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

What objective does Ordinary Least Squares minimise?

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

Give the OLS formula for the slope coefficient in a simple regression.

$\hat{\beta}_1=\frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sum(x_i-\bar{x})^{2}}=\frac{\operatorname{Cov}(x,y)}{\operatorname{Var}(x)}$, and $\hat{\beta}_0=\bar{y}-\hat{\beta}_1\bar{x}$.

How do you interpret the slope coefficient $\beta_1$ in a linear regression?

A one-unit increase in $x$ is associated with an average change of $\beta_1$ units in $y$, holding other variables constant (in multiple regression).

Interpret the coefficient in a log-log and a log-linear (semi-log) regression.

Log-log: $\beta_1$ is an elasticity — a $1\%$ rise in $x$ changes $y$ by $\beta_1\%$. Log-linear ($\ln y$ on $x$): a one-unit rise in $x$ changes $y$ by approximately $100\beta_1\%$.

What does $R^{2}$ measure and what are its limitations?

$R^{2}$ is the proportion of variance in $y$ explained by the model: $R^{2}=1-\frac{SS_{res}}{SS_{tot}}$. It never decreases when adding regressors and says nothing about causality or unbiasedness.

Why use adjusted $R^{2}$ instead of $R^{2}$?

Adjusted $R^{2}$ penalises adding regressors that do not improve fit: $\bar{R}^{2}=1-(1-R^{2})\frac{n-1}{n-k-1}$, so it can fall when useless variables are added, aiding model comparison.

In multiple regression, what does 'controlling for' a variable mean?

It means estimating the partial effect of one regressor on $y$ while holding the other included variables fixed, isolating its association net of those covariates (the 'ceteris paribus' interpretation).

What is omitted variable bias and what two conditions cause it?

It is bias in a coefficient from leaving out a relevant variable. It arises when the omitted variable (1) affects the outcome $y$ and (2) is correlated with an included regressor; the included coefficient then absorbs the omitted variable's effect.

List the key Gauss–Markov assumptions under which OLS is BLUE.

Linearity in parameters, random sampling, no perfect multicollinearity, zero conditional mean of errors $E(\varepsilon\mid X)=0$, and homoscedasticity (constant error variance). Under these, OLS is the Best Linear Unbiased Estimator.

State the null and alternative hypotheses framework and the meaning of a p-value.

$H_0$ is the no-effect/default claim; $H_1$ the alternative. The p-value is the probability of observing data at least as extreme as that seen, assuming $H_0$ is true. Small p-value gives evidence against $H_0$.

Define Type I and Type II errors and their associated probabilities.

Type I: rejecting a true $H_0$ (false positive), probability $\alpha$. Type II: failing to reject a false $H_0$ (false negative), probability $\beta$. Power $=1-\beta$.

What is the significance level and how does it relate to a confidence interval?

$\alpha$ is the threshold probability for rejecting $H_0$ (commonly $0.05$). A $(1-\alpha)$ confidence interval excludes the null value exactly when the two-sided test rejects $H_0$ at level $\alpha$.

How is a t-statistic for a regression coefficient computed and roughly what value signals significance?

$t=\frac{\hat{\beta}}{SE(\hat{\beta})}$. As a rule of thumb $|t|>1.96$ (large samples) indicates significance at the $5\%$ level for a two-sided test.

What does statistical significance NOT tell you about an effect?

It does not tell you the effect's size, practical/economic importance, or that the model is correctly specified. A tiny, unimportant effect can be statistically significant in a large sample.

Define heteroscedasticity and its consequence for OLS.

Heteroscedasticity is non-constant error variance across observations. OLS coefficients remain unbiased but standard errors are wrong, invalidating inference; remedy with robust (heteroscedasticity-consistent) standard errors.

What is multicollinearity and how does it affect regression estimates?

It is high correlation among regressors. It inflates coefficient standard errors and makes individual estimates unstable and hard to interpret, though it does not bias them or harm overall prediction.

What is autocorrelation (serial correlation) and where does it commonly arise?

It is correlation between error terms across observations, common in time-series data. It biases standard errors (understating them), so use Newey–West or other corrected standard errors.

Explain the distinction between correlation and causation.

Correlation means two variables move together statistically; causation means one produces a change in the other. Correlation can arise from reverse causality, confounding, or coincidence, so it does not establish cause.

What is a confounding variable (confounder)?

A confounder is a variable that influences both the treatment/explanatory variable and the outcome, creating a spurious association between them if not controlled for.

Name three reasons two variables might be correlated without a direct causal link.

(1) Reverse causality (Y causes X), (2) a common confounder driving both, and (3) coincidence/spurious correlation (especially with multiple comparisons or trending time series).

What defines a quasi-experiment and how does it differ from a true experiment?

A quasi-experiment estimates causal effects without random assignment, exploiting naturally occurring or policy-induced variation. Unlike a true experiment, treatment is not randomised, so identifying assumptions are needed to mimic randomisation.

Explain the difference-in-differences (DiD) method and its key assumption.

DiD compares the change in outcomes over time between a treated and a control group: $\hat{\delta}=(\bar{y}^{T}_{post}-\bar{y}^{T}_{pre})-(\bar{y}^{C}_{post}-\bar{y}^{C}_{pre})$. Key assumption: parallel trends — absent treatment, both groups would have moved similarly.

Describe regression discontinuity design (RDD).

RDD exploits a threshold in an assignment variable that determines treatment. Units just above and just below the cutoff are comparable, so the jump in outcomes at the cutoff identifies the local causal effect.

What is an instrumental variable and what two conditions must it satisfy?

An instrument $Z$ provides exogenous variation in an endogenous regressor $X$. It must be (1) relevant — correlated with $X$ — and (2) valid/exogenous — affecting $Y$ only through $X$ (the exclusion restriction).

Why is a randomised controlled trial (RCT) considered the gold standard for causal inference?

Random assignment makes treatment and control groups statistically equivalent in expectation on all characteristics (observed and unobserved), so any outcome difference can be attributed to the intervention, removing selection bias.

Distinguish internal validity from external validity in an RCT.

Internal validity is whether the study correctly identifies the causal effect within the sample. External validity is whether the result generalises to other populations, settings or times.

What is a counterfactual in programme evaluation?

The counterfactual is what would have happened to the treated group had they not received the intervention. Since it is unobservable, evaluation methods construct a credible comparison (control) group to estimate it.

Define the Average Treatment Effect (ATE) using potential outcomes notation.

$ATE=E[Y_i(1)-Y_i(0)]$, the expected difference between the potential outcome under treatment $Y_i(1)$ and under no treatment $Y_i(0)$ across the population.

How do you compute percentage change and percentage point difference, and why are they different?

Percentage change $=\frac{\text{new}-\text{old}}{\text{old}}\times 100\%$. A percentage point is the absolute difference between two percentages. E.g. a rise from $4\%$ to $5\%$ is a 1 percentage point increase but a $25\%$ relative increase.

How is a price index (e.g. base-year=100) constructed and interpreted?

$\text{Index}=\frac{\text{value in current period}}{\text{value in base period}}\times 100$. A value of 120 means a $20\%$ rise since the base year; the base period always equals 100.

What is the rule for estimation and back-of-envelope calculation, and why round to powers of ten?

Approximate inputs to convenient round numbers (often nearest power of ten or one significant figure), compute, then sanity-check the order of magnitude. Rounding keeps arithmetic fast while preserving the scale of the answer, e.g. $\approx 1{,}000$ rather than $983$. For speed in online numerical tests, estimate first to eliminate implausible multiple-choice options and convert percentages to fractions (e.g. $25\%=\frac{1}{4}$) before calculating.