3. Empirical Results
I estimate three different specifications. The dependent variable in each specification is performance, as measured by the percentage of games won. Pay inequality and total payroll are the independent variables. Table 2 shows the results. In the first specification, I regress performance on the share earned by the top 20% of players. The coefficient on the share of top 20% is negative and statistically significant. This indicates that teams with higher pay inequality tend to win fewer games. A one percentage point increase in the share of payroll earned by the top 20% of players is associated with about half of a percentage point decline in the percentage of games won.
Table 2: Regression Results
Dependent variable: winning percentage (in %)
Top20share (in %)
Payroll (in mil. USD)
Log of Payroll
Number of observations is 60.
In the second specification I include total payroll as an independent variable. Payroll is a measure of the financial resources which can affect performance - the higher the payroll, the higher the quality of players and, generally, the better the performance. Therefore, including payroll may increase the precision of the estimated coefficient on pay inequality. More importantly, it is possible that pay inequality is correlated with total payroll. If low payroll teams tend to have more pay inequality, then the coefficient on pay inequality in specification (1) is biased. Indeed, the correlation coefficient between the share earned by the top 20% of players and total payroll is -0.5. Teams with high pay inequality may perform worse not because of pay inequality, but because they are also the teams with a lower payroll. Therefore, in order to measure the effect of pay inequality on performance, I need to control for total payroll.
Once I control for total payroll, the coefficient on the share of the top 20% remains statistically significant but the magnitude drops substantially. Holding payroll constant, a one percentage point increase in the share earned by the highest paid 20% is associated with a 0.27 percentage point decline in the percentage of games won. The impact of inequality on performance does not seem enormous. For example, a five percentage point increase in inequality for the team with median inequality would shift the team up 13 spots in the inequality ranking, but its performance ranking would drop by only 2 spots. The coefficient on total payroll is positive and statistically significant. A one million dollar increase in total payroll is associated with about 0.1 percentage point increase in the percentage of games won. This indicates that greater financial resources tend to improve performance. Adding payroll as an independent variable led to an increase in R-squared from about 0.19 to 0.29.
Finally, in specification (3) I include the logarithm of payroll instead of payroll. I want to verify that the result in specification (2) is robust to different functional forms. In addition, the effect of an additional one million dollars may be smaller for a team with a 100 million payroll than for one with a 20 million payroll. Thus, including payroll in logarithm seems appropriate. The coefficient on the share of the top 20% remains statistically significant with roughly the same magnitude. The log of payroll is statistically significant. A one percent increase in payroll is associated with about 0.07 percentage points increase in the percentage of games won.
Writing in Economics :: Components of a Research Paper
An economics research paper includes the parts listed below. Some of these may be, and often are, combined into sections of the research paper. Depending on the nature of the research question, some parts may be emphasized more than others.
I've condensed information from several different sources. This is cursory content on how to write in economics, please make use of the additional resources. Also, every researcher has his or her own opinion about the best way to proceed. The information I've collected below is one of many possible ways to approach an undergraduate or graduate research project in Economics.
The abstract is a description of your research paper. The writing style of the abstract is very condensed - it should be no more than 350 words (or 5-6 sentences). The abstract is designed to identify the following to a potential reader:
- The research question
What is the question that is the focus of your research? A good research question is one that (i) doesn't have an obvious answer (otherwise, why bother researching it?) and (ii) is testable using data.
- Your contribution to the research on the subject
What has the previous literature found and what is your contribution to general understanding of the economic problem/question.
- How you answer the research question
How you use theoretical and/or empirical analysis to answer the research question.
Your findings based on the aforementioned analysis
The abstract is written when the paper is completed. It should not be the same as your introduction - the audience is different.
The introduction is designed to both identify and motivate your research question. Like an essay you would write in other subjects, the introduction begins with a broad statement, and then narrows down to your specific research question.
In the end, make sure that you've done the following in your introduction:
- State your research question
- Motivate why the subject of your research is important to economists and other stakeholders
- Explain to the reader where your research fits into the subject.
- Identify your contribution to general understanding on the subject/research question
- Summarize how you intend to answer the research question
- State your general results and answer to your research question.
The first paragraph of the introduction is used to motivate why this research is important and of interest to economists and other stakeholders (e.g., parents and teachers in education economics, central bankers in monetary policy, and residents and businesses affected by pollution). It may conclude with a statement of your research question, followed by a discussion of who is affected by the economic issue under study. It is not appropriate to include personal anecdotes in a written research paper. Remember, you are motivating why the research should be of interest to the reader.
The second paragraph typically has more detail about how you plan to answer the research question, possibly citing other work closely related to your own research. In fact, many authors combine the literature review with the introduction in order to streamline this discussion. This paragraph may conclude with your general findings.
You should be able to write the first paragraph when you begin your research. The second paragraph can be written as you are concluding your research, as it draws on information from subsequent sections of your paper.
The literature review serves two main purposes:
- motivate why your research question is important in the context of the broader subject
- provide the reader with information on what other researchers have found (highlighting your contribution)
If someone has done a similar analysis to yours, tell us, and then explain how yours is different. Explain their findings, and then follow up with what you expect to find in your own research, and compare.
Some things to keep in mind for your literature review:
- Conduct a comprehensive search of the research on your subject
Familiarize yourself with search engines in Economics (ECONLit is the most comprehensive) - do not rely on Google or other general search engines because they will link to you information that is not peer-reviewed research. A good general rule is as follows: if it is a paper not listed on ECONLit, it is probably not appropriate for a research paper in economics. Of course, there are exceptions. See my ECON 145 resources for more information on search engines.
- Create an annotated bibliography for the papers you plan to cite in your research paper.
More information on annotated bibliographies is given below. This is a good step to take early on in your literature review search because it helps you keep track of the papers you plan to cite, and helps you to summarize information in one place. This will help you with the subsequent steps below.
- Identify which papers are most relevant to your research question
It is easy to find lots of articles on one topic, but difficult to sort out which ones are important and relevant to your specific topic. You need to find the most relevant articles for your topic, and tell the reader why these are relevant articles for your topic specifically.
- Make an outline of your literature review
Write an outline of your literature review. When writing your literature review, you want to organize the research of others into themes that you want to convey to the reader. Do not simply list papers chronologically and summarize the results of others. You should group papers by common themes.
- Critically read research papers
You cannot read research papers like novels or the newspaper. Economics research papers are often dense and technical, requiring carefully reading. If you are not actively engaged as a reader, taking notes and writing questions to yourself as you go along, you are making poor use of your time and will not get much out of your literature review. See my page on Critical Reading for more information on strategies for how to read economics research papers.
- Be aware of plagiarism.
This is very difficult for the novice researcher because some information is generally taken as known, while other information is not. The best way to get a sense for how to appropriately cite and attribute material is to read economics research articles. Avoiding plagiarism doesn't mean rewriting someone else's ideas in your own words. If you are using someone else's idea, whether in quotes or not, you must cite it. When in doubt, cite.
- The literature review is critical to the success of the rest of your paper
Even though you are reviewing the work of others, this is a stepping stone to you conducting your own analysis. A weak or incomplete literature review will often result an inappropriate or insufficient economic model, empirical methodology, and or discussion of your results. You will use your literature review to familiarize yourself with :
- common research questions in the subject (introduction),
- economic models used to answer related research questions (economic model),
- empirical methodologies common in the field (empirical methodology),
- data sources you may use in your analysis (data description),
- how to report your results (empirical analysis), and
- how to identify your contribution to understanding of the research question/subject (conclusion/analysis).
You can see that the literature review is the foundation of your research paper.
Economic Model/Empirical Methodology
This section (or sections) or your paper are designed to show how you intend to answer your research question using economic theory (economic model) and empirically (using statistical tests). For the novice researcher, it is useful to think of these two approaches as separate. This avoids the temptation to confuse them.
This is what you have studied in most of your other economics classes. For example, what happens to the price of housing when the population increases? Using demand-supply model, we know that an increase in population leads to an increase in the demand for housing, increasing the equilibrium price. In reading economics research papers, the economic model is often not identified because it is assumed the reader (economic researchers) are familiar with the underlying model. However, to the novice researcher, the model may not be obvious, so it is important to outline the model and include it in your research paper.
Your economic model is how you make predictions of what you expect to find in the data. Based on the simple example above, we'd expect to see a positive relationship between housing prices and population, ceteris paribus (e.g., holding all other variables in the demand-supply model unchanged).
Another important point is that your economic model is what implies a causal relationship between the economic variables. While you may detect a positive or negative relationship in the data, this alone tells you nothing about which variable is causing a change in the other variable. The economic model can be used to model this relationship. In the example above, we assume that in the model, a change in population causes a change in the housing price.
The economic model should make no mention of data, regression analysis, or statistical tests. The model is a purely theoretical construct, based on an abstract notion of how the world works. The empirical methodology section of your paper is how you plan to test these relationships in the data. An economic model is NOT a regression equation.
Finally, you should use an economic model that is common in the literature on your subject. Unless you are proposing a new model, you should rely on those used by other researchers in the field. This will allow you to use your literature review to justify your choice of model. Also, this is why the economic model is often embedded in the literature review of the paper. For novice researchers, I recommend keeping it separate, to make sure you understand how to use your economic model to conduct theoretical analysis.
This is where you describe to the reader how you plan to test the relationships implied by your economic/theoretical model. First, you want to identify your dependent variable. This is the variable you are seeking to explain the behavior of. Next, you want to identify possible explanatory variables. These are the variables that could potentially affect your dependent variable.
Often in economic models, there are abstract notions of how some variables affect others. For example, human capital affects production, but how would we measure human capital in the data? You can find suitable proxies for a variable like human capital by familiarizing yourself with the literature.
So, how could a researcher go about testing the relationship between housing prices and population? First, we know that housing price is the dependent variable. Population is one explanatory variable, but are there others that affect housing prices? Yes. We know this from the demand and supply model that there are other variables that shift demand for housing (income, prices of substitutes and complements, expectations, tastes and preferences, etc.) and the supply of housing (input costs, expectations, the number of sellers, etc.). In order to isolate the effect of population on house price, we need to control for these other factors.
The most common strategy for empirical work regression analysis because it allows the researcher to isolate the correlation between two variables, while holding other explanatory variables constant (e.g., ceteris paribus from the model above). Often in the empirical methodology section, the researcher will point out potential estimation issues, highlighting the need for more advanced econometric techniques that go beyond ordinary least squares (OLS).
This section does not actually do any statistical analysis, but it may include a description of the data (see below). In advising students on research papers, I usually recommend the following breakdown for the empirical methodology section:
- Data description
This is a description of the data you plan to use for your analysis. It usually includes a citation of the primary source, data frequency, how the data are measured, the frequency of the data, etc. The amount of detail depends on the nature of the data. Also, this is the section where you would report any modifications you make to the data.
- Preliminary data analysis
This section reports summary statistics, histograms, time series plots, and other similar information. This section is designed to give the reader a sense of what your sample looks like. In reporting this information, you should be selective - more is not always better. You need to decide which information you need/want to convey to the reader and how to best convey it. See my Empirical Methods in Economics page for ideas on basic statistical analysis.
- Regression Equation
Now, you're ready to remind the reader of your particular test and how you are going to go about using regression to test it. This section should include a regression equation, a discussion justifying this equation, and a description of the expected signs on the coefficients for each of the explanatory variables (spending more time on those that are of particular interest for your study). Remember, the regression coefficient measure the marginal effects of the explanatory variable on the dependent variable (holding the other variables constant, ceteris paribus).
When justifying your regression equation and discussing the expected signs for the coefficients, you should make some clear connections back to your theory section and the literature review section of your paper. Also, make sure that you are using your regression equation to answer your research question. What is the testable hypothesis? Does this test answer your research question? See my Empirical Methods in Economics page for a simple primer on regression analysis.
An alternative to the ordering mentioned above is as follows. You can begin with a regression equation, then provide a detailed description of the data, along with some preliminary data analysis. It is most common to have the data description as its own section of the paper - mainly to make it easier for readers to reference it if they plan to do similar research. You could then follow this Data section with an Empirical Methodology section that consists of the #3 Regression equation described above.
This section is often titled "Results" in economic research papers, as it reports the results from your regression analysis above. There are commonly-used templates for reporting regression results. The best way to familiarize yourself with these templates is from the papers you cite in your literature review. You will see that it is common to report multiple regressions in one table, with the explanatory variables listed vertically on the left. See my page on Empirical Methods in Economics for more details.
The empirical analysis should include a table with your regression results, and your written analysis of these results. Note, this does not mean repeating the information in your regression tables. It means interpreting these coefficients in light of your economic model and comparing your findings to other papers from your literature review.
The conclusion usually consists of about three paragraphs. The first begins with a restatement of the research question, followed by a description of what we know about this research question from the literature (very concisely). Then the paragraph concludes with a brief description of the theoretical answer to the question.
The second paragraph begins with an answer to the research question, based on your empirical analysis. The researcher then proceeds to compare his/her findings to the consensus in the literature, pointing out possible reasons for differences and similarities. For example, perhaps you studied a different time period, or a different country. Perhaps you used a different measure of the dependent or explanatory variables.
In the final paragraph, it is common to draw policy implications from your research. In a practical sense, who cares about this research question (remember the stakeholders from the introduction..) and what can they do with this knowledge? Often the conclusion will point toward directions for future research, based on possible extensions to your research.
The bibliography contains complete references of the works that cited and referred to in your research.
It is essential that you give proper credit to all works that you cite, even if they are not included in your literature review. For example, if you obtained data from a publication that is not easily available, it would be appropriate to cite it in your data description and include it in your bibliography. Incomplete or inaccurate citations are akin to plagiarism, so please be sure to carefully check your references and keep track of them while completing your literature review.
In economics, it is most common to use APA style in citing references in the text of your paper and in creating a bibliography. For more information, see the APA style guide provided by the Library, or simply pick up a copy of the APA style guide if you will be using it frequently.
An annotated bibliography is one that includes the reference (mentioned above), along with a few sentences describing the research and how it relates to your research paper. Often the description will begin with a statement of what the research found, followed by one or two sentences that are relevant to the research question you are studying.
Even though APA style calls for a double-spaced annotated bibliography, many researchers prefer a single spaced one. The Library has information on annotated bibliographies and I have posted an outstanding example from undergraduate Economic Research Methods.
The best annotated bibliographies are those written by students who have read the literature critically. See my page on Critical Reading for more information on strategies for how to read economics research papers. Even if an annotated bibliography is not assigned as part of your research project, it is a useful exercise for you to engage in, especially if you have to present your research orally or using a poster. If you are unable to write an annotated bibliography, then you are probably writing a poor review of the literature on your subject and a less than satisfactory research paper.