So what would an NDP government do?

Evening Star · June 28, 2015

Doesn't almost every developed democracy use a system of progressive marginal rates? It just happened in every one of these countries with no logical basis?

-1=e^ipi · June 28, 2015

Doesn't almost every developed democracy use a system of progressive marginal rates? It just happened in every one of these countries with no logical basis?

Almost everyone believes in a god? Does that mean there is a logical basis for the belief in god?

There is a difference between a specific tax system and just having a progressive tax system. The set of progressive tax systems is infinitely dimensional, so a belief in a progressive system doesn't tell you what those rates should be.

Edited June 29, 2015 by -1=e^ipi

-1=e^ipi · June 28, 2015

= -1/(1.481+t) - 1/(1-t) + 9.9834/(1.7504 - 0.5*t)^3*(3*t - 0.519)*mean(1/((w/mean(w))^2 - ((3*t - 0.519)/(1.7504 - 0.5*t))^2))

I obtain a maximum social welfare when t = 24.73%.

To find T, I have T = (1.5*t - 0.2595)*mean(wL) = (1.5*t - 0.2595)*H*mean(w)*(1-t)/(1.7504 - 0.5*t). Using H = 6051 and t = 0.2473 gives T = $4588.

Sorry I made a mistake on the last line. It should be:

= -1/(1.481+t) - 1/(1-t) - 9.9834/(1.7504 - 0.5*t)^3*(3*t - 0.519)*mean(1/((w/mean(w))^2 - ((3*t - 0.519)/(1.7504 - 0.5*t))^2))

This gives a flat tax of 9.53% and a transfer of $-5509. Basically it's saying that under the model, the gains made from reducing taxes (due to people working more) far outweight the losses in social welfare due to a less equal distribution of income. One thing to point out is that the model's estimation of labour elasticity could be very wrong.

-1=e^ipi · June 28, 2015

For an average effective tax rate of 50.3%, this gives a labour elasticity of 0.498.

It seems plausible, although it might be a bit on the high end of empirical estimates:

The two links I provided earlier are not good for overall labour supply wage elasticity. Here is a paper that discusses various estimates for Australia, Canada, Britain and NZ: http://www.treasury.gov.au/PublicationsAndMedia/Publications/2007/Treasury-Working-Paper-2007-04.

It suggests Australia's labour supply wage elasticity is around 0.14, although Canada's is probably lower (let's say 0.1). So my model could be overestimating labour supply wage elasticity by a factor of 5.

-1=e^ipi · June 28, 2015

It suggests Australia's labour supply wage elasticity is around 0.14, although Canada's is probably lower (let's say 0.1). So my model could be overestimating labour supply wage elasticity by a factor of 5.

I can take into account this empirical evidence if I change my utility function from ln( c) + ln(l) to ln( c) + 1/B*ln(l), where B is some unknown coefficient.

Under the more generalized utility function, setting the derivative with respect to L to zero gives:

0 = 1/(L + T/w/(1-t_m)) - 1/B/(H - L)

=> L = (BH - T/w/(1-t_m))/(B+1)

The revenue neutrality condition for the representative consumer is still T = (1.5*t_e - 0.2595)*wL.

Thus the labour wage elasticity is 1/(B + 1)*(1.5*t_e - 0.2595)/(1 - t_m).

If we use t_e of 50.31% and t_m of 55.87% for the representative Canadian consumer, then this gives a labour wage elasticity of 1.122/(B+1). Setting this equal to 0.1 (to agree with empirical data) gives B = 10.22.

If I isolate for H, I get H = ((B+1)L + T/w/(1-t_m))/B = ((B+1)L + (1.5*t_e - 0.2595)*wL/w/(1-t_m))/B = L*((B+1) + (1.5*t_e - 0.2595)/(1-t_m))/B. Using L = 1706 for the average Canadian worker gives H = 2060.

So this means that I should have used a utility function of U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + T) + ln(2060-L)/10.22 to better reflect empirical observations of labour supply wage elasticity.

Edited June 28, 2015 by -1=e^ipi

-1=e^ipi · June 28, 2015

If I redo this post with the new social welfare function:

Firstly, I want to resolve an issue. There is quite a difference between the total income earned by the individuals on that table (~1170 billion) and Canada's 2013 GDP (~1894 billion) ...

With the utility function that agrees with observations of labour supply wage elasticity, I have:

Physical Capital's share of income is 1/3 condition: (1.481+t)*r*sum(K) = (1-t)*sum(wL) + sum(T)
Revenue Neutrality condition: sum(T) = (1.5*t - 0.2595)*sum(wL)
=> (1.481+t)*r*sum(K) = (0.7405 + 0.5*t)*sum(wL)
=> wL = i*(1.481+t)/(2.2215 + 1.5*t) (if rK is proportional to wL)

If I combine this with the utility maximization condition (L = (BH - T/w/(1-t_m))/(B+1)) I get:

BwH = (B+1)wL + (1.5*t - 0.2595)*mean(wL)/(1-t_m)
=> BwH = (B+1)*i*(1.481+t)/(2.2215 + 1.5*t) + (1.5*t - 0.2595)*mean(i)*(1.481+t)/(2.2215 + 1.5*t)/(1-t_m)
=> w = ((B+1)*i + (1.5*t - 0.2595)*mean(i)/(1-t_m))*(1.481+t)/(2.2215 + 1.5*t)/B/H

Using this I can recalculate the wages by income group under the model as I did before. Once I have w I can get L as L = i*(1.481+t)/(2.2215 + 1.5*t)/w. And again, I can adjust H (to correct for the error due to the earlier assumption of the representative consumer) so that the observed average hours worked per worker agree with empirical evidence. I get H = 2200.

Edited June 29, 2015 by -1=e^ipi

-1=e^ipi · June 29, 2015

Redoing the 3rd part of my analysis, my utility function is:
U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL)) + ln(H-L)/B

The social welfare function becomes:
mean(U) = ln(1-s) - ln(1.481+t) + mean(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL))) + mean(ln(H-L))/B

From individual utility maximization I obtained BwH = (B+1)wL + (1.5*t - 0.2595)*mean(wL)/(1-t).
=> BH*mean(w) = (B+1)*mean(wL) + (1.5*t - 0.2595)*mean(wL)/(1-t)
=> BH*mean(w) = ((B + 0.7504) + (0.5 - B )*t)*mean(wL)/(1-t)
=> mean(wL) = BH*mean(w)*(1-t)/((B + 0.7504) + (0.5 - B )*t)
=> BwH = (B+1)wL + (1.5*t - 0.2595)*BH*mean(w)*(1-t)/((B + 0.7504) + (0.5 - B )*t)/(1-t)
=> L = BH*(1 + mean(w)/w*(1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/(B+1)
Using B = 10.22 gives:

Substituting this back into the 3rd term of the social welfare function gives:
mean(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL)))
= ln(BH/(B+1)) + ln(1-t) + ln(mean(w)) + mean(ln(w/mean(w) + (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t) + (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t)))
ln(BH/(B+1)) is just an arbitrary constant, so can be dropped without loss of generality to get:
ln(1-t) + ln(mean(w)) + mean(ln(w/mean(w) + (3*t - 0.519)/((B + 0.7504) + (0.5 - B )*t)))

Substituting L into the 4th term of the social welfare function gives:
mean(ln(H-L))/B = mean(ln(BH/(B+1)*((B+1)/B - 1 - mean(w)/w*(1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t)))/B
= mean(ln(BH/(B+1)*mean(w)/w))/B + mean(ln((1/B*w/mean(w) - (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/B
The first term here is a constant, so it can be dropped, leaving:
mean(ln((1/B*w/mean(w) - (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/B

This means that the social welfare function becomes:
ln(1-s) + ln(mean(w)) - ln(1.481+t) + ln(1-t) + mean(ln(w/mean(w) + (3*t - 0.519)/((B + 0.7504) + (0.5 - B )*t))) + mean(ln((1/B*w/mean(w) - (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/B

Using B = 10.22 Gives:
ln(1-s) + ln(mean(w)) - ln(1.481+t) + ln(1-t) + mean(ln(w/mean(w) + (3*t - 0.519)/(10.9794 - 9.72*t))) + mean(ln((1/10.22*w/mean(w) - (1.5*t - 0.2595)/(10.9794 - 9.72*t))/10.22

To maximize social welfare, the derivative of social welfare with respect to t must be zero:
0 = -1/(1.481+t) - 1/(1-t) + (1.5*(10.9794 - 9.72*t) + 9.72*(1.5*t - 0.2595))/(10.9794 - 9.72*t)^2*(2*mean(1/(w/mean(w) + (3*t - 0.519)/(10.9794 - 9.72*t))) - mean(1/(1/10.22*w/mean(w) - (1.5*t - 0.2595)/(10.9794 - 9.72*t)))/10.22)
= -1/(1.481+t) - 1/(1-t) + 13.94676/(10.9794 - 9.72*t)^2*(2*mean(1/(w/mean(w) + (3*t - 0.519)/(10.9794 - 9.72*t))) - mean(1/(1/10.22*w/mean(w) - (1.5*t - 0.2595)/(10.9794 - 9.72*t)))/10.22)

This gives a maximum social utility when t = 70.0% and T = $20892. Although with a VAT of 25% one has t = 56.67% and T = $26321. This also results in the bottom 7.5% of current income earners (the ones that earn less than $5000) choosing not to work at all. This results depends on labour-wage elasticity being as low as 0.1, which is arguably on the low end.

Edited June 29, 2015 by -1=e^ipi

-1=e^ipi · June 29, 2015

Just for the sake of it, I'll redo the analysis using the Australian labour supply wage elasticity of 0.14. This gives B = 7.01, which gives H = 2222 (which becomes 2406 upon removal of representative consumer approximation). This results at an optimal social welfare with t = 66.65%, T = $19522 or a VAT of 25%, t = 53.52% and T = $24595.

I'll point out that I didn't change who the social welfare function values the additional dollar of a rich person to the additional dollar of a poor person (still log utility), I just changed how people value their leisure time vs their consumption.

Edited June 29, 2015 by -1=e^ipi

-1=e^ipi · June 30, 2015

I decided to look at the correlation between health/crime and income distribution using 2012 data from 28 OECD countries. I used life expectancy as my health indicator and the inverse logistic transform of 'how safe people feel' as my crime indicator. Using a constant, the logarithm of GDP per capita and the square of the gini coefficient as explanatory factors I can do population weighted regressions. I found that GDP per capita has a positive and the gini coefficient has a negative effect on health/crime. However, in both cases the magnitude of the effect of the Gini coefficient relative to the magnitude of the effect of GDP per capita was larger than what would be expected if health/crime outcomes were a linear function of my social welfare function (which uses logarithmic utility). This suggests that the crime/health effects of poverty reduction suggest that more income redistribution would be optimal relative to what is determined using my logarithmic social welfare function.

PIK · June 30, 2015

Just read tommy was to join harper in 2007, but turned down 180g's and wanted 300g's. Was on the computer.

Evening Star · June 30, 2015

The Conservatives should definitely run with this story: "He's so bad he considered working for US!"

On Guard for Thee · June 30, 2015

Maybe they will re think that pay hike when they look at the polls.

cybercoma · June 30, 2015

Just read tommy was to join harper in 2007, but turned down 180g's and wanted 300g's. Was on the computer.

You just read it, eh? Like people haven't been talking about that since he ran for leader of the NDP. :rolleyes:

-1=e^ipi · June 30, 2015

Now that I think about it, there is going to be a difference between long run and short run labour-supply wage elasticity so my elasticity value is probably too low.

Argus · June 30, 2015

The Conservatives should definitely run with this story: "He's so bad he considered working for US!"

Or more likely "He says we're so horrible but he was willing to work for us for more money."

Edited June 30, 2015 by Argus

PIK · June 30, 2015

Sorry cyber ,I do work for a living and do miss some stories.

Evening Star · June 30, 2015

Or more likely "He says we're so horrible but he was willing to work for us for more money."

Eight years ago, before they had much of a record. A lot of people, myself included, were happy to see a minority government and the end of corrupt Liberal rule in 2006. A politician and environmentalist would have to be blindly partisan or crazy to not even consider the opportunity to advise the PM on the environment. This is a non-story.

Edited June 30, 2015 by Evening Star

PIK · June 30, 2015

LOL everything to do with the NDOP or the liberals is a non story. This is huge ,it shows us what a type of man he really is. He goes with the highest bidder. Is he still a citizen of france?

Evening Star · June 30, 2015

He goes with the highest bidder.

Really? The NDP in a Quebec riding in 2007 was the highest bidder? Could I see the numbers?

Is he still a citizen of france?

I don't see why he would throw this away.

PrimeNumber · June 30, 2015

This is a non-story to anyone who can think logically. To the conservative base it's huge because they've been clammering for something, anything to get their party out of the hole its dug itself into. Unfortunately for them this won't be the hard hitting story they're looking for.

PIK · June 30, 2015

You want to be PM ,then get rid of it. And how much does he make being leader of the NDP.

cybercoma · June 30, 2015

Sorry cyber ,I do work for a living and do miss some stories.

Right. Because anyone who pays attention to the news must be unemployed. What a dick comment.

cybercoma · June 30, 2015

LOL everything to do with the NDOP or the liberals is a non story. This is huge ,it shows us what a type of man he really is. He goes with the highest bidder. Is he still a citizen of france?

It's a big deal because the Conservatives courted an extremely popular Québec provincial Liberal minister of the environment to be a policy advisor on the environment? Stop the presses. When has a politician EVER crossed the floor?

On Guard for Thee · June 30, 2015

This is a non-story to anyone who can think logically. To the conservative base it's huge because they've been clammering for something, anything to get their party out of the hole its dug itself into. Unfortunately for them this won't be the hard hitting story they're looking for.

Clammering is correct. Mulcair has already bee interviewed about this and clearly stated he questioned the party position on environmental issues, especially Kyoto, he ended the conversation. I suppose the Harper machine will try to keep it going, but its already yesterdays news.

cybercoma · June 30, 2015

This is a non-story to anyone who can think logically. To the conservative base it's huge because they've been clammering for something, anything to get their party out of the hole its dug itself into. Unfortunately for them this won't be the hard hitting story they're looking for.

Dean Del Mastro, Stephen Harper's parliamentary secretary who was the CPC spokesperson for ethics, is led away from the court in ankle shackles after being prosecuted and convicted for election fraud.

No big deal.

The Conservatives offer Mulcair a bunch of money to advise them on the environment and he turns them down because they were completely at odds with Mulcair on Kyoto. Scandal!

It's hilarious.