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    <h1>Methodology</h1>

    <h2>Boston in 2024</h2>
     <h4>Terminology</h4>
                            <ul style="margin-bottom: 20px;">
                                <li><strong>Tipping Fee:</strong> The cost per ton that municipalities pay to dispose of trash at incineration or landfill facilities. Boston's tipping fee is $103.38 per ton.</li>
                                <li><strong>Municipal Solid Waste:</strong> Trash collected through Boston's municipal waste management program.</li>
                                <li><strong>Household:</strong> A residential unit participating in Boston's municipal trash program. 322,000 households participated in 2024.</li>
                                <li><strong>Tonnage:</strong> The total weight of trash disposed by participating households, measured in tons. Boston disposed of 186,305 tons in 2024, which converts to 372,610,000 pounds.</li>
                            </ul>

                            <h4>Formulas</h4>
                            <ul style="padding-left: 20px; margin-bottom: 20px;">
                                <li><em>T</em> = Total tonnage disposed by Boston = 186,305 tons</li>
                                <li><em>H</em> = Number of participating households = 322,000</li>
                                <li><em>F</em> = Tipping fee per ton = $103.38</li>
                            </ul>
                            <h4>Calculation</h4>
                            <ul style="padding-left: 20px; margin-bottom: 15px;">
                                <li><strong>Total pounds of trash:</strong> <em>T</em> × 2,000 lbs/ton = 186,305 × 2,000 = 372,610,000 pounds</li>
                                <li><strong>Tons per household:</strong> <em>T</em> ÷ <em>H</em> = 186,305 ÷ 322,000 = 0.579 tons per household</li>
                                <li><strong>Total incineration cost:</strong> <em>T</em> × <em>F</em> = 186,305 × $103.38 = $19,260,210.90</li>
                            </ul>
                        </div>

    <h2>With Pay-As-You-Throw</h2>
    <h4>Terminology</h4>
                            <ul style="margin-bottom: 20px;">
                                <li><strong>Average Reduction:</strong> How much trash 5 cities reduced per household after 5 years with PAYT = 0.260 tons per household.</li>
                                <li><strong>Percent Reduction:</strong> How much less trash households threw away = 44.95%.</li>
                                <li><strong>Projected Reduction:</strong> How much trash Boston could reduce if it does as well as other cities = 83,629.87 tons over 5 years.</li>
                            </ul>

                            <h4>Variables</h4>
                            <ul style="padding-left: 20px; margin-bottom: 20px;">
                                <li><em>R</em> = Reduction per household = 0.260 tons</li>
                                <li><em>H</em> = Boston households = 322,000</li>
                                <li><em>F</em> = Cost per ton = $103.38</li>
                                <li><em>T<sub>current</sub></em> = Trash per household now = 0.579 tons</li>
                            </ul>

                            <h4>Calculations</h4>
                            <ul style="padding-left: 20px; margin-bottom: 15px;">
                                <li><strong>Trash per household after PAYT:</strong> 0.579 - 0.260 = 0.319 tons</li>
                                <li><strong>Percent reduction:</strong> (0.260 ÷ 0.579) × 100 = 44.95%</li>
                                <li><strong>Total reduction in 5 years:</strong> 0.260 × 322,000 = 83,629.87 tons</li>
                                <li><strong>Reduction per year:</strong> 83,629.87 ÷ 5 = 16,725.97 tons</li>
                                <li><strong>Total savings in 5 years:</strong> 83,629.87 × $103.38 = $8,646,580.35</li>
                                <li><strong>Savings per year:</strong> $8,646,580.35 ÷ 5 = $1,729,131.19</li>
                            </ul>
                        </div>

<h2>Malden: A Case Study</h2>
<h4>Terminology</h4>
                            <ul style="margin-bottom: 20px;">
                                <li><strong>Per-Household Revenue:</strong> How much money each household generates through PAYT bag and tag sales in Malden.</li>
                                <li><strong>Revenue Source:</strong> The different ways cities earn money from PAYT, like bag sales or trash tag sales.</li>
                                <li><strong>Scaling:</strong> Using Malden's revenue earned per household to estimate how much Boston could earn.</li>
                                <li><strong>Illustrative:</strong> This is an example calculation, not a prediction of what will actually happen.</li>
                            </ul>

                            <h4>Variables</h4>
                            <ul style="padding-left: 20px; margin-bottom: 20px;">
                                <li><em>M_rev</em> = Total money Malden makes from each PAYT source</li>
                                <li><em>M_hh</em> = Number of Malden households</li>
                                <li><em>B_hh</em> = Boston households = 272,500</li>
                                <li><em>B_rev</em> = Money Boston could make from PAYT</li>
                            </ul>

                            <h4>Calculations</h4>
                            <ul style="padding-left: 20px; margin-bottom: 15px;">
                                <li><strong>Step 1 - Malden's revenue per household:</strong> Divide Malden's total money by households.</li>
                                <li><strong>Step 2 - Scale to Boston:</strong> Multiply Malden's per-household amount by 272,500.</li>
                                <li><strong>Bag revenue example:</strong> $47.11 × 272,500 = $12,837,475</li>
                                <li><strong>Tag revenue example:</strong> $31.26 × 272,500 = $8,518,760</li>
                                <li><strong>Important note:</strong> This assumes Boston would work like Malden, which may not be true.</li>
                            </ul>
                        </div>
                    </div>


  <h2>Pre-Post Effect of PAYT Within a 5-year Time Period</h2>

  <strong>Step 1:</strong> Merge data sources to obtain key information
  <ul>
    <li>Data sources include the Massachusetts Department of Environmental Protection's Municipal Solid Waste and Recycling surveys from 2009 to 2024, inclusive; the Massachusetts Department of Revenue's Division of Local Services; and the Massachusetts Department of Environmental Protection's spreadsheet, "Massachusetts Municipalities with PAYT Programs, June 2025".</li>
    <li>Key information: PAYT adoption year, years pre- and post-PAYT adoption, number of households enrolled in each municipality's trash system, annual tonnage disposed per household.</li>
  </ul>

  <strong>Step 2:</strong> Generate annual tons of waste disposed per household
  <ul>
    <li>Tons per household are calculated by dividing the municipality's total annual disposal tonnage by the number of households served by the PAYT program.</li>
    <li>Tons per household standardizes our metric, as larger municipalities will dispose of more total trash than smaller municipalities.</li>
  </ul>

  <strong>Step 3:</strong> Remove records that would distort the "normal trash" comparison
  <ul>
    <li>Keep only rows of data in which bulky waste is excluded.</li>
    <li>Exclude years that did not record yearly tonnage.</li>
  </ul>

  <strong>Step 4:</strong> Identify the longest pre- and post-period for parallel trends
  <ul>
    <li>Filter data to contain municipalities with data 5 years before implementing PAYT through 5 years after implementing PAYT.</li>
    <li>If one town has 20 years of data and another has 3 years, comparisons may not follow parallel trends; therefore, we may not conclude that adopting PAYT had a statistically significant result.</li>
  </ul>

  <strong>Step 5:</strong> Select Harvard, Chicopee, Heath, Hinsdale, and Peru
  <ul></ul>
  <strong>Step 6:</strong> Create a time series chart
  <ul>
    <li><strong>IMPORTANT NOTE:</strong> Our time of adoption begins at -1 (the adoption year); Year 0 is the implementation year; Year 1 is one year after implementation.</li>
  </ul>

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