Lecture 1: Introduction

Economics 326 — Introduction to Econometrics II

Vadim Marmer, UBC

What is econometrics?

Econometrics develops statistical methods for:

  • Estimating economic relationships
  • Causal or counterfactual analysis: what happens to an outcome when we force a change in a factor.
  • Testing economic theories
  • Forecasting important economic variables
  • Evaluating government and business policy

Why statistics?

  • Economic theory motivates models of relationships between variables of interest.
  • Economic models are approximations, not exact descriptions of reality.
  • Even good models omit important factors that affect outcomes.
  • We replace a deterministic model with a probabilistic model.

Examples

  • Estimation of demand and supply functions
    Elasticities help evaluate the effects of taxation.

  • Mincer (1974), Schooling, Experience, and Earnings
    Uses individual data to estimate returns to schooling and experience.

    • Determine an “optimal” amount of schooling
    • Study education in developing countries
    • Study gender and race discrimination
    • Study the impact of immigration on labour markets

Types of data: cross-section

Definition

A cross-sectional dataset contains observations on individuals (e.g., workers or firms) collected in a single time period.

Example (wages and individual characteristics):

obs wage education experience female married
1 3.10 11 2 1 0
2 3.24 12 22 1 1
3 3.00 11 2 0 0
… … … … … …
  • The order of observations is not important.
  • It is often reasonable to assume observations are statistically independent.

Types of data: time series

Definition

A time series dataset contains observations on one or more variables over time.

Example (Puerto Rico minimum wage, unemployment, and GNP):

obs year minimum wage unemployment gnp
1 1950 0.20 15.4 878.7
2 1951 0.21 16.0 925.0
3 1952 0.23 14.8 1015.9
… … … … …
  • Data frequency can be daily/weekly/monthly/quarterly/annual; in finance, trade data can be very high frequency.
  • The order of observations is important.
  • Observations are often correlated (e.g., trends).

Types of data: panel

Definition

A panel dataset combines cross-section and time series: a time series for each cross-sectional unit.

Example (two-year panel on city crime):

obs city year murders population unempl police
1 1 1986 5 350000 8.7 440
2 1 1990 8 359200 7.2 471
3 2 1986 2 64300 5.4 75
4 2 1990 1 65100 5.5 75
… … … … … … …

Causality

  • We care about causal relationships, but data often only reveal correlations (associations).
  • To claim a causal effect, other factors affecting the outcome must be held fixed (controlled for).
  • Controlled experiments help with causality in the natural sciences.
  • Experiments are often impossible in economics (cost and ethics).
  • We typically work with observational data.

Examples (causality)

Education

\log(\text{Wage}) = \alpha + \beta \times \text{Years of Schooling} + U

U includes other factors (e.g., ability). If ability is hard to control for, simple correlations can overestimate returns to education.

Police and crime

\text{Number of Crimes} = \alpha + \beta \times \text{Size of the Police Force} + U

Cities with more crime often hire more police, so simple correlations can spuriously suggest police increase crime.

Forecasting vs estimation

Forecasting

  • Forecasting: predicting out-of-sample values of a variable: E.g.,
    • Predict next quarter’s GDP
    • Assess the probability of default on a loan given borrower characteristics (income, education, past history of defaults, etc.)
    • Predictive text: given previous words, predict the next word.
    • ChatGPT: given a prompt, generate the desired response.
    • Predict the number of crimes in a city next year given current police force size.
    • Forecasting equation: \widehat{\text{Number of Crimes}}= f(\text{Size of the Police Force}) where \widehat{\text{Number of Crimes}} is the forecasted number of crimes in a city with \text{Size of the Police Force}.
    • Use data to estimate or “learn” the best forecasting function f(\cdot).
    • Focus on prediction accuracy: minimizing some measure of forecast errors.

Estimation

  • Estimation: estimating structural parameters of an economic model: E.g.,
    • Effect of education on wages
    • Effect of police force size on crime
    • Structural equation: \text{Number of Crimes} = \alpha + \beta \times \text{Size of the Police Force} + U where \beta is the structural parameter measuring the effect of police force size on crime, and U includes other factors affecting crime.
    • Focus on causal or counterfactual interpretation: what happens to the outcome when we change a variable.
    • Best forecasting model may produce misleading counterfactual effects.
    • Good structural model may have poor forecasting performance.
    • Choose the right tool for the job!
    • Causal/counterfactual analysis always requires some assumptions about the data generating process.