Worthwhile Canadian Initiative

Rates, rents, shares, and capital theory

I think this is the technology that Paul Krugman has in mind:

1. C + Kdot = A.L^a.K^(1-a)

C is consumption, K is the capital stock, Kdot is investment, L is employment, A is a parameter that represents productivity, a is a parameter that (in competitive profit-maximising equilibrium) will equal labour's share of national income, so (1-a) is capital's share. (I've ignored physical depreciation of capital for simplicity).

Macroeconomists commonly assume this technology, mostly because it's easy to work with. But this technology creates a problem for Paul. That's because with this technology (in competitive profit-maximising equilibrium)  the (real) rate of interest equals the rental rate on capital goods (equals the Marginal Product of Kapital), and Paul wants to explain why capital income has gone up while the rate of interest has gone down. (So he has to assume that monopoly power has increased, and that what looks like an increase in capital income is really an increase in monopoly rents.)

Let me make one small change. Change 1 to:

2. C + Kdot/A = L^a.K^(1-a)

(I've divided both sides of 1 by 'A', then deleted the 'A' underneath 'C'.)

What is the link between labour's share of income, financialisation, and income concentration?

Bruce Bartlett draws attention to three developments in the US economy over the past 30 years or so:

1. The declining share of labour in national income in the US
2. The growing 'financialisation' of the US economy
3. The concentration of income at the top of the US income distribution.

Production of Robots by means of Robots.

(Sorry about the title. The devil made me write it.)

What are we afraid of? Let's think about the worst-case, nightmare scenario for the distribution of income.

Assume that all capital is robots, and robots are perfect substitutes for human workers. One robot can produce everything and anything one human worker can produce. And that includes producing more robots.

And assume that every year the technology of robot production improves, so that it takes less and less time for one robot to produce another robot.

That sounds nightmarish, right? Because robots will get cheaper and cheaper, and drive down human wages?

Well, no. They won't. Or rather, it all depends. It depends on whether we add other forms of capital, or land, to the model.

How much revenue can the Quebec government generate by increasing tax rates on high earners?

The newly-elected Parti québécois government wants to (among other things) eliminate the 'health tax' introduced in the 2010 budget and make up the shortfall by introducing two new tax brackets at the top end of the income distribution:

• 28% for taxable incomes above $130,000
• 31% for taxable incomes above $250,000

The current top Quebec rate is 24%, and it applies to taxable incomes above $78,000. The top federal rate of 29% kicks in at around $130,000, so the (net of the 16.5% Quebec abatement) federal + provincial top rates will be

• for taxable incomes above $130,000: 29*(1 - 0.165) + 28 = 52.215% (up from 48.215%).
• for taxable incomes above $250,000: 29*(1 - 0.165) + 31 = 55.215% (up from 48.215%).

If you assume that there are no behavioural responses to the new tax rates - that is, if you perform a static analysis - new revenues work out to around $835m. But if you incorporate the sort of behavioural responses based on available data - 'dynamic scoring' - you find that revenues will more likely to be half that, and probably less.

I'm going to work through the math below the fold.

Inequality rules

Last March, Bell Canada Enterprise circulated its 2012 executive compensation policy: 

we use three key elements of compensation with an aggregate target value positioned at the 60th percentile of what is paid in the competitive market for similar positions.

A few weeks later, Human Resources minister Diane Finley announced "a more efficient and responsive temporary foreign worker policy". This new policy allows employers to pay temporary foreign workers up to 15 percent less than the prevailing occupational wage rate:

"Does monetary policy have (bad) distributional consequences?"

Some questions are bad questions. This is one of them. We can get a clearer and more useful answer if we change the question. We can avoid wasting a lot of time arguing at cross purposes.

Here's a better question: "If we used fiscal policy instead of monetary policy to remove a shortage of aggregate demand, would that switch from one policy to another have distributional consequences?" The answer is almost certainly yes, though what those distributional consequences are will depend on the exact nature of the fiscal policy.

Here's an even better question: "If we assume that monetary policy always responds to changes in fiscal policy to keep aggregate demand at the same level, will changes in fiscal policy have distributional consequences?" Now the answer is certainly yes, though what those distributional consequences are will depend on the exact nature of the fiscal policy.

[Update: now I think about it, I think my third question is actually the same as my second question; just a clearer way of saying it.]

Morals? Can't afford them.

Noahpinion, Tyler Cowen and others have recently posted about the deserving poor. 

Some identification problems in the debate on taxing top earners

Two recent papers on top-earner taxation have made an important contribution to the policy debate on the topic, but it seems to me that we still have some way to go before we have an understanding of the phenomenon that is robust enough to use as a basis for policy.

Provincial Government Health Spending: The Equity Dimension

The meeting of the federal and provincial/territorial health ministers in Halifax on Thursday will be preoccupied with the sustainability of health expenditures and the coming negotiations over the renewal of the health care accord.  Naturally, the provinces want to ensure that federal transfers continue to rise to meet their needs while the federal government will be focused on the rate of increase of its health transfers as well as the need to ensure value for money from those transfers.

The rise in provincial government health spending and the tendency for its growth rate to outstrip revenue growth has been well chronicled.  However, another dimension to health spending is its distribution. 

On 'first-order' and 'top-end' inequality, and why the distinction is important

The debate about income inequality seems to be happening at two levels, which I'm going to label "first-order" and "top-end" inequality.

1. First-order inequality is visible in standard measures such the gini coefficient, and shows up as an increase in the gap between average and median incomes.
2. Top-end inequality refers to the share of income that goes to those whose income puts them above the 99th percentile and beyond.

No, we really don't want to reduce inequality

A few weeks ago, Mike Moffatt wrote an op-ed that ran in the Ottawa Citizen and several other PostMedia papers to the effect that there simply isn't the will on the part of 99% of the population to do much about inequality: if there were, there'd be more popular support for the sort of tax-and-redistribution measures that would actually be effective in reducing inequality. Instead, we get stuff like this:

Soldiers of fortune, department chairs, and CEO pay

Assume ten identical young men. One of them is needed to do a dangerous job which creates disutility for the person doing it. Assume they have diminishing marginal utility of consumption. Assume (though a weaker assumption can get the same results) that the utility function is separable in consumption and the type of job.

There are two ways to allocate resources:

1. Volunteer Army. The nine compensate the one at exactly the right level so that all are indifferent between doing and not doing the dangerous job.

2. Conscript Lottery. The ten hold a lottery, and the one who draws the shortest straw does the job.

"Just one more dying quail a week, and you're in Yankee Stadium"

The incomes earned by elite athletes are often cited as examples in arguments to the effect that high incomes aren't a problem that need solving. If large numbers of people are willing - eager, even - to give small sums of money to watch Wilt Chamberlain play basketball, then on what grounds would anyone begrudge Chamberlain's salary or the system that generated it?

I was thinking about this while watching Bull Durham for the umpteenth time. Especially this part:

Canada's redistribution policy: take from the rich, give to the ... median?

Much of the public debate on income inequality focuses on what is happening with market incomes. But most people generally accept that a certain level of inequality in market incomes is inevitable, and indeed necessary in order to provide the sort of incentives that generate economic growth. What really matters is inequality of income net of taxes and transfers. If increasing inequalities in market income are compensated by stronger redistribution, then there's less to worry about.

Unfortunately, that doesn't appear to be happening. A few weeks ago, I noted that Canada's tax-and-transfer system had become less effective in reducing inequality, as measured by the Gini coefficient. In this post, I'm going to look at how taxes and transfers have evolved for the various income quintiles. It reaches the same conclusion, but it also suggests a reason why the system has become less progressive.

Why the Gini?

Stephen Gordon recently posted an excellent analysis of trends in income inequality in Canada and elsewhere. Stephen, like almost all of the other authors cited in his post and the subsequent discussion, measured inequality using the Gini coefficient.

The very next day, I saw a paper by Francesca Greselin arguing that the Gini is inferior to the new Zenga inequality index and should be replaced.

Talk about deja vu all over again. Various limitations of the Gini inequality index have been known for years. Tony Atkinson described some and proposed an alternative to back in 1970; other indices for measuring inequality are the Theil index, and the Hoover index. Greselin and co-authors set out new arguments, and make a convincing case for replacing the Gini. But I don't expect to see the Zenga index in wide use any time soon.

We keep on using the Gini because that's the way people have always done it. But why did people even start using the Gini in the first place?

Can demographics explain why the income shares of high earners have increased?

The increasing concentration of incomes among a small number of high earners has been documented at length here ([1], [2], [3]) and elsewhere. Any sensible response to this development has to be based on at least a partial understanding of how and why this trend began - and we still don't have a theory that seems strong enough to use as a basis for policy.

Here is a story that makes sense to me. Then again, I may be putting one and one together and getting eleven.

On trends in inequality in Canada, the United Kingdom and Sweden

The Conference Board released a study on trends in inequality, so I decided to update the data from this old post. Here's what I found: if you measure inequality using the Gini index, you'd conclude that after increasing during the 1980's, inequality levels had stabilised since 1995.

Wealth and Its Distribution: Tomorrow is Yesterday

Wealth and income inequality is a big issue and I thought some historical perspective on wealth inequality might be interesting given that my research to date has led me to conclude that little has changed for the bottom of the wealth distribution at least in terms of relative wealth shares.  While there has been the growth of a middle wealth holding class over the last one hundred years in Canada, the wealth share of the bottom half of the wealth distribution is remarkably unchanged. 

Asset Management

My brother thinks of himself as a farmer, which he is. But I think of him as an asset manager. He has chosen to hold his assets in land, tractors, ploughs; and that's him, driving his tractor, pulling his plough over his land, fixing the tractor, fixing the plough, managing his assets. He earns his income doing the 1001 things he needs to do to get the best return from his assets.

Reconciling the Minimum Wage Literature

I'm a health and fitness nut, so I read a lot of health studies as well as using my own body as a guinea pig.  I've discovered a lot of things - for instance, I don't know if using creatine monohydrate leads to more strength gains than using a placebo, but I do know it makes you pee every 15 minutes.

Reading health studies (or even worse, hearing reports of health studies) can be incredibly frustrating as they often appear to be contradictory.  Caffeine is good for you. Caffeine is bad for you. Ephedrine and ECA stacks are dangerous. Ephedrine and ECA stacks are effective and safe to use, etc.  What to believe?