Hello World

This is a sample post to verify the MDX blog is working. You can write in plain Markdown — headings, lists, links, block quotes, code, and math — and it all renders with the site's existing typography.

Inline Math

The Euler identity $e^{i\pi} + 1 = 0$ is often called the most beautiful equation in mathematics. In a regression, we estimate $\hat{\beta} = (X'X)^{-1}X'y$.

Display Math

The normal distribution's probability density function:

$$f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right)$$

A summation you might see in economic history — the Gini coefficient:

$$G = \frac{\sum_{i=1}^{n} \sum_{j=1}^{n} |x_i - x_j|}{2n^2 \bar{x}}$$

Mixing Prose and Math

Consider a Cobb-Douglas production function $Y = AK^\alpha L^{1-\alpha}$. Taking logs:

$$\ln Y = \ln A + \alpha \ln K + (1 - \alpha) \ln L$$

This is the kind of expression you might encounter in a growth accounting exercise. The parameter $\alpha$ represents capital's share of output, typically estimated around $0.3$ for developed economies.

Other Formatting

A block quote looks like this. Useful for pulling out key passages or citing someone.

Lists work too

• First item
• Second item with $\LaTeX$ inline
• Third item with a longer description that wraps across multiple lines

That's it. Delete this file and replace it with a real post when you're ready.