Government Economic Service (GES) Assessment Centre 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 Government Economic Service (GES) Assessment Centre, not a summary of it.

1. 1

   Statistics and Probability Foundations

   4 topics

   • Descriptive statistics and distributions
     • Mean, median, variance, skewness
   • Probability rules and Bayes' theorem
   • Sampling and the central limit theorem
   • Confidence intervals and standard errors
2. 2

   Regression and Inference

   4 topics

   • Ordinary least squares and interpretation
     • Coefficients, R-squared, p-values
   • Multiple regression and control variables
   • Hypothesis testing and significance
     • Type I and Type II errors
   • Common regression pitfalls
     • Heteroscedasticity and autocorrelation
     • Multicollinearity and omitted variable bias
3. 3

   Causal Inference and Evaluation

   4 topics

   • Correlation versus causation
     • Endogeneity and identification
   • Quasi-experimental methods
     • Difference-in-differences
     • Instrumental variables
     • Regression discontinuity
   • Randomised controlled trials in policy
   • Counterfactuals and programme evaluation
4. 4

   Numerical Reasoning Under Test Conditions

   4 topics

   • Percentages, ratios and index numbers
   • Interpreting tables, charts and graphs
   • Estimation and back-of-envelope calculation
     • Fermi-style sanity checks
   • Speed techniques for online numerical tests

Quantitative Methods and Econometrics flashcards for Government Economic Service (GES) Assessment Centre

21 of 51 cards from the Quantitative Methods and Econometrics deck — real questions with worked answers.

1. In descriptive statistics, what is the difference between the mean, median, and mode, and which is most robust to outliers?

   The mean is the arithmetic average $\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i$; the median is the middle value when data are ordered; the mode is the most frequent value. The median is most robust to outliers and skew.

2. Define population variance and standard deviation, and state the formula for the (unbiased) sample variance.

   Variance measures average squared deviation from the mean. Population: $\sigma^{2}=\frac{1}{N}\sum(x_i-\mu)^{2}$. Sample (unbiased, Bessel's correction): $s^{2}=\frac{1}{n-1}\sum(x_i-\bar{x})^{2}$. Standard deviation is the square root: $s=\sqrt{s^{2}}$.

3. What does the coefficient of variation measure and how is it calculated?

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

4. Distinguish positive (right) skew from negative (left) skew in terms of the mean and median.

   In a right (positive) skew the long tail is to the right and $\text{mean} > \text{median}$. In a left (negative) skew the long tail is to the left and $\text{mean} < \text{median}$.

5. State the key properties of the normal distribution and the empirical (68–95–99.7) rule.

   The normal distribution $N(\mu,\sigma^{2})$ is symmetric and bell-shaped. Approximately $68\%$ of data lie within $\mu\pm\sigma$, $95\%$ within $\mu\pm 2\sigma$, and $99.7\%$ within $\mu\pm 3\sigma$.

6. How is a value converted to a standard (z) score, and what does it represent?

   $z=\frac{x-\mu}{\sigma}$. It expresses how many standard deviations a value lies from the mean, standardising any normal variable to $N(0,1)$.

7. What are the three axioms of probability (Kolmogorov)?

   (1) Non-negativity: $P(A)\geq 0$. (2) Normalisation: $P(\Omega)=1$. (3) Additivity: for mutually exclusive events, $P(A\cup B)=P(A)+P(B)$.

8. State the addition rule and the multiplication rule for probability.

   Addition (general): $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Multiplication: $P(A\cap B)=P(A)\,P(B\mid A)$; if independent, $P(A\cap B)=P(A)\,P(B)$.

9. Define conditional probability and state when two events are independent.

   $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$ for $P(B)>0$. Events are independent when $P(A\mid B)=P(A)$, equivalently $P(A\cap B)=P(A)P(B)$.

10. State Bayes' theorem and name its components.

    $P(A\mid B)=\frac{P(B\mid A)\,P(A)}{P(B)}$. Here $P(A)$ is the prior, $P(B\mid A)$ the likelihood, $P(B)$ the marginal/evidence, and $P(A\mid B)$ the posterior.

11. A test is 99% accurate for a disease affecting 1 in 1000 people. Why can a positive result still likely be a false positive (base-rate reasoning)?

    Because the prior (base rate) is tiny, the many true negatives generate numerous false positives that swamp the few true positives. By Bayes, $P(\text{disease}\mid +)$ stays low when $P(\text{disease})$ is very small, even with high test accuracy.

12. Distinguish a population parameter from a sample statistic, giving notation.

    A parameter describes the whole population (e.g. mean $\mu$, proportion $p$, sd $\sigma$) and is fixed but usually unknown. A statistic is computed from a sample (e.g. $\bar{x}$, $\hat{p}$, $s$) and estimates the parameter.

13. State the Central Limit Theorem.

    For a sample of size $n$ drawn from a population with mean $\mu$ and finite variance $\sigma^{2}$, the sampling distribution of the mean $\bar{x}$ approaches a normal distribution $N\!\left(\mu,\frac{\sigma^{2}}{n}\right)$ as $n$ grows, regardless of the population's shape (rule of thumb $n\geq 30$).

14. What is the standard error of the mean and how does it depend on sample size?

    $SE_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$ (or $\frac{s}{\sqrt{n}}$). It shrinks with the square root of $n$, so quadrupling the sample halves the standard error.

15. Distinguish sampling error from non-sampling (bias) error.

    Sampling error is random variation from observing only a subset of the population; it shrinks with larger $n$. Non-sampling error includes systematic biases (selection, measurement, non-response) that larger samples do NOT fix.

16. What does a 95% confidence interval mean, and give its general form for a mean.

    It means that 95% of intervals constructed this way over repeated sampling would contain the true parameter. Form: $\bar{x}\pm z^{*}\,\frac{s}{\sqrt{n}}$, with $z^{*}\approx 1.96$ for 95%.

17. What critical z-values correspond to 90%, 95% and 99% confidence intervals?

    $90\%\to z^{*}\approx 1.645$; $95\%\to z^{*}\approx 1.96$; $99\%\to z^{*}\approx 2.576$.

18. How does the width of a confidence interval change with confidence level and sample size?

    Width increases with higher confidence (larger $z^{*}$) and decreases with larger $n$ (since $SE\propto \frac{1}{\sqrt{n}}$). Greater certainty trades off against precision.

19. Give the standard error of a sample proportion and the corresponding confidence interval.

    $SE_{\hat{p}}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$; interval $\hat{p}\pm z^{*}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$.

20. Write the simple OLS regression model and name each term.

    $y_i=\beta_0+\beta_1 x_i+\varepsilon_i$, where $\beta_0$ is the intercept, $\beta_1$ the slope, $x_i$ the regressor, $y_i$ the outcome, and $\varepsilon_i$ the error term.

21. What objective does Ordinary Least Squares minimise?

    OLS chooses coefficients to minimise the sum of squared residuals: $\min_{\beta_0,\beta_1}\sum_{i=1}^{n}(y_i-\hat{y}_i)^{2}=\sum\hat{\varepsilon}_i^{2}$.

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