rafmacalaba/datause-encoder-data huggingface dataset:
WPS 3208

# **A Conceptual Framework For Retirement Products: Risk Sharing Arrangements Between Providers And Retirees**

Gregorio Impavido, Craig Thorburn, Mike Wadsworth<sup>†</sup> The World Bank and Watson Wyatt

### Abstract

Voluntary annuity markets are in most countries smaller than what the theoretical and part of the empirical literature would suggest. There are both demand and supply constraints that hamper the development of annuity markets. In particular, traditional products available in most countries can require excessive minimum capital requirements for given investment opportunities available to providers. Investment and longevity risk should be shared between providers and annuitants so that supply constraints can be relaxed. Alternative annuity products, which imply risk sharing, could be backed by substantially lower capital investments or, equivalently, provided at substantially lower prices to consumers.

### World Bank Policy Research Working Paper 3208, February 2004

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._

## **JEL Classification Codes** : G22, G23.

## **Keywords** : Annuities, Retirement benefits, Risk sharing.

> † Gregorio Impavido (gimpavido@worldbank.org) is Senior Financial Economist and Craig W. Thorburn (cthorburn@worldbank.org) is Senior Financial Specialist, both in the Financial Sector Operations and Policy Department of the World Bank.  Mike Wadsworth

> (mike.wadsworth@eu.watsonwyatt.com) is Partner at Watson Wyatt.  The authors are grateful to Mike Orszag and Sara Zervos for useful comments.
# **Table A.6a: Sustainability of Reform: Full Difference-in-Difference Estimates** **<u>(Margins Based on Current World Price of Crude Palm Oil)</u>**

||**Trading M**|**argins**|
|---|---|---|
||Wholesale-World Price|Retail-World Price|
|**Announcement Effects**|||
|Announcement Dummy|-4.958***|-5.792***|
||(-8.813)|(-9.251)|
|**Announcement*Palm (Intercept)**|**24.05**|**27.92**|
||(1.622)|(1.494)|
|**Announcement*Palm*World Price**|||
|**(Slope)**|**-0.210**|**-0.254**|
||(-1.141)|(-1.099)|
|**Effects of Policy Implementation**|||
|**Effects during first 6 months**|||
|Policy Implemt.|-2.825***|-3.992***|
||(-4.060)|(-5.664)|
|**Policy*Palm (Intercept)**|**66.99*****|**70.38*****|
||(8.692)|(12.04)|
|**Policy*Palm*World Price (Slope)**|**-0.813*****|**-0.827*****|
||(-7.677)|(-10.29)|
|**Effects after first 6 months**|||
|Policy Implement.|-4.782***|-5.176***|
||(-3.448)|(-4.438)|
|**Policy Implement.*Palm (Intercept)**|**13.43*****|**30.39*****|
||(3.394)|(7.491)|
|**Policy*Palm*World Price (Slope)**|**-0.125****|**-0.298*****|
||(-2.503)|(-5.931)|
|World Price*palm|0.0787|0.0158|
||(1.077)|(0.216)|
|World Price|-0.461***|-0.406***|
||(-6.198)|(-5.451)|
|Diesel Price|27.38***|0.208***|
||(10.08)|(3.771)|
|Dummy if World Price was rising (DW)|0.0718|0.235|
||(1.197)|(0.177)|
|DW*palm|0.303|-3.536***|
||(0.224)|(-2.968)|
|Palm|-3.649***|29.78***|
||(-2.753)|(12.16)|
|Relative world prices of palm-soy/wheat-rice|-3.140**|-4.068**|
||(-1.977)|(-2.558)|
|Relative world prices of palm/wheat|1.131***|1.010***|
||(3.787)|(3.089)|
|Intercept|<br>12.50***|<br>9.688***|
||(4.113)|(3.350)|
|Observations|1312|1312|
|Controls|||
|Year, Quarter, Product Fixed effects|Yes|Yes|
|Ramadan Dummies|Yes|Yes|
9 data from rural Gansu and Inner Mongolia are used. Both are agriculture based, lagging, inland provinces in western China. Gansu is the poorer of the two. It is mountainous and characterized by growing circular migration. Rural Inner Mongolia is somewhat richer and ethnically more diverse, with livelihoods still firmly anchored in agriculture. The data were collected by the National Bureau of Statistics of the Government of China as part of the monitoring and evaluation system for the World Bank supported Western Poverty Reduction Project.<sup>20</sup> Fifteen project counties were sampled (8 in Inner Mongolia and 7 in Gansu) and within each sample county, 10 villages were sampled in the ratio of 6 project villages to 4 nonproject villages. Within each sample village, 10 households were sampled randomly, yielding a sample of 800 households in Inner Mongolia and 700 in Gansu. Households were surveyed annually between 1999 and 2004. All data on household consumption, income and loans were collected using the daily diary method, with the exception of the baseline year 1999, when annual recall was used. To ensure comparability in the consumption data, the study is confined to the 2000-2004 panel. Data on household characteristics, e.g. demography, education, and assets were collected every year in December using the recall method.<sup>21</sup> As before, income is coded into earned and unearned income. Earned income includes wage income from temporary migration to urban areas, wage income from participating in off-farm wage-earning activities locally, and income from family business. Farming, forestry, fishery, animal husbandry, construction, transportation, restaurant and other services are all considered as family business. Unearned income includes remittances, gifts and other transfers. Most earned income is derived from family businesses (78% in Gansu and 86% in Inner Mongolia) (Tables 3 and 4).

Less than half of the households have wage income. In both provinces, households have on average between 300 and 400 (1999) Yuan unearned income. Yet, these averages hide a wide range of experiences, with about a third of the sample households not receiving any unearned income during the survey period, the majority having less unearned income than earned income and a small group (1%) having more unearned than earned income. Among those whose unearned income is strictly positive, but smaller than their earned income, it amounts on average to between 5% and 7% of earned income. Most households in both regions earn a substantial amount of income in kind (mostly food for auto-consumption),

> 20 The project operated in Inner Mongolia (IM) and Gansu (GS) between 1999 and 2004 and supported households in project villages through the provision of agricultural loans and rural infrastructure. 21 Because households were diligently visited every two weeks to collect the diaries, attrition has been very limited.
following the same households over time. As a result, there is a significant panel dimension to the household sample.<sup>12</sup> The scope of the survey is quite broad. Households are asked a range of questions regarding political status (e.g., household cadre status), education, sources of income, labor supply, land use, asset ownership, occupational choice and other household characteristics. Respondent households keep daily diaries of income earnings and expenditures and a resident survey administer/enumerator living in the county seat visits with households once a month to collect information from the diaries.

The data set used in our analysis comes from part of the complete RCRE survey.<sup>13</sup> It covers ten provinces (Shanxi, Jilin, Jiangsu, Zhejiang, Anhui, Henan, Hunan, Guangdong, Sichuan and Gansu) and spans the period 1986-2003 except 1992 and 1994 as RCRE was unable to conduct the survey in these years because of funding difficulties. As a result, the data set includes 14,417 households and has a total of 123,867 householdyear observations. RCRE‘s sampling is not proportional to provincial rural population. For example, the number of households surveyed in Sichuan is nearly the same as that surveyed in Gansu, despite the fact that Sichuan has a rural population that is nearly five times larger. Thus, in the descriptive statistics presented, we weight by rural population

> 12Despite the significant panel dimension, nearly one third of originally selected households were lost to attrition during the period 1986-1999.  This is mainly due to village attrition that occurred during two two-year gaps when RCRE was unable to conduct the survey in 1992 and 1994 because of funding difficulties.  To supplement the sample, RCRE replaced lost villages by comparable villages in the same counties.  Households lost through attrition were replaced (at least in principle) on the basis of random sampling. For a detailed discussion of the RCRE panel data set, including discussions of survey protocol, sampling, attrition, and comparisons with other data sources from rural China, see Benjamin, Brandt and Giles (2005). Other work exploiting the panel nature of this dataset includes: Benjamin, Brandt and Giles (2011), which examines the relationship between village inequality and income mobility; Giles (2006) and Giles and Yoo (2007), which analyze the risk-management and risk-coping behavior of households; and de Brauw and Giles (2008a, 2008b), which look at the effects of village-level migration on educational investment and household welfare, respectively. 13 The complete RCRE survey covers over 22,000 households in 300 villages in 31 provinces and administrative regions.  We have obtained access to data from 10 provinces, or roughly one third of the RCRE survey.

12
reasonable levels of risk aversion, below the measured risk aversion levels for our sample. This exercise provides a first suggestive source of evidence that non-price factors contribute to low observed rainfall insurance take-up rates.

# _B. Summary statistics_

We study households located in the Mahbubnagar and Anantapur districts of Andhra Pradesh, and the Ahmedabad, Anand, and Patan districts of Gujarat. Below we describe representative summary statistics of these households, based on surveys conducted in 2006. _Sample selection. –_ In Andhra Pradesh, summary statistics are based on a survey of 1,047 landowner households in 37 villages. This survey sample is exactly the same set of households used for our field experiments (details of the experimental design are presented in Section II). These households were originally selected in 2004 based on a stratified random sample from a census of approximately 7,000 landowner households (see Giné et al. 2008 for details).

In Gujarat, our survey data are drawn from 100 villages selected on two criteria: SEWA operated in the village, and the village was within 30 km of a rainfall station.<sup>6</sup> Field experiments in 2007 were conducted in a randomly selected 50 of these 100 villages. Survey data presented below are based on a baseline survey of 1,500 SEWA members in these villages, conducted in May 2006. The survey sample should be viewed as being representative of SEWA members in these 100 villages.<sup>7</sup> However, this sample is only a subset of the households subject to field experiments in 2007, the year of our Gujarat interventions. (Again, see Section II for details).

_Basic demographic characteristics. –_ Table 2 presents summary statistics for both sets of surveyed households. While there are differences in design across the Gujarat and Andhra Pradesh surveys, to the extent possible, we harmonize variable definitions. Full definitions of the construction of each variable are presented in the Data Appendix.

Overall, the state of Gujarat has richer soil and is substantially wealthier than Andhra Pradesh. However, in Gujarat, insurance is sold to poor households (SEWA members), while in

> 6 Subsequently, two of the 100 villages were deemed to be so close that it would not be possible to treat one and not the other, so they were grouped together and assigned the same treatment status.

> 7 For the Gujarat household survey 15 households were selected per village: five randomly selected from the SEWA member list; five randomly selected from the remaining SEWA members with a positive savings account balance; and five households selected (non-randomly) based on suggestions from a local SEWA employee that they would be likely to purchase rainfall insurance. However, the entire sample of 1,500 households has similar summary statistics to the 500 selected randomly from the SEWA list, implying that the overall sample is close to representative of SEWA’s overall membership in these 100 villages.

8
**Table 11.B. Model comparison: Diebold and Mariano (1995) test for aluminum prices**

|||||**Bivariate**|||**Machine**|
|---|---|---|---|---|---|---|---|
|**Approach**|**Horizon**|**Consensus**|**Futures**|**correlations**|**BVAR**|**OEM**|**learning**|
|Consensus<br>|3<br>|...|***||**|||
|Futures|3||...|||||
|Bivariate correlations|3|**|***|...|**|†|†|
|BVAR<br>|3<br>||***<br>||...<br>|||
|OEM|3||***||†|...||
|Machine learning|3|*|***||**|†|...|
|Consensus|6|...|***|||||
|Futures|6||...|||||
|Bivariate correlations|6|**|***|...|†|*|*|
|BVAR|6||†||...|||
|OEM|6|†|***|||...||
|Machine learning|6|*|***||†|*|...|
|Consensus|9|...|***||†|||
|Futures|9||...|||||
|Bivariate correlations|9|||...||||
|BVAR|9||||...|||
|OEM|9|†|***||†|...||
|Machine learning|9|*|***||†||...|
|Consensus|12|...|***||†|||
|Futures|12||...|||||
|Bivariate correlations|12|||...||||
|BVAR|12||†||...|||
|OEM|12|*||*|†|...||
|Machine learning|12|*|***||*|***|...|
|Consensus|15|...|...|...|†|||
|Futures|15|...|...|...|...|...|...|
|Bivariate correlations|15|...|...|...|...|...|...|
|BVAR|15||...|...|...|||
|OEM|15|**|...|...|†|...||
|Machine learning|15|**|...|...|†|†|...|
|Consensus|18|...|...|...|†|||
|Futures|18|...|...|...|...|...|...|
|Bivariate correlations|18|...|...|...|...|...|...|
|BVAR|18||...|...|...|||
|OEM|18|**|...|...|*|...||
|Machine learning|18||...|...|*||...|
|Consensus|21|...|...|...|*|||
|Futures|21|...|...|...|...|...|...|
|Bivariate correlations|21|...|...|...|...|...|...|
|BVAR<br>|21<br>||...|...|...<br>|||
|OEM|21|**|...|...|**|...||
|Machine learning|21||...|...|*||...|
|Consensus|24|...|...|...|*|||
|Futures|24|...|...|...|...|...|...|
|Bivariate correlations|24|...|...|...|...|...|...|
|BVAR|24||...|...|...|||
|OEM|24||...|...||...|*|
|Machine learning|24||...|...|**||...|

_Source_ : World Bank.

_Note_ : Diebold Mariano statistic tests whether the forecasts in the model indicated in the row is more accurate than the forecast of the model indicated in the column. *** indicates statistically significantly more accurate model in the row at the 0.1 percent significance level, ** at the 1 percent level, * at the 5 percent level, and † at the 10 percent level.

53
comparisons because data requirements for the estimation of log TFP result in varying sample attrition across countries, leading to non-representative country samples.

# **3. Estimation Methodology**

To estimate the impact of the business environment on firm performance, the two-year change in log TFP of manufacturing firms is regressed on lagged two-year changes in several aspects of the business environment as measured by a wide array of BEEPS variables.

## **_3.1. Estimation of TFP in the Presence of Simultaneity_**

Total factor productivity is measured as the residual from the estimation of a log-linear three factor Cobb-Douglas production function. For the analysis, the production function of firm _i_ in NACE 2-digit manufacturing industry (15-36) _j_ at time _t_ is assumed to have the following form: where _Y_ is a measure of output, and _L_ , _M_ , and _K_ are the usage of labor, material inputs, and capital with output shares _λ_ , _μ_ , and _κ_ , respectively. Drawing on the AMADEUS database, _Y_ is measured by operating revenues (thousands of 2001 U.S. dollars), _L_ is measured by the number of employees, _M_ is measured by material cost (thousands of 2001 U.S. dollars), and _K_ is measured by the value of tangible fixed assets (thousands of 2001 U.S. dollars). _Aijt_ represents TFP and increases the marginal product of all factors simultaneously. Transforming equation (1) into logarithms allows for linear estimation of TFP with the equation for the general form written as: where industry-specific coefficients— _λj_ , _μj_ , and _κj_ — are given by the estimation of the production function.

A simultaneity problem, however, arises when there is contemporaneous correlation between the factors of production and the errors, often thought as Hicks neutral productivity shocks. The firm, for example, may observe productivity shocks early enough to allow for a change in factor input decisions. In the context of the Cobb-Douglas production function, the error term is therefore assumed to be additively separable in two distinct components: 9
under LDO restrictions in Sri Lanka is of higher productivity compared to other land within the same sub-district (DSD). This unusual positive correlation between land productivity and incidence of land restrictions implies that if we ...nd a negative e¤ect of restrictions on equilibrium wage using simple OLS regression without controls for land productivity (but including human capital controls), it can be taken as particularly strong evidence. Because the OLS estimates are likely to be biased downward towards zero in this nonstandard case. The OLS estimates from this conservative speci...cation show that the coe¢ cient of incidence of land restrictions is, in fact, negative, numerically substantial and statistically signi...cant. This constitutes strong evidence of a negative e¤ect of land market restrictions on equilibrium wage.

To provide estimates of the magnitude of the causal e¤ect of land restrictions, we use an instrumental variables approach. We exploit a historical quasi-experiment in Sri Lanka that allows us to use variations in malaria prevalence across DSDs from 16th to early 20th centuries to identify the e¤ects of land restrictions on wages. For identi...cation of the interaction with distance (travel time) to the urban center, we rely on the insights from the transport engineering literature on the role of topography in road placement and in determining travel time. The instrumental variables estimates show that the e¤ect of LDO restrictions on wages is substantial; a 1 percent increase in the proportion of land under LDO restrictions in a DSD reduces the wage by about 6.6 percent (average of the estimates from di¤erent IV speci...cations in Tables 4 and 5, and evaluated at the median). The e¤ects of land restrictions depend on the location of a DSD, a 1 percent increase in the land under LDO restrictions leads to a reduction in the equilibrium wage by about 8.5 percent when the DSD is located about half an hour from the relevant urban center, but only to about 4 percent reduction when the DSD is about three and a half hours away from the urban center (again, averaging over the di¤erent IV results in Tables 4 and 5). We are not aware of any other paper in the literature that provides evidence on general equilibrium e¤ects of land market restrictions on wages and its spatial distribution.

# References

1. American Association of State Highway and Transportation O¢ cials, 2001, A Policy on Geometric Design Highways and Streets, Washington DC.

28
|**Table 1: Baseline S**|**urvey Summary**<br>Number of|**Statistics**<br>Contro|**by Treatme**<br> <br>l group|**nt Status**<br>Treatme|nt group<br>|P-value of<br>|
|---|---|---|---|---|---|---|
||households|Mean|Standard<br>deviation|Mean|Standard<br>deviation|difference in<br>means|
|_Background characteristics_|(1)|(2)|(3)|(4)|(5)|(6)|
|Household head is male|7112|0.75||0.77||0.126|
|Household head's age|7110|42.68|15.13|41.6|14.48|0.015**|
|No household member completed primary|7373|0.45||0.44||0.575|
|Experienced negative shock in last 6m|7399|0.82||0.82||0.994|
|Has access to a phone|7399|0.41||0.42||0.705|
|_Mobile money usage and remittances_|||||||
|Is aware of mobile money|7399|0.59||0.61||0.51|
|Used mobile money in last 3 months|7399|0.14||0.16||0.143|
|Saved money in last 6 months|||||||
|Any type of savings|7399|0.79||0.8||0.334|
|In mobile money account|7399|0.07||0.08||0.439|
|Received money in the last 6 months|||||||
|Via any channel|7399|0.14||0.15||0.203|
|Via mobile money|7399|0.06||0.07||0.172|
|Transportation costs (Ugandan Shilling)|1075|6782.39|68194.77|7401.81|85264.84|0.844|
|_Occupation_|||||||
|Does non-farm work|7379|0.09||0.11||0.054*|
|Self-employed(non-farm)<br>Note: The sample size varies from question t<br>households who received money via any cha<br>in treatment and control group means, clust|7379<br>o question due<br>nnel in the last<br>ered at the EA c|0.04<br>to nonres<br>6 months.<br>luster leve|ponse. Tran<br>Column 6 s<br>l and condit|0.05<br>sportatio<br>hows the<br>ional on s|n costs are f<br>p-value of t<br>trata dumm|0.108<br>or<br>he difference<br>ies.|

21
**<u>Table 1.</u>** <u>Descriptive statistics of average contributions in the public goods games.</u>

||Average c|ontribution|Proportion f|ree-riders|Average c<br>among c|ontribution<br>ontributors|Propor<br>contr|tion full<br>ibutors|Guessed<br>averaged<br>contribution|
|---|---|---|---|---|---|---|---|---|---|
||Standard|Agreement|Standard|Agreement|Standard|Agreement|Standard|Agreement|Standard|
|Nepal<br>(n=111)|61.7%|61.1%|5.4%|8.1%|65.2%|66.5%|27.0%|27.9%|62.7%|
|Ethiopia<br>(n=123)|43.6%|49.9%|1.6%|1.6%|44.3%|50.8%|7.3%|6.6%|41.5%|

**Figure 1.** Change in contribution levels when the agreement option is introduced.

<!-- Start of picture text -->
-10 -5 0 5 10 -5 0 5 10<br>Change_in_behavior Change_in_behavior<br>.4 .4<br>.3 .3<br>.2 .2<br>Density Density<br>.1 .1<br>0 0<br><!-- End of picture text -->

Nepal Ethiopia Let us now turn to our data from the Ethiopian experiment. Here, the average contributions in both games are lower than in Nepal: 43.6% vs. 61.7% in the standard game and 49.9% vs. 66.1% in the agreement game. Unlike in Nepal, the introduction of the possibility to form an agreement had an overall positive, albeit small, effect on contributions in Ethiopia. The average contributions increased by 14.4% (from 43.6% in the standard game to 49.9% in the agreement game), and by using a Wilcoxon sign-rank test we can reject the hypothesis of no difference (p-value=0.001).

As in Nepal, the proportion of free-riders is very low compared with the usual findings in student experiments: only 1.6% of the sample were free riders in both games. The proportion of full contributors was clearly lower in Ethiopia, with 7.3% of the sample in the 11