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 =
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...
Why is it important that
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
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
- formal experimental process
- typically designed by researchers
- rare, but behaviorial economists are doing it
- 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
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
some individuals over time, some individuals drop out along the way, and a new individual may enter
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
the deterministic component of the model
- 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 I-hat?
e (the residual)
I - I-hat (this tells us how accurate the estimate is to actual. we want e to be small)
True regression equation includes epsilon or e?
if you use I-hat as your model, do you include e?
- No. I can be equal to b_0-hat + bx_1 hat + e or I-hat is equal to b-hat + bx-hat, no e
- so i-hat is equal to all the hats, no e or i (no hat) is equal to all the hats plus e