Economics Quantitative Methods and Econometrics Syllabus

Quantitative Methods and Econometrics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Methods and Econometrics in Economics, not a summary of it.

1. 1

   Mathematical Economics

   3 topics

   • Functions and Graphs
   • Optimisation and Calculus
   • Matrix Algebra Applications
2. 2

   Statistics for Economics

   4 topics

   • Descriptive Statistics
   • Probability Distributions
   • Sampling and Estimation
   • Hypothesis Testing
3. 3

   Regression Analysis

   3 topics

   • Simple Linear Regression
   • Multiple Regression
   • Classical Assumptions and Violations
4. 4

   Applied Econometrics

   4 topics

   • Time Series Analysis
   • Panel Data Methods
   • Causal Inference
   • Interpreting Economic Data

Quantitative Methods and Econometrics flashcards for Economics

21 of 60 cards from the Quantitative Methods and Econometrics deck — real questions with worked answers.

1. What is a function, and what does its graph represent?

   A function $f$ is a rule assigning each input $x$ in the domain exactly one output $y=f(x)$. Its graph is the set of points $\{(x,f(x))\}$ in the plane, showing how $y$ varies with $x$.

2. State the slope-intercept form of a straight line and identify each parameter.

   $y = mx + b$, where $m$ is the slope (change in $y$ per unit change in $x$) and $b$ is the $y$-intercept (value of $y$ when $x=0$).

3. What distinguishes a linear function from a nonlinear one, giving the general quadratic as an example?

   A linear function graphs as a straight line with constant slope, e.g. $y=mx+b$. A nonlinear function has a changing slope; a quadratic $y = ax^{2}+bx+c$ (with $a\neq 0$) graphs as a parabola.

4. For an exponential function $y = a\,b^{x}$ with $b>1$, describe its growth and the meaning of $a$.

   It exhibits constant proportional (multiplicative) growth: $y$ multiplies by $b$ for each unit increase in $x$. The constant $a$ is the initial value at $x=0$.

5. What is the derivative $f'(x)$ interpreted as, both geometrically and economically?

   Geometrically, $f'(x)$ is the slope of the tangent to $f$ at $x$ (instantaneous rate of change). Economically it is the marginal value, e.g. marginal cost is the derivative of total cost.

6. State the power rule and product rule of differentiation.

   Power rule: $\frac{d}{dx}x^{n} = n x^{n-1}$. Product rule: $\frac{d}{dx}\big(u(x)v(x)\big) = u'v + uv'$.

7. State the first-order condition for an interior optimum of a differentiable function $f(x)$.

   Set the first derivative to zero: $f'(x)=0$. Solutions are critical (stationary) points that are candidate maxima or minima.

8. Give the second-order conditions distinguishing a local maximum from a local minimum at a stationary point $x^{*}$.

   If $f'(x^{*})=0$ and $f''(x^{*})<0$, it is a local maximum; if $f''(x^{*})>0$, it is a local minimum. If $f''(x^{*})=0$ the test is inconclusive.

9. In constrained optimisation, what does the Lagrange multiplier $\lambda$ measure?

   For maximising $f(x,y)$ subject to $g(x,y)=c$, $\lambda$ is the shadow price: the marginal change in the optimal objective value per unit relaxation of the constraint, $\lambda = \frac{\partial f^{*}}{\partial c}$.

10. What is a partial derivative $\frac{\partial f}{\partial x}$ of a multivariable function?

    The rate of change of $f(x,y,\dots)$ with respect to $x$ while holding all other variables constant; it isolates the marginal effect of $x$.

11. State the dimensions required for matrix multiplication and the resulting size.

    An $m\times n$ matrix times an $n\times p$ matrix is valid (inner dimensions match) and yields an $m\times p$ matrix.

12. Write the least-squares estimator of the coefficient vector in matrix form.

    $\hat{\boldsymbol{\beta}} = (\mathbf{X}^{\top}\mathbf{X})^{-1}\mathbf{X}^{\top}\mathbf{y}$, which requires $\mathbf{X}^{\top}\mathbf{X}$ to be invertible (full column rank).

13. What is the determinant of a $2\times 2$ matrix, and what does a zero determinant imply?

    For $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the determinant is $ad-bc$. A zero determinant means the matrix is singular (non-invertible) with linearly dependent rows/columns.

14. Define the identity matrix and the inverse of a square matrix.

    The identity $\mathbf{I}$ has $1$s on the diagonal and $0$s elsewhere, with $\mathbf{A}\mathbf{I}=\mathbf{A}$. The inverse $\mathbf{A}^{-1}$ satisfies $\mathbf{A}\mathbf{A}^{-1}=\mathbf{A}^{-1}\mathbf{A}=\mathbf{I}$; it exists only if $\det(\mathbf{A})\neq 0$.

15. What does the rank of a matrix tell you, and why does it matter for solving linear systems?

    Rank is the number of linearly independent rows (or columns). Full rank ensures a unique solution to $\mathbf{A}\mathbf{x}=\mathbf{b}$; deficient rank implies collinearity and no unique solution.

16. Compare the mean, median, and mode as measures of central tendency.

    Mean is the arithmetic average $\bar{x}=\frac{1}{n}\sum x_i$, sensitive to outliers; median is the middle value, robust to outliers; mode is the most frequent value, useful for categorical data.

17. Write the formula for the sample variance and explain the $n-1$ denominator.

    $s^{2} = \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^{2}$. The $n-1$ (Bessel's correction) provides an unbiased estimate of the population variance $\sigma^{2}$.

18. Define the coefficient of variation and state when it is useful.

    $CV = \frac{s}{\bar{x}}$ (often as a percentage). It expresses relative dispersion, allowing comparison of variability across data sets with different units or means.

19. How do you interpret skewness of a distribution?

    Skewness measures asymmetry. Positive (right) skew has a long right tail with mean $>$ median; negative (left) skew has a long left tail with mean $<$ median; zero skew is symmetric.

20. State the formula for the Pearson correlation coefficient and its range.

    $r = \frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum(x_i-\bar{x})^{2}\sum(y_i-\bar{y})^{2}}}$, with $-1 \leq r \leq 1$; it measures linear association only.

21. State the three axioms (Kolmogorov) of probability.

    (1) $P(A)\geq 0$ for any event $A$; (2) $P(S)=1$ for the sample space $S$; (3) for mutually exclusive events, $P(A\cup B)=P(A)+P(B)$.

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