Section 3: Some Basics, Econometrics, & Discounting Jisung Park: February 22 2013

Section 3: Some Basics,
Econometrics, & Discounting
Jisung Park: [email protected]
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
Economic
Theory
Empirics/
Econometrics
Policy
Analysis
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…
We often look at how two variables
relate to each other..
This red
line comes
from
Ordinary
Least
Square
Regression
(OLS),
which
shows the
impact of
income on
water use
9
Y (wateruse) = 1201.124 + 47.54*income
Bi-variate Regression (Y on one X)
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?
10
Multiple Regression (Y on many X’s)
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
11
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
Economic
Theory
e.g.
Hedonic
Regression,
Travel
Cost
e.g.
MicroTheory of
the Firm
Empirics/
Econometrics
Policy Analysis
e.g. CostBenefit
Analysis
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
Theory
Empirics
Policy Analysis

Stated Preference
Benefit Estimation Methods

Key Estimation Methods

Revealed Preference





Hedonic
Recreation Demand
Averting Behavior
Cost of Illness
Stated Preference


Contingent Valuation
Discrete Choice
Theory
Empirics
Policy Analysis
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


Information Problems


Purely hypothetical: seldom actually asked to pay
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.


Pros:


E.g. Back out value of better air quality through differences in
home prices.
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


Markets are operating well


Consumers “know” the true health impacts of air pollution
All Relevant “market participants” are included


Usual market failures aren’t in effect
Information Problems are minimal


E.g. Few behavioral biases like hyperbolic discounting
E.g. What of future generations?
All attributes and demands properly measured

E.g. Recall potential issues with travel cost and available
substitutes
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:
P
P
 MIPe  MWTPe 
e
e
21
Hedonic Pricing example
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
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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
22
Hedonic Pricing Example

Results of multiple regression
Regression Statistics
Multiple R
0.9630
R Square
0.9273
Adjusted R Square
0.9252
Standard Error
49620.07
Observations
209.00
Intercept
Num_Bedrooms
Num_Baths
Airport
Crime_Rate
Test_Scores
Sold2008

Coefficients Standard Error
-140,445.37
39,569.46
79,434.83
4,892.07
76,550.33
5,606.77
-49,197.76
9,136.00
-1,802.93
500.97
1,193.61
483.13
-73,671.17
9,298.15
t Stat
-3.55
16.24
13.65
-5.39
-3.60
2.47
-7.92
P-value
0.00
0.00
0.00
0.00
0.00
0.01
0.00
Fictional data
On average, a house near the airport sells for $49,198 less
than a house not near the airport, all else equal
23
Hedonic Pricing Model Issues and
Problems

Issues and problems

Simultaneity:


Selection:


Individuals’ perceptions of environmental attributes may differ from
measurements
Omitted variable bias:


Individuals differ in their tolerance of negative environmental
attributes
Information:


Prices are determined by both supply and demand, but these models
treat supply as exogenous (i.e., unaffected by environmental attributes)
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
24
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”.
26
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
27
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

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

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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?