ECON301 - Econometrics & Statistical Modeling Flashcards

Question 1

What is Econometrics?

Accepted Answer

Econometrics is the application of statistical methods to economic data. It aims to give empirical content to economic theory, test hypotheses, and forecast future trends using tools like regression analysis.

Question 2

What is a Statistical Model?

Accepted Answer

A statistical model is a mathematical representation of the relationship between variables, often including a random error component. In econometrics, these models are used to estimate parameters, test theories, and make predictions.

Question 3

Types of Economic Data

Accepted Answer

Economic data typically comes in three forms:
1.  **Cross-sectional data:** Observations on different entities (individuals, firms, countries) at a single point in time.
2.  **Time series data:** Observations on a single entity over multiple periods.
3.  **Panel data:** Observations on multiple entities over multiple periods (combines cross-sectional and time series).

Question 4

Simple Linear Regression (SLR) Model

Accepted Answer

The simple linear regression model describes the relationship between a dependent variable ($Y$) and a single independent variable ($X$) as: $Y = \beta_0 + \beta_1X + \epsilon$.
*   $Y$: Dependent variable
*   $X$: Independent variable
*   $\beta_0$: Intercept parameter
*   $\beta_1$: Slope parameter
*   $\epsilon$: Error term

Question 5

Interpretation of the Intercept ($\beta_0$) in SLR

Accepted Answer

The intercept parameter, $\beta_0$, represents the expected value of the dependent variable ($Y$) when the independent variable ($X$) is equal to zero. Its interpretation is only meaningful if $X=0$ is within the range of observed data and makes economic sense.

Question 6

Interpretation of the Slope Coefficient ($\beta_1$) in SLR

Accepted Answer

The slope coefficient, $\beta_1$, represents the expected change in the dependent variable ($Y$) for a one-unit increase in the independent variable ($X$), holding all other factors constant (though in SLR, there are no other factors explicitly in the model).

Question 7

The Error Term ($\epsilon$) in Regression

Accepted Answer

The error term, $\epsilon$, represents all unobserved factors that affect the dependent variable ($Y$) but are not included in the model. It captures measurement errors, omitted variables, and inherent randomness in human behavior.

Question 8

What is Ordinary Least Squares (OLS)?

Accepted Answer

Ordinary Least Squares (OLS) is a statistical method used to estimate the unknown parameters (coefficients) in a linear regression model. It works by minimizing the sum of the squared differences between the observed values of the dependent variable and the values predicted by the model (i.e., minimizing the sum of squared residuals).

Question 9

How OLS Works (Minimization Principle)

Accepted Answer

OLS estimates the regression coefficients ($\hat{\beta}_0$, $\hat{\beta}_1$) by finding the line that minimizes the sum of the squared residuals. The residual for each observation is $e_i = Y_i - \hat{Y}_i = Y_i - (\hat{\beta}_0 + \hat{\beta}_1X_i)$. OLS minimizes $\sum_{i=1}^n e_i^2$.

Question 10

Gauss-Markov Assumptions (Overview)

Accepted Answer

The Gauss-Markov assumptions are a set of conditions under which OLS estimators are the Best Linear Unbiased Estimators (BLUE). They include linearity, random sampling, no perfect multicollinearity, zero conditional mean of errors, homoskedasticity, and no autocorrelation (for time series).

Question 11

Gauss-Markov Assumption: Linearity in Parameters

Accepted Answer

The relationship between the dependent variable and the independent variables must be linear in the parameters. This means the model can be written as $Y = \beta_0 + \beta_1X_1 + \dots + \beta_kX_k + \epsilon$. The variables themselves can be non-linear (e.g., $X^2$, $\log(X)$).

Question 12

Gauss-Markov Assumption: Zero Conditional Mean of Error

Accepted Answer

The error term ($\epsilon$) has an expected value of zero, conditional on the independent variables ($X$). Mathematically, $E(\epsilon|X_1, \dots, X_k) = 0$. This is crucial for unbiasedness and implies that the independent variables are exogenous (not correlated with the error term).

Question 13

Gauss-Markov Assumption: Homoskedasticity

Accepted Answer

The variance of the error term ($\epsilon$) is constant across all levels of the independent variables ($X$). Mathematically, $Var(\epsilon|X_1, \dots, X_k) = \sigma^2$. This means the spread of the residuals should be roughly the same across the range of predicted values.

Question 14

What is Heteroskedasticity?

Accepted Answer

Heteroskedasticity is the violation of the homoskedasticity assumption, meaning the variance of the error term is *not* constant across all levels of the independent variables. For example, the errors might be larger for higher values of $X$.

Question 15

Consequences & Remedies for Heteroskedasticity

Accepted Answer

**Consequences:** OLS estimators remain unbiased and consistent, but they are no longer efficient (not BLUE). Standard errors are biased, leading to incorrect hypothesis tests and confidence intervals.
**Remedies:** Use heteroskedasticity-robust standard errors (e.g., White's standard errors) or transform the data (e.g., Weighted Least Squares).

Question 16

Gauss-Markov Assumption: No Perfect Multicollinearity

Accepted Answer

There should be no perfect linear relationships among the independent variables. This means no independent variable can be expressed as a perfect linear combination of other independent variables. If perfect multicollinearity exists, OLS estimators are indeterminate.

Question 17

What is Multicollinearity?

Accepted Answer

Multicollinearity refers to a high degree of linear correlation among two or more independent variables in a multiple regression model. While perfect multicollinearity prevents OLS estimation, high (imperfect) multicollinearity is more common.

Question 18

Consequences & Remedies for Multicollinearity

Accepted Answer

**Consequences:** OLS estimators remain unbiased and consistent, but their standard errors become very large, leading to imprecise estimates, wider confidence intervals, and difficulty in determining the individual impact of correlated variables.
**Remedies:** Increase sample size, drop one of the highly correlated variables, combine correlated variables, or use specialized techniques like Ridge Regression.

Question 19

What is R-squared ($R^2$)?

Accepted Answer

$R^2$ (R-squared) is a statistical measure that represents the proportion of the variance in the dependent variable ($Y$) that is predictable from the independent variable(s) ($X$) in a regression model. It ranges from 0 to 1, with higher values indicating a better fit. $R^2 = 1 - (SSR/SST)$, where SSR is the Sum of Squared Residuals and SST is the Total Sum of Squares.

Question 20

What is Adjusted R-squared?

Accepted Answer

Adjusted R-squared is a modified version of $R^2$ that accounts for the number of predictors in the model. It increases only if the new term improves the model more than would be expected by chance, making it useful for comparing models with different numbers of independent variables. It is always less than or equal to $R^2$.

Question 21

What is a p-value?

Accepted Answer

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, *assuming the null hypothesis is true*. A small p-value (typically < 0.05 or 0.01) suggests strong evidence against the null hypothesis, leading to its rejection.

Question 22

Hypothesis Testing (General Concept)

Accepted Answer

Hypothesis testing is a statistical method used to make inferences about a population parameter based on sample data. It involves formulating a null hypothesis ($H_0$) and an alternative hypothesis ($H_1$), collecting data, calculating a test statistic, and comparing its p-value to a predetermined significance level ($\alpha$) to decide whether to reject $H_0$.

Question 23

What is a Confidence Interval?

Accepted Answer

A confidence interval provides a range of values within which the true population parameter is likely to lie, with a specified level of confidence (e.g., 95%). It is constructed around the point estimate and reflects the precision of the estimate; wider intervals indicate less precision.

Question 24

What is Autocorrelation (Serial Correlation)?

Accepted Answer

Autocorrelation (or serial correlation) is the correlation of an error term with previous error terms in a time series model. Mathematically, $Cov(\epsilon_t, \epsilon_{t-s}) 
e 0$ for $s 
e 0$. It violates the assumption that errors are independently distributed.

Question 25

Consequences & Remedies for Autocorrelation

Accepted Answer

**Consequences:** OLS estimators remain unbiased and consistent, but standard errors are biased, leading to incorrect hypothesis tests and inefficient estimates. The $R^2$ can also be misleadingly high.
**Remedies:** Use robust standard errors (e.g., Newey-West standard errors), transform the data (e.g., Generalized Least Squares), or include lagged dependent variables in the model.

ECON301 - Econometrics & Statistical Modeling

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