<p><div><div><div><div data-show-faces="false" data-height="21" data-width="100" data-layout="button_count" data-send="true" data-href="https://www.r-bloggers.com/uss-proposals-tail-wagging-the-dog/"></div></div><div></div></div><div></div></div>
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(This article was first published on <strong><a href="https://statgeek.net/2018/03/15/uss-proposals-tail-wagging-the-dog/"> R – Let's Look at the Figures</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p>In response to my previous post, “<a rel="nofollow" href="https://statgeek.net/2018/03/13/latest-uss-proposal-who-would-lose-most/" target="_blank">Latest USS proposal: Who would lose most?</a>“, someone asked me about doing the same calculation for the USS JNC-supported proposals from January.  For a summary of those January proposals and my comments about their fairness, please see my earlier post “<a rel="nofollow" href="https://statgeek.net/2018/02/26/uss-pension-scheme-and-fairness/" target="_blank">USS pension scheme and fairness</a>“.</p>
<p>Anyway, the calculation is quite simple, and it led to the following graph.  The black curve is as in my previous post, and the <span>red</span> one is from the same calculation done for the <span>January</span> USS proposal.</p>
<p><img data-orig-file="https://statgeek.files.wordpress.com/2018/03/lost-comparison.png?w=456" data-orig-size="2940,1470" data-medium-file="https://statgeek.files.wordpress.com/2018/03/lost-comparison.png?w=456?w=300" data-attachment-id="739" data-image-meta="{" data-image-description="" src="https://statgeek.files.wordpress.com/2018/03/lost-comparison.png?w=456" data-permalink="https://statgeek.net/2018/03/15/uss-proposals-tail-wagging-the-dog/lost-comparison/" data-large-file="https://statgeek.files.wordpress.com/2018/03/lost-comparison.png?w=456?w=450" alt="lost-comparison" data-image-title="lost-comparison" sizes="(max-width: 450px) 100vw, 450px" data-comments-opened="1" class="wp-image-739" data-recalc-dims="1">The red curve shows just over 5% effective loss of salary for those below the current £55.55k USS threshold, and then a fairly sharp decline to less than 2% lost at the salaries of the very highest-paid professors, managers and administrators.  Under the January proposals, higher-paid staff would contribute proportionately less to the “rescue package” for USS — less, even, than under the March proposals.  (And if the salary axis were to be extended indefinitely, the <strong>red curve would actually cross the zero-line</strong>: that’s because in the January proposals the defined-contribution rate from employers would actually have <em>increased</em> from (max) 13% to 13.25%.)</p>
<p>In terms of unequal sharing of the “pain”, then, the January proposal was even worse than the March one.</p>
<p>At the bottom here I’ll give the <em>R</em> code and a few words of explanation for the calculation of the red curve above.</p>
<p>But the main topic of this post arises from <strong>a remarkable feature of the above graph!</strong> At the current USS threshold salary of £55.55k, the amount lost is <strong>the same — it’s 5.08% under both proposals</strong>.  Which led me to wonder: is that a <em>coincidence</em>, or was it actually a (pretty weird!) <em>constraint</em> used in the recent UUK-UCU negotiations?  And then to wonder: might the best solution (i.e., for the same cost) be to do <em>something that gives a better graph than <strong>either</strong> of the two proposals seen so far</em>?</p>
<h2>Tail wagging the dog?</h2>
<p>The fact that the loss under the March proposal tops out at 5.08%, exactly (to 2 decimals, anyway) the same as in the January proposal, seems unlikely to be a coincidence?</p>
<p>If it’s <em>not</em> a coincidence, then a plausible route to the March proposal, at the UUK-UCU negotiating table, could have been along the lines of:</p>
<blockquote>
<p>How can we re-work the January proposal to</p>
<ul>
<li>retain defined benefit, up to some (presumably reduced) threshold and with some (presumably reduced) accrual rate,</li>
</ul>
<p>while at the same time</p>
<ul>
<li>nobody loses more than the maximum 5.08% that’s in the January proposal</li>
<li>the employer contribution rate to the DC pots of high earners is not reduced below the current standard (i.e., without the “match”) level of 12%</li>
</ul>
<p>?</p>
</blockquote>
<p>Those constraints, coupled with total cost to employers, would lead naturally to a family of solutions indexed by just <em>two adjustable constants</em>, namely</p>
<ul>
<li>the threshold salary up to which DB pension applies (previously £55.55k)</li>
<li>the DB accrual rate (previously 1/75)</li>
</ul>
<p>— and it seems plausible that the suggested (12 March 2018) new threshold of £42k and accrual rate of 1/85 were simply selected as the preferred candidate (among many such potential solutions) to offer to UUK and UCU members.</p>
<h3>But the curve ought to be flat, or even increasing!</h3>
<p>The two constraints listed as second and third bullets in the above essentially <strong>fix the position of the part of the black curve that applies to salaries over £55.55k</strong>.  That’s what I mean by “tail wagging the dog”.  Those constraints inevitably result in a solution that implies substantial losses for those with low or moderate incomes.</p>
<p>Once this is recognised, it becomes natural to ask: what <strong>should</strong> the shape of that “percentage loss” curve be?</p>
<p>The answer is surely a matter of opinion.</p>
<p>Those wishing to preserve substantial pension contributions at high salary levels, at the expense of those at lower salary levels, would want a curve that decreases to the right — as seen in the above curves for the January and March proposals.</p>
<p>For myself, I would argue the opposite: <strong>The “percent lost” curve should either be roughly constant, or might reasonably even <em>increase</em> as salary increases</strong>.  (The obvious parallel being progressive rates of income tax: those who can afford to pay more, pay more.)</p>
<p>I had made a specific suggestion along these lines, in this earlier post:</p>
<ul>
<li><a rel="nofollow" href="https://statgeek.net/2018/03/01/future-uss-robin-hood-can-help/" target="_blank">Future USS: Robin Hood can help?</a></li>
</ul>
<p>The details of any solution that satisfies the “<strong>percent loss roughly constant, or even increasing</strong>” requirement clearly would need to depend on data that’s not so widely available (mainly, the distribution of all salaries for USS members).</p>
<p>But first the <strong>principle</strong> of fairness needs to be recognised.  And once that is accepted, the constraints underlying future UUK-UCU negotiations would need to change radically — i.e., definitely away from those last two bullets in the above display.</p>
<h2>Calculation of the red curve</h2>
<p>In the previous post I gave R code for the black curve.  Here is the corresponding calculation behind the <span>red</span> curve:</p>
<pre>sacrifice.Jan &lt;- function(salary) { # salary in thousands
    old_threshold &lt;- 55.55
    s &lt;- salary

## sacrifice arising from income up to old_threshold
    s2 &lt;- min(s, old_threshold)
    r2 &lt;- s2 * (19/75 + 1/100 - (13.25 + 8)/100)

## sacrifice (max) arising from income over the old threshold
## -- note that this is negative
    r3 &lt;- (s > old_threshold) * (s - old_threshold) * 
                (13 - 13.25)/100

    return(r2 + r3)
}

## A vector of salary values up to £150k
salaries &lt;- (1:1500) / 10

## Compute percent of salary that would be lost, 
## at each salary level
sacrifices &lt;- 100 * sapply(salaries, sacrifice.Jan) / salaries</pre>
<p>In essence:</p>
<ul>
<li>salary under £55.55k would lose the defined benefit (that’s the 19/75 part) and the 1% “match”, and in its place would get 21.25% as defined contribution.  The sum of these parts is the computed loss <em>r2</em>.</li>
<li>salary over £55.55k would <em>gain</em> the difference between potential 13% employer contribution and the proposed new rate of 13.25% (that’s the negative value <em>r3</em> in the code).</li>
</ul>
<hr>
<p>© David Firth, March 2018</p>
<p><strong>To cite this entry:</strong><br>
Firth, D (2018). USS proposals: Tail wagging the dog?. Weblog entry at <span>URL</span> <a rel="nofollow" href="https://statgeek.net/2018/03/15/uss-proposals-tail-wagging-the-dog/" target="_blank">https://statgeek.net/2018/03/15/uss-proposals-tail-wagging-the-dog/</a></p>
<p> </p>
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