Qustion 2:
The crime rate (dependent variable) is influenced by the opportunity cost of potential offenders and other socio-economic factors.
The following model can be constructed：
CrimeRatei = β0 + β1AverageWagei + β2Xi + αi
1. Dependent variable (CrimeRatei): Crime rate in area i. (For example: Number of crimes per 10,000 people)
2. Core independent variable (AverageWagei): Average wage (For example: Hourly or annual salary) in area i, with an expected negative sign. (Higher wages lead to higher opportunity costs of crime)
3. Control variable (Xi): Other factors that may affect the crime rate.
For example:
-Unemployment rate: The higher the unemployment rate, the stronger the incentive to commit crime is likely to be. (Positive expected sign)
-Education level: The average number of years of education. It may reduce the propensity to commit crimes. (Expected sign is negative)
-Population density: More opportunities for crime in densely populated areas. (Expected sign may be positive)
-Police investment: Number of police officers per 10,000 people, may deter crime. (Expected sign may be negative)
-Poverty rate: The proportion of low-income groups, which may correlate crime. (Expected sign may be positive).
4. Error term (αi): Unobserved factor.
The variables were selected on the basis of:
1. The core explanatory variable (AverageWage): It directly corresponds to the influence of Becker's theory of “legitimate income” on the decision to commit a crime.
2. Control variables: It needs to cover other drivers of crime to avoid omission bias.
For example:
-Unemployment and poverty rates reflect economic pressures
-Educational level may affect crime preferences
-Police commitment represents law enforcement deterrence
Final model：
CrimeRatei = β0 + β1AverageWagei + β2UnemploymentRatei + β3PopulationDensutyi + αi