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)

Outline Some Important Preambles The Bigger Picture Basic Econometric Techniques and Intuition Methods Used in Environmental Economics

Hedonic Pricing example Review of Discounting Questions

Some Important Preambles This Course in the context of Environmental

Economics and Sustainability Stavins and Weitzman Real-world policy relevance

Some Important Preambles Math and Economics

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

Welcome to the Club! MATH IS JUST A LANGUAGE

“Ϛ-σ = ∑√τλβ∞η”…

“Voulez-vous coucher avec moi, ce soir?”

Some Important Preambles 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.

Why do we need to learn Econometrics? The Bigger Picture

Policy Analysis

Empirics/Economet-rics

Economi

c

Theory

POLICY RECOMMENDATIONS

Some Basic Statistics 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

Data sets can vary in their means and distributions…

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We often look at how two variables relate to each other..

Y (wateruse) = 1201.124 + 47.54*income

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

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Bi-variate Regression (Y on one X)

Yi = β0 + β1Xi + εi

i = each observationY = 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 + β2Xi

2 + 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

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Multiple Regression (Y on many X’s)

Functional Form 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…

Vectors F(X, Z, e)

X is a vector of housing unit variables: X = (x1, x2, x3 … xn)

x1 = # of bedrooms x2 = size of kitchen …

Z is a vector of neighborhood characteristics: Z = (z1, z2, z3… zm)

Benefit Estimation Methods: Big Picture

Policy Analysis

Empirics/ Econometrics

Economic

Theory

e.g. Cost-Benefit Analysis

e.g. Hedonic Regression, Travel Cost

e.g. Micro-Theory of the Firm

Benefit Estimation Methods How would you estimate the benefits from

proposed Chinese air pollution control legislation? Think it through from what we’ve learned

Benefit Estimation Methods Key Estimation Methods

Revealed Preference

Stated PreferencePolicy

Analysis

Empirics

Theory

Benefit Estimation Methods Key Estimation Methods

Revealed Preference Hedonic Recreation Demand Averting Behavior Cost of Illness

Stated Preference Contingent Valuation Discrete Choice

Policy Analysis

Empirics

Theory

Stated Preference Techniques 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?”

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

Revealed Preference Techniques 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)

Key Assumptions for Revealed Preference Methods 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

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Example of Revealed Preference:Hedonic Pricing 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:

e

PMWTPMIP

e

Pee

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Hedonic Pricing exampleSuppose 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

Running this regression, we are interested in β3 Other applications: estimate how much people value air

quality, visibility

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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

Regression StatisticsMultiple R 0.9630R Square 0.9273Adjusted R Square 0.9252Standard Error 49620.07Observations 209.00

Coefficients Standard Error t Stat P-valueIntercept -140,445.37 39,569.46 -3.55 0.00Num_Bedrooms 79,434.83 4,892.07 16.24 0.00Num_Baths 76,550.33 5,606.77 13.65 0.00Airport -49,197.76 9,136.00 -5.39 0.00Crime_Rate -1,802.93 500.97 -3.60 0.00Test_Scores 1,193.61 483.13 2.47 0.01Sold2008 -73,671.17 9,298.15 -7.92 0.00 Fictional

data

Hedonic Pricing Example

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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

Hedonic Pricing Model Issues and Problems

Discounting

OMB Guidelines on Cost Benefit Analysis

“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 rates applied 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”.

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Why do we need discounting? Comparing apples to apples

U =

r = ρ + ηg r : discount rate ρ: pure rate of time preference (felicity

discounting, or “impatience”) η: elasticity of marginal utility g: future consumption growth rate

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Why do we need discounting? 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 (Principle of diminishing marginal utility).

What is the “correct” discount rate? 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

What is the appropriate discount rate in practice?

“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”. 30

Questions?