The forgotten caveats

The headline in the business standard reads : "India must grow at 18% to ensure jobs to growing workforce: World Bank".  The article is based on the recent world bank report titled "Jobless Growth" under the south Asia economic focus series. 

One would agree that 18% growth for a country of our size is not attainable. That being so, the headline implies that World Bank is saying that India cannot secure jobs to its growing workforce. Gloomy picture indeed. There is an element of certainty about the nice round number 18 which misleads a lay reader. 

It is not so if one reads the actual report. The actual report has pushed in enough caveats to survive any close scrutiny about the number 18. The problem is, the report presents things in a way that make newspapers pick up such headlines. That's a danger that any report writer should be wary about, and should factor in while presenting data to a lay reader. To expand the debate, the assumptions behind the models and the assumed simplifications should be made amply clear to the uninitiated audience lest they take the models on face value and start drawing conclusions for real world. The simplified models work, under set of circumstances and assumptions, to enlighten about some particular causal phenomenon under study. And it stops at that. A brief look at the calculation of the number 18 would throw some light. 

The first assumption the model makes is the roughly U shaped relation between employment rates and economic growth. It runs thus. 

GDP per capital Vs Employment rate - The U curve

Data indicates that employment and per capita income appear to exist in a U shaped relationship as shown above. When per capita income is low, the country has high employment as people start working young and remain employed due to sheer pressure of survival. If they drop out, they go hungry. As per capita income grows, children enroll in schools and stay there longer, old  people may get pensions, women may not go to work, and the abject need to work for survival decreases. This leads to decrease in employment till a certain stage is reached where the per capita income increases enough to reverse the trend. This happens as people in countries with high per capita income have higher education, they are less likely to drop out of employment, including women who now have access to better daycare and health facilities and can afford to be in the labour force. Also, better healthcare and life indicators ensure that one remains in labour force longer with less drop outs. The first set of assumptions while deriving the 18% growth is that such a curve exists, and India exists at a point on the curve where it is downward sloping, that is, more prosperity would lead to less employment with people dropping out. 

The second set of assumptions is that the employment data the model relies upon is good enough. That might not be so, even in the own words of the report: 

Economists in South Asia agree that the quality of the available employment data makes it difficult to credibly assess the labor market situation in their countries...PP34

One may recall the recent debate in the newspapers about the EPFO based employment data being used to prove the growth in employment numbers. Everyone took sides, but agreed on the point that we are far from getting reliable data on employment. So the report cleans up some sets of employment data that it has and goes ahead with whatever best it could manage. 

The report outlines the below equation to represent the approximation of the U curve mentioned above

Where Et is the employment rate, Yt is the total output, Nt is the population, Beta is the approximate slope of the U shaped curve around Yt, and negative for countries like India as mentioned above. 

Delta captures the responsiveness of employment to economic growth and is expected to be positive for India. Alpha and Gamma are short and long term constants arising while linearising the equations respectively. 

Then quarterly changes in employment are correlated with quarterly GDP growth, the report mentions that Okun's law (which roughly states that employment increases in direct relation to GDP growth) doesn't hold for India. For each percentage point increase in GDP growth, India's growth seems to drop by 0.11%. Counterintuitive? Yes, but the models say so. And within south asia, the law holds in Pakistan and Sri Lanka and fails for India. Nevertheless, we plough ahead with acceptable p values. 

See images below. 

Then the attention of report turns towards the question in hand. The one I have a problem with. How much growth is needed to create enough jobs? It takes three scenarios: 

a) Unambitious - let the Growth be whatever it is and lets see where employment would head

b) Constant - Growth needed to keep the level of employment constant

c) Catch-up or Ambitious - Growth needed to catch up in terms of employment levels and get pushed to the positive slope area of the U curve in a certain number of years. 

Based on T number of years to catch up, it models three equations by substituting above into the earlier two equations. Then the linear models look thus: 

Based on this, the model predicts the growth rates, and puts them on a neat bar chart. 

Now one may see that India needs a growth rate of around 18% to catch up with a time horizon T of 20 years. This chart doesn't contain any disclaimer. If one simply scrolls down the report and stops at it, it misleads. While the methodology is probably the best one could get in given circumstances of shaky data and inapplicable models, yet the chart doesn't mention any of those. It assumes a linear and deep reading of the text. 

If you observe, by the time you reach here in this post, you must have forgotten the first U curve assumptions I started with, unless you are econ types. Most policymakers in India are not Econ types. They are generalists who are more managers than policymakers. And that's why I have problems with data presented in this form. It has a ring of conclusiveness to it while the report embed the doubts about the U curve and Okun's law inside the text. To be fair, the report has been candid about employment data inaccuracies. 

If asked, I would present the following way. I would add up the uncertainties at each level in the modeling process as error terms. And when the final value is presented, and if forced to make a bar graph, I would include this cascaded final error term in the projection. It would be a range to reflect the uncertainties built into the model. 

Probably the headline then would read like this: 

India might need around between 7 to 25% growth rate for twenty years to ensure jobs for a growing workforce, depending on where we lie at the downward sloping U curve, and depending on the assumption that it's an U curve after all, with an inverse relation Okun's law holding tightly enough; which though counterintuitive, we shall somehow ignore, and depending on how much we believe on the employment data being generated, and given that other things remain constant in the time horizon considered. This after ignoring the inherent assumptions in data collection methods, which ignores pakora makers, and uncertainties in calculation of GDP growth. We are in bad shape. 

Probably that'll not be a click-bait headline. But then, who cares about the misleading headline too?