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Does Anxiety Affect Adolescent Academic Performance? The Inverted-U Hypothesis Revisited

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Abstract

The inverted-U relationship between anxiety and performance in the context of endogeneity has yet to be investigated. Junior high school students from Taiwan were used as the sample for investigating the effect of anxiety levels on the comprehensive analysis aptitude of students. The ordinary least square (OLS) analysis indeed confirmed the inverted-U relationship. In addition, both fixed-effect analysis and two-stage least square (2SLS) analysis using variation in acne severity to instrument for anxiety also concluded that anxiety increased performance at lower anxiety levels. However, this relationship was positive and insignificant at higher anxiety levels. Overall, our results supported the left (increasing) part of the inverted-U relationship between anxiety and performance, but found no evidence for the right (decreasing) part of the inverted-U relationship.

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Notes

  1. Mechanic and Volkart (1961) stated that anxiety and unease can be used as indicators to measure stress.

  2. Fig. 1 was obtained from Cochran et al. (2006).

  3. As we mentioned in “Introduction” section, a strong correlation between stress and anxiety exists. In addition, anxiety is easier to measure for students empirically.

  4. Muse et al. (2003) stated that most previous studies indicated a negative relationship. This relationship may be caused by difficulties in defining stress and inability to measure low stress levels (i.e., understressed conditions).

  5. In the following section, we explain how instrumental variables resolve simultaneity problems.

  6. The sample we used in our analysis was not the entire sample of data because tracking data had to be constructed. In “Instrumental Variable Second-Stage Regression Results” section, we re-analyzed the sample using an imputation method to investigate whether the problem of drop-outs is severe or not.

  7. This study used the estimated aptitudes of students on the comprehensive analysis aptitude test of the TEPS data as the dependent variable. These aptitudes were estimated using a 3-p model. These estimates could be compared between waves and students, facilitating our follow-up data analysis.

  8. Other than “whether families have experienced economic misfortune,” which was asked in both waves of questionnaires, other special events were asked in only the first wave of questionnaires. The special events encountered had a persistent effect on students. Thus, we still used the special events from the first wave as control variables in our regression analysis of the second-wave data.

  9. The mean age of the patients and the controls was approximately 22 years.

  10. The correlation of acne severity was 0.82 among monozygotic twins and 0.40 among dizygotic twins.

  11. The correlation of acne severity was 0.78 among monozygotic twins and 0.44 among dizygotic twins.

  12. Specifically, we regressed levels of study time (five levels) on acne severity. The reference group of acne severity is no acne. The coefficients of mild and severe acne were −0.0328 and −0.0464, respectively. Both of them were insignificant. We also used the midpoint of each level of study time to conduct study hours and regressed it on acne severity. The coefficients were still insignificant. In addition, we regressed levels of self-expectation regarding educational achievements (six levels) on acne severity. The results showed a positive correlation, implying that acne severity might affect the academic performance through the channel of self-expectation. Nevertheless, we could control study time and self-expectation in our analysis to mitigate the potential bias as far as possible.

  13. Anxiety measurement methods are explained in “Explanation of Variables” section of this paper. We also attempted the following method of measurement: For samples in which the total anxiety scores from the four questionnaires were equal to 0, we set the anxiety variable to 0 and other variables to 1. We found that these regression results were identical to those of the study (results not reported).

  14. For robustness, we also used the ratio of correct answers on the comprehensive analysis aptitude test as the dependent variable. These results are presented in Appendix 1. The regression results were identical to the student comprehensive analysis aptitude estimates obtained from the test. Therefore, only the student comprehensive analysis aptitude estimates obtained from the test are explained herein.

  15. The benchmark for the anxiety grouping was the average anxiety level. People above this benchmark were classified as the high-anxiety group and people below this benchmark were classified as the low-anxiety group.

  16. The level of significance for the male participants was 10%. The level of significance reached 1% for both the overall and female participants.

  17. We used the average anxiety level from the first-wave data as the anxiety grouping baseline to investigate how the influence of changes in anxiety levels on comprehensive analysis aptitude differed between the low-anxiety and high-anxiety groups during the first year of junior high school.

  18. Fitzpatrick and Aeling (1996) stated that severe acne was associated with disturbance in performance. Gonçalves et al. (2012) used questionnaires completed by 145 medical students, and observed that students with acne reported that there was no or merely a small negative effect on their academic performance.

  19. As mentioned previously, in the fixed effect model, we used the anxiety level from the first-wave data as the anxiety grouping baseline to investigate the difference of the effect of changes in anxiety levels on comprehensive analysis aptitude between the low-anxiety and high-anxiety groups during the first year of junior high school. In addition, because our IV is available only in the first-wave data, we performed 2SLS regression analysis on only the first-wave data.

  20. Although our IV was not weakly related to the endogenous regressor of interest, we utilized a Bayesian model for estimating the effect of anxiety as robustness verification. We used a Gibbs sampler for the 2SLS IV model and implemented it in the function rivGibbs of the R package bayesm developed by Rossi et al. (2005). Furthermore, we conducted our analysis again using a Bayesian OLS approach with the function runiregGibbs of the R package. Both the results of the Bayesian IV and Bayesian OLS approaches were similar to our main results (results not reported).

  21. Only one insignificant coefficient changes the sign.

  22. The influence was positive and insignificant in the high-anxiety groups.

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Acknowledgements

We thank Christopher Taber for his comments. All errors are ours.

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  1. Department of Economics, National Taiwan University, No.1, Sec 4, Roosevelt Road, Taipei, Taiwan

    Hsiu-Han Shih & Ming-Jen Lin

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  1. Hsiu-Han Shih
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The authors of this manuscript, Ming-Jen Lin and Hsiu-Han Shih, certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

Appendices

Appendix 1

For robustness, we used the ratio of correct answers on the comprehensive analysis aptitude test (RCAA) as the dependent variable. We divided every student’s number of correct answers on the CAA test by the highest number of correct answers of the data, and then multiplied the result by 100. The regression results presented in Appendix Table 13 was identical to the student comprehensive analysis aptitude estimates obtained from the test.

Table 13 The OLS and 2SLS results using RCAA
Full size table

Appendix 2

The sample we used in our main analysis was not the entire sample of data because of constructing the tracking data. We re-analyzed our sample using an imputation method to investigate whether the problem of drop-outs was serious or not. We did not have student data of variables obtained from the survey of the second wave for students who only appeared in the data from the first wave. Because our OLS and 2SLS analyses only required the data from the first wave, no problem of missing data occurred when we used the full sample from the first wave. For the fixed-effect model, we imputed the missing data of students who only appeared in the data from the first wave with the mean values of students who appeared in both waves for all variables that we included in our original analysis.

We did not have the data for the variables obtained from the survey of the first wave for the students who only appeared in the data from the second wave. To perform an OLS analysis for the full sample from the second wave, we imputed the missing data of these students with the mean values of students who appeared in both waves for all variables that we included in our original analysis. The results are presented in Appendix Table 14. These results were quite similar to our main results, implying that the problem of drop-outs is not severe.

Table 14 The results of imputation method
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Shih, HH., Lin, MJ. Does Anxiety Affect Adolescent Academic Performance? The Inverted-U Hypothesis Revisited. J Labor Res 38, 45–81 (2017). https://doi.org/10.1007/s12122-016-9238-z

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