Friday, April 19, 2013

Forecasting The 2020 High Income Threshold

This is going to be a technical post – feel free to skip to the end if you’re not comfortable with the math.

There’s apparently some question of why the ETP has a target of USD15,000 in per capita GNI by 2020, and how it was derived.

Scepticism over the target has always struck me as a little strange because of the uncertainty of forecasting over such a long horizon, and the desire for pseudo-precision involved in assuming such targets are meant to be operative. I mean – if you manage to get to USD14,999, does that mean we’ve failed? How about USD15,001? Would USD15,002 be significantly better?

Given the imprecision in aggregate economic statistics, particularly national account statistics, the desire for such accuracy is an exercise in futility. Nevertheless, doing a forecast projection is a more or less trivial exercise, which I’m going to try to demonstrate.

First the data – the ETP target is actually derived from the World Bank’s high income classification, which can be downloaded here, and the sample runs from 1988 to 2012. I had to fudge the data a bit, because the World Bank’s financial year starts in July, rather than January. And the reason why that’s important is because at an operational level, the income thresholds that the Bank uses is actually meant for determining loan eligibility.

Estimation

The plot of the data is as below (GNI per capita in USD):

01_wb

Note that while it is mostly increasing over time, the high income threshold isn’t exactly a linear progression. That presents a bit of a problem which I’ll get into later.

The model I’m using is an AR(1) model with a time trend:

Ln(GNI) = α + β*T + γ*AR(1) + ε

…where T is time. The auto-regressive term helps manage a serial correlation problem that’s present in the standard regression estimation.

Here ‘s the result of the preliminary run through:

Ln(GNI) = 8.15 + 0.02*T + [AR(1)=0.76]      R2 = 0.94

All the coefficients are statistically significant at the 0.1% level. There’s significant heteroscedasticity in the residuals, so the estimation uses White’s heteroscedasticity-consistent errors.

Summary Results

So what does all those numbers mean? Essentially, for every unit increase in T, Ln(GNI) increases by 0.02. In EconoEnglish: the high income threshold increases 2% every year. To be more precise, it increases by 2.04448753251947% every year, more or less. Yes, that was sarcasm.

Projecting that forward, we obtain a point estimate of USD14,492.89 by 2020 and a 95% confidence range forecast of USD16,470 to USD12,515 (standard error of USD1,149.7). The USD15,000 target is approximately just under the 66% boundary, i.e. there’s about a one-third probability of the high income threshold actually exceeding that level based on this projection.

In other words, the USD15,000 target is a “stretch” target that’s still achievable, and gives a better than 50% chance of Malaysia being classed as a high income country if we actually get there.

Caveat

Now, to return to that problem I mentioned – the heteroscedasticity problem means that the estimated coefficients and the forecast projections can be sensitive to the sample used in the estimation. Robustness checks via changing the sample size resulted in significant changes in the estimated coefficients and the final forecast.

However, going back to just 2009, which would be the latest known data point before the publication of the New Economic Model which originally established all these targets, doesn’t alter the results all that much:

Sample range: 1988-2009

Ln(GNI) = 8.16 + 0.02*T + [AR(1)=0.76]     R2 = 0.92

Coefficient of T: 2.026672335140296%
Std error: USD1,336.06
Point Forecast: USD14,434.73
Range Forecast: USD16,751-USD12,118

Conclusion

What it all boils down to is – the 2.0% adjustment factor that PEMANDU has been using to project forward the existing World Bank high income threshold to 2020 and set a target of USD15,000 for the ETP, has some statistical validation.

You could of course try the long way around and make a projection based on assumptions for the variables embedded in the World Bank’s calculation – exchange rates and GDP deflators for both Malaysia and the G5. But since all that information is incorporated in the high income time series, that’s probably more trouble than its worth. The univariate approach used here is more parsimonious, and likely to be less error-prone.

10 comments:

  1. >"Given the imprecision in aggregate economic statistics, particularly national account statistics, the desire for such accuracy is an exercise in futility. Nevertheless, doing a forecast projection is a more or less trivial exercise, which I’m going to try to demonstrate."
    >AR(1) time trend model
    >"In EconoEnglish: the high income threshold increases 2% every year. To be more precise, it increases by 2.04448753251947% every year, more or less. Yes, that was sarcasm."

    Not sure if satire...

    ReplyDelete
    Replies
    1. Poking fun at some people, is all.

      Delete
  2. Your Math worked out fine though just wondering whether the 'fudging' had had an unintentional impact. You could do better with the 'sarcastic' figure though, as your qualified 'more or less' still implies it is still not precisely accurate to the last decimal...; > (wink wink)

    Anyway while univariate analysis is acceptably less error prone in this case,it nevertheless is parsimonious with regard to accuracy plus the sample size will have an effect as your caveat suggests. I am just curious as to whether the cumbersome method will yield similar outcomes given the progression is non linear.

    Warrior 231

    ReplyDelete
    Replies
    1. Warrior,

      1) I checked using two samples with a time difference of one year, with mostly similar results, so the "fudging" didn't have much impact.

      2) While you might expect a more complex model to tend to generate more accurate forecasts, generally speaking the opposite is often found to be true. It's a trade-off between an accurate description of the past, and a better forecast of the future. These are not the same things.

      Delete
  3. My guess is the ~2% annual increase in the high income threshold from the World Bank is tied to the increase in global inflation. Now heres the bomb, IMF forecasted global inflation to increase by 3.7% from 2013-2018, that implies that the high income threshold to increase much faster than expected, implying much lower likelihood that Malaysia would be able to reach the 'actual' threshold of becoming high income by 2020.

    ReplyDelete
    Replies
    1. Actually, the increase is based on the rate of increase in the GDP deflator of the G5. Not that it matters - if inflation is higher, so will nominal income growth. Both the goal and the metric used is in nominal terms, not real terms.

      Delete
  4. Off topic, Reinhardt & Rogoff skewed by a uni kid. Love it:

    http://www.peri.umass.edu/fileadmin/pdf/working_papers/working_papers_301-350/WP322.pdf


    And people who talk about public debt blah blah blah should also have second and probably third thoughts on the perverse logical universe in which rating agencies belabor under:


    http://qz.com/77781/the-uk-downgrade-by-fitch-says-more-about-ratings-agencies-that-in-does-about-britain/


    Though to be fair to all sides, debt fear mongers can always fall back on face saving rationalisations to ease their pain.

    http://qz.com/76447/an-economists-mea-culpa-i-relied-on-rogoff-and-reinhart/

    But then again, gosh, don't economists ever submit to mea culpas? We engineers do.......just wondering

    Aside: just some interesting stuff especially points 2, 3 , 4

    http://qz.com/67532/tax-havens-five-not-so-convincing-justifications/

    Which inevitably leads to some yawn inducing ones with Danny Quah in it:

    http://online.wsj.com/article/SB10001424127887324662404578334330162556670.html?mod=wsj_valettop_email

    Warrior 231

    ReplyDelete
  5. ETP target is RM 1.7 trillion GNI in 2020 and not USD15k/capita.They also said GNI must grow at 6% per annum (excluding assumed inflation based on avg CPI of 3.2%).

    So,whats the target now? USD15k or RM1.7 trillion ?
    Confused...

    ReplyDelete
    Replies
    1. @anon 10.33

      The ETP target is USD15k per capita - the GNI target is derived from that, based on certain assumptions. Details are in the NEM part I document.

      Delete
  6. will you be writing a piece on if malaysia achieves this target of becoming a high income economy translates to ordinary citizens like me?

    will this mean i will have a better quality of life? For example, will the crime rate be low, healthcare is free and among the best in the world, will everyone be happy, can i afford to have a speedboat? is this the reality facing ordinary citizens of Malaysia once we achieve a high income nation?

    -sky2206

    ReplyDelete