Index

Additive dummy variables, 68–69

Assumptions

multiple linear regressions, 44

simple linear regressions, 24–25

Autocorrelation

autocorrelation function, 81–82

consequences, 81

HAC standard errors, 84

LM test, 82–84

multiple regression, 80

OLS estimator, 84–86

one lag error and k lag errors, 80

population correlation function, 81

regressing, 93–95

regression, 92–94

simple-regression model, 79

testing, 92–94

Autoregressive distributed lag (ARDL) model, 90–91

Autoregressive (AR) model

dependent variable, 86

first-difference model, 88–89

interval prediction, 87–88

one constant and two lag values, 87

point prediction, 87

random walk model, 86

Balanced panel, 98

Best linear unbiased estimators (BLUE), 25, 72, 84

Central Limit Theorem (CLT), 25, 29

Chow test, 74, 105

Coefficient estimates, 26–27

Column chart, 13

Conditional expectation function, 24

Confidence intervals, 29, 48

Correlations, 54

Critical t-value, 33

Cross-sectional dataset, 24

Data analyses

add-in tools, 12

calculation results in excel, 18–20

column chart, 13

data importing, 15–17

frequency distribution, 15

heteroscedasticity, 74–78

histogram, 14

panel data, 107–111

simple linear regression, 38–40

time-series data, 91–96

unwanted data deletion, 17–18

Dependent variable, 4, 23, 44, 45, 86

Descriptive statistics, 7–10, 20

Distributed lag (DL) models, 90, 95–96

Econometric model

multiple linear regression, 43–46

simple linear regression, 23–26

steps involved in, 5

vs. theoretical model, 3–4

wage and spending, 4

Elasticity, 27

Error

autocorrelation, 80, 84

heteroscedasticity, 72

Newey-West standard errors, 84

White’s standard errors, 72, 76, 84

Estimators and estimates

multiple linear regression

interval estimates, 47

point estimates, 46–47

predicted values, 47–48

simple linear regression

coefficient estimates, 26–27

interval estimates, 28–30

point estimates, 27–28

predicted value, 31–32

variance, 30–31

First-difference estimation, 100–102

First-difference model, 88–89

Fixed-effects estimators, 102–104

Frequency distribution, 15

F-tests

tests of joint significance, 48–50

tests of model significance, 51–52

vs. t-test, 52

Gauss-Markov theorem, 25

Generalized least squares estimators, 72

Goodness of fit measure

multiple linear regression, 52–53

panel data technique, 106

simple linear regression, 36–37

Heteroscedasticity

data analyses, 74–78

detection, 70–71

nature and consequences, 69–70

OLS estimator, 72–74

standard errors, 72

Heteroscedasticity and autocorrelation consistent (HAC) errors, 84

Histogram, 14

Hypothesis testing

F-tests, 48–52

t-tests, 32–35

Inferential statistics, 10–12

Intercept dummy variable, 68–69

Interval estimates

multiple linear regression, 47

simple linear regression, 28–30

Interval prediction, 31, 32, 47, 87–88

Lagrange multiplier (LM) test, 70–71, 82–84

Least square dummy variable (LSDV) method, 103

Left-tailed test, 34

Linear-log model, 66

Logarithmic model, 64–66

Log-linear model, 65–66

Log-log model, 64–65

Long-and narrow panels, 98

Mean squared error (MSE)

panel data technique, 106

Model transformations, 63–64

Multicollinearity, 45, 54

Multiple linear regression

data analyses, 54–58

econometric model, 43–46

estimators and estimates, 46–48

goodness-of-fit, 52–53

Newey-West standard errors, 84

Normal distribution, 3, 29, 82

One-tailed test, 34–35

Ordinary least squares (OLS)

autocorrelation, 84

autoregressive distributed lag model, 90

autoregressive model, 87

distributed lag model, 90

fixed-effects estimation, 102

heteroscedasticity, 72–74

panel dataset regression, 98

simple linear regression, 25–27

Panel data techniques

advantage, 97–98

balanced panels, 98

data analyses, 107–111

different characteristics detection, 105–106

first-difference estimation, 100–102

fixed-effects estimation, 102–104

goodness-of-fit, 106

identity differences, 98

long-and narrow panels, 98

pooled OLS estimation, 98

seemingly unrelated regressions, 104–105

short-and-wide panels, 98

unbalanced panels, 98

Point estimates

multiple linear regression, 46–47

simple linear regression, 27–28

Predicted value, 31–32

Probability, 5–7

P-value, 37–38, 53

Random walk model, 86

Right-tailed test, 34

Root mean squared error (RMSE), 106

R-squared (R²) value, 36–37

Seemingly unrelated regression (SUR), 104–105

Short-and-wide panel, 98

Simple linear regression

data analyses, 38–40

econometric models, 23–26

estimators and estimates, 26–32

hypothesis testing, 32–25

P-value, 37–38

R-squared value, 36–37

Simple model issues

function of training, 67–68

growth rate, 66–67

heteroscedasticity, 69–74

intercept dummy variable, 68–69

logarithmic model selection, 64–66

model transformations, 63–64

Standard error of the prediction (se(p)), 31

Standard error of the regression, 31

Stationary variable, 25, 80, 88, 89

Statistics primer

descriptive statistics, 7–10

inferential statistics, 10–12

probability, 5–7

t-distribution, 28

Tests of coefficient significance, 38

Tests of significance, 34–35

Theoretical model, 3–4

Three-period difference model, 102

Time-series data

autocorrelation, 79–86

autoregressive distributed lag models, 90–91

autoregressive model, 86–89

data analyses, 91–96

distributed lag models, 90

Time-series dataset, 24, 25

t-ratio, 35

t-test

vs. f-tests, 52

general hypothesis, 33–34

steps involved in, 32–33

tests of significance, 34–35

Two-tailed test, 35

Unbalanced panel, 98

White’s standard errors, 72, 76, 84