The Results section should follow directly from your Data & Methods section where you developed your model specification. However, your regression specification can/may have changed since you submitted your Data & Methods section and received feedback. This is acceptable and, in fact, encouraged. Just be sure to update the Data & Methods in the final version of your paper. Here, you provide a table of your regression results (potentially including multiple columns) – or several tables if necessary – and a brief description of those results. This section should be concise (1-3 pages, including tables), but will vary depending on the number of specifications included. Some things to consider in presenting and describing your results are:

1. QUESTION

2. Results & Discussion. This document includes what will become the Results and Discussion sections of your final paper.
3. The Results section should follow directly from your Data & Methods section where you developed your model specification. However, your regression specification can/may have changed since you submitted your Data & Methods section and received feedback. This is acceptable and, in fact, encouraged. Just be sure to update the Data & Methods in the final version of your paper. Here, you provide a table of your regression results (potentially including multiple columns) – or several tables if necessary – and a brief description of those results. This section should be concise (1-3 pages, including tables), but will vary depending on the number of specifications included. Some things to consider in presenting and describing your results are:
   1. Use outreg2 to generate your tables, or otherwise format them to disciplinary conventions – do not copy/paste tables from Stata.
   2. Do not report your estimates in terms of β’s or by using obscure abbreviations used in your codebook (such as lrgdppc). For the purposes of the results table, write out the variable name (such as logged real GDP per capita) that is consistent with the name you used in the Data & Methods section.

• Do not include too many significant digits. The goal is readability, not false precision.

1. Provide enough information so that the reader can understand your results without looking back at the text excessively. The notes on a table can be used for these purposes. For example, are you reporting standard errors or t-statistics in parentheses under the coefficient (standard errors are more common and generally preferred) and what do the “*” next to the coefficients denote (which level of significance)?
2. If you estimate several different specifications of your model (using the same dependent variable), include these as several different columns of the same table to facilitate comparison and improve readability. Table 1 below (from Nikolov, 2013) is a good example of this.
3. In describing your results – be brief. Your reader has already seen the table. For example, in a paper focused on the effect of education on wages, following Table 1, the text might say:

Table 1 shows that including a measure of ability in the wage equation dramatically lowers the predicted effect of education on earnings. Column 1 does not include an ability measure and indicates that a year of education raises wages by 9.1 percent. Column 2 adds the ability measure and the education effect drops to 3.1 percent. Columns 3 and 4 show that this general pattern is repeated even when state level dummy variables are included. The estimates in Table 1 are therefore consistent with the hypothesis that the OLS estimates suffer from an upward ability bias (Nikolov, 2013, p. 11).

• Notice that this description of the results begins and ends with statements that put the results in the context of the paper’s thesis. This is a good technique.
• Always interpret coefficients using the correct units.

1. If you are testing hypotheses other than standard significance tests (such as a test against a one-sided alternative, comparing two coefficients, or an exclusion restriction test), be sure to present the null and alternative hypothesis, compute the test statistic, report the p-value, and state your conclusion about the null hypothesis. You should not do this for every coefficient you estimate, your table will already make it clear to the reader which coefficients are statistically significant.
2. Pay attention to practical/economic significance (effect size), not just statistical significance. If you are using a large data set even very small effects can be statistically significant. Provide the reader with some context to put the effect in perspective.
3. If any of your results are strange or unexpected be sure to note this, you can and should return to it in your discussion section.

• Are your results consistent with or counter to the existing empirical research? Note this so that you can return to it in your discussion section.

The purpose of crafting these short descriptive paragraphs is to guide your reader through the results to focus their attention on the most important aspects of the table(s). Focus on what is important and be as clear as possible.

By the end of your results section, you should be able to draw a conclusion, even if it is not the one you expected. An unexpected result is a result nonetheless. Insignificant results can also be important and have significant policy implications. For example, perhaps we discover the 3-pt field goal percentage does not have an impact on a NBA team’s winning percentage, holding 2-pt field goal percentage (among other variables) constant. This might lead coaches to focus less of 3-pt field goals during practice and in recruiting players. As another example, suppose we find that after controlling for education and ability, work experience has no impact on worker productivity. This may lead employers to focus less on experience in employee recruitment. Remember, no study is a perfect study, but if you have done thorough empirical work, you should be able to reach some answer to your research question.

1. The Discussion section includes a discussion of the interpretation and implications of your empirical results, a discussion of potential explanations for the results based on your conceptual framework and/or previous literature, and a discussion of how your results are consistent with, an extension of, or at odds with the existing literature. This section should be concise (1-3 pages) and provide the reader with all of the relevant context needed to understand and interpret your results. Some things to consider in discussing your results are:
   1. If you have done a good job writing your results section, the discussion section should be relatively straightforward.
   2. Many good research questions in economics have policy implications. This is your chance to mention these (you may have already alluded to these in your introduction and/or literature review). Be careful not make value judgements – let your analysis speak for itself.

• If your results are strange or unexpected, suggest reasons why. This could be due to limitations of your methodology or data or perhaps inconsistencies in the theoretical framework.

1. Discuss these potential limitations of your research, such as: small sample size, less than ideal unit of analysis (state or national vs. individual), simplicity of the functional form, data (un)availability, selection bias, time period, omitted variables, etc.[1]
2. If there are several different possible explanations or interpretations of your results, which of these do you think are more likely? Are your interpretations based on a theoretical or conceptual understanding of the issue or based in the previous literature, or both?

[1] I am being hypocritical here. Academic writing should generally not use “etc.”

ANSWER

Results

Table 1: Regression Results

| Variable | Model 1 | Model 2 | Model 3 |
|———————————-|———|———|———|
| Independent Variable 1 | 0.12* | 0.18*** | 0.10** |
| Independent Variable 2 | 0.08** | 0.05* | 0.07*** |
| Control Variable 1 | 0.05 | 0.07** | 0.06* |
| Control Variable 2 | -0.03 | -0.02 | -0.01 |
| Constant | 1.20 | 1.10 | 1.25 |
| R-squared | 0.30 | 0.40 | 0.35 |

Note: Standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.

Table 1 presents the regression results for three different models (Model 1, Model 2, and Model 3). In Model 1, the coefficient for Independent Variable 1 is significant at the 5% level (p < 0.05), with a positive effect of 0.12. Model 2 shows that the effect of Independent Variable 1 increases in magnitude and remains significant at the 1% level (p < 0.01). Additionally, Independent Variable 2 exhibits a significant positive effect at the 5% level (p < 0.05) in Model 2. Model 3 confirms the significance of both Independent Variable 1 and Independent Variable 2, with similar effect sizes as in Model 2. Control Variable 1 also shows a significant positive effect at the 5% level (p < 0.05) in both Model 2 and Model 3.

The R-squared values indicate that the models explain a moderate proportion of the variation in the dependent variable, ranging from 0.30 to 0.40.

Discussion:

The regression results reveal several important findings. In Model 1, Independent Variable 1 has a positive and significant effect on the dependent variable, suggesting that an increase in Independent Variable 1 leads to an increase in the outcome variable. This result is consistent with previous research (cite relevant literature) that has shown the positive impact of Independent Variable 1 on similar outcomes.

In Model 2, the inclusion of Independent Variable 2 reveals an additional significant factor affecting the dependent variable. This finding suggests that Independent Variable 2 has an independent effect on the outcome, even after controlling for Independent Variable 1. This result adds to the existing literature by highlighting the importance of considering both Independent Variable 1 and Independent Variable 2 when studying the outcome variable.

The significance and stability of the coefficients in Model 3 further support the robustness of our findings. Control Variable 1 also demonstrates a positive and significant effect on the dependent variable, indicating its importance as a predictor of the outcome.

The results of this study have important policy implications. Based on the findings, policymakers should consider the positive effects of Independent Variable 1 and Independent Variable 2 when designing interventions or policies aimed at promoting the desired outcome. The magnitudes of the coefficients provide valuable insights into the effect sizes of these variables, indicating their practical significance.

However, it is essential to acknowledge the limitations of this study. First, the data used in the analysis may have certain limitations, such as potential measurement errors or missing variables that could influence the results. Second, the models employed in this study may have assumptions that limit their generalizability. Future research could address these limitations by using more

comprehensive datasets and employing alternative modeling techniques.

In conclusion, this study provides empirical evidence of the significant effects of Independent Variable 1, Independent Variable 2, and Control Variable 1 on the dependent variable. These findings contribute to the existing literature by expanding our understanding of the factors influencing the outcome variable. The policy implications of these results underscore the importance of considering these factors when formulating effective strategies and policies.