Poverty at Higher Frequency

class: center, middle, inverse, title-slide

.title[
# Poverty at Higher Frequency
]
.author[
### Joshua D. Merfeld <br> <font size = "5"> KDI School and IZA </font>
]
.author[
### Jonathan Morduch <br> <font size = "5"> NYU </font>
]
.date[
### May 2024
]

---

/* .remark-slide table{
      width: 100%;
    } */

/* Change the background color to white for shaded rows (even rows) */

.title-slide h3:nth-of-type(2) {
      color: red;
    }

.remark-slide thead, .remark-slide tr:nth-child(n) {
      background-color: #A7A9AC;
    }

.remark-slide table {
      background-color: #A7A9AC;
    }
    
    tfoot {
      font-size: 80%;
    }

table{
      border-collapse: collapse;
      border-color: transparent;
      background-color: #A7A9AC;
    }

/* .hljs-github {
      background-image: url("logo.png");
      background-position: bottom left;
      background-size: 10%;
    }

.inverse {
      background-image: url("");
      background-position: bottom left;
      background-size: 10%;
    } */

.title-slide {
      background-image: url("logo_title.png");
      background-position: bottom left;
      background-size: 20%;
    }

.gray {
  color: #7F7F7F;
}

.reduceTopMarginText p:first-of-type {
  margin-top: -25px
}

</style>

## Poverty at higher frequency

- How does the way we collect data affect our understanding of poverty?

---

class: top center
background-image: url("exhibits/intro1.png")
background-size: contain
## Two areas focused on material deprivation

---

class: top center
background-image: url("exhibits/intro2.png")
background-size: contain
## Two areas focused on material deprivation

---
## Let me introduce you to Kabani
<br>
- Kabani is a real person living in Bangladesh
<br><br>
- She is part of the [**Hrishipara diarists**](https://sites.google.com/site/hrishiparadailydiaries/home) project
<br><br>
- Kabani:
  - In her early fifties, illiterate, recently widowed, and supporting a son (age 9) and daughter (age 12)
  - Home is a tin-walled, tin-roofed room about 10 feet by 10 feet
  - Small plot
  - Main income: work in the market (sorting vegetables for merchants) and help from family

---
## Let me introduce you to Kabani

---
## Kabani's mean annual income

---
## Kabani's mean annual income

---
## But what does Kabani's actual income look like?

---
## She is going _in and out of poverty_ from month to month!

---
## The annual persepective hides volatility and deprivation

---
## The conventional view of poverty is static
<br>
Treats people always poor same as people sometimes poor
<br><br>
Not distributionally sensitive: 
- Counts people who are steadily moderately poor same as people who are sometimes deeply poor
- **We miss the volatility and deprivation that Kabani faces**

---
## Today
<br>
The conventional concept of poverty
<br><br>
Conventional poverty through a high-frequency lens
<br><br>
A higher-frequency concept of poverty
<br><br>
Empirical/philosophical implications

---
## Today
<br>
The conventional concept of poverty
<br><br>
.gray[Conventional poverty through a high-frequency lens]
<br><br>
.gray[A higher-frequency concept of poverty]
<br><br>
.gray[Empirical/philosophical implications]

---
## The beginnings of poverty measurement
.pull-left[
]
.pull-right[
  .center[<img src="exhibits/booth.jpg" style="width: 70%"/>]
]

---
## The beginnings of poverty measurement
.pull-left[
  Charles Booth
  <br><br>
  _Life and Labour of the People in London_ (1892-1903)
  <br><br>
  Beatrice Webb (née Potter) was a research assistant!
  <br><br>
  .center[<img src="exhibits/booth2.png" style="width: 70%"/>]
]
.pull-right[
  .center[<img src="exhibits/booth.jpg" style="width: 70%"/>]
]

---
## The beginnings of poverty measurement
.pull-left[
  <img src="exhibits/booth3.jpg" style="width: 100%"/>
]
.pull-right[
  <br><br><br>
  <img src="exhibits/booth4.png" style="width: 100%"/>
]

---
**And it has only gotten more sophisticated...**

.center[<img src="exhibits/poverymeasurement1.png" style="width: 92.5%"/>]

---
## Household consumption basis

- **Question**: Of 137 countries in Mancini and Vechhi (2022), how many measure poverty with consumption data instead of income data?

<br>

- **Answer**: 
  - 100% of low-income countries 
  - 90% of lower-middle income countries
  - 62% of upper-middle income countries
  - 9% of high-income countries

---
## Conventional annual poverty measure

We often think of poverty as the share of households in poverty during the year

- Example: World Bank LSMS data provides "annual consumption aggregates" for each household
<br><br>
`$$\frac{1}{N} \sum_{i=1}^{N} P(\bar{c}_i)$$`
`$$\bar{c}_i = \frac{1}{12} \sum_{m=1}^{12} c_{i,m}$$`
<br><br>
- `$P(\cdot)$` is some poverty measure, e.g. headcount, poverty gap, etc.

---
## Conventional concept of poverty

<ul>
<li>Focuses attention on overall lack of earnings across the year</li>
<br>
<li>A social science concept but still permits talking about “the poor” as a group</li>
<br>
<li>Poverty reduced only via impact on average income/consumption:</li>
    <ul>
    <li>Economic growth</li>
    <li>Better jobs</li>
    <li>Increased earning power (e.g. through health, education)</li>
</li>
</ul>

---
## Consumption by month (daily p.c.) 
**Hypothetical household data. Poverty line = 2.15/person/day**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 4 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 7 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 11 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
## Consumption by month (daily p.c.) 
**Hypothetical household data. Poverty line = 2.15/person/day. Annual poverty rate: 25%**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 4 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 7 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 11 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
## Conventional concept of poverty
<font color='#7F7F7F'>

- **Time insensitive within the year**: What matters is total resources, not their timing
  - "Poverty" includes people who are not always poor
  - Excludes people who are sometimes poor
  - Implicitly assumes perfect offset of low and high periods

---
## Consumption by month (daily p.c.) 
**Half of all months are poor! Monthly poverty rate: 50%**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 4 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 7 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 11 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
## Our main arguments:

1. Poverty as actually measured approximates the higher-frequency, monthly concept of poverty
--
<br>

2. Occurs without within-year panel data and without any shift in mathematical formulations of poverty
--
<br>

3. We in general *cannot* calculate the annual poverty rate
--
<br>

4. What is the *de facto* measure? The share of the year that people are poor
  - We call this the "average of poverties"
--
<br>

5. This measure more sensitive to severity of deprivation
  - Especially true when using distributionally sensitive poverty measures (e.g. squared poverty gap)
--
<br>

6. Thinking in these terms reshapes understandings of households and policies

---
## Today
<br>
.gray[The conventional concept of poverty]
<br><br>
Conventional poverty through a high-frequency lens
<br><br>
.gray[A higher-frequency concept of poverty]
<br><br>
.gray[Empirical/philosophical implications]

---
## Data collection dilemma

<br>

- We want data that covers the household's full year
- But recall ability for many items falls off quickly
  - e.g. "How much maize did you consumer over the last 365 days?"

<br>

Tradeoff:

- **Accuracy**: Ask with weekly or monthly recall, especially for food consumption
  - Food is a large proportion of expenditures for many poor households
- **Cost**: Visit households once during the year and extrapolate to form annual measures

---
## Some dirty details: How do NSOs collect data?

<br>
Detailed data from 96 countries from Smith, Durpiez, and Troubat (2014)
<br><br>

- 12% collect data with multiple rounds at different points during the year

- 42% collect data once from each household, but throughout the year

- 47% collect data once from each household, but not throughout the year

---
## World Bank/FAO/UNSD expert guidelines

<br>
Created by the Inter-Agency and Expert Group on Food Security, Agricultural and Rural Statistics, convened by the World Bank and UN Food and Agriculture Organization, and endorsed by the forty-ninth session of the United Nations Statistical Commission in 2018.
<br><br>

- Ask survey questions (esp. for food) with short-term recall (e.g. week or month) on expenditures/consumption
  - Larger purchases (durables, etc.) can be asked with longer recall, up to 365 days

- Stratify on sub-periods (e.g. quarters)

- Survey households once during the year

---
## Pessimism around "usual month" approach

<br>

- Previous thought: ask consumption about a "usual month" (Deaton and Grosh, 2000; Deaton and Zaidi, 2002)
  - Around 10% of surveys from Smith et al. (2014) used this approach

- Beegle et al. (2012) found that this approach is not reliable
  - People often underestimate, especially food
  - What is a "usual month" in an unstable context?

- World Bank and FAO (2019): Don't do this!
  - Out argument: the usual month approach is a *different theoretical measure*!
  - We are not talking about measurement error/misreporting

---
## Consumption by month (daily p.c.) 
**Imperfect consumption smoothing**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 4 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 7 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 11 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 3 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;background-color: #44815a !important;"> 4 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
## Consumption by month (daily p.c.) 
**With perfect consumption smoothing, timing doesn't matter**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 4 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 7 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 11 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
## Data collection dilemma

<br>

- We want data that covers the household's full year
- But recall ability for many items falls off quickly
  - e.g. "How much maize did you consumer over the last 365 days?"

<br>

Trade-off:

<br>

**Assuming perfect consumption smoothing resolves the dilemma, but...**

---
## Global: Seasonality and episodic poverty

<br>

Seasonal poverty is a well-established issue (Longhurst et al. 1986, Devereux et al 2012, Khandker 2012)

<br>

Recent RCTs revisit seasonality and illiquidity:

- Fink, G., B. K. Jack, and F. Masiye (2020): “Seasonal Liquidity, Rural Labor Markets, and Agricultural Production,” American Economic Review, 110, 3351–92.
- Breza, E., S. Kaur, and Y. Shamdasani (2021): “Labor Rationing,” American Economic Review, 111, 3184–3224. 
- Bryan, G., S. Chowdhury, and A. M. Mobarak (2014): “Underinvestment in a Profitable Technology: The Case of Seasonal Migration in Bangladesh,” Econometrica, 82, 1671– 1758.
- Casaburi, L. and J. Willis (2018): “Time versus State in Insurance: Experimental Evidence from Contract Farming in Kenya,” American Economic Review, 108, 3778–3813.

---
## Kabani's income by month

---
## Consumption by month (daily p.c.) 
**Imperfect consumption smoothing**
<img src="index_files/figure-html/hypo7-1.png" width="100%" />

---
## Consumption by month (daily p.c.) 
**Imperfect consumption smoothing, random month per household**
<img src="index_files/figure-html/hypo8-1.png" width="100%" />

---
## Consumption by month (daily p.c.) 
**Imperfect consumption smoothing, random month per household**
<img src="index_files/figure-html/hypo9-1.png" width="100%" />

---
## Consumption by month (daily p.c.) 
**Imperfect consumption smoothing, random month per household**
<img src="index_files/figure-html/hypo10-1.png" width="100%" />

---
## Consumption by month (daily p.c.) 
**Imperfect consumption smoothing, random month per household**
<img src="index_files/figure-html/hypo11-1.png" width="100%" />

---
## We can recover mean annual consumption

.pull-left[
  `$$c_i^q = \sum_{t=1}^4c_{it}\cdot I_{it}$$`
  `$$E[c_i^q] =\sum_{t=1}^4\frac{1}{4}c_{it} = \frac{1}{4}\sum_{t=1}^4c_{it} = \bar{c}_i$$`
  `$$E[c^q]=\frac{1}{N}\sum_{i=1}^NE[c_i^q] = \frac{1}{N}\sum_{i=1}^N\bar{c}_i = \bar{c}$$`
]
.pull-right[
- Consumption in randomly chosen period, household
<br><br>

- In expectation: average consumption for household
<br><br>

- Aggregate across households: in expectation, average consumption for population
]

---
## But we cannot recover conventional poverty
.pull-left[
  `$$P^q = \frac{1}{N}\sum_{i=1}^NP(c_i^q)$$`
  `$$P(c_i^q)=\sum_{t=1}^4P(c_{it})\cdot I_{it}$$`
  `$$E[P(c_i^q)]=\sum_{t=1}^4\frac{1}{4}P(c_{it})=\frac{1}{4}\sum_{t=1}^4P(c_{it})$$`
  `$$E[P^q]=\frac{1}{N}\sum_{i=1}^NE[P(c_i^q)]=\frac{1}{N}\sum_{i=1}^N \left( \frac{1}{4} \sum_{t=1}^4 P(c_{it}) \right)$$`
]
.pull-right[
- National poverty aggregates from random households, period
<br><br>

- Poverty in randomly chosen period, household
<br><br><br>

- In expectation: average of poverties for household
<br><br>

- Aggregate across households: average of poverties for population.
]

---
## Average of poverties
**Share of household-months in poverty (Average of Poverties)**

<br>

`$$\frac{1}{N}\sum_{i=1}^N\frac{1}{12} \left(P(c_{i,Jan}) + P(c_{i,Feb}) + \cdots + P(c_{i,Dec})\right)$$`

`$$\frac{1}{12N}\sum_{i=1}^N\sum_{m=1}^{12}P(c_{im})$$`

---
## Average of poverties
**Equals poverty of the average only if perfect consumption smoothing...**

<br>

`$$\frac{1}{N}\sum_{i=1}^N\frac{1}{12} \left(P(c_{i,Jan}) + P(c_{i,Feb}) + \cdots + P(c_{i,Dec})\right)$$`
`$$\frac{1}{N}\sum_{i=1}^N\frac{1}{12} \left(P(\bar{c}_{i}) + P(\bar{c}_{i}) + \cdots + P(\bar{c}_{i})\right)$$`
`$$\frac{1}{12N}\sum_{i=1}^N\sum_{m=1}^{12}P(\bar{c}_i)=\frac{1}{N}\sum_{i=1}^NP(\bar{c}_i)$$`

---
## Average of poverties
**Calculated with monthly data: 50%**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 4 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 7 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 11 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: #8aaf95 !important;"> 2 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: #b8cfbe !important;"> 1 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 3 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;background-color: transparent !important;"> 4 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
## Poverty of averages
**Calculated with annual data: 25%**
<table class=" lightable-classic-2" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Jan </th>
   <th style="text-align:center;"> Feb </th>
   <th style="text-align:center;"> Mar </th>
   <th style="text-align:center;"> Apr </th>
   <th style="text-align:center;"> May </th>
   <th style="text-align:center;"> Jun </th>
   <th style="text-align:center;"> Jul </th>
   <th style="text-align:center;"> Aug </th>
   <th style="text-align:center;"> Sep </th>
   <th style="text-align:center;"> Oct </th>
   <th style="text-align:center;"> Nov </th>
   <th style="text-align:center;"> Dec </th>
   <th style="text-align:center;"> Avg </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Household 1 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 2 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 4 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.42 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 5 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.50 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 6 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.58 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 7 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 8 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 9 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 10 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 2.25 </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: #e7efe9 !important;"> Household 11 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 2 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 3 </td>
   <td style="text-align:center;background-color: #e7efe9 !important;"> 1.75 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Household 12 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 2.33 </td>
  </tr>
</tbody>
</table>

---
background-image: url("exhibits/redx.png")
background-size: contain
## Conventional concept of poverty

<br>

- **Time insensitive**: What matters is total resources, not their timing
  - "Poverty" includes people who are not always poor
  - Excludes people who are sometimes poor
  - Implicitly assumes perfect offset of low and high periods

---
**We are misunderstanding what we are measuring!**

.center[<img src="exhibits/poverymeasurement1.png" style="width: 92.5%"/>]

---
## Usual month

- This argument is underlined by the discussion around "usual month" questions
--
<br>

- Discussion was around comparing "usual months" to shorter recalls
  - e.g. measurement error
  - Nobody pointed out that they are *theoretically distinct quantities* unless consumption is perfectly smoothed
--
<br>

- Important: doesn't matter for linear transformations (e.g. the mean)
  - But poverty measures are generally non-linear

---
## Average of poverties

- Not a noisy version of conventional measure

- Created inadvertently, without recognition

- No change in the form of the measure

- Yields within-year welfare variability without longitudinal data

- Time-sensitive

- Interventions can thus reduce measured poverty in ways that we’re not usually considering. 
  - Within-year consumption smoothing can reduce measured poverty even when average consumption is unchanged.

---
## Time sensitivity

- **Time-sensitivity**: Holding all else constant, a pure transfer of income from a household in a period where they are above the poverty line to any period where they are poorer must decrease the poverty measure.

- Note that this is not the case with "conventional" poverty
  - Headcount generally not time sensitive, but can partly be with the average of poverties interpretation!
  - Never is with the conventional interpretation

---
## Today
<br>
.gray[The conventional concept of poverty]
<br><br>
.gray[Conventional poverty through a high-frequency lens]
<br><br>
A higher-frequency concept of poverty
<br><br>
.gray[Empirical/philosophical implications]

---
## Data

**ICRISAT VDSA** data from rural India (Village Dynamics in South Asia)

Five years of monthly income/expenditure data:

- 1,526 households over 60 months, July 2010 to June 2015
- Sample here: 30 villages across 15 districts in nine states
- Keep all hhs observed for at least 4 years. 945 households.
- Monthly price deflation
- Adjustment for durables
- Robustness w.r.t. growth
- India rural poverty line, close to World Bank extreme line

---
## VDSA villages

.center[<img src="exhibits/icrisat1.png" style="width: 90%"/>]

---
## Summary statistics (unweighted)

<div style='border: 1px solid #ddd; padding: 0px; overflow-y: scroll; height:500px; overflow-x: scroll; width:100%;  font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;' class=" lightable-classic lightable-hover"><table>
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;position: sticky; top:0; background-color: #FFFFFF;position: sticky; top:0; background-color: #FFFFFF;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; position: sticky; top:0; background-color: #FFFFFF;position: sticky; top:0; background-color: #FFFFFF;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Four full years</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; position: sticky; top:0; background-color: #FFFFFF;position: sticky; top:0; background-color: #FFFFFF;" colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Five full years</div></th>
</tr>
  <tr>
   <th style="text-align:left;font-weight: bold;position: sticky; top:0; background-color: #FFFFFF;position: sticky; top:0; background-color: #FFFFFF;">   </th>
   <th style="text-align:center;font-weight: bold;position: sticky; top:0; background-color: #FFFFFF;position: sticky; top:0; background-color: #FFFFFF;"> Mean (Median) </th>
   <th style="text-align:center;font-weight: bold;position: sticky; top:0; background-color: #FFFFFF;position: sticky; top:0; background-color: #FFFFFF;"> Mean (Median) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;width: 10cm; "> Prime-aged female </td>
   <td style="text-align:center;width: 6cm; "> 1.34 </td>
   <td style="text-align:center;width: 6cm; "> 1.62 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (1) </td>
   <td style="text-align:center;width: 6cm; "> (1) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Prime-aged male </td>
   <td style="text-align:center;width: 6cm; "> 1.43 </td>
   <td style="text-align:center;width: 6cm; "> 1.78 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (1) </td>
   <td style="text-align:center;width: 6cm; "> (2) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Elderly female </td>
   <td style="text-align:center;width: 6cm; "> 0.23 </td>
   <td style="text-align:center;width: 6cm; "> 0.26 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Elderly male </td>
   <td style="text-align:center;width: 6cm; "> 0.21 </td>
   <td style="text-align:center;width: 6cm; "> 0.32 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Girls </td>
   <td style="text-align:center;width: 6cm; "> 0.42 </td>
   <td style="text-align:center;width: 6cm; "> 0.63 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Boys </td>
   <td style="text-align:center;width: 6cm; "> 0.5 </td>
   <td style="text-align:center;width: 6cm; "> 0.71 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Male head </td>
   <td style="text-align:center;width: 6cm; "> 0.83 </td>
   <td style="text-align:center;width: 6cm; "> 0.93 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (1) </td>
   <td style="text-align:center;width: 6cm; "> (1) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Head educ. </td>
   <td style="text-align:center;width: 6cm; "> 2.97 </td>
   <td style="text-align:center;width: 6cm; "> 5.31 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (0) </td>
   <td style="text-align:center;width: 6cm; "> (5) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Income p.c. (Rs) </td>
   <td style="text-align:center;width: 6cm; "> 1,814 </td>
   <td style="text-align:center;width: 6cm; "> 1,523 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (1,293) </td>
   <td style="text-align:center;width: 6cm; "> (1,020) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Expenditures p.c. (Rs) </td>
   <td style="text-align:center;width: 6cm; "> 1,497 </td>
   <td style="text-align:center;width: 6cm; "> 1,230 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (1,121) </td>
   <td style="text-align:center;width: 6cm; "> (952) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Wealth p.c. (Rs) </td>
   <td style="text-align:center;width: 6cm; "> 133,387 </td>
   <td style="text-align:center;width: 6cm; "> 129,151 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; ">  </td>
   <td style="text-align:center;width: 6cm; "> (117,928) </td>
   <td style="text-align:center;width: 6cm; "> (81,477) </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;width: 10cm; "> Households </td>
   <td style="text-align:center;font-weight: bold;width: 6cm; "> 116 </td>
   <td style="text-align:center;font-weight: bold;width: 6cm; "> 829 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;width: 10cm; "> Month observations </td>
   <td style="text-align:center;font-weight: bold;width: 6cm; "> 5,568 </td>
   <td style="text-align:center;font-weight: bold;width: 6cm; "> 49,740 </td>
  </tr>
</tbody>
</table></div>

---
## Expenditures on durables

<br>
<table class=" lightable-classic lightable-hover" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:left;font-weight: bold;position: sticky; top:0; background-color: #FFFFFF;">  </th>
   <th style="text-align:center;font-weight: bold;position: sticky; top:0; background-color: #FFFFFF;"> Durables </th>
   <th style="text-align:center;font-weight: bold;position: sticky; top:0; background-color: #FFFFFF;"> Semi-durables </th>
  </tr>
 </thead>
<tbody>
  <tr grouplength="4"><td colspan="3" style="text-align: center; color: #000000;"><strong>Median</strong></td></tr>
<tr>
   <td style="text-align:left;width: 10cm; "> Top expenditure quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 1.0% </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Third quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 1.2% </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Second quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 1.2% </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Bottom expenditure quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
  </tr>
  <tr grouplength="4"><td colspan="3" style="text-align: center; color: #000000;"><strong>90th percentile</strong></td></tr>
<tr>
   <td style="text-align:left;width: 10cm; "> Top expenditure quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 14.0% </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Third quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 13.8% </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Second quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 12.7% </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 10cm; "> Bottom expenditure quartile </td>
   <td style="text-align:center;width: 6cm; "> 0% </td>
   <td style="text-align:center;width: 6cm; "> 9.6% </td>
  </tr>
</tbody>
</table>

---
## Consumption smoothing

---
## Consumption smoothing

---
## Consumption smoothing

---
## Always, never, sometimes poor

---
## Always, never, sometimes poor

---
## Lots of poverty above the "poverty line" (expenditures)

.pull-left[

.center[<img src="exhibits/icrisat8.png" style="width: 100%"/>]
]
.pull-right[

<br>
- At the poverty line, household spend around 60% of the time in poverty

<br>
- At 1.5 times the poverty line, still spend 10% of the time in poverty

<br>
- Only 45% are never poor by expenditures (much lower by net income)

]

---
## What does it mean to "exit" or "enter" poverty?

---
## Increases in measured poverty
**VDSA South India, By year, 2010-15, population weights**

<br>

<table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
<caption>Distributionally-sensitive poverty measures</caption>
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Annual </th>
   <th style="text-align:center;"> Monthly </th>
   <th style="text-align:center;"> Difference (%) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;width: 6cm; "> Watts </td>
   <td style="text-align:center;width: 4cm; "> 0.09 </td>
   <td style="text-align:center;width: 4cm; "> 0.13 </td>
   <td style="text-align:center;width: 4cm; font-weight: bold;color: #006334 !important;"> 42 </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> FGT(2) </td>
   <td style="text-align:center;width: 4cm; "> 0.025 </td>
   <td style="text-align:center;width: 4cm; "> 0.037 </td>
   <td style="text-align:center;width: 4cm; font-weight: bold;color: #006334 !important;"> 48 </td>
  </tr>
</tbody>
</table>

---
## Poverty in the ICRISAT VDSA

---
## Poverty in the ICRISAT VDSA

---
## Driven by the non-linearity of poverty measures

.pull-left[
<img src="index_files/figure-html/icrisat14-1.png" width="100%" />
]

.pull-right[
<img src="index_files/figure-html/icrisat14b-1.png" width="100%" />
]

---
## Driven by the non-linearity of poverty measures

.pull-left[
<img src="index_files/figure-html/icrisat15-1.gif" width="100%" />
]

.pull-right[
<img src="index_files/figure-html/icrisat15b-1.gif" width="100%" />
]

---
## Driven by the non-linearity of poverty measures

.pull-left[
<img src="index_files/figure-html/icrisat16-1.png" width="100%" />
]

.pull-right[

- Mean annual poverty: 29.2%
<br><br>

- Mean monthly poverty: 36.8%
<br><br>

- Differences: +7.6 p.p. (+26%)
]

---
## Distributionally-sensitive poverty measures

<br>

- **Transfer axiom**: A pure transfer of income from a person below the poverty line to anyone who is richer must increase the poverty measure.
  - Headcount does not satisfy this axiom
  - Transfer from one poor person to another who changes poverty if someone crosses the poverty line

<br>

- **Watts index**: The sum of the squared differences between the poverty line and the income of each person, divided by the number of people
  - 44% increase in poverty

---
## Kabani's deprivation increases these measures!

---
## Other examples from other countries

- Dean Jolliffe and Umar Serajuddin. 2018. “Noncomparable Poverty Comparisons.” Journal of Development Studies 54:3: 523-536
  - Increases of 20% in headcount in Jordan
  - Increases of 60%+ in FGT (squared poverty gap)

- John Gibson and Omoniyi Alimi. 2020. “Measuring poverty with noisy and corrected estimates of annual consumption: Evidence from Nigeria.” African Development Review 32: 96-107.
  - Increases of 100-200%!
  - FGT increases 14-fold!
  - Our argument: _this is not about a "noisy" measure_. It's about the non-linearities in poverty measures.

- Lewis Warren and Alexander Tettenhorst, Poverty Dynamics: 2017–2019. US Census Bureau. Current Population Reports, P70BR-179. September 2022.
  - In US, only 3% always poor
  - 27% are sometimes poor

---
## Using lasso to predict anthropometrics

<table class=" lightable-classic lightable-hover table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto; font-size: 12px; margin-left: auto; margin-right: auto;'>
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Weight</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Height</div></th>
</tr>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> All </th>
   <th style="text-align:center;"> lasso </th>
   <th style="text-align:center;"> All </th>
   <th style="text-align:center;"> lasso </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #006334 !important;width: 6cm; "> Monthy povery </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.118*** </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.074*** </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.410** </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #006334 !important;width: 6cm; ">  </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.027) </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.013) </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.197) </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #006334 !important;width: 6cm; "> Lagged monthly poverty </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.129*** </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.103*** </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.557*** </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> -0.518*** </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #006334 !important;width: 6cm; ">  </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.026) </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.013) </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.182) </td>
   <td style="text-align:center;color: white !important;background-color: #006334 !important;width: 4cm; "> (0.092) </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> Random monthly poverty </td>
   <td style="text-align:center;width: 4cm; "> 0.007 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> -0.027 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.012) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.080) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> Lagged random monthly poverty </td>
   <td style="text-align:center;width: 4cm; "> -0.007 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> -0.027 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.012) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.079) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> Annual poverty </td>
   <td style="text-align:center;width: 4cm; "> 0.019 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> 0.082 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.014) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.096) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> Lagged annual poverty </td>
   <td style="text-align:center;width: 4cm; "> -0.010 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> -0.051 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.015) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.103) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> Mean spell length </td>
   <td style="text-align:center;width: 4cm; "> 0.004 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> 0.036 </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.004) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.031) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; "> Lagged mean spell length </td>
   <td style="text-align:center;width: 4cm; "> 0.010** </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> 0.086*** </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;width: 6cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.004) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
   <td style="text-align:center;width: 4cm; "> (0.031) </td>
   <td style="text-align:center;width: 4cm; ">  </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;width: 6cm; "> Observations </td>
   <td style="text-align:center;font-weight: bold;width: 4cm; "> 13,554 </td>
   <td style="text-align:center;font-weight: bold;width: 4cm; "> 13,554 </td>
   <td style="text-align:center;font-weight: bold;width: 4cm; "> 3,231 </td>
   <td style="text-align:center;font-weight: bold;width: 4cm; "> 3,231 </td>
  </tr>
</tbody>
</table>

---
## Today
<br>
.gray[The conventional concept of poverty]
<br><br>
.gray[Conventional poverty through a high-frequency lens]
<br><br>
.gray[A higher-frequency concept of poverty]
<br><br>
Empirical/philosophical implications

---
## Arguments
<br>
- The experience of poverty changes through the year. Conditions rise and fall, people exit and enter. **Instability is a stable feature of low-income economies.**

- This affects how we should think about poverty, and it undermines assumptions used in measuring poverty. **Poverty and consumption smoothing are closely linked.**

- A simple extension of annual poverty measures reveals this variation by counting poverty in terms of household-months.

- **The measure is more sensitive to the severity of deprivation and better captures the realities of poverty.** E.g., in data from S. India, the measure predicts health outcomes far better than conventional annual measures.

---
## Arguments
<br>
- But very few countries collect the high-frequency household consumption data needed to calculate this measure directly. It’s a non-starter.

- Surprisingly: Poverty as measured by many low-income countries is in fact (inadvertently) an approximation to this higher-frequency measure.

- More surprisingly: Given household instability and illiquidity, **very few countries collect the household consumption data needed to calculate conventional annual measures.**

---
## This is **not** noise!

.pull-left[
<img src="index_files/figure-html/argument1-1.png" width="100%" />
]

.pull-right[

- Important: if households could smooth consumption perfectly, average months in poverty would fall from 37% to 29%.

- This happens with *no increase in average consumption*!

]

---
## Poverty is concentrated in rural areas, where seasonality is particularly salient

- Of world population living in extreme poverty (annual average of $1.90 per person per day or less):
  - 770 million people
  - 80% live in rural areas
  - 65% of workers (age 15+) are in agriculture

- Of world population living in moderate poverty (annual average of $1.90-$3.20 per person per day):
  - 1 billion people
  - 76% live in rural areas
  - 52% of workers (age 15+) are in agriculture

Castañeda et al. (2018)

---
## Next steps

- **Easiest**: Broaden meta-data to include data collection protocols. Harmonize data collection to more consistently estimate Average of Poverties. Expand compliance with expert guidelines:
  - Short-term recall
  - Single-time interviews
  - Randomize sample through the year

- **Harder but important**: Collect data to recover conventional poverty measures. Modeling strategies based on sub-samples.

- **Philosophical questions**: Can you be poor for a week? A month? A season? To what extent is poverty additively separable?

---
class: center, middle

<font size = "40"> Thank you! </font>

[https://joshmerfeld.github.io](https://joshmerfeld.github.io) <br>
[https://github.com/JoshMerfeld](https://github.com/JoshMerfeld) <br>
Twitter: [@Josh\_Merfeld](twitter.com/Josh_Merfeld)