rafmacalaba/datause-encoder-data huggingface dataset:
The trigonometric approach is illustrated by comparing the estimated seasonal pattern with the estimated dummy variable coefficients for tomato prices in Morogoro, a provincial capital in central southern Tanzania – see Figure 1. Tomatoes, which are season bound and perishable, tend to exhibit acute price seasonality and therefore provide good illustrations of seasonality profiles. This is a case in which seasonality is high and well‐defined so the dummy variables procedure also works well. The estimated seasonal gap is 56% using the trigonometric specification, but 60% on the basis of the dummy variable estimates.

Although, the trigonometric specification is parsimonious, it is restrictive in that the post‐ harvest price decline is symmetric with respect to the pre‐harvest price rise. In practice, for many crops, prices drop more rapidly post‐harvest than that they rise in the remainder of the crop year. An alternative parametric specification is a sawtooth function in which prices fall sharply post‐harvest and then rise at a steady rate through the remainder of the crop year – see Samuelson (1957 and, for an application, Statistics New Zealand (2010). Suppose the peak seasonal factor of λ occurs in month _m_<sup>*</sup> and that the price falls by the seasonal gap of 2λ to –λ  in the harvest month _m_<sup>*</sup> +2. The seasonal factor then rises steadily by an amount over the 5 reminder of the year. Conditional on knowing the peak price month _m_<sup>*</sup> , the amplitude parameter λ may be estimated from the regression

* * * 1 Here  _zm_  _m_  is equal to ‐1 if _m_  _m_  1 or _m_  _m_  2 and 5<sup>otherwise. We estimate by</sup> performing a grid search choosing the value for _m_<sup>*</sup> which gives the maximum _R_<sup>2</sup> fit statistic.<sup>16</sup>

parameters to zero. It follows that the trigonometric equation (12) is nested within the dummy variables equation (6) and can be tested against it using a standard _F_ test.

16 * Strictly, if the peak month _m_ is estimated, equation (14) is not nested within the dummy variables representation (9). If _m_<sup>*</sup> were known, it would be nested and impose 10 restrictions on the dummy variables coefficients in equation (9). In what follows, we perform F tests against the dummy variables specification as if the two equations were estimated but adjust the degrees of freedom associated with the sawtooth representation to obtain correctly sized tests under the null hypothesis of no seasonality. See Meyer and Woodroofe (2000). Monte Carlo experiments led us to associate 4.1 degrees of freedom 15
# **I. Introduction**

In countries where there are few barriers to participation in social insurance erected by a segmented labor market - that is where covered jobs are not rationed and workers have access to formal cover wherever they may be employed - a substantial portion of the population can still fail to contribute. This may be due to poverty throughout their working lives (insufficient discretionary income to contribute), myopia (an irrational disregard for future needs), moral hazard (rational "gaming" of the system), constrained liquidity (limited access to credit that lowers affordable investment in illiquid assets), or a strong preference for alternative forms of income security.

Identifying which factors shape individual and household decisions with respect to the social insurance system is critical in determining whether low rates of participation are a cause for public concern. More importantly, a better understanding of household strategies to mitigate risks to income security can indicate whether further policy interventions beyond existing mandates would increase welfare or do harm. Greater knowledge of how constraints and preferences shape savings and insurance decisions can offer clues as to how formal social insurance systems might be further reformed to better accommodate the people they are designed to protect.

Earlier work on participation in formal social security among the working population in Latin America, has focussed primariiy on whether workers had _access_ to formal cover. While the large sample sizes of the data sets employed revealed broad regional patterns, the limitations of those data sets prevented a more thorough research of household choice. In this paper, new survey data from Chile allows a closer examination of the factors that shape _demand_ for formal cover, and how this is affected by expectations and perceptions of risk, the availability of alternative (market and household-based) resources of income security in old age, and the implicit set of incentives embedded in a particular social insurance regime.

Following this introduction, Section II outlines the structure of the old-age income security system in Chile, detailing the "rules of the game" in force since the country's pension reform in 1981. Readers familiar with the Chilean system are encouraged to skip to the next section. Section III introduces a simple analytical framework borrowed from the economics of insurance literature to guide the empirical investigation in later sections. Section IV presents the specific hypotheses to be tested. Section V describes the new data, focusing on previously unavailable variables - an affiliated workers' _density of contributions_ and subjective life expectancy. These data were collected during the PRIESO survey of households in Greater Metropolitan Santiago in December 1999 and January 2000.1 Section VI (a, b & c) presents and discusses the results of regression analysis using the new data. Section VII concludes.

> ' For more details on the implementation of the survey and structure of the questionnaire, see Appendices One and Two.

2
of these sectors. In the case of minerals, that share is less than one-third. Indeed, while the minerals sector generates the most direct labor value added, due to its dominance in the export basket and relatively high labor intensity, its weak backward links with the domestic economy limit its overall employment impact.

**Figure 6: Direct and indirect labor content of exports across sectors, South Africa 2011**

<!-- Start of picture text --> Minerals nec<br>Metals nec<br>Machinery and Equipment nec<br>Ferrous Metals<br>Transport Equipment<br>Chemical, Rubber, Plastic Products<br>Trade and Transport Services<br>Other Private Services<br>Agr, Forestry, Fisheries<br>Processed Foods<br>PubAdmin/Defence/Health/Educat<br>Energy Extraction<br>Paper Products, Publishing<br>Metal Products<br>Beverages and Tobacco Products<br>Manufactures nec<br>Wood Products<br>Textiles<br>Mineral Products nec<br>Wearing Apparel<br>Electricity, Gas, Water<br>Leather Products<br>Construction<br>Dwellings<br>0 2,000 4,000 6,000<br>US$ mil.<br>Direct LVAX Indirect LVAX<br><!-- End of picture text --> _Source:_ Authors’ elaboration based on LACEX.

Smaller export sectors instead generate labor value added more intensely. Exploring the labor intensity of exports shows that the labor content per $100 of exports also varies across sectors for 2001 and 2011 (Figure 7). For example, wearing apparel has a very high intensity of labor in its exports. Each $100 of gross wearing apparel exports generates $43 of wages, of which $18 go the workers directly producing these goods. At the lower end of the spectrum, $100 of metal exports generate only $21 of labor value added, shared equally between the direct and indirect components. With the exceptions of minerals and beverages and tobacco products, the labor intensity of sectors’ exports has declined, again confirming that the observed decline in the LVAX share is driven by exports becoming less labor intensive.

14
The recovery time estimation requires assessing the state of existing assets, evaluating possible damages, and estimating the construction works capacity and availability of financial and human resources. In addition, damage assessments and other estimations can be used to calculate the workforce needed in the event of a disaster. Furthermore, the gap between the workforce needed to recover functionality and actual available personnel provides essential inputs to estimate the time for recovery. If damage assessments are not available or not possible to estimate, proxies using historical data may provide an estimate of the likely resource demands and time required for recovery. Any of these cases will require empirical data obtained through expert interviews and by examining the input requirements for recovery in similar historical cases.

The time for recovery ( TfR ) associated with the various dimensions of functionality (i.e., lifesaving, relief, and economic) may be different. For lifesaving, functionality is reestablished with a minimal level of restored access (e.g. if one lane of a highway clears for passage of emergency vehicles). However, pre-event traffic demand cannot be restored to a functional level until the disrupted road is open to the public again. The time for recovery in terms of the economic dimension of functionality is often longer than that of lifesaving and relief.

In Japan, for example, a post-tsunami road clearance plan is currently under development that specifies required recovery times. The plan focuses on highways threatened by a potential large-scale tsunami resulting from an expected Nankai Trough Earthquake with 9.0 SI. At Wakayama Prefecture, the plan requires the clearance of at least one lane of the connecting highways leading to the coastal areas from inland highways within 24 hours after a tsunami. Within 48 hours, important places (e.g., city halls) in coastal areas are to be connected with inland highways by clearing at least one lane of coastal highway. All coastal highways required to provide life-saving services, conduct search and rescue activities, and deliver emergency relief must be cleared within 72 hours. To implement this plan, having in place an inland highway and connecting highways to coastal areas is critical. Also, ensuring the provision of key power and economic resources is essential. Pre-event treaties between government and key stakeholders, especially with local contractors, are crucial to guarantee the availability of resources for recovery.

20
- Carlana, M. 2019. "Implicit Stereotypes: Evidence from Teachers' Gender Bias." _Quarterly Journal of Economics_ 134(3): 1163–1224.

- Carlana, M., E. La Ferrara, and P. Pinotti. 2022. “Goals and Gaps: Educational Careers of Immigrant Children.” _Econometrica_ 90(1): 1–29.

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- Favara, M. 2017. “Do Dreams Come True? Aspirations and Educational Attainments of Ethiopian Boys and Girls.” _Journal of African Economies_ 26(5): 561–583.

- Favara, M., G. Chang, and A. Sánchez. 2018. “No longer children: What do Young Lives children do when they grow up? Transitions to post-secondary education and the labour market.” _Research Report_ . Oxford: Young Lives. Available at https://bit.ly/2N45uGv

- Fruttero, A., N. Muller, and O. Calvo-González. 2021. “The Power and Roots of Aspirations: A Survey of the Empirical Evidence.” _World Bank Policy Research Working Paper_ 9729. Washington, DC: World Bank.

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- Gagete-Miranda, J. 2021. “An Aspiring Friend Is a Friend Indeed: School Peers and College Aspirations in Brazil.” _Manuscript_ . Milan: Bocconi University. Available at: <u>https://cutt.ly/YRAB8mu</u>

- García, S., A. Harker, and J. Cuartas. 2019. “Building Dreams: The short-term impacts of a conditional cash transfer program on aspirations for higher education." _International Journal of Educational Development_ 64: 48–57.

- Genicot, G., and D. Ray. 2017. “Aspirations and Inequality.” _Econometrica_ 85(2): 489–519.

- ———. 2020. “Aspirations and Economic Behaviors.” _Annual Review of Economics_ 12: 715–746.

- Glewwe, P. Q. Huang, and A. Park. 2017. “Cognitive skills, noncognitive skills, and school-to-work transitions in rural China.” _Journal of Economic Behavior & Organization_ 134: 141–164.

- Guyon, N., and E. Huillery. 2021. “Biased Aspirations and Social Inequality at School: Evidence from French Teenagers.” _Economic Journal_ 131(634): 745–796.

- Jackson, C. K. 2018. "What Do Test Scores Miss? The Importance of Teacher Effects on Non–Test Score Outcomes." _Journal of Political Economy_ 126(5): 2072-2107.

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28
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# **Appendix 4. A Monte Carlo Assessment of the Effect of Long Run Time Trends in the Nunn and Qian Estimation Strategy**

# _A. A simple model of the confounding effect of trends_

NQ rely on predicting changes in aid through changes in the total quantity of wheat produced in the US. Since they argue that wheat production is mostly a function of climatic changes, then variation in aid conditional on climate is plausibly exogenous. This is an appealing argument if wheat production varies considerably from year to year so that wheat production in adjacent years is unrelated, because it would be hard to explain fluctuations in aid and conflict that vary from year to year in exactly the same way as wheat. As we show below, however, wheat production and conflict in regular aid recipients both show pronounced parallel trend patterns in the time series. Given that the trend in conflict incidence in irregular aid recipients does not parallel the others, these trends can generate spurious correlation that fully explains the NQ results, much like the violation of the parallel trends assumption in DID estimation can lead to spurious results.

We motivate the importance of these patterns by presenting a simple model that highlights how persistent and parallel trends of wheat production and conflict can generate patterns similar to those reported by NQ without any underlying causal effect of aid producing or extending conflict. We then simulate coefficient estimates using the NQ estimation strategy to show via Monte Carlo analysis that even when food aid flows do not cause conflict in the true data generating process (DGP), the NQ estimation strategy yield estimates spuriously suggesting a causal effect in the presence of these heterogeneous trends among potentially endogenous groups.

Suppose that wheat production follows the following pattern: Where f(t) is a function of time and z is a random variable distributed N(0,1) that is independently distributed across years. Define a random variable ft =f(t) for a fixed time period that over the study period where the variance of ft over the studied period, σf, is substantially larger than the variance of zt, σz. In such a framework, observations of wheat 57
PRE WorkinC Paper Series

||BI6|Auihnr||Contact<br>for paper|
|---|---|---|---|---|
|WPS469|Modeling Economic Behavior in<br>Peru's Informal Urban Retail Sector|J. Barry Smith<br>Morton Stelcner|August 1990|M. Abundo<br>36820|
|WPS470|What Do Alternative Measures of<br>Comparative Advantage Reveal<br>About the Composition of Developing<br>Countries' Exports?|Alexander J. Yeats<br>|August 1990|J. Epps<br>33710|
|WPS471|The Determinants<br>of Farm<br>Investment and Residential<br>Construction in Post-Reform China|Gershon Feder<br>Lawrence J. Lau<br>Justin Lin<br>Xiaopeng Luo|August 1990|C. Spooner<br>30464|
|WPS472|Gains in the Education of Peruvian<br>Women, 1940 to 1980|Elizabeth M. King<br>Rosemary Bellew|August 1990|C. Cristobal<br>33640|
|WPS473|Adjustment, Investment, and the<br>Real Exchange Rate in Developing<br>Countries|Riccardo Faini<br>Jaime de Melo|August 1990|R. Sugui<br>37951|
|WPS474|Methods for Measuring the Effect<br>of Adjustment Policies on Income<br>Distribution|Anne Maasland|August 1990|P. Dixon<br>39175|
|WPS475|Does Divestiture Matter? A<br>Framework for Learning from Experie|Ahmed Galal<br>nce|August 1990|G. Orraca-Tetteh<br>37646|
|WPS476|Health Insurance in Sub-Saharan<br>Africa: A Survey and Analysis|Ronald J. Vogel|August 1990|K. Brown<br>35073|
|WPS477|Private Participation in the Delivery<br>of Guinea's Water Supply Services|Thelma A. Triche|August 1990|M. Dhokai<br>33970|
|WPS478|Interrelations Among Child Mortality,<br>Breastfeeding, and Fertility in<br>Egypt, 1975-80|John Marcotte<br>John B. Casterline|August 1990|S. Cochrane<br>33222|
|WPS479|Conversion Factors: A Discussion<br>of Alternate Rates and Correspondin<br>Weights|Michael Hee<br>g|August 1990|E. Zamora<br>33706|
|WPS480|An Evaluation of Neutral Trade Policy<br>Incentives Under Increasing Returns<br>to Scale|Jaime de Melo<br>David Roland-Holst|August 1990|R. Sugui<br>37951|
|WPS481|The Effects of Trade Reforms on<br> <br>Scale and Technical Efficiency:<br> <br>New Evidence from Chile|James Tybout<br>Jaime de Melo<br>Vittorio Corbo|August 1990|R. Sugui<br>37951|
|WPC 482|Membership in the CFA Zone:<br> <br>Odyssean Journey or Trojan Horse?|Shantayanan Devarajan<br>Jaime de Melo|August 1990|R. Sugui<br>37951|
<mark>. : |</mark>

<!-- Start of picture text --> Happiness scores, 2013-2020<br>6.4<br>6.2<br>6<br>5.8<br>5.6<br>5.4<br>5.2<br>o)<br>4.8<br>” wn wo Ss oo ep) oO<br>a a ca a a a N<br>oON fo)N oON oON oON fo)N oON<br><!-- End of picture text -->
ownership, expenditures, labor force participation and social protection dynamics was administered in both years, in addition to a community questionnaire that included information on access to services and infrastructure in the locality, and price information. All variables used in our analysis were constructed from answers to identical questions in ALSMS02 and ALSMS05.

The data used for the panel, individual-level analysis are drawn from the APS. The nationally representative APS is a subsample of the 3,599 households interviewed for ALSMS02. More specifically, as part of the APS, 7,973 members of 1,782 ALSMS02 households were tracked and re-interviewed in 2003 and 2004. New members that joined the original 1,782 ALSMS02 households also participated in the panel survey, as well as the members of new households which were formed by original ALSMS02 individuals. Starting in 2003, only individuals aged 15 years and over were eligible for interview. Sample members that were abroad at the time of a particular wave of the APS were not tracked, but they remained eligible for interview at a future wave if they returned to their households in Albania. As a result, the panel survey collected information on 8,542 individuals living in more than 1,800 households from 2002 to 2004.

For the purposes of panel analysis, our sample is restricted to work-eligible individuals (i) for whom information is available for all three years, (ii) who have not been full-time students at any point between 2002 and 2004, and (iii) who were between the ages 15 and 55 in 2002. As the retirement age in Albania is 57 and 62 for women and men respectively, the age cut-off allows the sample individuals to be of working age throughout the period of analysis. Our results are robust to marginal changes in the ceiling age. Most importantly, heads of household have also been excluded because eligibility to NE is tied to their employment status. Including heads 14
Table 10 Regreasions of S etor Frnctioan of iploy.eat an Ineome: (1) Co- nbution of Initial and Final Year **Cros** Sectien of **Coantries** and (2) Aral Rates of **Change** Withi1n C-trles, by Sez of oer I

|Sector|Sam|ple||Man|||Wo.n||
|---|---|---|---|---|---|---|---|---|
||Siz|e|Intercep|t LogGNPIA|R|Intercept|LogGNPIA|R|
|Agriculture|1<br>2|122<br>61|1.620<br>(54.2)<br>-|-.177<br>(40.3)<br>-. 183<br>|.931<br>.673|1.846<br>(32.2)<br>-|-.207<br>(25.7)<br>.199<br>|.847<br>.673|
|||||(11.1)|||(10.3)||
|Mining|1<br>2|122<br>61|-. 0160<br>(3.96)<br>-|<br>.00413<br>(6.94)<br>-. 00516<br>|.297<br>.055|.00157<br>(1.16)<br>-|.00014<br>(.71)<br>.00115<br>|.005<br>.029|
|||||(1.81)|||(1.26)||
|Manufacturing|1<br>2|122<br>61|-. 224<br>(11.2)<br>-|<br>.0599<br>(20.4)<br>.0191<br>(2.46)|.777<br>.092|.109<br>(3.89)<br>-|.0384<br>(9.78)<br>.00861<br>(.59)|.444<br>.006|
|Utilities|1|122|-. 0181<br>|<br>.00397<br>|.738|-. 0041<br>|.0010<br>|.491|
||2|61|(12.3)<br>-|(18.1)<br>.00104<br>(1.01)|.017|(6.22)<br>-|(10.6)<br>.0001<br>(.12)|.000|
|Construction|1|122|-. 126<br>128|<br>.0282<br>195|.760|-. 0120<br>482|.00293<br>836|.368|
||2|61|(.)<br>-|(.)<br>.9347<br>(5.85)|.363|(.)<br>-|(.)<br>.00946<br>(9.07)|.578|
|Commerce|1|122|-. 0977<br>839|<br>.0302<br>176|.721|-. 195<br>769|.0486<br>136|.608|
||2|61|(.)<br>-|(.)<br>.0319<br>(7.29)|.470|(.)<br>-|(.)<br>.0622<br>(6.48)|.412|
|Transportation|1|122|-. 0534<br>107|<br>.0157<br>214|.793|-. 0448<br>203|.00879<br>284|.871|
||2|61|(.)<br>-|(.)<br>(.0187<br>(8.33)|.536|(.)<br>-|(.)<br>.00735<br>(6.14)|.386|
|Serviees|1|122|-. 0881<br>(561)|<br>.0356<br>(154)|.665|-. 483<br>(120)|.108<br>(190)|.751|
||2|61|.<br>-|.<br>.0827|.495|.<br>-|.<br>.120|.539|
|||||(7.66)|||(8.38)||
|Nonagriculture|1|122|-. 620<br>(20.7)|<br>.177<br>(40.3)|.931|-. 846<br>(14.7)|.207<br>(25.7)|.847|
||2|61|-|.183<br>(11.1)|.673|-|.199<br>(10.3)|.637|
|**Table 8. Co**|OLS<br>**efficients of int**|**erest at the sub-n**<br>Uncondit|**ational level**<br>ional Quantile R|egression|
|---|---|---|---|---|
|||_25th quantile _|_50th quantile _|_75th quantile_|
||_Log Real Val_|_ue of Monthly Per_|_Capita Food_|_Consumption_|
|Lo Price of Wheat Flour|-0.437***|-0.220***|-0.416***|-0.615***|
|g|[0.0401]|[0.0460]|[0.0540]|[0.0608]|
|Log Price of Wheat Flour X|0.0196|-0.0355|-0.0275|-0.0072|
|Agricultural Household|[0.0288]|[0.0349]|[0.0336]|[0.0410]|
|P-value of F-Statistic of Joint<br>|0.00|0.00|0.00|0.00|
|Significance|||||
||_L_|_og Daily Calorie P_|_er Capita Inta_|_ke_|
|L Pi f Wht Fl|-0.138***|-0.0641**|-0.136***|-0.237***|
|og rce o ea our|[0.0263]|[0.0298]|[0.0285]|[0.0356]|
|Log Price of Wheat Flour X|-0.0750***|-0.037|-0.0837***|-0.0700***|
|Agricultural Household|[0.0203]|[0.0231]|[0.0206]|[0.0267]|
|P-value of F-Statistic of Joint<br>Significance|0.00|0.01|0.00|0.00|
|||_Log Food Consu_|_mption Score_||
|L Pi f Wh Fl|-0.229***|-0.317***|-0.201***|-0.156***|
|og rce o eat our|[0.0300]|[0.0551]|[0.0316]|[0.0341]|
|Log Price of Wheat Flour X|0.0665***|0.117***|0.0459**|-0.00321|
|Agricultural Household|[0.0195]|[0.0368]|[0.0215]|[0.0240]|
|P-value of F-Statistic of Joint<br>Significance|0.00|0.00|0.00|0.00|

Note: Each set of coefficients and standard errors are from separate, population weighted regression, with the dependent variable listed above the estimates. Total observations: 20,483. OLS standard errors are corrected for clustering and stratification, UQR standard errors are clustered bootstrap (with replacement) estimates. *, **, and *** denote significance at 10%, 5%, and 1%, respectively.

31