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In this VoxEU text, «Promising ideas for future research on the employment effects of minimum wages », how do I interpret the elasticity of employment?

I would think of it as percentual change in quantity of labour demanded over percentual change in minimum wage. However, if I google the concept, I get % change in employment associated with a % change in output. Ok, Factor Incomes = Expenditures = Output. However, although at a national level they are the same, at a micro level, I don't see how both definitions would equate...

Any help would be appreciated.

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I'm citing the first two lines of the article you refer to (emphasis mine):

The debate among researchers about the employment effects of minimum wages remains intense and unsettled. There is clear variation in the magnitude of estimated employment effects across studies, with the debate often being between an elasticity for low-skilled groups equal to (or indistinguishable from) zero, or an elasticity in the range of −0.1 to −0.2.

Mechanically, you can always compute elasticities of any two variables w.r.t. each other at an initial point $b$, which is defined as

$$\eta_{a, b} = \frac{\partial a(b)}{\partial b}\frac{b}{ a(b)}$$

Simply googling employment elasticity gives you

$$\eta_{employment, X}$$

where $X$ is the unknown. What is it, that employment is elastic towards?

The article makes clear that indeed, $a$ in this context is the employment rate, while $b$ is the level of the minimum wage.

Instead of googling, you could have looked at any of the studies cited in the article. The first sentence in Dube et al (2010) actually states that

We use policy discontinuities at state borders to identify the effects of minimum wages on earnings and employment in restaurants and other low-wage sectors.

So they're interested in two related elasticities, one of which was the one you initially suspected. Their table 2 will give you some estimates of those elasticities.

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Employment elasticity is the growth of employment relative to growth of Economy. Reforms of 1991 is a shift in era in Indian economic realm. Post Liberalization the major change occurred is the shift in population from agriculture to Manufacturing and Services. India traditionally being an agrarian economy, the low growth and heavy population pressure on land, disguised unemployment have led to people waiting for opportunity to change to a rapid growth environment and liberalisation provided a medium.

Despite aspiring for an Industrial economy during Nehruvian era, there was a marginal growth which could not sustain momentum resulting in low productivity in manufacturing as well. Post liberalization period gave an opportunity for people to turn to services with the growth of banking, financial sector, BPO industry, coming of internet. Though new employment opportunities have come but the rapid rise of population, urbanisation have made it mandatory to raise the employment growth. So, unlike expected post liberalisation has led to stagnation in employment growth. With deregulation of sectors and removal of licenses, emergence of private sector and employment in trade and tourism etc also tried to provide employment. But overall Employment Elasticity in India has been flexible till 1991 and post liberalization has made it rigid and sectoral composition to GDP of the country changed especially with rapid growth in services sector and marginal growth in manufacturing, and not much change in agriculture. The low employed industry of services is contributing maximum share to GDP is an evidence that employment elasticity is rigid posing a challenge to the current Indian government and revival of manufacturing through 'Make in India' could be a great opportunity to meet the growing requirements.

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