Econ 3451. Effect of Opioid on Death Rates in the United States

Effect of Opioids on death rate

Econ 3451
Handout 4: The Empirical Project
Objective
This project is meant to give you experience writing a simple research paper that combines economic analysis/thinking with quantitative statistics and data work.  You will be using a specific quantitative methodology known as multivariate linear regression analysis.  While this may seem intimidating, It's really not very difficult, and I think you’ll find it to be a valuable professional tool that has many applications in business and government. The paper should be around 6 double spaced pages (not including graphs/figures/ tables/and references).  The goal of the paper is for you to explore the relationship between a health-related variable and one of its key explanatory (ie. independent) variables. Your paper should frame the economic, theoretical, and policy importance of the relationship between the two by drawing on secondary source citations.  Your statistical analysis should relate back to the importance of these variables, especially in terms of how they relate to economic theory, and provide us insight into the overall health phenomena you are investigating.      
You may work with one other student in the class, but doing so is not required. I will not be taking measures to align your incentives, so if you do decide to work with another student, then choose carefully.  In other words, if your group partner does not do their part, I will not be penalizing them.
  Getting started:
You may want to start your project by simply identifying some general area of health economics that interests you.  Note, that health economics is really quite broad and can include the evaluation of any behavioral or economic phenomena that affects health. Some areas that students have researched in the past include: drinking and driving, marijuana legalization, physician supply, teen suicides, fertility, health insurance coverage, domestic violence, etc. Once you've identified a general area that you want to study, you need to think about a specific health-related variable that you want to examine more closely.  For example, I might be broadly interested in female access to medical care, but more specifically I'd like to know why the % of women who do not go to preventative doctor visits varies from state to state (or across counties in the nation, or across towns within a particular state).  Other examples might be the number of physicians, or the number of hospital beds, or the number of heart transplants, or prescription drug consumption per capita, etc. The list of potential topics is lengthy, so pick something that genuinely interests you but that is also practical to get information/data on and analyze effectively.
Once you've selected a specific variable to study, and the type of geographic areas you will use as a source of data (states, counties, metro areas, towns, etc.), you’ll need to think about the likely sources of variation in this measure—things that would potentially cause this measure to vary across different locations.  For example, suppose you are interested in woman’s health issues, particularly the access that women have to preventative health care.  What particular things might cause the % of women who had a preventative health care visit in the past 12 months to vary across the 50 states? [It’s actually very difficult to establish true causality, but you want to be thinking about this as a causal relationship, relating one or more “explanatory” or independent variables to the dependent variable.] The proportion of women with a regular physician is not evenly distributed, so what factors might “explain” this variation?  Some possibilities include: population in various age groups (not all age groups equally demand physician services); income (visits to a doctor is generally regarded as a “normal good”); average insurance coverage (access to insurance can greatly decrease the cost of having a regular doctor), etc. As you’re thinking about the “explanatory” variables, also think about whether each variable is likely to increase or decrease access to a regular physician.  This is where your economic reasoning should be useful. Think about the most important explanatory factors and how each might influence your variable of interest.  Try to avoid simply throwing in any variable that comes to mind.  The more thought you invest in this part of the exercise, the more likely your results will be interesting and meaningful.  
Ultimately your paper should focus on the relationship between a key independent/explanatory variable of interest and the health variable you are trying to understand.  You should focus the discussion of your paper on this major factor or independent variable that you feel explains the variation in your health outcome.  In the example of female access to health care if the key dependent variable was the % of women in a state who had a preventative health care visit in the past 12 months the key independent variable could be the % of women in a state who live near a community health care clinic.
I divide the parts of the handout by the parts of the paper I expect you to include in your final project:
I. Introduction / Overview of the Issue
The first part of the paper should introduce the issue you are interested in. Explain why it is important, and discuss what is known from earlier research about the dependent variable you are studying (the dependent variable is the key variable you are interested in). Here is where you should make use of secondary sources.  Well documented, and reliable Internet resources are fine, however Wikipedia is not an acceptable secondary source.  That being said, Wikipedia is a good place to get a general sense of a topic and to find some good sources if they are cited in the article.  
In the example above, I could begin with finding several academic papers or news articles about what factors cause some women not to have a regular doctor.  I would then highlight the major factors (access to community health clinics, income, age, insurance coverage, education, poverty) that causes variation in the dependent variable.  These different factors are known as independent variables: you should try to include all of these in your analysis. 
The introduction is also a good time to introduce simple economic theory or a simple model into your analysis.  For example, is the paper about the supply side creation of health care clinics?  If so, then a production function for clinics might make sense to look at / talk about.  
Typically, this section should be 1-2 pages.  
Note, From the beginning focus your discussion on one major factor or independent variable that you are interested in looking at in more detail (for example how access to a community health care clinic affects preventative health care).   
What I am looking for in this section: An explanation for why your topic is important and how your key independent variable may relate to you key dependent variable.  Why the relationship between the two is important and what previous work has said about this relationship.  What other independent variables should be included in the multivariate regression model.
II. Descriptive Statistics
The next step is to understand the correlation between the dependent variable and main independent variable of interest and how this varies across the data.  This can be done by making scatter plots, calculating the mean of the dependent variable, and calculating the mean of the dependent variable by different regions or social groups.  For example, you could calculate the average % of women who had a preventative health care visit in the past 12 months for different geographic regions in the US (North, South, New England, etc) or for different racial/ethnic groups (Black, White, Hispanic, etc).  Of particular importance you could calculate how the mean value of the dependent variable varies by different levels of the key independent variable of interest.  From our example: you could make a table of how the % of women who had a preventative health care visit in the past 12 months varies for states where fewer than 25% of women live near a community health clinic relative to states where more than 25% of women live near a community health clinic.  
You will calculate these correlations, present them in a table, and discuss what you find in your paper.  This section should be around 1 page.
III. Economic Model 
The next step is to develop a model that makes a hypothesis about how one variable causes another.  In our example this would be arguing for how variation in the availability of community health clinics causes women in different states to have differences in preventative health visits.  To do this, you need to present an empirical “model.”  A model is a mathematical formulation for how the independent variable is related to the dependent variable. In this example, making use of data for all 50 states and DC, the relationship or “model” I've described might take the general functional form:
A = f(%HC, POP 20-34, POP 35-64, POP 65+, %POV, EDU),
Where the variables are defined as:
A % of adult women who had a preventative check up in the past 12 months   % HC               % of adult women who live near a community health clini
POP 20-34   fraction of population 20-34 years old  
POP 35-64 population 35-64 years old 
POP 65+ population 65 years and older 
%POV percent of families in poverty
EDU Average total years of schooling
The above model basically states that major factors (often inputs into a production function, utility function, or demand function) that cause A.
You will be expected to use at least four to five independent variables.  However, you are welcome to get data on more independent variables (if you do, be careful not to have more independent variables than observations.  For example in the above model I have 51 observations--data on 50 states and DC-- and only 5 independent variables).  Either way, you will want to focus your analysis and research on a single independent variable that is of particular interest.
To estimate this relationship in your model, you need to assume some specific functional form.  You should use a simple linear function.  If we limit our analysis to the 6 explanatory variables I've suggested, this linear function would be written:
A = a0 + a1(%HC)+ a2(POP 20-34) + a3(POP 35-64) + a4(POP 65+) + a5(% POV) + a6(EDU) 
The function is linear because none of the variables is raised to a power, multiplied by another variable, logged, or appears as an exponent. Intuitively this assumes you are fitting a straight regression line between the two variables. In addition to a constant or intercept (a0), the equation contains 5 coefficients (a1, a2, …, a5), one for each explanatory variable.  These coefficients (a1, a2, …, a5) give the slope for that variable, or how the dependent variable changes with a change in the relevant independent variable.   The 6 parameters of the model can be estimated using data (the values of A and the 6 independent variables) from all 51 units (50 states plus DC). 
The signs and magnitudes of the estimated parameters (and some other statistics that will be calculated) will tell you more about the empirical relationship between female access to care and community health clinics.  For example, %pov is estimated as the percent of women living at or below the poverty level, the estimated coefficient a5 would be interpreted as the change in A (percent of women with a preventative visit in the past 12 months) for a 1% change in the share of women living in poverty.  If a1 > 0, it would be consistent with our expectation that we would find more women do not have regular care in areas where there is greater poverty.  
This type of statistical analysis is called linear regression and the particular estimation method you'll probably be using in this assignment is called ordinary least squares, or simply OLS.  
You should spend about 1 page discussing your model, how you estimate the relationship (including data used).
IV. Results
Then you should spend 1-2 pages, discussing the findings from your estimation, and what this shows about your question.  Specifically you should refer to a table of the slope coefficient estimates of the various independent variables.  These estimates say how the dependent variable changes with the independent variable and reflect the key findings of the paper. Such a table should look similar as to what was on homework 4 (though with more columns) or the midterm
V. Conclusion / Output
You can then spend about half a page to a page on a conclusion where you tie together your statistical findings with previous research and/or discuss the greater implications of your results.  Among other things the conclusion is the place to discuss the policy importance of your findings, and to put your regression estimates into prospective.  
 At the end of the paper also include the statistical output: scatter plots, regression output, table of means, etc. that you reference in your paper.  You also must include your bibliographic references.
Getting Data:
One small obstacle: to estimate this relationship (that is, to determine the parameters a0, a1, …, ), you need data—information about the specific variables in your model for a particular sample.  In the model I've outlined, the data would be cross-sectional (data for all 50 states in a particular year).  But we also could study this type of relationship using time-series data (data for one geographic area over 40 years, for example).  Sometimes researchers use pooled data (data for a series of cross-sectional samples taken at various points in time).  If the sample consists of the same units in each period, the pooled-data are also called panel data. 
We have an Internet and library full of data, but let me suggest a few specific websites that you might want to explore in your search for topics and for the necessary data. 
http://www.kff.org/statedata/
http://www.statehealthfacts.org/
http://www.cdc.gov/datastatistics/http://datacenter.shadac.org
http://researchguides.library.tufts.edu/content.php?pid=49955&sid=366979
http://quickfacts.census.gov/qfd/index.html
http://www.cerc.com/townprofiles/list.asp
http://www.census.gov/
http://www.fedstats.gov/
http://www.bls.gov/
http://www.bea.gov/
http://www.statemaster.com/index.php
http://www.econdata.net
http://einstein.library.emory.edu/econlinks.html
http://www.usa.gov/Topics/Reference-Shelf/Data.shtml
Proposal Due Date: Thursday October 31st   (as a homework assignment)
Project Due Date: Tuesday December 3rd. (tentative).