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Three major uses for econometrics
 describing economic reality
 testing hypotheses about economic theory
 forecasting future economic activity

y is a linear function of x. why?
the change in y is relative to a change in x is always =

represents what?
the marginal effect of change in X_1 on y.

Extending the marginal effect that is β_1 in a single variable regression model, how would β_1 and β_2 be interpreted in a multiple variable regression?
They're now referred to as partial effects of the change in X_1 or X_2 on y. Remember, all other things are constant in economics.

Difference between proportional change and percent change?
Percent change is proportional change times 100. This is important because it's where mistakes are made. Think about the difference in GDP  .032 (proportion) compared to 3.2 percent. Could be quite a bit of $ there.

When are quadratic equations helpful?
diminishing returns, for example

One of the most useful natural logorithm uses to us?
can be used to approximate proportionate changes.

the natural log of x is typically defined as
the power to which the base e must be raised to obtain the number x.

properties of the natural logarithm
 No negatives. Only defined for x > 0
 ln(x) < 0 for 0 < x < 1 (if x is between 0 and 1, the ln is less than 0)
 If x = 1, then ln(x) = 0
 ln(x) > 0 for x >1

when applying the approximation
it generally works best when
 the change in x is by a smaller amount
 (expect β_1 to be positive, b/c increasing and β_2 to be negative most of the time)

ln (x_1/x_0) is approximately equal to?
the proportionate change in x when x changes from x_0 to x_1

To approximate the percent change in x, we can multiply the ln(x) by...
 100

Why is it important that
duh. elasticity.

When there is a log of the variable on the left and log of the variable on the right, the coefficients can be interpreted as
elasticities

exponential function
this is the inverse of the natural log function

Three main uses of econometrics?
 1. describe economic reality (estimating the parameters of a market demand curve)
 2. test economic hypotheses (is hamburger an inferior good?)
 3. forecast future economic activity (forecast future housing demand for a region)

7 steps in econometric analysis?
 1. formulate a precise question
 2. develop some kind of model that addresses the question
 3. convert model to an econometric model
 4. state the hypothesis in terms of coefficients in the model
 5. collect data
 6. estimate the econometric model
 7. test the hypothesis as stated in 4

experimental data
 formal experimental process
 typically designed by researchers
 rare, but behaviorial economists are doing it

nonexperimental
 passive collection
 researcher does not design the process that creates data
 most common in economics
 survey  for most part

cross sectional data
collect on indvididuals at a single point in time

time series
1 individual across time

pooled cross section
 data on a bunch of individuals at a single point in time, then data on a bunch at different points in time
 then pool it together

panel dataset
some individuals over time, some individuals drop out along the way, and a new individual may enter

unbalanced panel
individuals that are there don't necessarily exist throughout (different numbers of observations for each individual)

why shouldn't we confuse correlation with causation?
  omitted variables
 reverse causality (student performance can be because of self esteem, or better performance can improve self esteem)

Regression analysis, defined
a statistical technique that attempts to explain movements in one variable (dependent) as a function of movements in a set of other (independent) variables

the purpose of regression analysis
to find the betas

is..
the deterministic component of the model

What does do?
 There's always some randomness we can't control. Epsilon does this.
 It's the stochiastic (random) error term. It captures variation in the dependent variable that is not captured by movements in the independent variables

captures at least four sources of variation not accounted for by the deterministic model
 1. some influence on dependent variable that may not be included in model
 2. there is likely measurement error in at least one of the variables
 3. we might have chosen the wrong functional form
 4. there is randomness in the world we can't account for with measured variables

the difference between I and Ihat?
e (the residual)

e equals
I  Ihat (this tells us how accurate the estimate is to actual. we want e to be small)

True regression equation includes epsilon or e?
epsilon

if you use Ihat as your model, do you include e?
 No. I can be equal to b_0hat + bx_1 hat + e or Ihat is equal to bhat + bxhat, no e
 so ihat is equal to all the hats, no e or i (no hat) is equal to all the hats plus e

