rafmacalaba/datause-encoder-data huggingface dataset:
# **2.2. Formulas for the optimal sample size and the optimal allocation of samples across areas**

In his influential book on survey sampling, Cochran (1977) presents two key formulas for designing any stratified simple random sampling. The first formula determines the minimum sample size required to achieve a certain level of statistical reliability regarding the relationship between one statistic and another targeted variable. The second formula, based on Neyman’s (1934) original allocation rule, determines the optimal allocation of the sample across strata.<sup>3</sup> These two key formulas, presented in Cochran’s (1977) book, assume that the sample follows a simple stratified random sampling design.<sup>4</sup> However, most surveys that we are interested in—that is, household income and expenditure surveys and integrated household surveys designed to measure living standards and monitor poverty and welfare patterns—are not a simple stratified random sample, but rather use multi-stage stratified clustered sampling designs.<sup>5</sup> Therefore, the original Cochran (1977) formulas for designing a sample for a living standards household survey is generally not appropriate and would result in an inadequate determination of the sample size and a sub-optimal allocation of the sample across strata. Nevertheless, the formulas are widely used for the selection of the sample size and allocations across strata.

In this paper, we propose a modification to Cochran’s sample size formula to estimate adequate sample sizes for multi-stage stratified clustered surveys. Cochran’s (1977) original formula, building on work by C <mark>ornfield (1951) and Kish (1965), estimates sample size by</mark> calculating the minimum sample size required to achieve a certain level of precision (plus or minus x

> 3 The Neyman’s (1934) original allocation rule minimizes the variance of the sample mean of a targeted variable given a fixed pre-established sample size assuming that the cost of sampling in each stratum is constant.

> 4In sampling, stratification is the process of dividing members of a population into homogeneous subgroups before selecting the sample. This provides two main advantages over simple random sampling (SRS). First, it ensures that different subgroups of the population are properly represented in the sample. Second, it allows to gain statistical precision in the estimation of the variance of the mean of a targeted variable because the variability within the subgroups is lower compared to the variations across the entire population.

> 5 A stratified clustered sampling design consists in selecting the sample using multiple stages. In the first stage, the population is divided into groups (or clusters). In the second stage, one or more clusters are chosen at random and for everyone within the chosen cluster a second sampling unit (or ultimate sampling unit) is selected.

6
- food supplements or an asset replacement were options for the program participants; and

- b. Promote activities encouraging improved behavior across a range of dimensions (health, education, women’s empowerment, financial inclusion, and social cohesion/community support) by providing advice and linking households directly to education, health, and financial institutions where appropriate. This included helping households to apply for national ID (Tazkira) cards if they did not yet have one.

The program applied a sequenced approach. The recipient received support for their livelihood selection, which included an intensive and repeated consultation between MISFA, the partner field staff, and the UP women, so that participants could make an informed choice among different enterprise options. The livestock asset was worth USD 1,136 – 1,488 PPP (USD 309 – 405 nominal) at time of delivery and was replaced if it became sick or died. The consumption stipend aimed to support the household with basic food needs, initially to replace the potential forgone income or productive time that the TUP recipient spent learning about and initiating their business rather than attending to their usual duties. Once the household began work on their enterprise, they received follow-up visits on a biweekly basis from program staff to provide guidance on both business and social issues. After 12 months of continued support, households were assessed on a set of performance indicators and formally “graduated,” after which no further support was provided through the program.

While the program is similar to the standard TUP program model, a few important differences exist (a cross-country comparison of intervention components is reported in Table A2 of the <u>Online Appendix):</u>

1. Coaching support lasts for 12 months instead of 18 – 24 months.

2. A health subsidy is included that does not exist in other programs.

3. The focus of asset provision is on cows rather than smaller livestock assets like goats, pigs and chickens.

4. Asset values transferred are larger than other programs where data exist.

The program variations were decided by MISFA based on earlier pilots conducted in Bamyan Province, where the program attributes were finetuned to address local constraints.

# 4. DESIGN AND METHODS

## **Experimental Design and Sample**

We use a household-level randomized experimental design to estimate the causal effect of the intervention on socioeconomic outcomes of UP households. The evaluation sample comes from 80 villages in four districts of Balkh province (Dehdadi, Dawlatabad, Nahr-e Shahi and Khulm). The participatory wealth ranking was conducted in all study villages of Balkh 12
# **1. Introduction**

Why is our money ever less valuable? Perhaps it is simply that we have inflation because we expect inflation, and we expect inflation because we’ve had it.

—Robert M. Solow<sup>1</sup> Contrary to many emerging market economies, which have experienced noticeable declines in inflation owing to a combination of relatively favorable external factors and implementation of sound domestic policies, Turkey is still attempting to curb chronic high inflation and attain price stability (Table 1). The absence of a permanent fiscal adjustment coupled with unsatisfactory progress with the implementation of key structural reforms lie at the heart of the chronic high inflation in Turkey. The experiences from a variety of approaches to stabilization adopted by emerging market economies (exchange rate-based orthodox programs and heterodox programs) also confirm that inflation does not stay permanently low in the absence of a permanent fiscal adjustment.<sup>2</sup>

**Table 1. Evolution of the Inflation Rate in Selected Emerging Market Economies**<sup>a</sup>

||1981-1990|1991-1995|1996-2000|2000|2001|2002|
|---|---|---|---|---|---|---|
|Turkey|46.3|79.3|74.1|54.9|54.4|45|
|Israel|118.3|12.9|6.4|1.1|1.1|5.7|
|South Africa|14.7|11.3|6.5|4.5|5.7|10|
|Korea|6.4|6.2|4.0|2.3|4.1|2.8|
|Malaysia|3.2|4.3|3.1|1.3|1.4|1.8|
|Thailand|4.4|4.8|4.3|1.5|1.7|0.6|
|Hungary|10.9|25.4|15.1|9.7|9.2|5.3|
|Chile|20.4|13.9|5.2|3.8|3.6|2.5|
|Mexico|69.1|18.0|19.4|9.5|6.4|5.0|

a: Average inflation rates obtained from IMF WEO (2003) and the CBRT.

Evidence suggests that countries that adopted exchange rate based stabilization arrangements appear to have been more successful in bringing inflation down. This monetary regime, however, is prone to balance of payment crises as countries often fail to

> 1 Technology Review (December/January 1979, page.31).

2
# **1. Introduction**

In assessing the extent of poverty in a given country one naturally uses a poverty line that is considered appropriate for that country. However, the purchasing power of national poverty lines varies across countries, with richer countries tending to adopt higher lines. For the purposes of measuring poverty in the world as a whole, the World Bank’s “$1 a day” measures have aimed to apply a common standard, such that any two people with the same purchasing power over commodities are treated the same way—both are either poor or not poor, even if they live in different countries. A deliberately conservative standard has been used by the Bank, anchored to what “poverty” means in the world’s poorest countries. By focusing on how poverty is defined in the poorest countries, the $1 a day line gives the global poverty measure a salience in focusing on the world’s poorest, though it is recognized that higher lines also need to be considered to obtain a complete picture of the distribution of living standards.

Following this approach, Ravallion, Datt and van de Walle (RDV) (1991), in research for the 1990 _World Development Report_ (World Bank, 1990), compiled data on national poverty lines across 33 countries and proposed a poverty line of $1 per day at 1985 Purchasing Power Parity (PPP) as being typical of low-income countries.<sup>2</sup> They estimated that one third of the population of the developing world in 1985 lived below this line.<sup>3</sup> Since then the Bank’s researchers have updated the original RDV estimates of global poverty measures in the light of new and often better data. The estimates done for the 2000/01 _World Development Report_ (World Bank, 2000) used an international poverty line of $1.08 a day, at 1993 PPP, based on the original set of national poverty lines in RDV (Chen and Ravallion, 2001). In 2004, about one in five people in the developing world—slightly less than one billion people—were deemed to be poor by this standard (Chen and Ravallion, 2007).

This paper reports on the most extensive revision yet of these past estimates of poverty measures for the developing world. In the light of a great deal of new data and under various assumptions pertaining to the key methodological choices, we estimate the global poverty count for 2005 and update all our past estimates back to 1981. This puts our knowledge of the extent of poverty in the world on a firmer footing.

> 2 RDV also used a lower line of $0.75 per day, which was the predicted line in the poorest country in their data set, Somalia, though it also happened to coincide with India’s line at the time.

> 3 By the “developing world” we mean all low and middle income countries—essentially the Part 2 member countries of the World Bank (based on Gross National Income per capita in 2005).

2
**Table 2 Average share of the working age population by World Bank region and income** **<u>group classification</u>**

|**Region/Income groups**|**1950**<br>**1960**|**1970 1980 1990 2000 2010 2015**|
|---|---|---|
|EAP|55.8 53.8|52.5 54.7 57.4 59.4 63.1 63.8|
|ECA|61.3 59.3|58.0 61.6 62.9 64.5 68.4 68.3|
|LAC|54.1 51.4|50.5 53.6 56.8 59.7 63.7 65.5|
|MENA|56.0 53.1|51.3 51.3 53.1 58.7 63.7 63.6|
|SAS|55.7 56.1|54.2 54.5 54.4 57.2 61.7 63.6|
|SSA|55.5 54.2|52.7 51.7 51.5 52.8 54.4 55.2|
|Low income|55.6 54.8|53.3 52.5 51.7 52.4 53.8 54.7|
|Lower-middle income|56.2 54.3|52.6 53.4 54.6 56.8 60.5 61.5|
|Upper-middle income|56.6 54.3|53.2 56.0 58.7 62.0 65.9 66.4|
|High income: OECD|64.5 62.6|62.9 64.3 66.4 67.2 67.4 65.9|
|High income: non- OECD|59.7 56.9|57.9 61.7 64.0 66.1 70.1 69.9|
|Total|58.2 56.2|55.5 57.1 58.7 60.6 63.5 63.7|

# _Source:_ United Nations (2015).

_Note:_ HIC refers to high-income countries; EAP refers to low and middle-income East Asia and the Pacific; ECA refers to low and middle-income Europe and Central Asia; LAC refers to low and middle-income Latin America and the Caribbean; MNA refers to low and middle-income Middle East and North Africa; SAR refers to low and middle-income South Asia; and SSA refers to low and middle-income Sub-Saharan Africa.

**Table 3 Average years of schooling by World Bank region and income group classification**

|**Region/Income groups**|**1950**|**1960**|**1970**|**1980**|**1990**|**2000**|**2010**|
|---|---|---|---|---|---|---|---|
|EAP|1.77|2.32|3.03|4.09|5.06|6.16|7.49|
|ECA|3.59|4.33|5.52|7.06|8.49|9.80|10.60|
|LAC|2.66|3.08|3.68|4.66|5.79|6.99|8.08|
|MENA|0.51|0.74|1.28|2.22|3.55|4.98|6.58|
|SAR|1.32|1.52|2.14|2.69|3.53|4.47|5.47|
|SSA|0.96|1.24|1.68|2.36|3.26|4.02|4.99|
|Low income|0.48|0.66|0.96|1.50|2.23|2.92|3.84|
|Lower-middle income|1.66|2.03|2.68|3.56|4.49|5.51|6.44|
|Upper-middle income|2.37|2.87|3.62|4.75|6.11|7.39|8.77|
|High income: OECD|6.11|6.66|7.70|8.81|9.71|10.77|11.71|
|High income: non- OECD|3.05|3.77|4.87|5.94|7.33|8.65|9.80|
|Total|2.88|3.35|4.13|5.11|6.18|7.26|8.34|

_Source:_ Barro and Lee (2013).

_Note:_ HIC refers to high-income countries; EAP refers to low and middle-income East Asia and the Pacific; ECA refers to low and middle-income Europe and Central Asia; LAC refers to low and middle-income Latin America and the Caribbean; MNA refers to low and middle-income Middle East and North Africa; SAR refers to low and middle-income South Asia; and SSA refers to low and middle-income Sub-Saharan Africa.

13
all age groups (World Bank 2005). Data on child poverty are published separately but not data on poverty in old age. Only recently have there been efforts to publish internationally comparable indicators of welfare from an age-specific perspective for rich and poor countries (HelpAge International 2004; Kakwani and Subbarao 2005).

In developed countries, the old age poverty rates are generally not much lower than those for the total population but this is a relatively recent trend. A few decades ago, the average income of the elderly was substantially lower than that of other age groups and their rate of poverty much higher (Förster, Fuchs and Makovec 2003). In developing countries, patterns are different and there is no obvious trend. As far as Latin America is concerned, the poverty headcount for the elderly is clearly lower than for the population average in the cases of Argentina, Brazil, Chile and Uruguay and to a lesser extent in Nicaragua and Panama. It is higher in the other countries as shown in figure 1 below. Argentina, Brazil, Chile and Uruguay—which are among the richest countries in our sample—will often behave differently from the rest.

Poverty in old age can still be observed even in countries—for instance in the OECD—that have generous transfers for the elderly including targeted minimum pensions. This seems puzzling at first sight since the pension is universal and its level is above the poverty line (generally half the median income). There are at least three reasons for this apparent puzzle: family composition (if the other family members do not have any resource. the equivalent income of each member can be below the poverty line); take-up issue (when the pension is means-tested some individuals can be reluctant to claim it) and finally, given that it is subject to a means-test, some elderly people prefer to keep their assets even if these assets do not generate much income (Pestieau 2006).

6
# **3. Patent Data**

Our primary research objective is to estimate how the formation of IPAs affects bilateral flows of patent applications, from origin country to destination country across all potential patent-country pairs. In this context, we distinguish among the effects on within-IPA members, the impacts on patenting from member countries to nations outside IPAs, and the effects on flows from origin countries that do not join specific IPAs to countries within them. Our patent data come from the PATSTAT database organized by the European Patent Office (EPO). The database lists the origin nation, from which the patent is originally filed, and the destination nation, which is the patent authority in which registration is desired, as well as the filing date for each application. Because our interest lies in assessing where patents are filed, we include each destination listed in a patent family as a separate application. Similarly, for patents filed through the Patent Cooperation Treaty (PCT) or the EPO, both of which list countries in which protection may be sought during a grace period, we include only those that reached an ultimate national authority. Many applications list only a filing authority, which indicates that the origin is the same country, implying an application that does not cross an international border. Though our focus lies primarily on measuring international patenting effects, we include domestic applications in our empirical setting in order to account for within-country patenting as a reference category in the gravity-model analysis that follows.<sup>6</sup> Our analysis extends over the period 1995 to 2015, during which multiple IPAs were established. We cut off the end date in order to avoid truncation of patents in recent years, which exists due to lags in application filings. Our data covers patent applications originating from 187 origin countries that are ultimately filed in 82 different destination countries. The fact that there are fewer destination countries than origins in our data is a result of the set of patent offices covered in the PATSTAT data set.<sup>7</sup> Figure 2 depicts changes in average patent shares and volumes in the years before and after the entry into force of three types of IPAs and another simple form of policy protection. Our definition of which trade agreements constitute IPAs is as follows. First, does an agreement include at least three of what we call “core TRIPS-Plus requirements,” which are key elements of

> 6 In the trade-gravity context, the inclusion of intranational trade volumes has been shown to be an important consideration for recovering accurate estimates of trade-policy impacts (Yotov, 2022). For instance, Larch et al. (2018) find that the inclusion of intranational trade volumes in the empirical gravity setting leads to substantially different estimates on the impact of countries’ accession to the Eurozone relative to specifications based solely on international trade flows.

> 7 Details on extracting these data are explained in Appendix B.

9
(ODI) Overseas Development Institute. 2014. “Case Studies to Support _Realising the Resilience Dividend_ , Climate and Environment Programme, ODI, London, UK.

Perera, Alex, De Pino, Samantha Putt, and Oliveira, Barbara. 2013. “Aligning Profit and Environmental Sustainability: Stories from Industry.” World Resources Institute Working Paper. Washington, DC.

Pisano, Mark and Callahan, Richard F. 2012. “Case Study I: Fiscal Sustainability in Los Angeles County.” _National Civic Review_ 101(1): 11–17.

Rose, Adam. 2004a. “Economic Principles, Issues, and Research Priorities in Natural Hazard Loss Estimation.” In _Modeling the Spatial Economic Impacts of Natural Hazards_ , Yasuhide Okuyama and Stephanie Chang, 13–36. Heidelberg: Springer.

Rose, Adam. 2004b. “Defining and Measuring Economic Resilience to Disasters.” _Disaster Prevention and Management_ , 13(4): 307–14.

Rose, Adam. 2009a. _Economic Resilience to Disasters._ CARRI Research Report #8. ORNL.

Rose, Adam. 2009b. Th _e Economics of Climate Change Mitigation Policy: International, National and Regional Perspectives_ . Cheltenham, UK: Edward Elgar.

Rose, Adam. 2014. “Economic Resilience and the Sustainability of Cities in the Face of Climate Change: An Ecological Economics Framework,” In _Handbook of Sustainable Cities,_ edited by Daniel A. Mazmanian and Hilda Blanco _._ Cheltenham, UK: Edward Elgar.

Rose, Adam. 2015. “Macroeconomic Consequences of Terrorist Attacks: Estimation for the Analysis of Policies and Rules." In _Benefit Transfer for the Analysis of DHS Policies and Rules,_ edited by Carol Mansfield and V. Kerry. Cheltenham, UK: Edward Elgar.

Rose, Adam and Krausmann, Elisabeth. 2013. “An Economic Framework for the Development of a Resilience Index for Business Recovery.” _International Journal of Disaster Risk Reduction_ 5(September): 73–83.

Rose, Adam and Kustra, Tyler. 2013. “Economic Considerations in Designing Emergency Management Institutions and Policies for Transboundary Disasters.” _Public Management Review_ (15)3: 446–64.

Rose, Adam and Lim, Dongsoon. 2002 “Business Interruption Losses from Natural Hazards: Conceptual and Methodological Issues in the Case of the Northridge Earthquake.” _Environmental Hazards: Human and Policy Dimensions_ 4(1): 1–14.

Rose, Adam and Wei, Dan. 2013. “Estimating the Economic Consequences of a Port Shutdown: The Special Role of Resilience.” _Economic Systems Research_ 25(2): 212–32.

Rose, Adam, Avetisyan, Misak, and Chatterjee, Samrat. 2014. “A Framework for Analyzing the Economic Tradeoffs between Urban Commerce and Security.” _Risk Analysis_ 14(8): 1554–79.

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# **Table A3.3: Transition matrices including East European countries (14-year transitions)**

||[0-0.15)<br>**_Panel I:_**|[0.15-0.3) <br>**_Total numbe_**|[0.3-0.45) <br>**_r of transit_**|[0.45-0.6)<br>**_ions_**|≥0.6||[0-0.15)<br>**_Panel I_**|[0.15-0.3) <br>**_II: Mean firs_**|[0.3-0.45) <br>**_t passage ti_**|[0.45-0.6)<br>**_me_**|≥0.6|
|---|---|---|---|---|---|---|---|---|---|---|---|
|[0-0.15)|234|12|1|0|0|[0-0.15)|35.6|116.2|53.8|59.3|51.0|
|[0.15-0.3)|20|55|18|2|0|[0.15-0.3)|611.1|49.0|37.7|41.8|33.6|
|[0.3-0.45)|0|5|12|12|4|[0.3-0.45)|1200.7|105.3|95.0|21.8|12.3|
|[0.45-0.6)|0|0|3|8|9|[0.45-0.6)|1369.3|168.7|168.7|28.6|4.7|
|≥0.6|0|0|0|1|53|≥0.6|1423.3|222.7|222.7|54.0|1.1|
||**_Pan_**|**_el II: Transit_**|**_ion matrix_**|||||||||
|p(i,j)|[0-0.15)|[0.15-0.3)|[0.3-0.45)|[0.45-0.6)|≥0.6|**_Ergodic distrib_**|**_ution for t_**|**_ransition m_**|**_atrix_**|||
|[0-0.15)|0.95|0.05|0.00|0.00|0.00||0.03|0.01|0.01|0.04|0.92|
|[0.15-0.3)|0.21|0.58|0.19|0.02|0.00|**_Eigenvalues fo_**|**_r transitio_**|**_n matrix_**||||
|[0.3-0.45)|0.00|0.15|0.36|0.36|0.12||0.11|0.48|0.70|0.98|1.00|
|[0.45-0.6)|0.00|0.00|0.15|0.40|0.45|**_Half-life for tr_**|**_ansition ma_**|**_trix_**||||
|≥0.6|0.00|0.00|0.00|0.02|0.98||29.8|||||
||**_Panel I:_**|**_Total numbe_**|**_r of transit_**|**_ions_**|||**_Panel I_**|**_II: Mean firs_**|**_t passage ti_**|**_me_**||
||[0-1/16)|[1/16-1/8)|[1/8-1/4)|[1/4-1/2)|≥1/2||[0-1/16)|[1/16-1/8)|[1/8-1/4)|[1/4-1/2)|≥1/2|
|[0-1/16)|113|10|0|0|0|[0-1/16)|7.0|43.9|38.1|68.0|91.7|
|[1/16-1/8)|28|50|17|0|0|[1/16-1/8)|74.0|19.6|25.8|55.7|79.4|
|[1/8-1/4)|1|20|58|22|0|[1/8-1/4)|190.3|31.6|30.4|29.8|53.6|
|[1/4-1/2)|0|0|9|41|14|[1/4-1/2)|300.1|109.8|109.8|19.6|23.7|
|≥1/2|0|0|0|1|65|≥1/2|366.1|175.8|175.8|66.0|1.4|
||**_Pan_**|**_el II: Transit_**|**_ion matrix_**|||||||||
|p(i,j)|[0-1/16)|[1/16-1/8)|[1/8-1/4)|[1/4-1/2)|≥1/2|**_Ergodic distrib_**|**_ution for t_**|**_ransition m_**|**_atrix_**|||
|[0-1/16)|0.92|0.08|0.00|0.00|0.00||0.14|0.04|0.03|0.05|0.74|
|[1/16-1/8)|0.29|0.53|0.18|0.00|0.00|**_Eigenvalues fo_**|**_r transitio_**|**_n matrix_**||||
|[1/8-1/4)|0.01|0.20|0.57|0.22|0.00||0.30|0.55|0.81|0.98|1.00|
|[1/4-1/2)|0.00|0.00|0.14|0.64|0.22|**_Half-life for tr_**|**_ansition ma_**|**_trix_**||||
|≥1/2|0.00|0.00|0.00|0.02|0.98||43.8|||||

33
# Contents

|1|Introduction<br>3|
|---|---|
|2|The Model<br>6|
||2.1<br>Firms<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br>7|
||2.2<br>Households<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . .<br>9|
||2.3<br>Commercial Bank . . . . . . . . . . . . . . . . . . . . . . . . .<br>11|
||2.3.1<br>Interest Rate Pricing Rules<br>. . . . . . . . . . . . . . .<br>11|
||2.3.2<br>Capital Requirements . . . . . . . . . . . . . . . . . . .<br>14|
||2.3.3<br>Borrowing from the Central Bank . . . . . . . . . . . .<br>16|
||2.4<br>Central Bank . . . . . . . . . . . . . . . . . . . . . . . . . . .<br>17|
||2.5<br>Market-Clearing Conditions . . . . . . . . . . . . . . . . . . .<br>17|
|3|Non-Binding Capital Requirements<br>18|
||3.1<br>Negative Supply Shock . . . . . . . . . . . . . . . . . . . . . .<br>21|
||3.2<br>Increase in Ofcial Refnance Rate . . . . . . . . . . . . . . . .<br>25|
||3.3<br>Increase in Capital Adequacy Ratio . . . . . . . . . . . . . . .<br>27|
|4|Binding Capital Requirements<br>28|
||4.1<br>Constant Risk Weights . . . . . . . . . . . . . . . . . . . . . .<br>29|
||4.2<br>Endogenous Risk Weights<br>. . . . . . . . . . . . . . . . . . . .<br>32|
|5|Concluding Remarks<br>35|
|Re|ferences<br>39|
|Fi|gures 1 to 12<br>42|
|Ap|pendix<br>43|

2