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Econometrics

Week 1

08/26/2025

  • Midterm:

    • October 9

    • December 2

  • Final:

    • Work in groups of 2

    • Write Empirical paper

    • Need to use Strata

    • Represent what you learn

  • Buy textbook and read it

Homework (08/28/2025)

  • Important statistical concepts used in Econometrics:

    • Measure of central tendency:

      • Mean

      • Median

    • Measures of dispersion:

      • Variance

      • Standard Deviation

    • Minimum, Maximum, and Range

    • Skewness and Kurtosis

    • Correlation, covariance

    • Confidence interval

  • Mean

    • Measure of central tendency

    • The mean is the arithmetic average of the data.

    • Suppose to have N observation of X, then Mean is the sum of X’s divided by N

  • Median

    • Another measure of central tendency

    • Median is the middle observation when the data are arranged from smallest to largest.

    • Sometimes called the 50th percentile.

    • Half the observations lie below the median and half the observations live above the median.

    • Central observation for an odd number of observations and an average of the two middle data points for an even number of observations.

Measures of Dispersion:

  • Variance

    • Measure of dispersion (how scattered the data is)

    • The variance (sample) is calculated by subtracting the mean from each observation, squaring that value, adding up all N values, and then dividing that by the number of observations less one.

  • Standard deviation

    • Another measure of dispersion

    • Measures the average deviation of the values in the dataset away from the mean

    • It is the square root of the variance

Covariance and Correlation Coefficient

  • Provides numerical value to the strength and direction of the linear relationship between two variables.

  • Only concerned with strength of the relationship.

  • No casual effect is implied!

  • Covariance:

    • Measure of linear relationship between two random variables Think of variance (measures how X varies with itself)

  • Correlation Coefficient:

    • Degree of joint variation between Y and X as a fraction for the individual variations in Y and X scaled, removes the interpretation problem:

Covariance and Correlation Coefficient Interpretation

  • Covariance:

    • Positive:

      • Above average values of X associated with above values of Y

    • Negative:

      • Above average values of X associated with below average values of Y

    • Problem with the covariance measure:

      • We do not know whether the magnitude is large or small because of the units that we choose.

  • Correlation Coefficient:

    • If all data points in a data set fall on a positively sloped line, rxy =1.

      • The closer to positive 1, the stronger the positive linear relationship.

    • If all the data points in a data set fall on a negatively sloped line, rxy =-1.

      • The closer to negative 1, the stronger the negative linear relationship.

    • If there is no linear relationship between X and Y, then rxy =0.

      • The closer to 0, the weaker the linear relationship.

Random Variables

  • A random variable is a numerical outcome of a random process.

    • Two types:

      • Discrete random variables - take on countable values (number of heads in a coin toss basically).

      • Continuous random variables - take on any variable within an interval (height or income basically)

  • Notation:

    • Often denoted by capital letters (X,Y)

  • Values:

    • Represented by lowercase letters (x,y)

  • In econometrics, random variables are used to model uncertainty data.

Random Variable and Expectation

  • Expectation (or expected value) represents the long-run average of a random variable.

  • It provides a measure of the “center” of the distribution.

  • For a discrete random variable X:

      • Where P(X = x) is the probability that the random variable, X takes value “x”.

08/28/2025

Econometrics

  • Literally means “economic measurement”

  • Econometrics is a science and art of using economic theory and statistical techniques to analyze economic data.

  • Econometrics attempts to quantitatively bridge the gap between economic theory and the real world.

  • Venn Diagram:

    • Economic on the left

    • Statistics on the right

    • Econometrics in the middle

Week 2

09/02/2025

  • Regression Equation

    • Y = B0 + B1X