# Economics 105: Statistics

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Economics 105: Statistics

Economics 105: Statistics Go over GH 22 GH 23 due Monday Individual Oral Presentations see RAP handout. Dates are Tue April 24th and Thur April 26th in lab. But we cant fit them all into 75 minutes so extra sessions to be announced. Consider a change in X1 of X1X2 is held constant!Average effect on Y is difference in pop reg models

Estimate of this pop difference is

Average Effect on Y of a change in X in Nonlinear Models

Example

Example

What is the average effect of an increase in Age from 30 to 40 years? 40 to 50 years?2.03*(40-30) - .02*(1600 900) = 20.3 14 = 6.32.03*(50-40) - .02*(2500 1600) = 20.3 18 = 2.3Units?!

http://xkcd.com/985/5Example

Example

Log Functional Forms

Linear-Log

Log-linear

Log-log

Log of a variable means interpretation is a percentage change in the variable (dont forget Marks pet peeve)

Log Functional Forms Heres why:ln(x+x) ln(x) =

calculus:

Numerically:ln(1.01) = .00995 = .01 ln(1.10) = .0953 = .10 (sort of)

10Linear-Log Functional Form

Linear-Log Functional Form

Log-Linear Functional Form

Log-Linear Functional Form

Log-Log Functional Form

Log-Log Functional Form

Examples

Examples

Examples

Examples

Dummy VariablesA dummy variable is a categorical explanatory variable with two levels:yes or no, on or off, male or femalecoded as 0s and 1sRegression intercepts are different if the variable is significantAssumes equal slopes for other explanatory variablesIf more than two categories, the number of dummy variables included is (number of categories - 1)Dummy Variable Example (with 2 categories) E[ GPA | EconMajor = 1] = ? E[ GPA | EconMajor = 0] = ? Take the difference to interpret EconMajor

Y = (0 + (1ln(X)

(b)

Now change X:

Y + (Y = (0 + (1ln(X + (X)

(a)

Subtract (a) (b):

(Y = (1[ln(X + (X) ln(X)]

now

ln(X + (X) ln(X) ,

so

(Y (1

or

(1 (small (X)

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Yi = (0 + (1ln(Xi) + uifor small (X,

(1

Now 100* = percentage change in X, so a 1% increase in X (multiplying X by 1.01) is associated with a .01(1 change in Y.

(1% increase in X ( .01 increase in ln(X)

( .01(1 increase in Y)

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ln(Y) = (0 + (1X

(b)

Now change X: ln(Y + (Y) = (0 + (1(X + (X)

(a)

Subtract (a) (b): ln(Y + (Y) ln(Y) = (1(Xso

(1(X

or

(1 (small (X)

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ln(Yi) = (0 + (1Xi + uifor small (X,

(1

Now 100* = percentage change in Y, so a change in X by one unit ((X = 1) is associated with a 100(1% change in Y. 1 unit increase in X ( (1 increase in ln(Y) ( 100(1% increase in Y_1126969052.unknown

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ln(Yi) = (0 + (1ln(Xi) + ui

(b)

Now change X:

ln(Y + (Y) = (0 + (1ln(X + (X)

(a)

Subtract:

ln(Y + (Y) ln(Y) = (1[ln(X + (X) ln(X)]

so

(1

or

(1 (small (X)

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ln(Yi) = (0 + (1ln(Xi) + uifor small (X,

(1

Now 100* = percentage change in Y, and 100* = percentage change in X, so a 1% change in X is associated with a (1% change in Y.

In the log-log specification, (1 has the interpretation of an elasticity.

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