Greek Letters
The alphabet
The 24 letters of the Greek alphabet, in alphabetical order. Uppercase and lowercase letters can represent different quantities in mathematical notation.
In Quarto, put inline mathematics between dollar signs. For example, type $\beta$ to display \(\beta\). The commands below also work in LaTeX math mode.
For uppercase Greek letters that share the shape of a Latin letter, standard LaTeX uses that Latin letter, such as $A$ for alpha. Lowercase omicron uses $o$.
| Name | Uppercase | LaTeX/Quarto | Lowercase | LaTeX/Quarto |
|---|---|---|---|---|
| Alpha | \(A\) | $A$ |
\(\alpha\) | $\alpha$ |
| Beta | \(B\) | $B$ |
\(\beta\) | $\beta$ |
| Gamma | \(\Gamma\) | $\Gamma$ |
\(\gamma\) | $\gamma$ |
| Delta | \(\Delta\) | $\Delta$ |
\(\delta\) | $\delta$ |
| Epsilon | \(E\) | $E$ |
\(\epsilon\) | $\epsilon$ |
| Zeta | \(Z\) | $Z$ |
\(\zeta\) | $\zeta$ |
| Eta | \(H\) | $H$ |
\(\eta\) | $\eta$ |
| Theta | \(\Theta\) | $\Theta$ |
\(\theta\) | $\theta$ |
| Iota | \(I\) | $I$ |
\(\iota\) | $\iota$ |
| Kappa | \(K\) | $K$ |
\(\kappa\) | $\kappa$ |
| Lambda | \(\Lambda\) | $\Lambda$ |
\(\lambda\) | $\lambda$ |
| Mu | \(M\) | $M$ |
\(\mu\) | $\mu$ |
| Nu | \(N\) | $N$ |
\(\nu\) | $\nu$ |
| Xi | \(\Xi\) | $\Xi$ |
\(\xi\) | $\xi$ |
| Omicron | \(O\) | $O$ |
\(o\) | $o$ |
| Pi | \(\Pi\) | $\Pi$ |
\(\pi\) | $\pi$ |
| Rho | \(P\) | $P$ |
\(\rho\) | $\rho$ |
| Sigma | \(\Sigma\) | $\Sigma$ |
\(\sigma\) | $\sigma$ |
| Tau | \(T\) | $T$ |
\(\tau\) | $\tau$ |
| Upsilon | \(\Upsilon\) | $\Upsilon$ |
\(\upsilon\) | $\upsilon$ |
| Phi | \(\Phi\) | $\Phi$ |
\(\phi\) | $\phi$ |
| Chi | \(X\) | $X$ |
\(\chi\) | $\chi$ |
| Psi | \(\Psi\) | $\Psi$ |
\(\psi\) | $\psi$ |
| Omega | \(\Omega\) | $\Omega$ |
\(\omega\) | $\omega$ |
Alternative forms
Some lowercase letters have alternative forms that you may encounter in mathematical notation.
| Name | Usual form | LaTeX/Quarto | Alternative | LaTeX/Quarto |
|---|---|---|---|---|
| Epsilon | \(\epsilon\) | $\epsilon$ |
\(\varepsilon\) | $\varepsilon$ |
| Theta | \(\theta\) | $\theta$ |
\(\vartheta\) | $\vartheta$ |
| Kappa | \(\kappa\) | $\kappa$ |
\(\varkappa\) | $\varkappa$ |
| Pi | \(\pi\) | $\pi$ |
\(\varpi\) | $\varpi$ |
| Rho | \(\rho\) | $\rho$ |
\(\varrho\) | $\varrho$ |
| Phi | \(\phi\) | $\phi$ |
\(\varphi\) | $\varphi$ |
The form \(\varsigma\) ($\varsigma$) is used for sigma at the end of a Greek word. In our mathematical notation, we generally use \(\sigma\) ($\sigma$).
How we use these symbols
These are common conventions. Always check how a symbol is defined in the model or paper you are reading. The examples below follow our notes. See Formulae for the main results together with the conditions under which they apply.
| Symbol | Use | Example from the module |
|---|---|---|
| \(\beta_0,\beta_1,\ldots\) | Population regression coefficients | \(\beta_1\) is the coefficient on treatment or schooling in Weeks 1–4. Week 5 writes the schooling coefficient as \(\beta\), following BJB. |
| \(\widehat\beta_1\) | Estimated regression coefficient | The hat indicates an estimate calculated from a sample. |
| \(\gamma_0,\gamma_1,\ldots\) | Coefficients in another relationship | Ability regressed on university attendance in Week 1, the logit model in Week 2, and slope differences in RDD. |
| \(\pi_0,\pi_1,\ldots\) | First-stage coefficients | \(\pi_1\) measures how the instrument changes the endogenous explanatory variable. |
| \(\delta_0,\delta_1,\ldots\) | Reduced-form coefficients | In Weeks 3–4, \(\delta_1\) measures how the instrument changes the outcome. Elsewhere, \(\delta\) can label other regression coefficients. |
| \(\tau\) | Treatment effect | \(\tau_{\mathrm{ATT}}\) in matching and \(\tau_{\mathrm{LATE}}\) in IV. |
| \(\rho\) | Correlation, or a treatment-effect coefficient | \(\rho_{x,z}\) is a correlation in Week 5. In Week 7, \(\rho\) is the RD effect at the cutoff. |
| \(\varepsilon,\epsilon,\nu,\eta,\xi\) | Disturbances or unobserved components | Week 1 uses \(\varepsilon_i\) in the earnings relationship and \(\eta_i=Y_i^0-E[Y_i^0]\). Week 5 uses \(\nu_i\) for the first-stage disturbance. |
| \(\mu\) | A mean, or an unobserved group component | \(\mu_0=E[Y_i^0]\) in Week 1. In the class-size application, \(\mu_s\) is an unobserved school effect. |
| \(\sigma\) | Population standard deviation | The outcome standard deviation in the power calculation. |
| \(\sigma^2\) | Population variance | The common outcome variance assumed in that calculation. |
| \(\sigma_{x,y}\) | Population covariance | Week 5 uses \(\sigma_{x,\epsilon}\) for the covariance between schooling and the outcome disturbance. |
| \(\alpha\) | Significance level, or a regression coefficient | \(\alpha=0.05\) in a five-percent test. The class-size application also uses \(\alpha\) for a coefficient. |
| \(\beta\) in power calculations | Probability of a Type II error at a specified alternative | Power is \(1-\beta\). This use is separate from the regression coefficients. |
| \(\Delta\) | A difference or specified effect size | The effect a study is designed to detect in Week 1. |
| \(\theta,\lambda\) | Additional regression coefficients | Coefficients on controls or interactions. |
| \(\sum\) | Summation | \(\sum_{i=1}^{n}Y_i\) adds the outcomes of all \(n\) observations. The summation symbol is based on uppercase sigma, \(\Sigma\). |
We also use the Latin letters \(u\), \(v\) and \(e\) for disturbances. In particular, Latin \(v\) and Greek \(\nu\) can look similar. A hat on a disturbance, such as \(\widehat v_i\), denotes an estimated residual.