Econometrics Key Terms Chpt 1-4

Front 1

Chapter 1 - Key Terms

Back 1

Definition

Front 2

Causal Effect

Back 2

a ceteris paribus change in one variable has an effect on another variable

Front 3

Ceteris Paribus

Back 3

all other relevant factors are held fixed

Front 4

Cross-Sectional Data Set

Back 4

s data set collected by sampling a population at a given point in time

Front 5

Data Frequency

Back 5

the interval at which time series data are collected. Yearly, Quarterly and Monthly are the most common data frequencies

Front 6

Econometric Model

Back 6

an equation relating the dependent variable to a set of explanatory variables and unobserved disturbances, where unknown population parameters determine the ceteris parabus effect of each explanatory variable

Front 7

Economic Model

Back 7

a relationship derived from economic theory or less formal economic reasoning

Front 8

Empirical Analysis

Back 8

a study that uses data in a formal econometric analysis to test a theory, estimate a relationship, or determine the effectiveness of a policy

Front 9

Experimental Data

Back 9

data that have been obtained y running a controlled experiment

Front 10

Nonexperimental Data

Back 10

data that have not been obtained through a controlled experiement

Front 11

Observational Data

Back 11

see nonexperimental data- data that have not been obtained through a controlled experiement

Front 12

Panel Data

Back 12

a data set constructed from repeated cross sections over time. With a balanced panel, the same units appear in each time period. With an unbalanced panel, some units do not appear in each time period, often due to attrition

Front 13

Pooled Cross Section

Back 13

a data configuration where independent cross sections, usually collected at different points in time, are combined to produce a single data set

Front 14

Random Sampling

Back 14

a sampling scheme whereby each observation is drawn at random from the population. In particular, no unit is more likely to be selected than any oter unit, and each draw is independet of all other draws

Front 15

Retrospective Data

Back 15

data collected based on past, rather than current, information

Front 16

Time Series

Back 16

data collected over time on one or more variables

Front 18

Chapter 2

Front 19

Coefficient of Determination

Back 19

R squared -It is the proportion of variability in a data set that is accounted for by the statistical model

Front 20

Constant Elasticity Model

Back 20

a model where the elasticity of the dependent variable, with respect to an explanatory variable, is constant; in multiple regression, both variables appear in logarithmic form

Front 21

control Variable

Front 22

Covariate

Front 23

Degrees of Freedom

Back 23

in multiple regression analysis, the number of observations minus the number of estimated parameters

Front 24

Dependent Variable

Back 24

the variable to be explained in a multiple regression model (and a variety of other models)

Front 25

Elasticity

Back 25

the percentage change in one variable given a 1% ceteris paribus increase in another variable

Front 26

Error Term (Disturbance)

Back 26

the variable in a simple or multiple regression equation that contains unobserved factors that affect the dependent variable. The error term may also include measurement errors in the observed dependent or independent variables.

Front 27

Error Variance

Back 27

the variance of the error term in a multiple regression model

Front 28

Explained Sum of Squares (SSE)

Back 28

the total sample variation of the fitted values in a multiple regression model

Front 29

Explained Variable

Back 29

dependent variable

Front 30

Explanatory Variable

Back 30

in regression analysis, a variable that is used to explain variation in the dependent variable

Front 31

First Order Conditions

Back 31

the set of linear equations used to solve for the OLS estimates

Front 32

Fitted Values

Back 32

the estimated values of the dependent variable when the values of the independent variables for each observation are plugged into the OLS regression line

Front 33

Gauss-Markov Assumptions

Back 33

The set of assumptions (Assumptions MLR.1 through MLR.5 or TS.1 through TS.5) under which OLS is BLUE

Front 34

Heteroskedasticity

Back 34

The variance of the error term, given that the explanatory variables, is not constant

Front 35

Homoskedasticity

Back 35

the errors in a regression midel have constant variance conditional on the explanatory variables

Front 36

Independent Variable

Back 36

explanatory variable

Front 37

Intercept Parameter

Back 37

the parameter in a multiple linear regression model that gives the expected value of the dependent variable when all independent variables equal zero

Front 38

Mean Independent

Back 38

expected value-a measure of central tendency in the distribution of a random variable, including an estimator

Front 39

OLS Regression Line

Back 39

the equation relating the predicted value of the dependent variable to the independent variables, where the parameter estimates have been obtained by OLS

Front 40

Ordinary Least Squares (OLS)

Back 40

a method for estimating the parameters of a multiple linear regression model. The ordinary least squares estimates are obtained by minimizing the sum of squared residuals

Front 41

Population Regression Function (PRF)

Back 41

see conditional expectation- the expected or average value of one random variable, called the dependent or explained variable, tht dependes on the values of one or more other variables, called the independent or explanatory variables

Front 42

Predicted Variable

Back 42

see dependent variable

Front 43

Predictor Variable

Back 43

explanatory variable

Front 44

Regressand

Back 44

dependent variable

Front 45

Regression through the Origin

Back 45

regression analysis where the intercept is set to zero; the slopes are obtained by minimizing the sum of squared residuals, as usual

Front 46

Regressor

Back 46

explanatory variable

Front 47

Residual

Back 47

the difference between the actual value and the fitted (or predicted) value; there is a residual for each observation in the sample used to obtain an OLS regression line

Front 48

Residual Sum of Squares (SSR)

Back 48

see Sum of Squares Residuals (SSR)- in multiple regression analysis the sum of the squared OLS residuals across all observations

Front 49

Response Variable

Back 49

dependent variable

Front 50

R-Squared

Back 50

in a multiple regression midel, the proportion of the total sample variation in the dependent variable that is explained by the independent variable

Front 51

Sample Regression Function (SRF)

Back 51

see OLS regression line- the equation relating the predicted value of the dependent variable to the independent variables, where the parameter estimates have been obtained by OLS

Front 52

Semi-elasticity

Back 52

the percentage change in the dependent variable given a one-unit increase in an independent variable

Front 53

Simple Linear Regression Model

Back 53

a model where the dependent variable isa linear function of a single independent variable, plus an error term

Front 54

Slope Parameter

Back 54

the coefficient on an independent varaible in a multiple regression

Front 55

Standard Error of Beta hat 1

Back 55

an estimate of the standard deviation in the sampling distribution of Beta hat 1

Front 56

Standard Error of the Regression (SER)

Back 56

in multiple regression analysis, the estimate of the standard deviation of the population error, obtained as the square root of the sum of squared residuals over the degrees of freedom

Front 57

Total Sum of Squares (SST)

Back 57

the total sample variation in a dependent variable about its sample average

Front 58

Zero Conditional Mean Assumption

Back 58

a key assumption used in multiple regression analysis that states that, given any values of the explanatory variables, the expected value of the error equals zero (see Assumptions MLR.4, TS.3 and TS.3

Front 60

Chapter 3

Front 61

Best Linear Unbiased Estimator (BLUE)

Back 61

among all linear unbiased estimators, the estimator with the smallest variance. OLS is BLUE, conditional on the sample values of the explanatory variables, under the Gauss-Markov assumptions

Front 62

Biased Toward Zero

Back 62

a description of an estimator whose expectation in absolute value is less than the absolute value of the population parameter

Front 63

Ceteris Paribus

Back 63

all other relevant factors are held fixed

Front 64

Degrees of Freedom (df)

Back 64

in multiple regression analysis, the number of observations minus the number of estimated parameters

Front 65

Disturbance

Back 65

error term

Front 66

Downward Bias

Back 66

the expected value of an estimator is below the population value of the parameter

Front 67

Endogenous Explanatory Variable

Back 67

an explanatory variable in a multiple regression model that is correlated with the error term, either because of an omitted varaible, measurement error, or simultaneity

Front 68

Error Term

Back 68

the variable in a simple of multiple regression equation that contains unobserved factors that affect the dependent variable. The error term may also include measurement errors in the observed dependent or independent variables

Front 69

Excluding a Relevant Variable

Back 69

in multiple regression analysis, leaving out a variable that has a nonzero partial effect on the dependent variable

Front 70

Exogenous Explanatory Variable

Back 70

an explanatory variable that is uncorrelated with the error term

Front 71

Explained Sum of Squares (SSE)

Back 71

the total sample variation of the fitted values in a multiple regression model

Front 72

First Order Conditions

Back 72

the set of linear equations used to solve the OLS estimates

Front 73

Gauss-Markov Assumptions

Back 73

the set of assumptions (Assumptions MLR.1 through MLR.5 or TS.1 through TS.5) under which OLS is BLUE

Front 74

Gauss-Markov Theorem

Back 74

the theorem that states that under the five Gauss-Markov assumptions (for cross-sectional or time series models) the OLS estimator is BLUE (conditional on the sample values of the explanatory variables)

Front 75

Inclusion of an Irrelevant Variable

Back 75

the including of an explanatory variable in a regression model that has a zero population parameter in estimateing an equation by OLS

Front 76

Intercept

Back 76

in the equation of a line, the value of the y variable when the x variable is zero

Front 77

Micronumerosity

Back 77

a term introduced by Arthur Goldberger to describe properties of econometric estimators with small sample sizes

Front 78

Misspecification Analysis

Back 78

the process of determining likely biases that can arise from omitted variables, measurement error, simultaneity, and other kinds of model misspecification

Front 79

Multicollinearity

Back 79

A term that refers to correlation among the independent variables in a multiple regression model; it is usually invoked when some correlations are "large", but an actual magniture is not well defined.

Front 80

Multiple Linear Regression Model

Back 80

a model linear it its parameters, where the dependent variable is a function of independent variables plus an error term

Front 81

Multiple Regression Analysis

Back 81

a type of analysis that is used to describe estimation of and inference in the multiple linear regression

Front 82

OLS Intercept Estimate

Back 82

the intercept in an OLS regression line

Front 83

OLS Regression Line

Back 83

the equation relating the predicted value of the dependent variables, where the parameter estimates have been obtained by OLS

Front 84

OLS Slope Estimate

Back 84

A slope in an OLS regression line

Front 85

Omitted Variable Bias

Back 85

the bias that arises in the OLS estimators when a relevant variable is omitted from the regression

Front 86

Ordinary Least Squares

Back 86

a method for estimating the parameters of a multiple linear regression model. The ordinary least squares estimates are obtained by minimizing the sum of squared residuals

Front 87

Overspecifying the Model

Back 87

See inclusion of an irrelevant variable

Front 88

Partial Effect

Back 88

the effect of an explanatory variable on the dependent variable, holding other factors in the regression model fixed

Front 89

Perfect Collinearity

Back 89

in multiple regression, one independent variable is an exact linear function of one or more other independent varaibles

Front 90

Population Model

Back 90

a model, especially a multiple linear regression model, that describes a population

Front 91

Residual

Back 91

the difference between the actual value and fitted (or predicted) value; there is a residual for each observation in the sample used to obtain an OLS regression line

Front 92

Residual Sum of Squares

Back 92

see Sum of Squared Residuals - in multiple regression analysis, the sum of the squared OLS residuals across all observations

Front 93

Sample Regression Function (SRF)

Back 93

See OLS regression line- the equation relating the predicted value of the dependent variables, where the parameter estimates have been obtained by OLS

Front 94

Slope Parameter

Back 94

the coefficient on an independent variable in a multiple regression model

Front 95

Standard Deviation of B hat j

Back 95

a common measure of spread in the distribution of B hat j

Front 96

Standard Error of B hat j

Back 96

and estimate of the standard deviation in the sampling distribution of beta hat 1

Front 97

Standard Error of the Regression (SER)

Back 97

in multiple regression analysis, the estimate of the standard deviation of the population error, obtained as the square root of the sum of squared residuals over the degrees of freedom

Front 98

Sum of Squared Residuals (SSR)

Back 98

in multiple regression analysis, the sum of squared OLS residuals across all observations

Front 99

Total Sum of Squares (SST)

Back 99

the total sample variation in a dependent variable about its sample average

Front 100

True Model

Back 100

the actual population model relating the dependent variable to the relevant independent variables, plus a disturbance, where the zero conditional mean assumption holds

Front 101

Underspecifying the Model

Back 101

see excluding a relevant variable- in multiple regression analysis, leaving out a variable that has a nonzero partial effect on the dependent variable

Front 102

Upward Bias

Back 102

the expected value of an estimator is greater than the population parameter value

Front 103

Variance Inflation Factor (VIF)

Back 103

in multiple regression analysis under the Gauss-Markov assumptions, the term in the sampling variance affected by correlation amot the explanatory variables

Front 105

Chapter 4

Front 106

Alternative Hypothesis

Back 106

the hypothesis against which the null hypothesis is tested

Front 107

Classical Linear Model

Back 107

the multiple linear regression model under the full set of classical linear model assumptions

Front 108

Classical Linear Model (CLM) Assumptions

Back 108

the ideal set of assumptions for multiple regression analysis: for cross sectional analysis, Assumptions MLR.1 through MLR.6 and for time series analysis, Assumptions TS.1 through TS.6. The assumptions include linearity in the parameters, no perfect collinearity, the zero conditional mean assumption, homoskedasticity, no serial correlation, and normality of the errors

Front 109

Confidence Interval (CI)

Back 109

a rule used to construct a random interval so that a certain percentage of all data sets, determined by the confidence interval, yields an interval that contains the population value

Front 110

Critical Value

Back 110

in hypothesis testing, the value against which a test statistic is compared to determine whether or not the null hypothesis is rejected

Front 111

Denominator Degress of Freedom

Back 111

in the F-test, the degrees of freedom in the unrestricted model

Front 112

Economic Significance

Front 113

Exclusion Restrictions

Back 113

restrictions that state that certain variables are excluded from the model (or have zero population coefficients)

Front 114

F Statistic

Back 114

a statistic used to test multiple hypotheses about the parameters in a multiple regression model

Front 115

Joint Hypothesis Test

Back 115

a test involving more than one restriction on the parameters in a model

Front 116

Jointly Insignificant

Back 116

failure to reject, using an F test at a specified significance level, that all coefficients for a group of explanatory variables are zero

Front 117

Jointly Statistically Significant

Back 117

the null hypothesis that two or more variables have zero population coefficients is rejected at tehe chosen significance level

Front 118

Minimum Variance Unbiased Estimators

Back 118

an estimator with the smallest variance in the class of all unbiased estimators

Front 119

Multiple Hypotheses Test

Back 119

a test of a null hypothesis involving more than one restriction on its parameters

Front 120

Multiple Restrictions

Back 120

more than one restriction on the parameters in an econometric model

Front 121

Normality Assumption

Back 121

the classical linear model assumption that states that the error (or dependent varaible) has a normal distribution, conditional on the explanatory variables

Front 122

Null Hypothesis

Back 122

in classical hypothesis testing, we take this hypothesis as true and require the data to provide substantial evidence against it

Front 123

Numerator Degrees of Freedom

Back 123

in the F-test, the number of restrictions being tested

Front 124

One-Sided Alternative

Back 124

an alternative hypothesis that states that a parameteris greater than (or less than) the value hypothesized under the null

Front 125

One-Tailed Test

Back 125

a hypothesis test against a one sided alternative

Front 126

Overall Significance of the Regression

Back 126

a test of the joint significance of all explanatory variables appearing in a multiple regression equation

Front 127

p-value

Back 127

the smalled significance level at which the null hypothesis can be rejected. Equivalently, the largest significance level at which the null hypothesis cannot be rejected

Front 128

Practical Significance

Back 128

the practical or economic importance of an estimate, which is measured by its sign and magnitude, as opposed to its statistical significance

Front 129

R-Squared Form of the F-Statistic

Back 129

the F statisticfor testing exclusion restrictions expressed in terms of the R-squareds from the restricted and unrestricted models

Front 130

Rejection Rule

Back 130

in hypothesis testing, the rule that determines when the null hypothesis is rejected in favor of the alternative hypothesis

Front 131

Restricted Model

Back 131

in hypothesis testing, the model obtained after imposing all the restrictions required under the null

Front 132

Significance Level

Back 132

the probability of Type 1 error in hypothesis testing

Front 133

Statistically Insignificant

Back 133

failure to reject the null hypothesis that a population parameter is equal to zero, at the chosen significance level

Front 134

Statistically Significant

Back 134

rejecting the null hypothesis that a parameter is equal to zero against the specified alternative, at the chosen significance level

Front 135

t- ratio

Back 135

see t-ratio

Front 136

t- statistic

Back 136

the statistic used to test a single hypothesis about the parameters in an econometric model

Front 137

Two-Sided Alternative

Back 137

an alternative where the population parameter can be either less than or greater than the value stated under the null hypothesis

Front 138

Two-Tailed Test

Back 138

a test against a two sided alternative

Front 139

Unrestricted Model

Back 139

in hypothesis testing, the model that has no restrictions placed on its parameters