New Economist

Is the BoE inflation fan flawed?

Kevin Dowd at Nottingham certainly thinks so. In an article in the March 2007 Journal of Macroeconomics, Too good to be true? The (In)credibility of the UK inflation fan charts, he argues that the Bank of England's model overestimates inflation risk:

This paper presents some simple methods to estimate the probability that realized inflation will breach a given inflation target range over a specified period, based on the Bank of England’s RPIX inflation forecasting model and the Monetary Policy Committee’s forecasts of the parameters on which this model is built. Illustrative results for plausible target ranges over the period up to 04Q1 indicate that these probabilities are low, if not very low, and strongly suggest that the Bank’s model over-estimates inflation risk.

Here is an ungated version.

I have always found it a tad ludicrous that the Bank's central CPI projection invariably manages to revert to the inflation target two year's out. Implied message: current rates are always appropriate. Could they not either use the fan to indicate upside or downside medium-term risks to their outlook, or as some other central banks do, publish their internal interest rate forecasts rather than just talk about implied market forecasts? Like Dowd, I'm not a great fan of the fan.

Evaluating probabilistic predictions

David Pennock of Oddheads blog asks a good question: what is the “right” way to evaluate probabilistic predictions?

There is no single absolute best way, though several tests are appropriate, and probably can be considered stronger tests than the calibration test. In our paper “Does Money Matter?” we use four evaluation metrics:

1. Absolute error: The average over many events of lose_PR, the probability assigned to the losing outcome(s)
2. Mean squared error: The square root of the average of (lose_PR)²
3. Quadratic score: The average of 100 - 400*(lose_PR)²
4. Logarithmic score: The average of log(win_PR), where win_PR is the probability assigned to the winning outcome

Note that the absolute value of these metrics is not very meaningful. The metrics are useful only when comparing one predictor against another (e.g., a market against an expert).

My personal favorite (advocated in papers and presentations) is the logarithmic score.

New book: 'Data Analysis Using Regression and Multilevel/Hierarchical Models'

Anyone familiar with Andrew Gelman's excellent blog, Statistical Modeling, Causal Inference, and Social Science, would be keen to see his new book, aco-authored with Jennifer Hill. The book is titled Data Analysis Using Regression and Multilevel/Hierarchical Models, and has just been published by Cambridge University Press.

Judging by its table of contents it covers plenty of ground, including several that have been neglected by other authors:

1. Why?; 2. Concepts and methods from basic probability and statistics;

Part IA. Single-level Regression: 3. Linear regression: the basics; 4. Linear regression: before and after fitting the model; 5. Logistic regression; 6. Generalized linear models;

Part IB. Working with Regression Inferences: 7. Simulation of probability models and statistical inferences; 8. Simulation for checking statistical procedures and model fits; 9. Causal inference using regression on the treatment variable; 10. Causal inference using more advanced models;

Part IIA. Multilevel Regression: 11. Multilevel structures; 12. Multilevel linear models: the basics; 13. Multilevel linear models: varying slopes, non-nested models and other complexities; 14. Multilevel logistic regression; 15. Multilevel generalized linear models;

Part IIB. Fitting Multilevel Models: 16. Multilevel modeling in bugs and R: the basics; 17. Fitting multilevel linear and generalized linear models in bugs and R; 18. Likelihood and Bayesian inference and computation; 19. Debugging and speeding convergence;

Part III. From Data Collection to Model Understanding to Model Checking: 20. Sample size and power calculations; 21. Understanding and summarizing the fitted models; 22. Analysis of variance; 23. Causal inference using multilevel models; 24. Model checking and comparison; 25. Missing data imputation;

Appendixes: A. Six quick tips to improve your regression modeling; B. Statistical graphics for research and presentation; C. Software; References.

Caveat: I've ordered it but have not yet seen a copy. Comments welcome from those who have.

Happiness in Whitehall

Whitehall has been looking at happiness and well-being, according to the Sunday Times, citing a new 193 page Defra report Review of research on the influences on personal well-being and application to policy making (PDF) by Paul Dolan and Tessa Peasgood from Imperial College London and Mathew White from the Centre for Well-being in Public Policy, University of Sheffield. John Elliott writes in his piece, Happiness is a chat over the fence, that:

The attempt to quantify what the report calls “SWB” — a personal “sense of wellbeing” — is part of a move by all the main political parties to go beyond purely financial measures of wellbeing in setting goals for policy.

The Whitehall Wellbeing Working Group (W3G for short), a committee of civil servants, has been charged with finding out how ministers can make citizens more cheerful. The report was commissioned by the environment department, which is leading the Whitehall effort. It consists of a review of research carried out around the world into the factors influencing happiness and how governments can affect it.

But what does happiness research mean for policy makers?

“It’s shown that married people are happier — so what does that mean for politics? Does it follow that we should be encouraging people to marry?” asked Dolan, whose next task for the government is to draw up a reliable “happiness unit” to measure wellbeing. He added: “Is that the realm of politics . . . or something that should be left to individual choice?”

While the idea of a Whitehall-defined unit of happiness may not fill that many people with joy, its supporters hope that by pinpointing what makes people happy, taxpayers’ money could be spent with greater effect on national wellbeing.

“If the aim of policy were to alleviate misery, there may be some justification for targeting women as they tend to exhibit higher levels of depression.”

...Although the government has not yet reached many specific conclusions, the health department is working on advice to primary care trusts on promoting wellbeing. The environment department added that the transport and culture ministries were also “interested” in measuring how their policies affected people’s happiness. Meanwhile, the Department of Trade and Industry has just launched a two-year research project into “Mental Capital and Wellbeing”, which, said Defra, “aims to produce a challenging and long-term vision that maximises mental capital in the UK in the 21st century for the benefit of both individuals and society”.

Simon Parker, head of public services research at the think tank Demos, welcomed the new emphasis on wellbeing. He said: “You are starting to see politicians talking about issues that reflect how life isn’t just about cash . . . but it’s important to inject a note of realism, there is only a certain amount a government can do.”

Of course, not everyone is enamoured. Times columnist Libby Purves (In Grey Britain it's always your fault, 9 January) is just back from abroad and thinks it all quite banal:

The latest political buzz is a “wellbeing index”, masterminded by 3WG, the Whitehall Wellbeing Working Group, whose civil servants now have a report in their hands commissioned by the Department for the Environment. It reveals that people are happier if they get plenty of sleep and a social life, are not too fat and get promotion at work; and that they get unhappy if they are jilted, sacked or soaked by heavy rain.

With discoveries as startling as this, it cannot be long before another costly Whitehall survey finds that our wellbeing suffers when we are treated like pointless nuisances by services and authorities that we are paying for.

A tad unfair. The report itself provides a very useful review of the literature and discussion of the various measures of subjectve well-being and their relative merits. For anyone researching this area, it's a must read.

Beware pseudoneglect!

What's not to like about a Likert scale? Perhaps the most commonly used method in social surveys for geting people to provide scaled opinions and preferences, you'll find it just about everywhere. To be sure, it has some well known biases. The Wikipedia entry lists three:

Likert scales may be subject to distortion from several causes. Respondents may avoid using extreme response categories (central tendency bias); agree with statements as presented (acquiescence response bias); or try to portray themselves or their organization in a more favorable light (social desirability bias).

Alas, new research - highlighted by the ever useful BPS Research Digest - identifies a fourth: spatial bias. Melbourne University researchers at the Laterality Laboratory explain it thus:

Most people have a leftward attentional bias that occurs in normally functioning individuals. This bias, also known as pseudoneglect, causes people to bisect lines         slightly to the left of their true centre.

Scary stuff. Here's how the BPS blog post explains it:

Andrea Loftus and colleagues have reported this spatial bias could be distorting survey results.The researchers presented two groups of students with the same questionnaire statements about their experience at university (e.g. “My course has been enjoyable”), except that one group answered using a 5-item Likert scale that ranged left-to-right, from ‘definitely disagree’ to ‘definitely agree’, whereas the other group answered using a scale that ranged left-to-right across the page, from ‘definitely agree’ to ‘definitely disagree’. The positive questionnaire statements were the same as those used by the Higher Education Funding Council for England (HEFCE) in its survey of 250,000 students.

In the current study, the students’ natural bias for the left meant those answering using the Likert scale that started on the left with ‘definitely agree’, responded with that answer to 27 per cent more statements than did the other group of students – that is, their views came out as more positive. By contrast, those students who answered using the scale that began on the left with ‘definitely disagree’ responded more often with ‘mostly disagree’, meaning their views came out overall as more negative.

The observation has profound implications for surveys ..that seek respondents’ agreement, or not, with consistently positive or negative statements, and which use the same Likert scale for answers throughout. The researchers said one solution in the future is for the Likert scale direction to be reversed for half of the survey sample.
__________________________________

Nicholls, M.E.R., Orr, C.A., Okubo, M., and Loftus, A. (2006). Satisfaction Guaranteed. The Effect of Spatial Biases on Responses to Likert Scales. Psychological Science, 17, 1027-1028.

It appears this bias only occurs when respondents complete a left-rught scale themselves, not when it is read out to them. So it should not affect telephone polling, nor presumably face-to-face surveys (unless a showcard is used). Nonetheless, these findings will raise doubts about a good many survey results.

98 ways to visualise data

Economists tend to focus on sophisticated econometric methods, but often ignore the quality of the underlying data they're using, along with simpler methods of analysis - such as visualisations. This week I will be including a few posts on data, statistics and alternative quantitative methods.

Let's start with the visualisation of data. Aleks Jakulins at the Statistical Modeling, Causal Inference, and Social Science blog points us to a stunning periodic table of visualisation methods. The table provides 98 methods of visualising information.

Go to the original table here (or click the table below), and hover your mouse over some of the 'elements'. While you may be familiar with mindmaps, fishbone diagrams and even Chernoff faces, I'll bet you find some methods new to you.

More on the US gender gap

The New York Times piece I posted about earlier today implies that the gender pay gap has stopped narrowing in the United States. In aggregate terms this is not the case - as the accompanying picture shows. The unadjusted median hourly pay gap continued to close through the late 1980s and early 1990s, reaching a low of 20.2% in 2003 compared with 25.0% in 1993. (Although the pay gap did widen a little in 2004 and 2005, to 20.4% and 20.6% respectively).

But when one adjusts the raw numbers for changing employee characteristics, especially education, the picture looks more bleak - suggesting little change in the gender pay gap since the early 1990s.

This chart comes from a very useful website on the End of the Gender Revolution?, maintained by David A. Cotter (Union College), Joan M. Hermsen (University of Missouri) and Reeve Vanneman (University of Maryland). The site also makes available most of the time series data used for the charts in Excel spreadsheets, updated to 2005. Recommended.

The US gender pay gap - slow progress

A long piece by the New York Times' David Leonhardt explains why in the United States the Gender Pay Gap, Once Narrowing, Is Stuck in Place. The accompanying graphic is worth clicking on.

Throughout the 1980s and early ’90s, women of all economic levels — poor, middle class and rich — were steadily gaining ground on their male counterparts in the work force. By the mid-’90s, women earned more than 75 cents for every dollar in hourly pay that men did, up from 65 cents just 15 years earlier.

Largely without notice, however, one big group of women has stopped making progress: those with a four-year college degree. The gap between their pay and the pay of male college graduates has actually widened slightly since the mid-’90s.

For women without a college education, the pay gap with men has narrowed only slightly over the same span.

These trends suggest that all the recent high-profile achievements — the first female secretary of state, the first female lead anchor of a nightly newscast, the first female president of Princeton, and, next month, the first female speaker of the House — do not reflect what is happening to most women, researchers say.

A decade ago, it was possible to imagine that men and women with similar qualifications might one day soon be making nearly identical salaries. Today, that is far harder to envision.

“Nothing happened to the pay gap from the mid-1950s to the late ’70s,” said Francine D. Blau, an economist at Cornell and a leading researcher of gender and pay. “Then the ’80s stood out as a period of sharp increases in women’s pay. And it’s much less impressive after that.”

Last year, college-educated women between 36 and 45 years old, for example, earned 74.7 cents in hourly pay for every dollar that men in the same group did, according to Labor Department data analyzed by the Economic Policy Institute. A decade earlier, the women earned 75.7 cents.

The reasons for the stagnation are complicated and appear to include both discrimination and women’s own choices. The number of women staying home with young children has risen recently, according to the Labor Department; the increase has been sharpest among highly educated mothers, who might otherwise be earning high salaries. The pace at which women are flowing into highly paid fields also appears to have slowed.

Which matters: nature or nurture?

Both do, according to a pathbreaking paper presented to Harvard's Inequality Summer Institute earlier this year. Using a quite remarkable Swedish dataset by merging data from administrative sources and censuses, the authors Anders Björklund (Stockholm University), Markus Jäntti (Abo Akademi University) and Gary Solon (University of Michigan) examine the correlation of socioeconomic status  between parents and children, and find that both nature and nurture matter. The paper, Nature and Nurture in the Intergenerational Transmission of Socioeconomic Status: Evidence from Swedish Children and Their Biological and Rearing Parents (PDF), concludes:

The adult socioeconomic status of Swedes born between 1962 and 1965 appears to be positively associated with the socioeconomic status of both their biological parents and their rearing parents, when those parents are not the same as each other as well as when they are. Accordingly, our paper is entitled “Nature and Nurture,” not “Nature vs. Nurture.” We see no logical or empirical need to choose between the two. Our evidence suggests substantial importance for both.

Note: An earlier paper by the two authors, Influences of Nature and Nurture on Earnings Variation:
A Report on a Study of Various Sibling Types in Sweden (PDF), published in 2005, used data from the Swedish Twin Registry, to examine the importance of genes and environment in accounting for earnings variation. It concluded that genetic influences were important:

Even our smallest estimates of the genetic component of earnings variation, however, suggest that it accounts for about 20 percent of earnings inequality among men and more than 10 percent among women.

However, almost two-thirds of earnings variation could be explained neither by genetics or environment:

Although our results point to a significant role for genetic variation, perhaps the most striking finding is the most obvious one – about the importance of non-shared environment. The largest sibling correlation in earnings that we estimate is a 0.36 correlation for monozygotic twin brothers. Even though these brothers have identical genes and, according to our preferred model, experience even more similar environments than other sibling pairs do, an estimated 64 percent of their earnings variation is explained by neither genetic nor environmental resemblance. In other words, much and perhaps most of earnings variation in Sweden stems from environmental factors that are not shared even by monozygotic twins.

Neither genes nor the environment in which we are raised determine (most of) our future earnings.

Who are the world's wealthy?

Both the BBC News and The Economist point to a new World Institute for Development Economics Research study on The World Distribution of Household Wealth. The report was written by James Davies (University of Western Ontario), Anthony Shorrocks and Susanna Sandstrom (WIDER), and Edward Wolff (New York University).

The study finds that wealth is shared much less equitably than income: the richest 2% of adults in the world own more than half of global household wealth. The definition of wealth used is broad: the value of physical and financial assets less debts, not just money. Here is an excerpt from the paper's (PDF) conclusions:

This paper has provided a first estimate of the world distribution of household wealth. We have seen that the distribution is highly concentrated - in fact much more concentrated than the world distribution of income, or the distribution of wealth within all but a few of the world’s countries.

While a typical share of the top 10 per cent of wealth-holders within a country would be about 50 per cent, and the median Gini around 0.7, we have estimated that for the world as a whole the share of the top 10 per cent was 85 per cent in the year 2000 and the Gini equalled 0.892 using official exchange rates, Milanovic (2005) estimates that the world income Gini was 0.795 in 1998.

While wealth (and income) concentration is somewhat less when the estimates are done on a PPP basis, we have argued that the large share of wealth that is owned by people who can readily travel and invest globally means that converting at official exchange rates is preferable for many purposes when one is studying the distribution of wealth, rather than income distribution or poverty.

According to the study, almost all of the world’s richest individuals live in North America, Europe, and rich Asia-Pacific countries. Each of these groups account for about one-third of the world’s wealthiest 10%. The Economist is not wrong to have called its piece Winner takes (almost) all.