can only be allocated to eliminate or reduce inequities when the forms of inequity present are determined (Sunderman et al. 1990). The aggregative nature of standard measures recommended by the IAAO for identifying assessment inequity is observed by Sunderman et al. (1990b). Their study proposes breaking the coefficient of dispersion (COD) into vertical and horizontal components, since the coefficient measures both forms of inequity combined.

Additionally, the use of a bivariate model to explain assessed values in terms of sale prices may bias the interpretation of the vertical inequity, since assessment levels are likely to contain horizontal inequities. When considering only two variables in the analysis, the variability of the assessment levels that are not caused by groups of properties defined by value is also present in the model and might be interpreted incorrectly as vertical inequity.

In the present study, the use of sale prices to represent market value in the assessment ratio studies is assumed to be the best alternative available. Considering that assessment equity, by definition, is the degree to which assessment bears a consistent relationship to market value “at the assessment date", the analyses of assessment equity on which assessed values are compared with future sale prices should be avoided. As discussed earlier, these studies only indicate how well current assessments predict future sale prices (Benson and Schwartz 1997).

The need for adjusting sale prices to the assessment date and to represent the full cash value, prior to undertaking any analysis of the assessment performance, is recognised in the majority of the studies and guides on assessment equity. The focus of interest concerns the most appropriate technique for adjusting sale prices.

In this study, the use of multiple regression analysis (MRA) for adjusting sale prices is suggested. Several advantages may result from using the technique in comparison to the usual procedures adopted for adjusting sale prices. These advantages are summarised below:

The adjusting factors are derived from a regression model that is established based on current market information and identifies the most important factors determining prices, instead of adopting a subjective and arbitrary factor.

MRA can be used to develop non-linear adjustments for time and specific models can be developed for different groups of properties (IAAO, 1990).

For instance, in the empirical analysis undertaken, the existence of different housing sub-markets in the city of Porto Alegre was identified. Relative market values in four

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geographic regions were found to change at differential rates over time. It should be taken into account when adjusting sale prices.

The adjusting factors derived from the regression models tend to be more precise than when general price indexes are adopted.

MRA can employ practically all available sales information during the period of the analysis. As a result, the models can be based on larger sample sizes. Other techniques suggested by the IAAO (1990), such as paired sale analysis and resales analysis, are likely to generate adjusting factors based on a small group of sales that might not be representative of the property population being analysed.

The models generated explain variations in the sale prices regarding several independent factors, such as sales date, mortgage, building year, and other property characteristics. Assessed values are not included in these models. Therefore, eventual vertical or horizontal inequities on estimates of assessed values do not bias the analysis.

An analysis of residuals of a model that explains sale prices according to housing attributes and other social and economic variables may be helpful in suggesting the information about sale prices to be examined further or rejected for consideration in the analysis. In the present study, the same models generated to adjust sale prices were employed to indicate the exclusion of non-representative sales from the analysis.

Regarding vertical equity, only models based on the traditional approach are supported and, therefore, analysed. As discussed earlier, the traditional approach reflects better the economic behaviour than do the alternative approaches. Additionally, sale price is likely to be the best alternative for representing market value available.

The effects of using a multivariate model for analysing vertical equity were explored. According to the empirical analysis undertaken, the coefficients estimated using those models are different from those using only two variables. The multivariate models present better explanatory power than the usual models supported by the traditional approach.

This methodology may make it possible to isolate, in fact, vertical assessment equity. Further investigation is required, but those models seem to be more appropriate to indicate vertical assessment bias than the usual models employed. Additionally, the multivariate models are able to identify the other property attributes that cause differences in assessment levels.

The IAAO (1990) recognises multivariate analysis as a power tool for identifying assessment bias. According to the IAAO, multivariate analyses are able to analyse assessment bias in relation to many independent variables offering more precision and efficiency than the scatter diagrams and tables.

Indeed, multivariate models are able to identify simultaneously bias caused by level of sale prices, floor area, age, and so forth. In other words, they can analyse vertical and horizontal assessment inequities simultaneously. Finally, adjusting factors for equalising assessments could be derived from the coefficients provided by those models in order to reduce the overall inequity.

16

A false indication of assessment regressivity/progressivity might be related to a wrong methodology of the analysis carried out. Assessment inequities must be clearly and properly identified in order to develop policy guidelines for reducing both types of inequity. Neither academic community nor professionals involved in the taxing process have been able to propose a universally accepted methodology for that. The methodology proposed in the present study might make it possible to identify assessment bias properly.

Acknowledgements

The authors wish to thank the support offered by Prof. G. Brown during the preparation of the paper and the access to the data on property taxation provided by the Secretariat of Finance of the city of Porto Alegre. The Brazilian government through the National Council for Scientific and Technological Development [CNPq] sponsored the present study.

17

References

Bell, E. J. 1984. Administrative Inequity and Property Assessment: The Case for the Traditional Approach. Property Tax Journal 3:123-131.

Benson, E. D., and A. L. Schwartz, Jr. 1997. Vertical Equity in the Taxation of Single Family Homes. The 13th Annual Meeting of the American Real Estate Society: Sarasota, FL, USA.

Cannaday, R. E., E. W. Stunard, and M. A. Sunderman. 1987. Property Tax Assessment: Measures and Tests of Uniformity Applied to Chicago Condominiums. Illinois Business Review, Vol. 44, No. 2, pp. 9-13.

De Cesare, C. M., and L. Ruddock. 1997. An Empirical Analysis of a Property Tax System: A Case Study from Brazil. The International Conference on Assessment Administration (63rd Annual Meeting): Toronto, Canada.

Cheng, P. L. 1974. Property Taxation, Assessment Performance, and its Measurement. Public Finance XXIX: 268- 284.

Clapp, J. M. 1990. A New Test for Equitable Real Estate Tax Assessment. Journal of Real Estate Finance and Economics 3: 233-249.

Edelstein, R. H. 1979. An Appraisal of Residential Property Tax Regressivity. Journal of Finance and Quantitative Analysis XIV- 4: 753-768.

Gaston, P. 1984. Redeeming the Assessment Ratio Equity Test. Property Tax Journal: 3:181-198.

Evans, A. E. 1995. The Property Market: Ninety Per Cent Efficient? Urban Studies 32 – 1:5-29.

International Association of Assessing Officers [IAAO]. 1978. Improving Real Property Assessment: A Reference Manual. IAAO: USA.

_____________ 1990. Property Appraisal and Assessment Administration. Ed. By J.K. Eckert, IAAO: USA.

Kitchen, H. M. 1992. Property Taxation in Canada. Canadian Paper No. 92. Canada: Canadian Tax Foundation [CTF].

Kennedy, P. 1984. On an Unfair Appraisal of Vertical Equity in Real Estate Assessment. Economic Inquiry. XXII: 287-289.

Kochin, L. A., and R. W. Parks. 1982a. Vertical Equity in Real Estate Assessment: A Fair Appraisal. Economic Inquiry XX:511-532.

_____________ 1982b. Testing for Assessment Uniformity: A Reappraisal. Property Tax Journal 3:27-54.

Paglin, M., and M. Fogarty. 1973. Equity and the Property Tax: A New Conceptual Focus. National Tax Journal 25-4:557-565.

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Sirmans, G. S., B. A. Diskin, and H. S. Friday. 1995. Vertical Inequity in the Taxation of Real Property. National Tax Journal 48-1:71-84.

Sunderman, M. A., J. W. Birch, R. E. Cannaday; and T. W. Hamilton. 1990a. Testing for Vertical Inequity in Property Tax Systems. Journal of Real Estate Research 5- 3:319-334.

_____________1990b. Components of Coefficient of Dispersion. Property Tax Journal 9- 2:127-139.

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Table 1 – Tests for Vertical Equity

General Form of the Models Test Reference

A. Traditional Approach

AV= β0 + β1 SP + ε β0 = 0 Paglin and Fogarty (1972)

Ln AV = β0 + β1 ln SP + ε β1= 1 Cheng (1974)

AV/SP= β0 + β1 SP + ε β1= 0 IAAO (1978)

AV= β0 + β1 SP + β2 SP2 + ε β0 = β2 = 0 Bell (1984)

AV= β00 + β10 SP+ β01 Low + β02 High + β11 Low SP + β12 High SP + ε

β00=β01 =β02= 0

Sunderman et al. (1990)

B. Alternative Approaches

Ln SP = β0 + β1 ln AV + ε β1= 1 Kochin and Parks (1982)

Ln SP = β0 + β1 ln AV + ε ln AV = b0 + b1 Z + ε

β1= 1 Clapp (1990)

Where AV is assessed value; SP is sale price; and, βs are the coefficients estimated by the models. Low (High) is a dichotomous variable equal to one if the sale price of the property is less (more) than the first (second) knot and zero, otherwise. Additionally, Low SP (High SP) is the sale price of the property if the sale price on the property is less (more) than the first (second) knot and zero, otherwise. Finally, Z is an instrumental variable that is equal to “-1” when AV and SP rank in the bottom one-third of the data. Z is equal to “1” when AV and SP rank in the top one-third of the data. Otherwise, Z is equal to zero.

20

Table 2 - Models for Adjusting Sale Prices

Dependent Variable: SPu [USA$/m2] Models (1)- St: Standard error of β SPu Ln (SPu)

Geographical Region Heart North Centre South Independent Variables (χ) β St(1) β St(1) β St(1) β St(1)

Constant - Intercept term -45.99 24.21 37.54 12.11 7.10 0.49 3.73 0.22

Sale date 10.58 0.20 9.43 0.21 0.033 0.0009 0.035 0.0009

% mortgage 0.77 0.10 0.18 0.08 0.001 0.0004 0.0007 0.0004

Neighbourhood 1- Centre - - - - 0.15 0.026 - -

Neighbourhood 2- Centre - - - - 0.075 0.022 - -

Neighbourhood1- North - - 41.93 10.28 - - - -

Quality of district 12.21 1.24 - - - - 0.039 0.006

Land value index: Ln (χ) - - - - - - 0.12 0.045

Distance to shopping centre 1[m] - - 9.2E10-7 1.8E10-7 - - - -

Free site area [m2] 0.19 0.091 - - 0.0016 0.0004 - -

Building year (age): (χ2)

(χ4)

0.024

-

0.001

-

0.029

-

0.0018

-

-

4.3E10-9

-

5E10-10

-

5.8E10-9

-

7E10-10

Luxurious quality flat 212.03 21.33 - - - - - -

High quality flat 23.66 5.40 - - - - - -

Presence of lift 25.19 4.86 - - 0.082 0.020 0.10 0.027

Frontal flat (position) 150.27 5.79 - - - - 0.31 0.022

Middle flat (position) -124.06 5.75 -107.50 4.68 - - -0.13 0.27

Car parking spaces - - 20.47 6.33 - - - -

Blocks of flats per site - - -5.02 0.62 - - - -

Property sales per month

Ln(χ)

-0.042- 0.012

-

-

-

-

-

-

-0.30

0.067

-

-

-

-

-

Data 484 467 437 257 2R [%] 92.49 88.69 79.12 87.34

Where SPu is sale price per unit floor area in [USA$/m2]; βs are the regression coefficients of the independent variables; Sts are the standard errors of the regression coefficients; and, 2R is the adjusted coefficient of determination for each model.

21

Figure 1- The Median and the Coefficient of Dispersion of the Median (COD) of the Assessed Value to Sale Price Ratio (AV/SP)

0.400 0.371

0.274

0.000

0.100

0.200

0.300

0.400

0.500

Assessment Year

Med

ian

of A

V/S

P

1993 1994 1995

29.12 28.40 28.40

0.005.0010.0015.0020.0025.0030.0035.00

Assessment Year

CO

D o

f AV

/SP

1993 1994 1995

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Figure 2- The Median of the Assessed Value to Sale Price Ratio (AV/SP) for Sets of Data Sample Classified According to Three Ranges of Price

0.419

0.320 0.329

0.000

0.100

0.200

0.300

0.400

0.500

Med

ian

of A

V/S

P

25% low 50% middle 25% high

Property Price

23

Figure 3- The Median of the Assessed Value to Sale Price Ratio (AV/SP) for Sets of Data Sample Classified According to Assessment Year and Three Range of Price

0.000

0.100

0.200

0.300

0.400

0.500

Med

ian

of A

V/S

Pall cases 1993 assessment year1994 assessment year 1995 assessment year

25% low 50% middle 25% high

Property Prices

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Table 3 – Price-related Differential [PRD]

AV/SP Assessment Year Mean Weighted Mean

PRD Data

all cases 0.36 0.34 1.06 ➨ regressivity 1646

1993 0.42 0.40 1.05 ➨ regressivity 551

1994 0.39 0.38 1.03 ➨ neutral 560

1995 0.29 0.30 0.97 ➨ progressivity 535

Where AV is assessed value; SP is sale price; and, PRD is the price-related differential.

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Table 4 – Models for Analysing Vertical Equity: ln AV = β0 + β1 ln adjSP + ε

Assessment Year β0 β1 Data 2R [%] Outliers

all cases 0.032 0.89 ➨ regressivity 1645 76.27 1

Standard error of β (0.13) (0.0123)

1993 -0.245 0.93 ➨ regressivity 550 77.91 2

Standard error of β (0.21) (0.0211)

1994 -0.619 0.96 ➨ regressivity 560 75.33 0

Standard error of β (0.24) (0.023)

1995 -2.150 1.08 ➨ progressivity 523 83.19 12

Standard error of β (0.23) (0.021)

Where AV is assessed value; adjSP is adjusted sale price; βs are the coefficients estimated by the regression models; and, 2R is the adjusted coefficient of determination of the regression models. β0 is the regression coefficient estimated for the intercept term and β1 is the regression coefficient estimated for the variable adjusted sale price. The number of residuals removed from each model are indicated in the column entitled “outlier”.

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Table 5 - Models for Vertical Equity: ln AV = β0 + β1 ln adjSP + Other Variables + ε

Dependent Variable: ln (Assessed Values) [USA$] Models (1)- St: Standard error of β All cases 1993 1994 1995 Independent Variables (χ) β St(1) β St(1) β St(1) β St(1)

Constant - β0 1.22 0.13 1.17 0.20 19.27 4.41 -0.96 0.26

Ln (Sale Prices) - β1 0.81 0.013 0.80 0.02 0.86 0.024 0.97 0.02

Sales date - - 0.013 0.004 -0.00054 0.0001 0.02 0.003

Assessment year 1995 -0.24 0.016 - - - - - -

Centre 0.092 0.032 - - 0.30 0.04 -0.12 0.031

Heart 0.24 0.031 - - 0.41 0.04

North -0.071 0.03 -0.18 0.029 0.13 0.038 -0.26 0.029

Penthouse 0.26 0.04 - - - - - -

Distance to nearest shopping centre [m]

-0.00007 7E10-6 -0.00009 8E10-6 - - -0.0001 9E10-6

Building year (age) -0.004 0.0007 - - -0.005 0.0012 -0.004 0.001

Luxurious quality flat 0.29 0.11 - - - - 0.38 0.18

Popular quality flat - - -0.16 0.07 - - - -

Presence of lift 0.12 0.016 0.096 0.029 0.13 0.027 - -

Number of flats per floor - 0.0037 0.0009 -0.0034 0.0012 -0.007 0.002 -0.004 0.0017

Blocks of flats per site - - -0.011 0.0047 -0.011 0.005 - -

Data 1642 550 559 523 2R [%] 87.55 85.15 84.60 89.71

Where βs are the regression coefficients of the independent variables; Sts are the standard errors of the regression coefficients; and, 2R is the adjusted coefficient of determination for each model. β1 is the regression coefficient estimated for the variable adjusted sale price.

27

Table 6 – Comparing Models for Analysing Vertical Equity

ln (AV) = f (lnadj SP) ln (AV)= f (lnadjSP) + other variables Assessment Year β1 2R [%] Data β1

2R [%] Data

All cases 0.89 76.27 1645 0.81 87.55 1642

1993 0.93 77.91 550 0.80 85.15 550

1994 0.96 75.33 560 0.86 84.60 560

1995 1.08 83.19 523 0.97 89.71 523

Where AV is assessed value; adjSP is adjusted sale price; and, 2R is the adjusted coefficient of determination for each model. β1 is the regression coefficient estimated for the variable adjusted sale prices in the models.