For example, say we have specified that we will be using the criteria of efficiency, cost, political acceptability, and equity to make our decision. We have defined what we mean by each of these and how they will be measured. For example, efficiency is defined as the amount of reduction in the teenage driving accident rate, and is measured by the Department of Motor Vehicles as the number of accident involving teen drivers divided by the total number of teens in the state.
We must then look at each proposed policy alternative, one at a time, and ask, what would be the efficiency of this alternative? What would be the cost of this alternative? What would be the political acceptability of this alternative? And how will this alternative affect equity? We then repeat this process for every alternative, including the no-action alternative.
How do we know what the efficiency of each alternative will be? That involves forecasting.
There are a variety of methods used to make forecasts. Forecasting methods range from simple stereotyping to complex statistical formulas.
Intuition may use techniques such as Delphi, scenario writing, or feasibility assessment. However, it requires that the participants be quite knowledgeable, and it needs to be checked for logical consistency.
Theoretical models identify important variables and specify the nature of the linkages among them. Then the model is used to predict outcomes when one or more of the variables are changed. Models are built from information, experience, expert advice, etc.
Constructing a model helps to get to the key elements of the situation, and focus on the most important concerns. It identifies the key factors and the relationships among them which will likely be impacted by any proposed policy alternative. It demonstrates the likely consequences of either the no action alternative, or any other rival alternative.
Models may be expressed in words, in physical dimensions (e.g., architectural models), or in numerical form.
Extrapolation uses the past to predict the future, assuming there are stable patterns. For example, if the population of Arizona has been growing at 50% every ten years, then a graph showing past growth can be extended into coming years to predict future growth.
Extrapolation is useful for conducting a baseline analysis, showing what is expected if the status quo or no action alternative is adopted. It is relatively simple and cheap and can be accurate in many circumstances. Data can be either raw numbers or a computed rate of change.
Extrapolation requires precise definitions of criteria and measures, and accurate measurement. It is most often used when there are linear patterns in the data. Extrapolation is less useful in the case of new problems, new issues, or new policy areas, where there is little or no past data.
The most commonly used form of regression is linear regression, and the most common type of linear regression is called ordinary least squares regression. Linear regression uses the values from an existing data set consisting of measurements of the values of two variables, X and Y, to develop a model that is useful for predicting the value of the dependent variable, Y for given values of X.
Year | Actual Population | Predicted Population |
1910 | 15000000 | |
1920 | 18000000 | |
1930 | 21000000 | |
1940 | 24000000 | |
1950 | 27000000 | |
1960 | 30000000 | |
1970 | 33000000 | |
1980 | 36000000 | |
1990 | 3900000 | |
2000 | 42000000 | |
2010 | 45000000 |
If the data are not linear, that is, if on a graph the line that best shows the relationship between the two variables is not a straight line, then simple linear regression cannot be used to extrapolate into the future. Instead, the data must be converted, for example, to logarithms, or a different sort of regression must be used.
To calculate the long term costs and long term benefits of a proposed policy alternative, the policy analyst must assemble estimates of the initial or implementation year costs and benefits of the alternative, and the subsequent costs and values for each additional year the project will be in effect.
Say that the city wants to upgrade its data processing function. It asks for bids showing costs to be submitted by different vendors. It also estimates the savings that will occur from each bid (for example, from a reduction in personnel).
For the first bid, the policy analyst estimates the following
YEAR: | 0 | 1 | 2 | 3 | 4 | 5 |
Costs | $15,000 | 0 | 0 | $1,223 | 0 | 0 |
Benefits | 0 | $4,000 | $4,000 | $4,000 | $4,000 | $4,000 |
The next step is for the policy analyst to decide on a discount rate. The discount rate assumes that money spent in the future will not cost as much as money spent today. Similarly, money gained in the future will not be worth as much as money gained today. This is based on the human preference for wanting to put off costs (or payments) as long as possible, and wanting to receive benefits (or pay) as soon as possible.
The discount rate is usually obtained from economists, from agency policy, or from the nature of the project being considered (i.e., whether a large infrastructure project, a revenue-bond based project, or a general obligation bond based project). Another source is the discount rate charged by the Federal Bank, or the interest rate paid on government bonds.
At times, the choice of which discount rate to use has been highly politicized. Because many government projects have high initial costs but a long stream of benefits, a low discount rate will make a project look more favorable, and a high discount rate will make a project look less favorable.
The same discount rate is generally applied to both the project costs and the project benefits. If inflation is going to be factored in, it should be applied to both the costs and benefits separately, before the discount factor is applied.
To calculate the discounted costs, multiply each year's costs by that
year's discount factor (the discount rate factor be obtained from a table
of discount rates):
YEAR: | 0 | 1 | 2 | 3 | 4 | 5 | Total |
Costs | $15,000 | 0 | 0 | $1,223 | 0 | 0 | $16,223 |
Discount rate | 4% | 4% | 4% | 4% | 4% | 4% | |
Discount factor | 1.0 | .9615 | .9246 | .8890 | .8548 | .8219 | |
Discounted costs | $15,000 | 0 | 0 | $1087 | 0 | 0 | $16,087 |
To calculate the discounted benefits, multiply each year's benefits
by that year's discount factor (the discount rate factor be obtained from
a table of discount rates):
YEAR: | 0 | 1 | 2 | 3 | 4 | 5 | Total |
Benefits | 0 | $4,000 | $4,000 | $4,000 | $4,000 | $4,000 | $20,000 |
Discount rate | 4% | 4% | 4% | 4% | 4% | 4% | |
Discount factor | 1.0 | .9615 | .9246 | .8890 | .8548 | .8219 | |
Discounted benefits | 0 | $3846 | $3698 | $3556 | $3419 | $3288 | $17,807 |
The Net Present Value is the value of the project if all the costs were paid today and all the benefits were gained today. To find NPV, subtract discounted costs from discounted benefits: Discounted Benefits $17,807 - Discounted Costs $16,087 = $1,720
The Net Present Value of each policy alternative must be calculated separately, and then it can be compared to the NPV of each other policy alternative, to find the one with the highest NPV.
The costs and the benefits of any policy alternative can be compared in a number of ways. Cost-benefit ratios are obtained by dividing discounted benefits by discounted costs:
Discounted benefits =$17,807
Discounted costs =$16,087
Benefit/Cost ratio =1.1
Note that the highest benefit-cost ratio may not have the highest NPV. These are two different types of analysis. The most efficient projects have the highest benefits-to-costs ratio, but many policy analysts prefer to maximize NPV. In any case, NPV should be a positive number, and the benefit-cost ratio should be greater than 1.0
The internal rate of return is an expression of the discount rate at which discounted benefits would equal discounted costs. For the example above, at an 8% discount rate, discounted benefits would equal $15,971 and discounted costs would also equal $15,971.
If the calculated IRR is greater than the discount rate being used for the project, then that is an indication that the project should be carried out. Generally, IRR is not comparable to either NPV or the benefits-to-costs ratio. The IRR from one project, however, can be directly compared to the IRR from an alternative project.
Often there is no clearly superior potential policy alternative, but several that seem equally acceptable. One alternative may be better on the criterion of efficiency, while another is better on costs, and a third on political acceptability.
Or does a project still have a positive NPV if the discount rate is raised from 4% to 6%? Is the IRR still greater than the discount rate? Is the benefit-to-cost ratio still greater than 1.0 ?
In another example, the city assumes that building a new parking garage will raise an additional $2,000 per parking space per year in sales taxes, as well as the revenues from parking. What if only $1,000 is raised?
Or say a university wants to get more students to park on campus instead of on nearby neighborhood streets. It thinks that if it reduces the parking permit fee by $10, then 25% more students will buy one and park on campus. What if only 5% more students buy one?
A city has vacant land that it can sell, lease, or keep. The city wants to sell. It assumes that someone will buy the land and develop it, increasing the city's property tax revenues. But what if the office building remains mostly vacant? Would this change the city's decision on selling? What are the probabilities of the different outcomes? What if the probabilities for the favored outcome decrease?
A fortiori analysis examines the likelihood that any one factor will take on a value that makes the project infeasible. For example, what if the project takes two years to complete instead of one? What if interest rates rise dramatically? What if new regulations are adopted that make the project technically impossible?
Another way to begin the appreciate the different possible outcomes of different policy alternatives is to use quick decision analysis. This is a way to visually represent a small number of alternatives and their consequences.
Quick decision analysis identifies key issues, and helps the policy analyst to decide what information is necessary to assess each possible alternative. It helps to structure thinking about the probability or likelihood that certain outcomes will occur. It also helps the policy analysts or decision-makers to reveal their attitudes about risk and uncertainty. And it alerts the policy analyst to the possible political ramifications of predicted outcomes.
Each possible policy alternative has two possible outcomes: new economic
development occurs, or new economic development does not occur.
Likely Outcomes |
Do Nothing | Offer Abatement | ||
Development
Occurs |
No new development | Development
Occurs |
No new
development |
|
Change in Property Tax Revenues | +$100 m | 0 | +$900 m | 0 |
Cost of offering the abatement | 0 | 0 | -$600 m | -$200 m |
Cost of additional city services | -$25 m | 0 | -$100 m | 0 |
Net | +$75 m | 0 | +$200 m | -$200 m |
Probability of this outcome | p=0.3 | p=0.7 | p=0.6 | p=0.4 |
Expected Value of this alternative |
0.3 x $75 m =
$22.5 m |
0.7 x $0 m =
$0 m |
0.6 x $200 m =
$120 m |
0.4 x-$200 m =
-$80 m |
+$22.5 m | +$40 m |