Introduction to Econometrics

• Econometrics deals with the application of statistical methods to economic data for estimating relationships, testing theories, and policy evaluation.
• It is used to forecast macroeconomic variables like interest rates, inflation, and GDP, but also non-macro areas like political campaign effects and school spending impacts.
• Econometrics differs from mathematical statistics due to its focus on analyzing nonexperimental economic data, which is data not collected through controlled experiments.
• Nonexperimental data is also called observational or retrospective data, highlighting the researcher's passive role in data collection.
• The method of multiple regression analysis is a key tool, econometricians have also developed new techniques to handle complexities in economic data and test economic theories.

Steps in Empirical Economic Analysis

• Empirical analysis uses data to test a theory or estimate a relationship between variables.
• The first step in empirical analysis is formulating a clear question of interest. Questions can involve testing economic theories or evaluating government policies.
• Economic models consist of mathematical equations describing various relationships, such as utility maximization leading to demand equations.
• Utility maximization relates quantity demanded of a commodity to prices of related goods, consumer income, and individual characteristics.
• Economists can use tools like utility maximization to explain behaviors that may initially seem non-economic.
• Formal economic models guide empirical analysis, one can rely on economic theory less formally or even intuition. Common sense can also inform the process

Economic Model of Crime

• Gary Becker's model explains an individual's participation in crime using utility maximization which is weighing rewards against opportunity costs and potential penalties.
• An equation can represent time spent in criminal activity (y) as a function of factors like "wage" from crime (x1), legal wage (x2), other income (x3), probability of getting caught (x4), conviction probability (x5), expected sentence (x6), and age (x7).
• Economic theory, combined with introspection, can predict the impact of each variable on criminal activity, forming the basis for econometric analysis

Job Training and Worker Productivity

• A labor economist assesses job training effects on productivity. A formal economic theory is unnecessary.
• It is known that education, experience, and training affect worker productivity, which dictates wages.
• A model example is: wage = f(educ, exper, training).
• 'wage' is hourly wage, 'educ' is education in years, 'exper' is workforce experience, 'training' is weeks in job training.

Econometric Model Specification

• An economic model needs transformation into an econometric model, which needs function (f()) specification.
• Deal with variables that cannot be observed practically.
• The below equation resolves ambiguities by setting some relationship with econometrics and economic model: crime = β₀ + β₁wage + β₂othinc + β₃freqarr + β₄freqconv + β₅avgsen + β₆age + u
• The choice of variables is a blend of data and economic theory.
• Term "u" includes intangible parameters like morality, wage for criminal activity, family background etc.
• constants (β₀, β₁,..., β₆) describe the strength and direction between factors and crime used to determine crime.
• Researchers begin econometric analysis by specifying an econometric model, merging economic theory into the model specification.
• Variables selected using economic reasoning and common sense.
• Hypotheses of interest are stated in terms of the unknown parameters.
• β₁ = 0 means wage (from legal) has no effect on the criminal behavior.

Structure of Economic Data

• Economic data sets come in different types where the special features must be accounted for or exploited. Next are the most important data structures.
• A cross-sectional data set samples units (individuals, firms, etc.) at a point in time.
• Data can be taken from the same time period.
• It assumes a random sample from the overall population, which simplifies the analysis.
• Problems can occur when random sampling is not appropriate, e.g) wealthier sampled families do not report sampling
• Issues arise when sampling from large units.
• Cross-sectional data are used in microeconomics fields for testing microeconomic policies.
• Data includes individuals, households, firms and cities at a given time.

Time Series

• Consists of observations of a or several variables over time
• Examples include GDP, supply, homicide rates and sales figures
• Time is an important dimension
• Chronological order carries important information.
• Economic observations cannot be assumed independent across time can often be related to recent history
• Should specify Econometric models for time series data for standard methods before embellishments or modifications
• Some variables show special tendencies over a period of time
• Data frequency at the collection point can require special attention
• Stock prices are recorded at daily intervals
• Supply is reported weekly
• Series are recorded less frequently, for example inflation and rates of unemployment

Pooled Cross Sections

• Some data sets have cross-sectional and time series features and characteristics
• Two cross-sectional household surveys are in the US one each in 1985 and 1990.
• Each with a sample of households on common variables such income and family
• Combining increases sample size
• Examine the effect of a new policy
• Data is collected before and after a policy change
• Analyzed much like a standard cross-section needs to account for differences.

Panel or Longitudinal Data

• This set consists of a time series for cross-sectional member in the data set.
• This could be educational, wage, and employment history for a time period
• In financial data and investment about data firms over a 5 year period
• Data firms or counties are followed
• Data can be collected over counties immigration flow tax rates wage rates for the years, for example, 1980, 1985, and 1990
• Units are followed over a given time period
• Houses sold that tend to show up in a cross-sectional dataset not considered is panel dataset.
• Difficult to obtain in the time series where units show some type of replication
• Can control for certain unobserved characteristics