2. Distinguish between the following pairs of econometric concepts: (a) Ordinary

Question

2. Distinguish between the following pairs of econometric concepts:

(a) Ordinary Least Squares and Two-Stage Least Squares

(b) Heteroscedasticity and Autocorrelation

(c) t-statistic and F-statistic

(d) Autoregressive Process (AR) and Moving Average Process (MA)

(e) Regression and Correlation

(f) Cross-sectional data and Time series data

(g) R-Square and Adjusted R-Square

(h) Linear Regression Model and Non-linear Regression Model

(i) Skewness and Kurtosis

(j) Jarque-Bera test and Ramsey RESET test

Explanation / Answer

Sol)

h) Linear regression requires a linear model.

A model is linear when each term is either a constant or the product of a parameter and a predictor variable. A linear equation is constructed by adding the results for each term. This constrains the equation to just one basic form:

Response = constant + parameter * predictor + ... + parameter * predictor

While a linear equation has one basic form, nonlinear equations can take many different forms. The easiest way to determine whether an equation is nonlinear is to focus on the term “nonlinear” itself. Literally, it’s not linear. If the equation doesn’t meet the criteria above for a linear equation, it’s nonlinear.

i)

Skewness
A measure of the asymmetry of a distribution. The normal distribution is
symmetric, and has a skewness value of zero. A distribution with a
significant positive skewness has a long right tail. A distribution with a
significant negative skewness has a long left tail. As a rough guide, a
skewness value more than twice it's standard error is taken to indicate a
departure from symmetry.

Kurtosis
A measure of the extent to which observations cluster around a central
point. For a normal distribution, the value of the kurtosis statistic is 0.
Positive kurtosis indicates that the observations cluster more and have
longer tails than those in the normal distribution and negative kurtosis
indicates the observations cluster less and have shorter tails.

In practical terms, skewness is probably more important than kurtosis, and
positive skew is probably more common than negative skew. Most variables
with a fixed lower limit but no fixed upper limit (for example, income --
assuming income can't be less than 0) will tend to be positively skewed.

e) Correlation quantifies the degree to which two variables are related. Correlation does not fit a line through the data points. You simply are computing a correlation coefficient (r) that tells you how much one variable tends to change when the other one does. When r is 0.0, there is no relationship. When r is positive, there is a trend that one variable goes up as the other one goes up. When r is negative, there is a trend that one variable goes up as the other one goes down.

Linear regression finds the best line that predicts Y from X.

c)

T test Vs F test

Typically a t-test is used to examine the differences between the means of two groups. For example, in an experiment you may want to compare the overall mean for the group on which the manipulation took place vs a control group.

To examine whether there are differences between the groups you would use the F-ratio, which essentially measures the improvement due to fitting the model i.e. the group means versus the grand mean of scores for all participant and compares this against the error remaining in the model, which is the difference between the actual scores and the respective means of the groups. Therefore, the F-test is the ratio of systematic variance : unsystematic variance, so higher scores are better.

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