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Section 3: Some Basics, Econometrics, & Discounting

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Section 3: Some Basics, Econometrics, & Discounting

Jisung Park: jisungpark@fas.harvard.edu

February 22 2013

(Based in part on slides by Liz Walker and Rich Sweeney)

- Some Important Preambles
- The Bigger Picture
- Basic Econometric Techniques and Intuition
- Methods Used in Environmental Economics
- Hedonic Pricing example

- Review of Discounting
- Questions

- This Course in the context of Environmental Economics and Sustainability
- Stavins and Weitzman
- Real-world policy relevance

- Math and Economics
- “Math just isn’t my thing, but I think I like economics.”
Welcome to the Club!

- MATH IS JUST A LANGUAGE

- “Math just isn’t my thing, but I think I like economics.”

“Ϛ-σ = ∑√τλβ∞η”

…

“Voulez-vouscoucher avec moi, cesoir?”

- Policy Applications as the End-Goal
- Most of you, I would imagine, are taking this course because you actually care about or are interested in environmental policy and big-picture problems like Climate Change or Sustainable Development.
- “These models and methods are so unrealistic”
- True, but they can help us clarify our thinking about complex issues.

- The Bigger Picture

POLICY RECOMMENDATIONS

- Econometrics ~ Statistics
- Mean
- Mean = ∑Xi /n
- Mean takes all data points into account
- Mean is sensitive to outliers. Outliers have a lot of weight on mean (e.g. mean income and Bill Gates)

- Measures of Dispersion
- Variance = (Xi – mean)2/N
- Standard Deviation =[(Xi – m)2/N]1/2 = (Variance)1/2

- More dispersed data have higher variance
- Like mean, standard deviation is also sensitive to outliers

This red line comes from Ordinary Least Square Regression (OLS), which shows the impact of income on water use

Y (wateruse) = 1201.124 + 47.54*income

Yi = β0 + β1Xi + εi

i = each observation

Y = Dependent Variable (water use)

X = Independent Variable (income)

εi= Error term

β0 = intercept. It tells us the predicted value of Y when X = 0.

β1 = The coefficient that tells us how Y changes for unit change in X.

What sources of error can you imagine?

Yi= β0 + β1Xi1 + β2Xi2 + β3Xi3 + εi

- More than one independent variables
- Now, β1 is the change in value of Y for a unit change in X1 while holding constant (or controlling for) X2 and X3 (the marginal interpretation)
- Recall Hedonic example in class

- F(x, z, e)
- Just a “general” way of representing the relationship between variables. (As opposed to a “specific functional form”.)
- Some examples of functional forms:
- Linear: F(x, z,e) = ax + bz - ce
- Quadratic: F(x, z, e) = ax + bz^2 -ce
- Cubic, Exponential, Power, etc…

- F(X, Z, e)
- X is a vector of housing unit variables:
- X = (x1, x2, x3 … xn)
- x1 = # of bedrooms
- x2 = size of kitchen
- …

- X = (x1, x2, x3 … xn)
- Z is a vector of neighborhood characteristics:
- Z = (z1, z2, z3… zm)

- X is a vector of housing unit variables:

e.g.

Micro-Theory of the Firm

e.g. Hedonic Regression, Travel Cost

e.g. Cost-Benefit Analysis

- How would you estimate the benefits from proposed Chinese air pollution control legislation?
- Think it through from what we’ve learned

- Key Estimation Methods
- Revealed Preference
- Stated Preference

- Key Estimation Methods
- Revealed Preference
- Hedonic
- Recreation Demand
- Averting Behavior
- Cost of Illness

- Stated Preference
- Contingent Valuation
- Discrete Choice

- Revealed Preference

- The short definition: Think surveys
- Pros:
- Can design surveys to target the “good” in question directly
- E.g. “How much do you value the existence of Polar Bears?”

- Can design surveys to target the “good” in question directly
- Cons:
- Incentive Compatibility
- Purely hypothetical: seldom actually asked to pay

- Information Problems
- Do respondents really know the science behind ecosystem services, air pollution’s impact on health, biodiversity conservation?

- Framing and other biases (Prospect Theory)
- Scale Issues
- Loss Aversion

- Incentive Compatibility

- The short definition: Backing out implied valuation using observed behavior.
- E.g. Back out value of better air quality through differences in home prices.

- Pros:
- Suffers fewer problems of incentive compatibility, framing bias

- Cons:
- Sensitive to study design and key assumptions (more overleaf)

- Prices are good indicators of true value
- E.g. Few behavioral biases like hyperbolic discounting

- Markets are operating well
- Usual market failures aren’t in effect

- Information Problems are minimal
- Consumers “know” the true health impacts of air pollution

- All Relevant “market participants” are included
- E.g. What of future generations?

- All attributes and demands properly measured
- E.g. Recall potential issues with travel cost and available substitutes

- These models use attributes of market products, including environmental attributes to explain variation in product prices
- P = F(x, z, e)
- P: price of market product (e.g., house)
- x: vector of non-env. product attributes (e.g., lot size, bedrooms)
- z: vector of non-env. local attributes (e.g., crime rate)
- e: environmental attribute (e.g., local air pollution)

- Marginal implicit price of environmental attribute or marginal willingness to pay for environmental attribute:

Suppose we wanted to study the variation in housing prices due to proximity to an airport (which generates noise, a negative environmental externality)

Price = β0+ β1*Bedrooms + β2*Bathrooms + β3*Airport + β4*Crime + β5*Scores + β6*Sold2008 + error

- Price: Sale price of house in dollars
- Number of Bedrooms
- Number of Bathrooms
- Near Airport: Dummy variable equal to 1 if the house is near the airport and 0 otherwise (so coefficient is not a slope in this case)
- Crime Rate: Annual number of incidents per 10,000 population
- Test Scores: Average test scores at public high school (out of 100)
- Sold in 2008: Dummy variable equal to 1 if the house sold this year

- Results of multiple regression
- On average, a house near the airport sells for $49,198 less than a house not near the airport, all else equal

Fictional data

- Issues and problems
- Simultaneity:
- Prices are determined by both supply and demand, but these models treat supply as exogenous (i.e., unaffected by environmental attributes)

- Selection:
- Individuals differ in their tolerance of negative environmental attributes

- Information:
- Individuals’ perceptions of environmental attributes may differ from measurements

- Omitted variable bias:
- Coefficients are too large or small if an explanatory variable associated with the dependent variable and correlated with other explanatory variables is left out

- Scope:
- Relatively narrow range of applications

- Simultaneity:

- “For transparency’s sake, you should state in your report what assumptions were used, such as the time horizon for the analysis and the discount ratesapplied to future benefits and costs.
- It is usually necessary to provide a sensitivity analysis to reveal whether, and to what extent, the results of the analysis are sensitive to plausible changes in the main assumptions and numeric inputs”.

- Comparing apples to apples
- U =
r = ρ + ηg

- U =
- r : discount rate
- ρ: pure rate of time preference (felicity discounting, or “impatience”)
- η: elasticity of marginal utility
- g: future consumption growth rate

- Benefits or costs that occur sooner are often (though not necessarily) more valuable
- Resources invested earn a positive return, so current consumption is more expensive than future consumption, since you are giving up that expected return on investment when you consume today. (Opportunity Cost).
- Postponed benefits also have a cost because people generally prefer present to future consumption. (Positive time preference).
- Also, if consumption continues to increase over time, as it has for most of U.S. history, an increment of consumption will be less valuable in the future than it would be today (Principleof diminishing marginal utility).

- Big Debate, with philosophical dimensions
- Especially in the context of long-T problems like Climate Change (stay tuned!)
- (Weitzman, Nordhaus, Stern, Goulder, Stavins…)

- “The problem of discounting for projects with payoffs in the far future is largely ethical.” - Kenneth Arrow
- “Discounting later enjoyments versus earlier ones is simply a practice that is ethically indefensible.” - Frank P. Ramsey
- Descriptive Reality ≠ Normative Desirability
- “People tend to be impatient and value present goodies over future goodies” is not the same statement as
- “Societies should value present generations over future generations”
- Philosopher Bryan Norton (2009): Levels of analysis matter

- An active area of research

- “a real discount rate of 7 percent should be used as a base-case for regulatory analysis” (OMB)
- Why?
- “The 7 percent rate is an estimate of the average before-tax rate of return to private capital in the U.S. economy.
- the returns to real estate and small business capital as well as corporate capital.
- It approximates the opportunity cost of capital
- it is the appropriate discount rate whenever the main effect of a regulation is to displace or alter the use of capital in the private sector”.