Methodology - Yuan-032/Econometrics_pre GitHub Wiki

The research question we want to test is what is the causal relationship between the change in the effective minimum wage and the change in the unemployment rate. Before entering into the model development part, we spend some time figuring out the dependent and independent variables which are the minimum wage and unemployment rate. According to the International Labour Organization, the setup and consideration of minimum wage are related to the factors including the general level and distribution of wages, the evolution and differences across regions in the cost of living, as well as national or sectoral levels of labor productivity and rates of economic growth. The domestic factors affecting the U.S. labor force, employment, and unemployment levels including economic growth, cyclical and structural factors, demographics, education and training, innovation, labor unions, and industry consolidation, etc. Except for the macro level, there exist other individual level variables that influence unemployment, for instance, gender, race, family background, level of job tenure, and so on and so for. Those factors related to the dependent and independent variables may lead to endogeneity bias.

We apply three models in our regression. Model 1: The OLS regression model [formula1 here]

By using the OLS model to our data and analysis, Assumption 1 fails here. The potential problem is their exits omitted variables which lead to the covariance between the error term and effective minimum wage is not equal to zero. As for the analysis above, the confounding variables including the cost of living, labor productivity, as well as economic growth. Another potential problem that will cause Assumption 1 to fail is the reverse causality. Not only the minimum wage affect the unemployment rate, but the unemployment rate is also an index to set up and determine the minimum wage in the U.S. In this way, the coefficient we estimated could not reveal causality.

Model 2: Regression model with dummy variables

[formula2 here]

By separating the time periods into three parts which are 1980-1989, 1990-1999, 2000-2009, we regress the change in the unemployment rate on the change in the effective minimum wage. In this way, we could find the associated relationship among them across three different time periods. One reason for implementing this regression is that the time period from 1980 to 2018 is relatively long in the first model, and we hope by breaking it down into three periods, we could explore more insights on the data as well as the macro-level impact will be more obvious. However, the failure of Assumption 1 is not addressed in this case.

Model 3: Panel Data

[formula3 here] Our dataset is panel data and it includes the 50 states in the U.S. and the time period from 1980 to 2018. In the panel data model, we include both the time fixed effect and the state fixed effect. State fixed effect in the regression is a fixed constant over time which is different across entities. In this way, we could capture the factors which are different among states but not vary from the time, for instance, the education level, the cost of living, and so on and so for. Year fixed effect is constant across entities but changes over time which allows us to capture the variables which are varied by time but not the states, for instance, the labor productivity, the economic growth, price level, and etc. In this way, the panel data capture many underlying factors which may cause a problem in the previous models. However, the coefficient of the panel data model is still not causal as reverse causality exists. To further address this problem, we need the instrumental variable for help.