MBIE-min-wage-model
This project reviews the model used by MBIE in their 2020 minimum wage review.
The OIA on which this review is based is available in the OIA subfolder.
In my tweets, I made three claims. In this document I will substantiate each.
1) ``The model was trained on data from 1996 to 2017. If you instead train the model on data from 1996 to 2020, you find that higher minimum wages create jobs.''
In code.txt, we see that the model MBIE use to predict the effect of minimum wage increases is
change in employment =
( (proposed min wage ÷ forecast average hourly rate)
- (current min wage ÷ current average hourly rate)
) × elasticity × population.
From code.txt, we have that:
- forecast average hourly rate = 1.009 × current average hourly rate
- current average hourly rate = 33.33
- current min wage = 18.90
- elasticity = -0.172
From page 59 of the review, we have that the population of all wage earners is 1914900.
Substituting these into the above equation, we calculate that the predicted change in employment from a $20 minimum wage is -9123 jobs. This matches page 7 of the review.
The elasticity of -0.172 comes from worksheet `M' of this Excel document. It's not obvious from that document what the variable names mean, but from sleuthing around the rest of the OIA and comparing different data sources, I've concluded that the elasticity comes from a first-difference log regression of employment on the real minimum wage, GDP, lagged GDP and average earnings. That worksheet also specifies that only years 1996-2017 are used in the regression.
I replicate that regression in the Stata do file replicate.do. When I use data from the years 1996-2017, I calculate an elasticity = -0.178, which is very similar to that calculated by MBIE. When I use data from the years 1996-2020, I calculate an elasticity = 0.017. This elasticity is greater than zero, implying that higher minimum wages increase employment.
2) ``The model predicts that higher minimum wages increase Māori employment. MBIE obfuscated this finding by grouping effects on Māori with the effects on young people, Pasifika & women, as the `groups most affected'.''
In code.txt, MBIE present a positive elasticity for Māori. In fact they also present a positive (but somewhat smaller) elasticity for Pasifika. The `groups most affected' language comes from the review.
3) ``The model has a coding error which results in the estimated impact being off by a factor of 2.''
Recall the model used to predict the effect of minimum wage increases:
change in employment =
( (proposed min wage ÷ forecast average hourly rate)
- (current min wage ÷ current average hourly rate)
) × elasticity × population.
That is evidently different to the log-linear model with which the elasticity is estimated. From my reading through the OIA files, I think that the model was, at some point, meant to have been changed -- but only the estimating equation was changed, while the code used to extrapolate that equation was unchanged. If MBIE had consistently used the log-linear model, they would have predicted that increasing the minimum wage from $18.90 to $20 would have reduced employment by 0.172×(log(20)-log(18.90)) = 0.9 percent. That would equal a loss of roughly 19000 jobs -- twice as many as they actually predicted.