Statistics, state benefits, and reproduction: some sort of unholy trinity

Over the past week, there has been some discussion regarding a book written by Adam Perkins (a Lecturer in the Neurobiology of Personality at King’s College London) regarding the impact of state benefits on personal outcomes (the title of the book – “The Welfare Trait: how state benefits affect personality” – probably gives that away).

Of particular focus has been one table that Perkins claims demonstrates that being on benefits is associated with a higher number of children in that household – i.e. that being on state benefits encourages reproduction (according to Perkins). The table, reproduced from here below, appears to indicate that households in which no-one is employed have higher numbers of children than do households with one or two workers.

[Children%2520per%2520household%255B4%255D.png]

Perkins’ conclusions were criticised by Jonathan Portes (a Senior Fellow at the NIESR) for a number of reasons, to which Perkins provided a response – see here.

However, this response is entirely unsatisfactory as it fails to acknowledge the actual problems with using the table above to make meaningful inferences. First, it does nothing to demonstrate that the results in the table are statistically significant – that is to say that the results in the are not just due to “random chance” (i.e. an artefact of the data used) and are, in fact, a “true” result. Without testing the results for statistical significance, there is no way to determine whether or not there is actually a meaningful difference between the number of children in working households as compared to workless household. Indeed, Perkins does not appear to even acknowledge this as an issue of his reliance on this table.

Second, Perkins’ numbers deliberately exclude households in which there are no children. This is an egregious decision that Perkins has tried to justify using baseless arguments. The issue is that Perkins could have deliberately introduced a bias into the numbers in the table that directly affects the inferences drawn from the results in the table. To see this, suppose that a higher proportion of workless households have no children than the proportion of working households that have no children.

Indeed, suppose that 500,000 working households do not have children, but 1,000,000 workless households do not have children. The table below, shows the impact of this hypothetical example – including households that do not have children actually reverses the direction. Once childless households are included in this hypothetical example, workless households actually have fewer children that do working households. Hence, it is essential that the number of childless households are included when trying to see if state benefits affect reproduction.

Hypothetical childless

In fact, when one uses the actual total number of households available from the ONS (rather than the hypothetical example above), we actually find a mixed set of results. The number of children per workless household is indeed lower than the number of children in working and mixed households, but the number of children per mixed household is higher than that in working households.

Actual childless

Hence, Perkins’ conclusions regarding the impact of benefits on reproduction are incorrect. The actual results suggest that there does not appear to be a systematic relationship between the employment status of a household and the number of children in that household. This goes to show how excluding certain groups from a dataset can introduce bias in any results obtained from analysing that dataset.

UK price levels and inflation targeting

Over the weekend, Andrew Sentance tweeted the graph below in an attempt to show that price levels in the UK are above where they “should” be given the Bank of England’s inflation-targeting regime. In particular, he tried to use this graph as a justification for his continued demands that the Bank of England increase interest rates soon (if not immediately).Sentance inflation

If one were to take Sentance’s graph at face value, then it might seem that he has a point- price levels are above where they would be if the Bank of England had followed its 2% CPI target since 2004.

However, of course one should not take this graph at face value. For a start, it ignores the fact that the Bank of England’s inflation target is not just the central point of 2% per year, but is actually a range around that central point. In fact, the Bank of England’s official inflation target is 2% +/- 1% – in other words, inflation can be as much as 2.9% or as low as 1.1% and the Bank of England would still be within its target. Hence, the graph below also plots these upper and lower bounds of the price level over time (the top dotted line shows the upper bound, while the bottom dotted line shows the lower bound).

Clearly, the path of prices in the UK has always remained within the Bank of England’s target (assuming a start date of January 2004). Moreover, even though the price level came relatively close to breaching the upper bound in 2011/2012, more recently those prices levels are well within the upper bound (albeit above the central target).

CPI Inflation

Of course, the Bank of England did not just start targeting inflation in January 2004 – in actual fact it first started targeting inflation in 1992. However, given that it was only granted independence in May 1997, it is more appropriate to examine the path of prices from that date. This is shown in the graph below, which also takes into account the July 2003 move from targeting RPIX to targeting CPI instead.

Specifically, the red line shows the path of RPIX inflation (re-based to equal 100 in May 1997) until June 2003, from which point it shows the path of CPI. Likewise, the dashed line shows the path of prices under central target of 2.5% from May 1997 until June 2003, and then the path under the central target of 2.0% from July 2003 onwards. The dotted lines show the upper and lower bounds of +/-1% around the central target.

The picture here is even more striking than before. Due to inflation generally being below the centre of the target until about 2007, the price level was below what it would have been if the central target had been achieved (although prices did generally stay within the lower bound). Only more recently (i.e. since about 2007/2008) has inflation been above the central target for a sustained period of time, such that the price level “caught up with” where it would have been if inflation had followed the central target.

RPIX and CPI Inflation

Indeed, the end result is that the prevailing level of prices in the UK of the past 4-5 years have been close to the level that would have been achieved if inflation had stayed at the central target since 1997. In other words, the graph used by Andrew Sentance to try to claim that the level of prices in the UK is higher than it “should” be is mis-leading in the extreme – instead of prices being above the level of the central target, they are actually around the central target level and well within the upper and lower bounds of the inflation target. Hence, trying to claim that interest rates should be raised due to the price level being above “target” is not valid.