The Declining Effect of Insurance on Life Expectancy
Round 1
Reviewer 1 Report
Dear Author!
The manuscript provides a contribution to the research area effect of insurance on life expectancy. The title of the manuscript is appropriate. The title reflects the content of the manuscript.
There is a balanced relationship between the objective, content of the manuscript.
It is appropriate to finalize the abstract.
The abstract must include sufficient information for readers to judge the nature and significance of the topic. The abstract should contain the main idea of the paper, the subject and the goal of the research, methods used, hypotheses, research results and a brief conclusion.
The style of presenting the material should be adjusted. In a scientific article, it is not appropriate to write in the first person.
I am grateful to the author for developing an interesting material.
Best regards,
Author Response
First, I would like to thank the referees for their time and efforts on my behalf. Below, I have copied your referee reports and inserted my responses with indented text.
Dear Author
The manuscript provides a contribution to the research area effect of insurance on life expectancy. The title of the manuscript is appropriate. The title reflects the content of the manuscript.
There is a balanced relationship between the objective, content of the manuscript.
It is appropriate to finalize the abstract.
The abstract must include sufficient information for readers to judge the nature and significance of the topic. The abstract should contain the main idea of the paper, the subject and the goal of the research, methods used, hypotheses, research results and a brief conclusion.
I think that my abstract does all the above.
The style of presenting the material should be adjusted. In a scientific article, it is not appropriate to write in the first person.
I have eliminated the use of the first person.
I am grateful to the author for developing an interesting material.
Thank you, very much.
Best regards,
Reviewer 2 Report
The paper addresses an important concern, which is related to the impact of life insurance on life expectation. The results seems to indicate a moderate impact of life insurance on life expectation.
The empirical approach adopted by the author is not extremely popular, as also indicated by the fact that papers using that methodology are not published in top Economics/Statistics journal.
I have two main concerns:
1) You should remove the list of journals, which published papers using the same methodology as yours. This is not informative and does not add any value to the paper.
2) I would elaborate more about the methodology. After reading it, I was not still convinced that the chosen empirical strategy is the appropriate one. As far as I understood, you want to mitigate the consequence of omitted variable problem. But is there no any other way? Possibly checking for variables that can be included in the model? I know the OECS stats database and it contains a lot of variables that can be included (consistently with the literature). If you do not have any available variable, that is fine. But it seems to me that you start from the idea that you need to "show" the goodness of your approach and, therefore, you did not make any effort in finding variables that can be included in the model. Moreover, I am not entirely convinced that the omitted variable problem is relevant only when variables are related each other. If this is the case, you may have a multicollinearity problem, which necessarily leads to dropping one or more variables.
3) I am not very clear with the discussion about Iceland. If you suspect that there is a mistake in the data, I would simply remove that country from the analysis. Discussing whether the number is 148 or 1480 generates only confusion;
4) Table 1 reports the per capita insurance premia. If I understood correctly this are data that you used in your regression. If so, I am not very sympathetic with reproducing data in your paper. You indicated the source and that is all you need to do. If you want to show the evolution of data over time, it would be more convenient to include a graph. The same applies to the discussion of the results. It would be much more effective to include a graph showing the evolution of the values over time rather than a table, which in my view is not informative.
5) While you discussed the estimation approach, it is not clear to me which is the equation you are going to estimate. Rather than presenting the model in a general form (eqs. 1 to 8) you can rewrite it using exactly the same variables you are going to use in your analysis
6) Tables should be edited properly rather than copying and pasting them from excel.
In general, I found your reserarch question interesting. However in my view the paper needs some improvements to make it more palatable for publication. In particular I would like to see a deeper discussion of the empirical approach. This is the main point to address. Other suggestions can be addressed quickly, but the discussion/justification of the empirical model is a crucial step.
Author Response
First, I would like to thank the referees for their time and efforts on my behalf. Below, I have copied your referee reports and inserted my responses with indented text (the indent disappeared in this window, but is retained in the attached file). Please note that I have done my best to make the improvements in my paper that you requested. However, please be aware that JRFM gave me only 10 days to make this revision. Furthermore, this revise and resubmit has come at a very bad time for me. It arrived the day before Thanksgiving – one of the USA’s biggest three holidays (Christmas, Easter, and Thanksgiving). I hosted out of town guests for Thanksgiving for 4 days. During this holiday, I got up at 5:30am to work on these revisions before my guests got up. My guests have now left, but in the week after Thanksgiving I will receive term papers from my students which will need to be graded. I also need to write final exams this week (I do not use multiple choice exams from test banks). However, I am happy with how I have changed the paper and doubt that the changes would have been substantially different even if I had been given more than 10 days.
The paper addresses an important concern, which is related to the impact of life insurance on life expectation. The results seems to indicate a moderate impact of life insurance on life expectation.
The empirical approach adopted by the author is not extremely popular, as also indicated by the fact that papers using that methodology are not published in top Economics/Statistics journal.
One A+ journal (as ranked by the Australian Deans’ List) has published two RTPLS papers – The European Journal of Operational Research. Furthermore, I have published 28 peer reviewed journal articles that use RTPLS; most of these articles are in B or C level journals. When I developed RTPLS in 1999, I expected the world to enthusiastically embrace it – the data requirements to conduct it are minimal as are the modelling assumptions needed; furthermore, often policy makers need total derivative estimates not the partial derivative estimates found through normal regression analysis. Many years ago, I submitted an RTPLS paper to the top statistics journal in the world – Journal of the American Statistical Association. The editor was extremely interested in my ideas, but he told me that I needed to include in the paper a proof of the asymptotic properties of RTPLS before he would send it out to referees. I revised the paper including a proof of RTPLS being unbiased and consistent (I do not know how to prove efficiency). The editor said that my proofs were not good enough, and he did not send it out for review. Thomas Kuhn, in his seminal book The Structure of Scientific Revolutions, says that it takes a generation for a new paradigm to be accepted. RTPLS is a paradigm shift in doing statistical analyses. I hope that someday the statistics world will fully embrace it, but that is likely to be long after I am dead. In the meantime, I have successfully published with it – two A+ publications any many B and C publications.
I have two main concerns:
- You should remove the list of journals, which published papers using the same methodology as yours. This is not informative and does not add any value to the paper.
I have done this.
- I would elaborate more about the methodology. After reading it, I was not still convinced that the chosen empirical strategy is the appropriate one. As far as I understood, you want to mitigate the consequence of omitted variable problem. But is there no any other way? Possibly checking for variables that can be included in the model? I know the OECS stats database and it contains a lot of variables that can be included (consistently with the literature). If you do not have any available variable, that is fine. But it seems to me that you start from the idea that you need to "show" the goodness of your approach and, therefore, you did not make any effort in finding variables that can be included in the model. Moreover, I am not entirely convinced that the omitted variable problem is relevant only when variables are related each other. If this is the case, you may have a multicollinearity problem, which necessarily leads to dropping one or more variables.
Another way is Variable Slope Generalized Least Squares (VSGLS) as explained in Leightner, Inoue, and Lafaye de Micheaux (2021) – see references. Under most circumstances, RTPLS and VSGLS preform equally well; however, under some conditions RTPLS noticeably outperforms VSGLS. I have used the best technique possible.
I address the idea of adding other variables when I write immediately before the conclusion: It is important to remember that RTPLS estimates are total derivatives (not partial derivatives) that show all the ways that the dependent and independent variables are related. Thus if insurance premium increases are correlated with advances in health technology, then the RTPLS estimates presented here capture that correlation. Indeed it is likely that one of the major ways that insurance and life expectancy are correlated is by insurance making it possible for people to receive medical treatments that use advance health technology that without insurance would be prohibitively expensive. If a researcher were to estimate d(life expectancy)/d(insurance) holding medical technology constant, then that researcher might find no relationship between life expectance and insurance when (in truth) insurance is playing a key role by making modern medical technology affordable. Furthermore, holding per capita GDP constant while estimating the effects of insurance on life expectancy is also problematic because higher per capita GDP could be viewed as a substitute for insurance or higher per capita GDP increasing wealth (which can be used to sustain the lives of the elderly) could stimulate more insurance to protect that wealth. The total derivatives found in this paper for d(life expectancy)/d(insurance) capture all the ways that insurance and life expectancy are related. It is impossible to test the robustness of this paper’s results by comparing them to the results of different multivariate analyses that use varying sets of independent variables because RTPLS produces total derivatives while multivariate analysis produces partial derivatives. Apples and oranges are both fruits (RTPLS and multivariate analyses are both statistical methods), but beyond that one similarity, apples and oranges are very different
If there is absolutely no relationship between an included independent variable and an omitted variable, then that omitted variable just adds more random variation to the dependent variable (which decreases the statistical significance) and does not affect the estimated coefficient for the included variable. I have rewritten the text to make this clearer.
- I am not very clear with the discussion about Iceland. If you suspect that there is a mistake in the data, I would simply remove that country from the analysis. Discussing whether the number is 148 or 1480 generates only confusion;
I was given only 10 days to make these revisions, and those 10 days include a major holiday for the USA and days needed to grade term papers. Eliminating Iceland would not change the results substantially but honesty in publishing would require that I make adjustments in all tables and text even if the changes were only 1/1000 th of the original numbers (100.1 becoming 100.2). I have tried to clarify what I say about Iceland. Also the two graphs added show how that decimal place error affected the data and results.
- Table 1 reports the per capita insurance premiums. If I understood correctly this are data that you used in your regression. If so, I am not very sympathetic with reproducing data in your paper. You indicated the source and that is all you need to do. If you want to show the evolution of data over time, it would be more convenient to include a graph. The same applies to the discussion of the results. It would be much more effective to include a graph showing the evolution of the values over time rather than a table, which in my view is not informative.
I have eliminated the original Table 1, but not the original Table 2 (which is now Table 1). I eliminated the original Table 1 because you are correct in saying that a reader could find that data on the OECD website; however, a reader could not find the information on the original Table 2 (which is now Table 1). Furthermore, there was no way to show all the information given on the original Table 2 in one graph, thus I included the original Table 2 and a graph of the most important original Table 2 results. Some of the data is also shown in an added graph.
- While you discussed the estimation approach, it is not clear to me which is the equation you are going to estimate. Rather than presenting the model in a general form (eqs. 1 to 8) you can rewrite it using exactly the same variables you are going to use in your analysis
I have added the following sentence: In this paper’s application, Y is life expectancy and X is insurance premiums per capita.
- Tables should be edited properly rather than copying and pasting them from excel.
I did not copy and paste from excel; I copy and pasted from Lotus. Why is that a problem? Copy and pasting makes sure that the numbers I generated using RTPLS made it correctly into the paper. Retyping those numbers adds the possibility of typos and takes a lot of time. Unless I know of a good reason to not cut and paste, I will continue to cut and paste.
In general, I found your research question interesting. However in my view the paper needs some improvements to make it more palatable for publication. In particular I would like to see a deeper discussion of the empirical approach. This is the main point to address. Other suggestions can be addressed quickly, but the discussion/justification of the empirical model is a crucial step.
I have greatly expanded my explanation of RTPLS.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The paper is potentially interesting but there are important statistical weaknesses that make the results unreliable.
1. I was not aware of the RTPLS technique and I will read the papers in which it is introduced to better understand how it works. However, I am convinced that it is not possible to isolate the relation between life expectancy and insurance expenditures (per capita) without controlling for at least the following variables: country GDP (per capita) and the presence of a public health system. Indeed, the former variable has an extremely strong correlation with both variable (insurance expenditure and life expectancy), the latter makes the share of health insurance much less relevant in the total amount of insurance expenditures for those countries.
2. In the paper all expenses are expressed in US dollars according to exchange rates, however, given that the cost of living is much different among the considered countries, PPP dollars should be used instead. You can find them here: https://data.oecd.org/conversion/purchasing-power-parities-ppp.htm
3. I would suggest to robustify your results by also including the estimates produced by a multilevel model, which can reduce the estimation bias for omitted variables that characterize the countries, for example by introducing a fixed- or random-effect for each country.
I attach the pdf of your paper with all the embedded comments. Please fix all points raised within that document.
Comments for author File: Comments.pdf
Author Response
First, I would like to thank the referees for their time and efforts on my behalf. Below, I have copied your referee reports and inserted my responses with indented text. Please note that I have done my best to make the improvements in my paper that you requested. However, please be aware that JRFM gave me only 10 days to make this revision. Furthermore, this revise and resubmit has come at a very bad time for me. It arrived the day before Thanksgiving – one of the USA’s biggest three holidays (Christmas, Easter, and Thanksgiving). I hosted out of town guests for Thanksgiving for 4 days. During this holiday, I got up at 5:30am to work on these revisions before my guests got up. My guests have now left, but in the week after Thanksgiving I will receive term papers from my students which will need to be graded. I also need to write final exams this week (I do not use multiple choice exams from test banks). However, I am happy with how I have changed the paper and doubt that the changes would have been substantially different even if I had been given more than 10 days.
The paper is potentially interesting but there are important statistical weaknesses that make the results unreliable.
- I was not aware of the RTPLS technique and I will read the papers in which it is introduced to better understand how it works. However, I am convinced that it is not possible to isolate the relation between life expectancy and insurance expenditures (per capita) without controlling for at least the following variables: country GDP (per capita) and the presence of a public health system. Indeed, the former variable has an extremely strong correlation with both variable (insurance expenditure and life expectancy), the latter makes the share of health insurance much less relevant in the total amount of insurance expenditures for those countries.
I have added the following (immediately before the conclusion): It is important to remember that RTPLS estimates are total derivatives (not partial derivatives) that show all the ways that the dependent and independent variables are related. Thus if insurance premium increases are correlated with advances in health technology, then the RTPLS estimates presented here capture that correlation. Indeed it is likely that one of the major ways that insurance and life expectancy are correlated is by insurance making it possible for people to receive medical treatments that use advance health technology that without insurance would be prohibitively expensive. If a researcher were to estimate d(life expectancy)/d(insurance) holding medical technology constant, then that researcher might find no relationship between life expectance and insurance when (in truth) insurance is playing a key role by making modern medical technology affordable. Furthermore, holding per capita GDP constant while estimating the effects of insurance on life expectancy is also problematic because higher per capita GDP could be viewed as a substitute for insurance or higher per capita GDP increasing wealth (which can be used to sustain the lives of the elderly) could stimulate more insurance to protect that wealth. The total derivatives found in this paper for d(life expectancy)/d(insurance) capture all the ways that insurance and life expectancy are related. It is impossible to test the robustness of this paper’s results by comparing them to the results of different multivariate analyses that use varying sets of independent variables because RTPLS produces total derivatives while multivariate analysis produces partial derivatives. Apples and oranges are both fruits (RTPLS and multivariate analyses are both statistical methods), but beyond that one similarity, apples and oranges are very different
- In the paper all expenses are expressed in US dollars according to exchange rates, however, given that the cost of living is much different among the considered countries, PPP dollars should be used instead. You can find them here: https://data.oecd.org/conversion/purchasing-power-parities-ppp.htm
By leaving the results in US dollars, the results are better understood and are comparable. If I switched to PPP, then how do I interpret the results – would I estimate how much life expectancy is gained by one eighth of a hamburger’s worth of local currency being put into insurance? That is awkward. Furthermore there are major problems with PPP. For example, there are no comparable baskets of goods that are common to all 43 of the countries I analyze. Furthermore, the amount of each good in the PPP baskets that are purchased in the different countries vary. Third the quality of the goods in the PPP baskets vary between the different countries. Switching to PPP, in my view would make the analysis awkward, less understandable, harder to make comparisons, and less precise. Furthermore, the 10 day limit that the journal gave me prohibits me from collecting more data, redoing all the analysis, reconstructing all the tables and graphs, and rewriting the entire paper.
- I would suggest to robustify your results by also including the estimates produced by a multilevel model, which can reduce the estimation bias for omitted variables that characterize the countries, for example by introducing a fixed- or random-effect for each country.
Please see my response to your points number 1 and 2 above.
I attach the pdf of your paper with all the embedded comments. Please fix all points raised within that document.
For the embedded comments, I list the old line number, followed by the new line number, followed by my response.
Old Line 29 (new line 29) I changed “that” to “who.”
Old line 91 (new line 93) I added “if |Xt| > 1”
Old line 95 (new lines 104-165) “layers” is explained with the example given on lines 104-165.
Old line 143 (new line 199) singular verb changed to plural verb
Old line 144 (new line 200) singular verb changed to plural verb
Old line 145 the JRFM gave me only 10 days to make these revisions – too little time to redo all the analysis using PPP, create new tables and charts, and rewrite the results.
Old line 149 (new line 205) singular verb changed to plural verb
Old line 150 (new line 206) singular verb changed to plural verb
Old line 151 this sentence and Table 1 were deleted
Old line 152 (new line 207) singular verb changed to plural verb
Old line 153 (new line 209) reworded this to eliminate the first person
Old line 154 (new line 210) singular verb changed to plural verb
Old line 155 This sentence was deleted
Old line 158 Your idea is interesting, but it is beyond the scope of this paper
Old line 182 (new line 233) I rewrote this sentence
Old line 195 (new line 246) I added “(but less suspicious when one considers Luxembourg’s unusually high GDP per capita
Old line 225 Turkey has changed the spelling of her name to Turkiye
Old line 226 Consider Figure 1. In this Figure there is not much vertical variation for observations with the lowest values for X (the known independent variable). Since RTPLS uses the relative vertical distance to capture the effects of omitted variables, RTPLS has the most difficulty producing accurate estimates for the observations with the lowest values for X. Turkiye had the lowest values for per capita insurance premiums. In spite of this, the thousands of simulations testing RTPLS (which are summarized in the paper) show that RTPLS noticeably out performs using OLS and assuming that there are no omitted variables except for the case when random error is as important as the omitted variable.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I think the revision addressed most of my concerns. I am still convinced that copy and paste table from Excel (or Lotus or any other software) is not approprate. I can understand that it may take time to edit properly tables, but this is something that must be done.
I do not think that other personal/academic commitments are a valid justification. I had many things to do in the last weeks. Nonetheless, I found time to revise the paper.
Therefore, I suggest the author to find the time to edit tables in a proper manner in the way it is done every time something is published. I have never seen a table without a proper editing in 20+ years of my academic career. So this is the reason: tables must be presented in an accurate way.
