Statistical Analysis
Statistical Analysis
To aid stakeholders in evaluating the merits of the current Tiebreaker and to determine relationships between total costs, square footage, and project location, Kingdom Development (Kingdom) performed statistical analysis on new construction projects awarded credits in the 9% competition.
Executive Summary
The 9% Tiebreaker is based on public funds divided by total project costs and it should come as no surprise that it is strongly correlated with public funds per unit. The real surprise—the Tiebreaker is also correlated with higher cost per unit and not correlated with lower credits per unit. Applicants are getting huge amounts of public funds per unit ($132,020) and simultaneously asking for a huge amount of credits per unit ($267,367), which pays for 93% of project costs. The Tiebreaker fails to leverage the scarce 9% credit like it was intended to do.
If California desired a Tiebreaker that leverages credits by rewarding credit efficiency, projects proposing less square footage would have lower costs, need fewer credits, and receive an advantage in the competition. However, since project costs are strongly correlated with square footage, this advantage can be quantified and offset. Similarly, projects located in densely populated locations, in high income counties, and or in high rent zip codes would be at a disadvantage. However, these location based characteristics are correlated with cost per unit and so their effect on costs can be quantified and offset.
Hypotheses Tested
1. Public funding per unit is the primary driver of the Tiebreaker.
2. The Tiebreaker causes higher cost per unit.
3. Credits per unit is not significantly correlated with the Tiebreaker.
4. Projects cost more if they provide more residential square footage and cost less when they provide less.
5. Projects cost more to develop in densely populated locations, in high income counties, and in high rent zip codes.
Data Set
Kingdom created a table containing all 9% awarded new construction projects since 2014. New construction was defined as projects where new construction costs were at least three times rehabilitation costs. This criteria resulted in a list of 241 new construction projects. However, 3 outlier projects were removed for having nonsensical costs per unit given their location and square footage (ironically they had great Tiebreakers). As a result the data set contains 238 records with data on size, location, costs, and financing (for more details, see the Meta Data tab in the accompanying Cost Analysis spreadsheet).
While checking the data set for errors Kingdom corrected 5 pieces of data: one missing land cost, two with exorbitant land costs, one with residential square footage below the TCAC limits, and one small area fair market rent zip code that was double surrounding zip codes. These adjustments are denoted with purple text on the Data tab and were brought in line with similar projects.
Download the data set and analysis tool.
Methodology
Besides simple arithmetic and statistical calculations (average, quartile, standard deviation, etc.) we utilized Pearson correlation values, simple linear regressions, and multiple linear regressions (using the “least squares regression” method). We mostly relied on Excel functions but had to use the data analysis toolkit to obtain p-values (needed for confidence measurement). Functions include: LINEST, SLOPE, INTERCEPT, RSQ, PEARSON, CORREL, SUMIFS, and COUNTIFS (see the fully functional accompanying Cost Analysis.xlsx).
Tiebreaker Driver
Test: Public funding per unit is the primary driver of the Tiebreaker.
Background: The average project received $132,020 of public funding per low-income unit, which equates to 32% of funding sources. Public funding ranged from $0 per unit to $386,798 per unit.
Finding: The more public funding per unit a project received the higher its Tiebreaker. The two variables shared a 0.81 correlation (+ or - 1.0 is a perfect correlation, 0.0 is no correlation). According to a linear regression, public funding can explain 65% of the all variances in Tiebreaker. Each $1,000 of public funding per unit will increase the Tiebreaker 0.18%. For example, to go from a 40% Tiebreaker to a 41% the project would need $5,427 more public funding per unit.
Higher Costs!
Test: The Tiebreaker causes higher cost per unit.
Background: The Tiebreaker was introduced to leverage the tax credit, by inducing investment of Redevelopment Agency funds, at a time when public funds were not being deployed. Over the last four years, the average Tiebreaker has been 44% and has trended up to 47% in 2017. The low and high in the data set were 8% and 83% and half of the projects fell between 30% and 57%.
Finding: The higher the Tiebreaker the higher cost per unit gets. The two variables shared a 0.35 correlation. According to a linear regression, Tiebreaker can explain 12% of the all variances in cost per unit.
Lower Credits?
Test: Credits per unit is not significantly correlated with the Tiebreaker.
Background: The Tiebreaker was introduced to leverage tax credits with public funds. If the Tiebreaker was successful in doing so it would have a strong negative correlation (< -0.50) with tax credits per unit similar to its strong positive correlation with public funding per unit (0.86).
Finding: Credits per unit has a weak correlation (-0.20) with the Tiebreaker above $325,000 credits per unit and no correlation (-0.09) with the Tiebreaker below $325,000 credits per unit.
Square Footage Effects
Test: Projects cost more if they provide more residential square footage and cost less when they provide less.
Background: If California desired a Tiebreaker that leveraged credits by rewarding credit efficiency, projects proposing less square footage would have lower costs, need fewer credits, and receive an advantage in the competition. Can square footage based cost differences be quantified and then offset in the competition?
Finding: Residential square footage is highly correlated with project costs (0.67) and explains 44% of all variations in project costs. Using a simple linear regression we are given the following equation to calculate total project cost given residential square footage:
ProjectCost = 347*ResidentialSqFt + 7,171,479
Let’s compare two examples, the state average project and CA-16-115 (a 57 unit senior project).
The state average costs $22,867,232 (347*45,281 + 7,171,479)
CA-16-115 should cost $17,050,434 (347*28,500 + 7,171,479)
CA-16-115 would have a tremendous advantage against other projects by proposing 1-BR Senior units at the minimum square footage. However, The regression model provides a means of quantifying the project’s square footage based cost differences, which can be used to level the playing field.
Location Effects
Test: Projects cost more to develop in densely populated locations, in high income counties, and in high rent zip codes.
Background: If California desired a Tiebreaker that leveraged credits by rewarding credit efficiency, projects in certain areas with inherently higher costs would be disadvantaged. Can location based cost differences be quantified and then offset in the competition?
Finding: Individually the following location based characteristics were correlated with higher costs per unit (see the table below and the graphs on the following pages).
Using a multiple linear regression, which forces these characteristics to work together in explaining variances, they are able to explain 45% of all variances in cost per unit with a 99.5% confidence level. The approximate difference in cost from one location to the next can be calculated using the following model:
CostPerUnit = 54,485*PrevWage + 1.2*Population + 2.4*CountyAMI + 44.7*FairMarketRent + 99,265
Let’s compare two examples, the state average project and CA-17-141 (an 83 unit project in Santa Clara).
The state average costs $404,193 per unit (54,485*0.6 + 1.2*24,949 + 2.4*72,744 + 44.7*1,427 + 99,265)
CA-17-141 should costs $512,276 per unit (54,485*1.0 + 1.2*31,536 + 2.4*113,300 + 44.7*1,660 + 99,265)
The regression model provides a means of quantifying a project’s location based cost differences, which can be used to level the competitive playing field.
Characteristic |
Correlation |
Explains |
CA Avg. |
CA-17-141 |
X_{1} Prevailing Wages |
37 |
14% |
0.62 |
1 |
X_{2} Population in 1-mile |
31 |
9% |
24,949 |
31,536 |
X_{3} County AMI |
57 |
32% |
72,744 |
113,300 |
X_{4} Fair Market Rents |
52 |
27% |
1,427 |
1,660 |
Conclusion
The current Tiebreaker is driven solely by public funding per unit, is correlated with higher costs per unit, and therefore drives costs up. The Tiebreaker has no significant correlation with credits per unit and therefore fails to leverage tax credits.
The effect of increased (or decreased) residential square footage can be measured as it is strongly correlated with total project costs.
The effects of location based characteristics on cost per unit can be measured as they are all correlated with cost per unit. Combined in a multiple linear regression model, these characteristics can explain the inherent cost differences of different locations.