Khaki Economist

While Eviews may be a more limited system than R overall, it has a couple of really cool features. One, which I have found very useful, is the ability to put strings on the left hand side of an assignment. This allows the user to generate objects with names obtained from a string list. This is useful when you want to do the same thing for data in lots of different industries (treating them seperately).

For example, you could define a list of industries:

%industries = “Ag Manu Services”

then run a loop, generating, say, nominal values

for %i %industries

series nominal_output_{%i} = real_output_{%i} * price_{%i}

next

which generates appropriately named series for each industry. This is considerably more difficult in R, at least to my knowledge. Here’s my workaround:

industries <- c(“Ag”, “Manu”, “Services”)

for(i in 1:length(industries)){

a <- industries[i] # a becomes a string variable containing, sequentially, the industry name

real <- paste(“real_output_”,”a”, sep = “”) # real becomes a string obtained by concatenating “real_output_” and the string

real_series <- eval(parse(text = paste(“price”,”a”,sep=”"))) * eval(parse(text = paste(“real_output_”,”a”,sep = “”))) # eval(parse(text = … is a way of evaluating a string as the name of an object, so here we generate a series called “real_series” which contains the relevant value for that loop

assign(real, real_series, inherits = TRUE) # and here we assign the series to the name.

}

It’s a pretty ugly workaround (and what I’ve found in my short stint of being an R coder is that when something’s not elegant, there already exists a better way, or you’re trying to do something that you shouldn’t be trying to do), but it works. If you do know of a better way, please let me know!

Mexico City’s Buena Vista Walmart is the first super-market I’ve ever seen paralised by a trolley-jam. It is not more busy than any other large city supermarket, and not understaffed. No: the reason it takes ten minutes to walk from one side of the store to the other every single night is because they have no baskets—only large trolleys. To my sample of Mexican Walmarts, this is unique; most Mexican Walmarts have trolleys and baskets. And so the error must have been made by the managers of that particular outlet. Of course, this is only a small example of inept management in Mexico, but it’s sadly representative—labour productivity in Mexico is about a third of that in the US. If Mexico were as well managed as the US, it would be as rich.

This all raises a few questions: why are managers in Mexico (and the developing world in general) so terrible? why are those in the US so good? and how much of the difference is able to be affected by policy?

Management in Mexico

There are many well managed businesses in Mexico, and they do very well. This suggests there are large returns to good management, and we should expect, over time, well managed businesses to displace poorly managed businesses. To an extent, this has occurred already; Walmart and Appleby’s have slowly usurped street markets and cantinas. But the pace of this transition is slow, and still most of the businesses most Mexicans deal with are run terribly, exacerbating poverty. I attribute this poor management to three causes: Mexico’s caste system, nepotistic/senioric hiring, and its abysmal school and university system.

First, Mexico actually has a caste of idle rich, which surprised me. In Australia, it’s typical that small business owners (and most large business owners) work harder than any of their employees. In Mexico however, it seems the entire point of owning a business is to avoid any painful task.

To characterise, there are some jobs which appear to be below Mexico’s entrepreneurs, and so potentially labour-saving or product-improving changes to businesses are either not realised or not acted on. In the restaurant I worked at for 3 weeks, the owner never looked inside the fridge. Had she, she’d have discovered motzarella, stored on top of raw pork sausages, which were placed directly on top of (not above: on) raw lettuce. This didn’t bother the kitchen workers—generally poor and uneducated—and so nothing changed. I lost 3kg in a day after eating from that kitchen.

So if the business owners don’t want to work, why don’t they just hire a good manager, and incentivise them with a suitably-worded contract? This problem confused me, until hearing an anecdote from a former classmate who now works in a Mexican central government department.

All public-sector job openings in Mexico have a selection process that involves, as the second-last hurdle, completing an exam. Of course, preferential hiring always finds a way: on helping to fill a senior position, my former classmate, who had worked with the preferred candidate, was instructed to write an exam that only the pre-chosen candidate could pass.

We sadly expect corruption like this in the public service of poor countries, but not in private enterprise. However we still see well-run businesses (like Walmart) hiring incompetent managers, and then not firing them. My suspicion is that much of the cause for this is the low level of security, which has begot Mexicans’ low levels of trust for those with whom they’re not acquainted. They hire an incompetent manager not because they know the manager is good, but because they know he’s not a thief.

Of course the first two reasons can be remedied by educating people. Caste can be dissolved when there’s some prospect for dish-pigs to become hotelliers, and hiring a stranger can be easier when you know that their education probably indicates competence. But on almost any metric, Mexico’s education fails. In the OECD league tables, only Brazil and Indonesia do worse. It’s not poverty—in the 90s when Korea was as well off as Mexico (it’s now twice as well off, which is telling), it still did better than the US. Of course, if children aren’t being taught to do difficult things well, universities have to pick up the slack, but in this respect, Mexico still lags: only a handful of universities educate their students to anything near a world standard. So there’s probably little reason to expect a new generation of world-class managers.

Management in the US

On returning from holidays in the US, Australians usually rave on about two things: terrible coffee served by excellent waiters. These two things are really a symptom of the same phenomenon: Americans’ desire for well-priced consistency. This is centuries old: economic historian Nathan Rosenberg points out that the great immigration westward was facilitated by cheap (not fancy) balloon houses; that the conveyor-belts of early factories were more standardised than abroad, lowering down-time when piece of machinery broke; while on the Continent skilled craftsmen made excellent, expensive things, the uneducated of America produced, by the million, less-good, less-expensive things. There is no way of producing many good, cheap things without deliberate management.

While much has been said about the Taylorism of American management—the reduction of food making to a production-line job requiring little training, for instance—I’ve seen little written about the accompanying phenomenon: the desire of American managers to turn their business into an institution. It may be gimmicky, but it seems to work. In Seattle WA, fishmongers throw fish at each other in front of tourists’ cameras; in Bakersfield CA, the town’s most popular Italian restaurant has hundreds, no thousands of photos of footballers and old newspapers pinned up on the wall; in Austin TX the best tacos are the Korean ones; LA’s favourite fast-food burger joint has an off-menu menu; and all through the country, evening road-trippers pull in at Denny’s diner to be greeted “Good morning, and welcome to Denny’s”.

The fact is that managers of businesses in the US take their role as managers far more seriously than anywhere else I’ve spent any time.

The Role of Public Policy

If I am attributing the differences in productivity between Mexico and the US to private-sector management, then what role policy? We surely can’t force businesses to be better managed. But there are some public policies (or lack of) in Mexico today which, if continued, are likely to perpetuate poverty.

- Mexico has an abysmal education system, particularly in fostering critical thinking and mathematics. It also has a culture of ‘rule-of-thumb’ (as do many relatively uneducated countries), and so getting people to accept new ideas is incredibly difficult relative to the US. Unsurprisingly, the Mexican education system is terribly corrupt, with tenured teaching jobs effectively sold or bequested, and La Maestra, the head of the the Union, being one of the most powerful political players in Mexico. Short of a very costly industrial war, there does not seem to be an easy way out of this equilibrium.

- There is no Productivity Commission in Mexico. There are plenty of great economists, especially in Mexico City and Guanajuato, but neither Federal nor (more powerful) state governments give them toothy roles in government. In Australia, where we have a very well respected Productivity Commission, commissioned reports serve as talking point documents for both sides of parliament. The result ends up being that on both sides of parliament there is nominal acquiescence to themes of productivity, especially over the long-run. Even union bosses aren’t arguing for a return to the bad old days.

- Mexico’s informal economy and poorly-developed banking system go hand in hand. Because so many businesses work solely in cash, they have no financial history able to be verified by banks: a prerequisite for any serious lending.

This leads to incredibly low deposit and loan rates. According to MarketWatch, in 2010 total bank deposits were about 15 per cent of GDP, compared with over 100 per cent of GDP in Australia. There is little surprise that small businesses–even the ones that are more productive–fail to grow if credit market access is off the table.

This is partly the fault of Mexican banks, which, despite being private institutions, are ridiculously poorly managed. Electronic banking is hardly used (for payments, salaries, anything!) and queues at major banks can be several hours long. Forcing businesses to formalise could only work if banks come up to speed, and if bad policies like deposit taxes (!!!) are removed.

While Mexico’s poverty is almost solely a result of poor management (even within the private sector), there are some policies which affect productivity in the long-term. I’d be interested to hear your ideas.

Many large organisations use internal “performance management” “systems” to check up on and rate their staff. Unfortunately, this task isn’t easy: managers typically observe only a part of an employee’s work, and so can only give a biased appraisal. Most managers know this, and so ask colleagues for their thoughts on other colleagues. This process has, in the management textbooks (and probably on the Weasel Words website), become known as 360 Degree Feedback.

To some, this process causes undue stress, and in particular teams or organisations, may be unproductive; people generally don’t like being made to bitch about their colleagues (even those who voluntarily do it!), perhaps because they themselves don’t like the idea of other people bitching about them.

While monitoring staff is an essential function of management, there must be an easier way. Below I describe a method of collecting the relevant data, without the potentially disruptive side effects. It is based on a Hamming code, a type of linear error-correcting code used in information theory.

First, I contest that the only thing that really matters in a monitoring context  is whether someone is below an acceptable threshold or above it. It is obvious when someone is clearly above a threshold (at which their wage is set), because they will ask for a promotion or leave.

This makes the job easier—all we need to do is rate people on whether they can or can’t do certain aspects of their job. And so the process works like this:

1: Each person in the organisation nominates a list of people they feel able to give an assessment on.

2: Management creates a list of criteria, which needn’t be applicable to all levels of the job function. There are always two wordings of each criteria.

3: Each person then completes a questionnaire, in a room by themselves. This questionnaire gives three names (which have been randomly drawn from the list provided at step 1), and a criteria to assess the three names against.

4: The person then has to write whether there is an odd or an even number of people in the list of three who satisfy the threshold.  They do not specify who they consider competent, nor how many.  This may be replaced with a question asking how many of the three satisfy the threshold, and this improves quality slightly.

5: The manager ranks each person for each of the necessary criteria.

By Hamming’s 1950 insight, it turns out this is sufficient to determine with an arbitrary degree of accuracy (for large groups) who exactly is incompetent. By auditing employees on several characteristics, it’s possible to then create a ranking of employees. This ranking should, in general, match up with the pay and hierarchy of the organisation. That is, people in more senior positions should not be failing on criteria passed by junior employees, while junior employees should not be showing “strategic leadership”.

I am a hopeless addict of economics blogs. So I thought I’d compile a short list of blogs that are relatively un-read, despite being better than the blogs which seem to get a lot of attention.

1. David Warsh’s Economic Principles. Warsh has about a thousand subscribers on Google Reader, versus forty-five thousand for the drivel produced by Brad DeLong. His posts are long, well written, and, importantly, not written by Brad DeLong.
2. James Hamilton’s and Menzie Chin’s Econbrowser, which ahs 3000 odd subscribers relative to the 70,000 had by Paul Krugman. Unlike Krugman, this blog has nice, considered long posts which consider the data above politics. It is also the best econ-blog.
3. Andrew Gelman’s blog, which has 4000 subscribers relative to Freakonomics’ 13000. While this is not strictly an econ-blog, it contains more thought than most of them, and has a lively, well-behaved considerate comments section.
4. John Cochrane’s new blog, which has a thousand subscribers. It’s perhaps a bit too early to tell, but the posts are long, fairly well considered, and, except for one spat with DeLong, have largely avoided mudslinging. Cochrane’s a pretty serious character in the field, and I really hope the blog turns into him imparting his wisdom on the readers.
5. Austin Contrarian is a great little blog (130 subscribers) on town-planning issues, especially considering the intersection between urban economics, local politics, and law. These issues actually affect our lives far more than what DeLong writes about, and so you should subscribe!. Unfortunately, it’s been a bit quiet lately, but I’m sure with enough pestering, Chris will blog frequently again!
6. Harry Clarke’s blog. Again, another small blog (130 subscribers) though highly respected in the Australian econ-blogging community. His longer posts on environmental econ are especially good.
7. Andrew Norton’s blog. Andrew has a small but loyal following in Australia. His posts are data-driven posts, primarily on higher education. Definitely worth reading.
8. Zero Intelligence Agents. Drew Conway is a PhD student in political science, who seems to have become an R addict in the mean-time. I relate to this, as it’s also become my addiction.
9. VOX. I really can’t believe this only has 6000 subscribers on Google Reader. Hundreds of authors, thousands of posts, all driven by the latest research. Kind of like a repository for extended abstracts.
10. ?

Below I outline an idea to address the productivity growth shortfalls in the electricity, gas, and water industries recently experienced in Australia. Especially given the likely increases in electricity and gas costs from the carbon price, now is a good time to reconsider the structure of the retail utilities market.

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In December, Martin Ferguson announced that the Productivity Commission would be commencing an investigation into electricity network regulation. This move is welcome: after large gains in productivity growth following partial or full privatisation in the 1990s, water, electricity and gas distribution have seen their productivity growth rates plummet.

“In electricity, gas and water supply, the level of productivity fell by around one-quarter this decade and, though this fall is largely inscrutable, it is clear that productivity improvements from streamlining workforces and running capital closer to capacity have run their course.” –Dolman, B., 2009

Such a slowdown affects Australians far more than the much-publicised decline of Australian manufacturing. While manufactured goods can generally be imported, our utilities can’t, and so increases in productivity leads to equivalent real price decreases.  Because we haven’t seen productivity increases in utilities as we have in other consumer-industries (been to Aldi or Costco lately?), this means that the real cost of utilities has been increasing recently, and now takes a larger proportion of household final consumption expenditure than in any time in the last half century.

Source: ABS, 5204 Table 42—Household Final Consumption Expenditure (including imputed rents). Data construction is (Water and sewerage services + Electricity and gas services) / HFCE (all current prices).

Of course, this increase could be driven by an increase in relative prices of utilities to other consumption goods, or an increase in the amount of utilities demanded to other goods, or both. However, the data tend to suggest that the large increases in costs are due primarily to price increases (see figures below). While this recent period has also seen large increases in input costs (due to a commodity price surge and a drought), the same forces were at work before the recent increase in prices, which leads me to suspect there’s something else going on.

Source: ABS, 5204, Table 42. 

There are reasons to suspect that there are economic rents made in the utilities rent business. These rents occur because there are fairly real transaction costs in account switching providers. That’s why second-tier retailers (ie. the retailers who don’t own wholesale or distribution businesses) send people door-to-door trying to get you to switch. If rents do exist in this industry, then there are productivity and welfare gains to be had by redesigning the retail market in order to eliminate them.

The cost of choice?

In a paper investigating different models of retirement pensions, Peter Diamond (1996) looks at the Chilean pension model. In the early 1980s, Chile privatised its pension in a system (resulting in a system similar to Australia’s Superannuation system, only with tightly regulated private fund managers competing to manage the retirement savings of workers). While their returns were good, their management costs were excessive—up to about 3% of the average annual income of an employee. The overheads of these firms were so high partly because the returns to marketing were so high—if you didn’t market, you didn’t get any funds to manage, and you went broke. This means higher fixed costs: Chilean pension-fund managers had 3.5 salespeople for every 1000 accounts, whereas the total employment of Social Security was 0.5 people per 1000 accounts.

Diamond’s more recent insight is that this excessive ‘cost of choice’ can be remedied by the state taking a somewhat more active role in market design. His proposal is for the government to aggregate groups of people with similar levels of risk-tolerance, and run a closed-envelope tender for the business of managing the groups’ pooled funds (which simply take some combination of an index and government bonds, depending on the risk profile of the portfolio). Because a) the cost of managing an index is minimal, b) the marketing costs of this type of operation are the cost of submitting a tender, and c) the price elasticity facing any firm becomes very high, the equilibrium management fees for this sort of retirement plan become very low: the TSP, which runs in this fashion, had management fees of 2.5 basis points in 2011; Australian Super had 16-79 basis points + other expenses.

Diamond extended this idea to insurance in the early 1990s: you could group people together, geographically, in large enough groups to eliminate selection problems, and offer their collective business (well enough defined) to the cheapest insurer, you would see large falls in insurance prices.

But what about choice?

Choice is good to the extent that it offers people the quality they want at a price that is reasonable to them. However, with homogeneous products, there is less of a quality/price trade-off.  This means that, if a reduction in choice of contracts for a homogeneous commodity is accompanied in a reduction in prices, there exists a number of (reduced) choices which can leave everyone’s welfare improved. One only need to choose the contract which is closest to their ideal contract, and, so long as the person’s preferences aren’t odd, the reduction in price should offset or more than offset the decrease in utility that occurs by the person not being to purchase the perfect contract.

The flip-side of this is that the fewer choices offered, the greater the saving must be to compensate people (in utility terms) for the reduced choice.

So what to do about utilities retailing?

IF there are large marketing costs in utility retailing, or there are rents in utilities retailing, or both, then prices could almost certainly be decreased by adopting a geographic-pooling scheme.

This would involve drawing squares on a map, and designating each of these squares a ”pool”. The members of each pool would then elect a contract “type”, roughly equivalent to the sorts of choices your electricity provider would provide you. The information on aggregated types for each geographic pool would then be sent to the retailers, who could then nominate a price for service which would bind for the following 6 months. Towards the end of the period, the firms could re-contest the pools.

The result of this would be that utility retailing firms would not need a marketing division, and would simply need to offer the lowest price in order to get business. Their monitoring costs would also be reduced, as metering agents would not need to travel as far (every building in the pool would be a customer, rather than some smaller share).

If, in period, there were things like black-outs or water interruptions, the firm would loose the ability to re-bid for the pool’s contract the next period.

The potential problems would lie in the potential for collusion, and the problem of introduction. The returns to collusive behaviour would increase as the potential spoils increase, and so this would need to be monitored. The problem of introduction would be that there are pre-existing contracts made between retailers and households. I don’t know anything about contracts, and so I’m not sure how this would be remedied.

Diamond, P., Proposals to restructure Social Security, The Journal of Economic Perspectives, vol 10, no. 3, 1996

Dolman, B., What happened to Australia’s productivity surge, The Australian Economic Review, vol  42, no. 3, 2009

Overview:

In the long run, standards of living are almost entirely determined by productivity—the ability to produce more with the same resources.  However, sometimes “productivity improvements” are used as an excuse for bad policy. These types of productivity improvements, while improving productivity, don’t actually improve the welfare maximising consumption possibilities of the population over the long run.

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Differences in levels of productivity explain most of the difference in living standards between poor countries and rich countries. However, the way in which it is commonly measured may give politicians the wrong idea when they use public funds to promote pet industries in the name of “improving productivity”.  This is because there is an inherent difference between the productivity measure reported in the National Accounts and that which describes the improvement in “consumption possibilities” (sorry, terrible jargon) of the population. This insight is due to William Nordhaus (2000).

How do we measure productivity?

Productivity is simply the amount of output of a firm or economy, divided by the amount of inputs. A commonly used measure, which I alluded to yesterday, is “labour productivity”, which is total output divided by the amount of labour used (we normally use an estimate of the number of hours worked for this).

It makes sense that improving productivity should improve living standards. Say I am living on an island, and I eat only corn. In the first year I produce 40 bushels of corn; in the second year I produce 50. It’s clear that I am able to eat more the second year. This seems to be how politicians think about productivity, which is fare, as this is how it’s published by the ABS also.

There are three main problems with carrying the island analogy across to an entire economy. The first is that in a real economy, we have many different products and industries, and these change over time. The second is that we trade with foreigners. The third is that while improvements in productivity are more feasible in some industries than others, “feasible” isn’t the benchmark which should be used.

The first one and a half of these problems is what Nordhaus discusses in his paper, which I encourage interested people to read.

The implication of there being many sectors is that “productivity”, as measured by the ABS, can be attributable to:

1) The pure productivity effect. This is when firms produce more with the same amount of inputs. You measure this by holding industry shares constant, and looking at the increase in productivity. Some people call this the “Shift effect”.

2) The so-called Baumol effect. This is when, although no industries improve their rates of productivity, a relatively productive industry increases in size by a greater amount than an unproductive industry. To measure this, we hold the levels of productivity constant and look at the difference in industry shares, which is why we call this the “Share effect”. William Baumol gets the naming rights as he noticed that industries with relatively high productivity growth seemed to grow faster than industries with low rates of productivity growth, and this improved the total productivity of the economy.

3) The Denison effect. This happens due to an interaction between the first two. You can think of it as the pure effect of having some people leave the unproductive sector and start working in the more productive sector. If we say that both sectors grow at the same rate, this means that the average productivity of the remaining workers in the unproductive industry is higher, as is the productivity of the workers who left to work in the productive sector (even though the average productivity of those in the productive sector has decreased). The net effect is the Denison effect.

The next problem raised by Nordhaus is that if you want to measure productivity as it actually affects livelihoods you shouldn’t look so much at production as you should at consumption. While this can’t be wholly divorced from the trade argument I will make below, I will try.

Let’s suppose for a sec that the country does not trade, and that all industries produce final consumption goods. Then which components of productivity above should we include in the “welfare maximising” productivity measure? The reader should realise that the first two (the pure productivity and Baumol effects) both imply that the country makes more stuff without more effort. As such, they improve welfare. The third effect occurs due to differences in inter-industry productivity, which may be due to heterogeneity in the inputs. To the extent this is true, we’re not comparing apples with apples; the inputs we use in a sector with vastly lower productivity aren’t likely to be the same inputs we use in a more productive industry. Consequently our welfare maximising productivity growth does not include the Denison effect (Nordhaus’s argument is slightly more nuanced).

For simplicity, the model used by Nordhaus to deduce the above relies on there being perfectly competitive markets. One of the main consequences of that assumption is that the producers produce consumption goods exactly in concordance with the desires of consumers. In real life, things ain’t so simple. If governments encourage certain types of production (by subsidising) and discourage others (by taxing/imposing tariffs) there is no reason to expect the levels of production of goods to match up with what people want to buy.

The unfortunate result of policies like the car subsidy package is that, while they are perhaps inspired by claims of higher productivity in heavy industry, they resulting changes in productivity are largely due to the Denison effect, and so don’t improve productivity in a meaningful way as much as advertised. That is, the policy doesn’t lead to higher consumption in cars in Australia, and almost certainly reduces the consumption of other things. This becomes a stronger argument once we accept that we trade with foreigners.

So what does trade imply?

A difficulty is that some sectors are able to improve in productivity, while others cannot. This latter category includes the likes of hairdressers and string quartets—non-tradable goods and services with almost no scope for productivity changes. Of those sectors able to improve in technology, we can break them into non-tradeable and tradeable sectors.

In Australia, there are some sectors like banking, telecoms and other utilities who have had strong growth in productivity, and are almost untraded. As a paper by my old boss Ben Dolman points out, there is still much scope for improvement in these sectors (by international standards). Because gains in productivity in these sectors are reaped by Australians, productivity improvements in these sectors are very likely to lead to welfare improvements.

Other industries, like mining and manufacturing, are also traded, and there is also scope for improvements to productivity. In mining, Australia’s productivity is above world norms (though this is likely a remnant of our coal being at surface rather than deep underground). However, in manufacturing Australian productivity is about half the US’s. This likely due to scale (see table below, from Dolman’s Productivity Commission working paper).

Australian wages are in exchange-rate weighted terms about the same as the US’s. American workers are also better trained, and have more capital per worker. So why would any foreigner in their right mind buy an Australian manufactured good over an American one? It will almost certainly be more expensive, and equal or lesser quality. To close this price differential, Australian manufacturers would have to more or less double their productivity—and almost impossible task without the scale possible in the US.

Put a bit more plainly, this means that the only way that a policy like car subsidies would improve Australian welfare is if it improved productivity by so much that Australian cars weren’t so expensive by world standards, and this resulted in more exports, and this allowed us to buy at lease one more of the goods that we gave up in order to subsidise the car industry.

But industry policy aimed at boosting Australian productivity (the good kind, not the fake kind) needn’t be so difficult. Simply reduce bottlenecks in infrastructure impeding the industries which do already export—like mining. Each dollar invested there will improve Australian welfare by multiples of the dollars used to make V8 sports-cars nobody wants.

–Nordhaus, W., “Alternative methods of measuring productivity growth”, Cowles Foundation Discussion Paper 1282, 2000

–Dolman, B., Parham, D., Zheng, S., “Can Australia Match US Productivity Performance?”, Productivity Commission Staff Working Paper, 2007.

Overview:

A popular model which is often used to teach economic growth (and explain why some countries are richer than others) is the Exogenous Growth Model, attributable to the work of Trevow Swan (ANU) and Rober Solow (MIT) in the 1950s. This model says that for most countries, economic growth occurs due to the relentless ability of firms to work out ways of doing the same work with fewer inputs. This contrasted with earlier models which said that all countries needed to do was save more in order to buy machines.

While simple, the model captures some of the interesting relations in an economy, and can help non-economists with high-school mathematics understand why some countries are rich and others poor.

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At the core of most contemporary macroeconomic thinking lies some notion of “exogenous growth”. This post describes this important concept as intuitively as possible, for economics students, or for people who may be interested in why some countries are richer than other countries.

Before launching into the details of the model, though, it’s important to recognise why economists like it so much. When building a toy model of the economy, you must keep in mind a set of things which you want your model to replicate. The rules Swan and Solow wanted to replicate were Nicholas (later Lord) Kaldor’s Facts:

Lord Kaldor, a British economist, noticed a few rules which tended to hold across countries and time. These are:

1. There is no long-run trend in the return to capital. This is contrary to the Marxian conclusion that capitalists earn more and more on the same investment. While there are periods when capital earns more, and less, there is little time-trend to these.

2. There is no long-run trend in the capital share or labour share of income. This is a bit different to #1. In #1, we were interested in the return to invested capital. In #2 we are interested in how income is split between wages and retained earnings/dividend payments. #2 says that the amount of income that goes to capital (which in turn may be owned by anyone) has no time trend.

This is not to say that it is impossible for such a thing to occur (it may have in the past while in the US), just that it’s not such a dominant force as to include it in a toy model of the economy.

3. Income per capita seems to show fairly constant growth over time.

4. The ratio of national income to labour-force exhibits a (positive) time trend. That is to say, I could make a fairly safe bet that the GDP per person will be higher in 2030 than now.

5. The ratio of invested capital to income, or income to invested capital, exhibits no such time trend. That means that on average, the stock of invested capital grows as quickly as the economy.

6. We see capital deepening; more capital per worker over time. This simply follows from #4 and #5. If you’re studying a course on growth or macroeconomics, you will definitely want to memorise these facts.

While they are a crass generalisation (and may not describe economies like Australia’s very well) they do describe most economies most of the time, and also underpin this exceptionally powerful little model. In particular the related concept of a Balanced Growth Path, which is something you want a growth model to replicate, is one that complies with these facts.

The Model

There are a few key ingredients in the model. They are:

1. The savings rate of the economy: s. This is the proportion of production that is not consumed;

2. The rate at which the average unit of capital (building, computer, whatever) depreciates each year: d;

3. The rate at which Labour Augmenting Technological Change occurs: g (this is described in more detail below);

4. The rate at which the population grows: n;

There are also a few assumptions needed for the model. All are unrealistic, and most growth modelling is focussed on relaxing the assumptions:

1. There is no trade, and no international capital flows;

2. All people work, and the 1 product they produce is one they consume and invest (think about corn: you can eat it, plant it, and harvest it);

3. All the people who work live in the same house and live forever;

4. Contracts (and insurance) exist, and always work, and so there is no economic risk;

5. People do not get to decide their savings rate, I just tell them what it is;

6. The technology which grows doesn’t require that you need to invest in research to get it. This is a bit like technological growth outside the US; in Australia, we don’t need to invent things, just buy the snazzy capital equipment from Seimens, Toshiba, or Westinghouse;

7. Finally, the amount of stuff produced in the economy is determined by the amount of capital, the amount of people, and the amount of technology.

A short note on Labour Augmenting Technical Change

Labour augmenting technology is technology which allows us to use less people to do the same amount of stuff. In Mexico, where I am at the moment, they don’t seem to have caught on to the idea of automatically-wringing mop-buckets. They wring their mops out by hand, taking twice as long and getting bleach all over their skin.

If you had a very large area to mop, and only one mop bucket, you would need fewer people to mop it if your mop bucket had an automatic-wringer. And so the automatic wringer is labour-augmenting. If Mexico adopted automatically-wringing mop buckets, this would be labour-augmenting technical change.

Note that not all labour-augmenting technologies need to be encapsulted in a capital good, like a mop bucket. Methods used in businesses can determine how many people you need to do a particular thing. Last January, I wanted to climb a mountain right next to Solo (Surakarta) in Central Java. We figured it would be cold up top, and went to buy some jumpers from the local equivalent of Myer or Sears. Instead of there being a lot of employees, as in Myer or Sears, there were thousands of them. The process to buy a jumper included dealing with a sales assistant, then giving the chosen jumper it to another person, and another person giving you an identifying ticket. When you were done collecting tickets you took them to the cash register. The cashier then gave your tickets to another person, who collected your goods while you paid. That meant there were five people doing the job one or two would do in Australia. The difference is in method, not in capital, yet is still labour-augmenting technology.

A formal statement of the model:

We have a production function Y(t) = F(K(t),L(t)E(t)), where Y is output, L is the number of people, and E is labour-augmenting technology. This is continuous, upward sloping, and concave. These assumptions say that if I have a pizza shop and employ more people, I can make more pizzas, but as I put on more and more staff, the increase in pizza-making is hampered by crowding. Likewise, we cannot indefinitely add pizza ovens and expect that we can make more and more pizzas without increasing the number of workers.

The t subscripts indicate that the value of the variable is for perid t; t-1 was the value for last period, and t+1 is for the next period.

A capital accumulation function

K(t+1) = K(t)(1-d) + I(t), where I is investment, and capital takes one period to come online. This equation simply states that next period’s capital is all the capital which existed today that did not depreciate, plus whatever we invested in new capital today.

Because we have a closed economy, savings must equal investment, and so

I(t) = sY

Because n and g are growth rates:

L(t+1) = L(t)(1+n)

E(t+1) = E(t)(1+g)

Remember growth facts 4 and 5? They state that while capital per person K/L grows over time and income per person Y/L grows over time, income per unit of capital Y/K does not grow over time. This means we can define a growth rate of E, g, such that y=Y/LE and k=K/LE do not grow over time. This gives the capital accumulation equation (expressed in terms of effective units of labour, LE):

K(t+1)/L(t)E(t) = K(t)(1-d)/L(t)E(t) + sY(t)/L(t)E(t)

= K(t+1)/L(t+1)E(t+1)*L(t+1)E(t+1)/L(t)E(t)= k(t)(1-d) +sy(t)

= k(t+1)*L(t)E(t)(1+n)(1+g)/L(t)E(t)= k(t)(1-d) +sy(t)

= k(t+1)*(1+n+g+ng) = k(t)(1-d) +sy(t)

Now recall under Balanced Growth, when the Kaldor rules hold, both k and y have no time trend. This implies k(t+1) = k(t) = k, and y(t+1) = y(t) = y, and so: k(1+n+g+ng) = k(1-d) +sy which gives:

sy = k(n+g+d+ng), or because both n and g are small,

sy = k(n+g+d) under balanced growth.

We should really take some time to discuss this result. The term (n+g+d)k is the amount you need to invest to simply not go backwards (in terms of capital per effective unit of labour). To invest this much, your savings need to be sufficient. So what happens if your savings decrease? Then your capital will depreciate, and your population will grow, and your technology will progress, until there is less capital per effective labour unit.

How about what happens when you save more? Exactly the opposite happens– you acquire more capital, which will allow you to produce a bit more, but not as much as the existing capital helped you produce. You can see this in the following chart.

GRAPH TIME!

The top curve is the amount you can produce at all the given levels of capital per effective unit of labour. The curve below (that has a similar shape) is the amount of production saved given some savings rate s, for all the different possible levels of capital. The straight line is the “necessary replacement” line in order to keep capital growing as quickly as effective labour units (as it does in the Kaldor Fact). The intersection of the straight line and the savings line determines the amount of capital per effective unit of labour, which in turn determines output.

Two basic extensions:

1. The Golden Rule of savings.

The Golden Rule savings rate is the rate that maximises consumption over time. So what would consumption be? Clearly, it is the difference between income and savings. We can graph Balanced Growth Rate of consumption (per effective unit of labour; if you want the per-person measure, multiply this by the amount of technology) as being the difference between y and sy. But in balanced growth, the rate of investment, sy = k(n+g+d).

This has an intuitive appeal. To be investing the amount required to maintain the same capital stock per effective unit of labour, you must invest to keep up with population growth, technology growth, and the depreciation of capital. If you look at the graph of y-sy (below) you see that it has a maximum point.

For this point, there is an associated savings rate which will maintain this level of consumption.

y – sy = f(k) – s f(k) = f(k) – k(n+g+d)

We want the maximum point, so we take the derivative of this function with respect to capital per augmented labour unit and set to zero:

f’(k) – (n+g+d) = 0

And so the savings rate which gets us the most consumption is that which matches the marginal product of effective units of capital (ie, the additional output you get by having one additional unit of capital for each technology-improved worker) to the sum of population growth, technological improvement, and depreciation.

This is found by substituting: recall that sf(k) = (n + g + d)k Then the golden rate of savings s* is s*f(k) = f’(k)k Which, intuitively, is when the total amount saved (LHS) is equal to the total payments to capital plus the total amount used to replace depreciated capital (RHS), all in effective units of labour terms.

2. The International Flow of Capital, or why do the Chinese and Germans send it to Australia and the US?:

Imagine if you had two countries without trade or capital-market relationships. One country has distinctly better legal institutions, rule of law, and a fairly developed pension system (discouraging savings). The other is poorly developed political or legal institutions, and no pension system (encouraging savings). Basic economic theory may tell us that poor countries have more to exploit (so to speak) and so should attract capital from rich countries.

A quick view of these two countries through the lense of the Solow model will tell you that capital will flow not from the rich to the poor country, as you may believe, but from the poor to the rich country. This is because there is less risk in a country with well developed legal institutions. Even if returns on SOME projects in China are very high, returns on all projects are not high enough to compensate for the considerable difficulty of being an inward investor in China (relative to being an inward investor in Australia or the US).

Compounding this is the higher domestic savings rates in China. The investment of savings tends to have a home-bias (that is, even if rates of return on foreign investments are higher, people still invest at home), owing to imperfect global capital markets an information problems across borders. This means that we should otherwise expect returns in China to be LOWER than in perfect capital markets (as more will be invested, decreasing the returns to capital).

IMPLICATIONS OF THE MODEL:

So here’s the juicy bit: what does the model predict?

1) While increased savings will lead you to acquire more capital in the short run, it does not allow your growth rate to permanently increase—this only occurs due to technological progress.

2) A decrease in population growth, likewise, will improve growth, as the amount of investment that needs to cover population growth decreases. However, this increase in growth is temporary, and in the end, only technological growth will help.

3) Countries who face very high capital costs or have crappy neighbours, and so can’t get world-market prices for their products, need to pay a lot more for additional capital, and so need a higher savings rate to afford the capital. However if they have production technologies which are away from the frontier but affordable, this may mean that they get stuck in a poverty trap.

Consider a farmer in Burundi who grows a crop but uses a donkey to plough. If he could save enough, he could afford a tractor from China. However, Burundi is landlocked and has relatively unstable neighbours with poor infrastructure. This makes the Chinese tractors more expensive in Burundi. Also, this lack of market access means the cropper can only sell his crops to others in Burundi, or maybe people in Rawanda, DRC, or Tanzania, who are unable to offer the world price for the crop.

The cropper is stuck in a POVERTY TRAP, whereby saving enough for the tractor—which would make him better off—would involve starving himself.

———–

This concludes my description of a basic growth model. Coming up: how does productivity relate to a growth model like this?

Government econometricians, as in the Treasury or Productivity Commission, do most of their work in either a) estimating elasticities, or b) preparing forecasts. They estimate elasticities (the expected percentage change in one variable attributable to a 1% change in another) because governments may be interested in answering interesting questions like “if we reduce tax rates on a second job by x, how much more can we expect people to work?” They use forecasts to inform governments how much certain events are likely to affect budget positions, policy viability, etc. This is all very important work when designing policy.

The primary tools of government agencies to make these predictions are reasonably basic statistical models (or CGE models based on statistically-deduced elasticities). These are the sorts of models one would learn in an advanced econometrics class—they are (in general) linear, non-Bayesian methods which estimate (by definition) the parameters of a (defined) continuous function. In the Treasury at least, these are generally basic Error Correction Models and VARs/SVECMs (though there are a few people there doing more advanced stuff).

The confusing aspect of this is that outside econometrics, when people need to predict or forecast events AND have a lot of money (and bonus upside) riding on whether their forecasts are correct (like in insurance or credit markets), the tools of econometrics are barely used. Indeed, many models, like the couple I will describe below, completely ignore some of the fundamental building-blocks of classical econometrics (like parameters, continuous functions), simply because getting it right is so much more important. After describing a couple of different types of these non-classical-econometric models, I will spend some time hypothesising why they’re not used much in policy.

Decision Tree

An important building block for several of these methods (especially the popular Random Forest algorithm) is the decision tree. I’ll describe how these work here. Bear in mind I am a complete novice at this stuff, and I’m describing it as my intuition understands it. Please let me know if I have anything wrong. For a more technical discussion, please see here
http://www.mayo.edu/hsr/techrpt/61.pdf

Let’s say we are interested in estimating the probability of whether a parent will send at least one of their children to a private school (1 for yes, 0 for no; while I use a binary classification here, your dependent variable can be a classifier, survival rate, continuous variable, etc.).  My independent variables are {Income, # times attend church/month, # children, proportion of children = girl, immigrant?}. Let’s say the data look like this:

Each of the rows relates to a particular family, with the first column being our dependent variable (the one we want to predict) and the other columns being those we use to help us. Such a problem may exist in urban planning; for example, we may have all the independent variables for a suburb, but no information on the proportion of families in the suburb sending their children to private school. Or we may be interested in what is likely to happen to a suburb undergoing demographic change.

The idea of decision tree building is to identify “split points” in the independent variables which neatly separate the dependent variables into groups which are less “impure” than the un-split group. I should define these two concepts:

1. First, impurity. An econometrician may think of this as being “heterogeneity”. There are a couple of ways of measuring this. Let p_{iA} be the proportion of class i in group A. “i” would be {public school, private school} in the case above. “A” would simply be the sample represented by the entire table. We want to work out the “impurity” of dependent variable column in the sample. If everyone sends their children to public school, we want it to be 0; likewise if everyone sends their children to public school. We want there to be maximum impurity when there is an equal proportion of every class in the sample. There are two simple functions which we use for this:Let’s say there are K classes in the independent variable column, then the impurity of the sample A is either:$I(A) = \sum_{i=1}^{K} -p_{iA}ln(p_{iA})$  (information index)or$I(A) = \sum_{i=1}^{K} p_{iA}(1-p_{iA})$ (Gini index).

   These can be thought of intuitively as a simply function which is bigger when the sample is more heterogeneous, and zero when it is perfectly homogeneous.

2. A “split point” can be thought of like this. Let’s say we rank the entire sample by each of the independent variables in turn. So when we rank it in terms of income, it looks like this:

The aim is to split the sample into two (or more) groups, based on one of these independent variables, and in doing so, reduce the impurity of the total sample. So letting A_{1} be the first sub-group created, and A_{2} the second sub-group, we want to find the split-point (in one of the independent variables) which maximises I(A)-I(A_{1})-I(A_{2}).

Working so many calculations out by hand is exhausting, so we let computers do it. In the sample above, we split it into two sub groups, one with incomes at or above 130,000 (impurity = 0, all families in this classification have a child in private school), and the other with incomes below 130,000 (impurity = 0.24, one of the seven have a child in private school). Thus the total impurity of the sample is reduced from 0.48 to 0.24.

In building decision trees, this process is iterated on again for each of the sub-groups created, using all of the independent variables which improve purity (in many cases, for more than one split). At the end of the process we get many terminal nodes, each far less “impure” than the original sample. Consequently, for a new observation, we can assign them to a terminal node and so determine the probability the observation will be of each class.

Extensions:

There are several extensions to the basic decision tree. First, a decision tree tends to over-fit, leading to increased probability of the mis-classification of out-of-sample data. This is remedied by attaching a “cost” to having each additional node: a cost of infinity will result in the “tree” just being the initial data set, while a cost of zero will result in the full tree. By increasing the cost, the least efficient splits are not done, and so the tree is “pruned”.

We can also create a matrix of “costs” incurred by misclassifying an observation with type j as a type k. This is especially useful if the costs of a false negative are greater than a false-positive, as would be the case in cancer diagnosis. This works by altering the impurity measure of each split, so that if misclassifying a {public school} as a {private school} family is twice as bad as the opposite (it will result in fewer public schools built), then the maximum impurity occurs at proportion(public) = 0.75, proportion(private) = 0.25, rather than the 50/50 ratio before.

Random Forests:

The Random Forests algorithm is a popular method in predictive analytics which builds on decision-trees. The idea is that a large number of trees are grown using most (but not all) of the data available, randomly selecting the independent variables included in the trees. The remaining data are used to calculate the robustness of the trees. Each tree then has a “vote” on the membership of each of the observations, and the mode of these votes is the winner.

What’s so great about these models?

These models do not assume any structure of the data or the underlying relationships, are Bayesian, non-linear, and in no way are concerned with the continuity of the underlying model (if there is one). They (and their derivatives) are used by practically all contestants in the data-analysis competitions on Kaggle, and do very well.

So why aren’t they the port of first-call for econometricians?

Distributional issues: In economics, many macro variables are dominated by trends, and so their growth rates are not as broadly dispersed as in other types of data. Consequently, the risk of split-points occurring near the mode of growth data leads to increased risk of mis-classification.

Time-series issues: With the exception of the auto-regressive tree models of the Meek, Chickering and Heckerman (2002) and the distance between tuples-approach of Yamada and Yokoi (2003), these models don’t seem especially well developed in time-series analysis, especially in a multi-variate setting. As much econometrics is done on time-series, and as there is a large toolbox of powerful methods already in existence, it may just be that the switching costs between methods could be too large.

The most salient issue, though, is that most econometrics has been devised to estimate parameters for theoretical or argumentative constructs, rather than truly pursuing out-of-sample predictive power. An example of this is the idea of an elasticity: a constant, estimable relationship describing how much one thing changes when another does. Even if we abandon that it must be a constant, and instead try to identify the “deep” parameters of a function describing an elasticity, we have to believe that at some point there must be “deep” parameters which are not functions of other things. Due to the limitations of macroeconomic data (monthly, quarterly or yearly release, underlying data not released, small variance, short samples) these sorts of deep parameters are unlikely to be estimable with any real precision.

In contrast, if you were to try to estimate an elasticity using a random-forest approach, you may well end up with several elasticity estimates, each conditional on the variables in your model. For the theoretical modeller, this isn’t all that acceptable.

Most of all, though, I doubt these modelling methods would become very popular in policy circles simply because five elasticities are far harder to describe to a politician than one. 

Terrible bureaucracies keep people in poverty. They encourage corruption, make it more expensive to obey the law, start businesses, and attract foreign skill and capital.  And they are solely the result of political systems which emphasise personalities over results, viewing the public as voters rather than consumers of government services.  I am more than sold that the famous analysis of Parente and Prescott (2000)* is correct: ‘big man syndrome’ prevents backward societies from adopting best practice, especially in bureaucracies. And Mexican bureaucracy is where Big Men feel most comfortable.

For the last week, I’ve been trying to regularise my Mexican visa, and in doing so I’ve had a glimpse inside a truly terrible bureaucracy. Below I’ll give you a quick run-through on the set of processes I had to go through, then speculate on the causes and a potential fix. I am left with the impression that the best thing the Mexican Government could do is pay Walmart or OXXO to process immigration documents.

The Instituto Nacional de Migración (INM)

My wife and I have been to the Guadalajara office of the INM three times in the last week, each time requiring 2-5 hours, and we anticipate going another two times in the coming week.  Some observations:

• The requisite documents for the visa application are not listed online, and are not available in a brochure in the INM office—the only way to access the documents is to wait in a queue. We waited about half an hour.
• After waiting another two hours to submit the documents listed on the requisites form given to us, we were told that one of the documents listed was not actually required, and there was another form which needed completion which was not listed. On the unlisted form, the date box indicated the form had been in use since 200_—clearly insufficient time to update the requisites list.
• After three days, the INM website gave indication that I should present myself at their office.
• When arriving at the office, I took a number “74″, then saw on the screen “11″. We asked how long each number took: “about 20 minutes”. It seems the only reason we were served on the same day is because people in the queue got fed up and went home. We also saw a couple in the queue who we spoke to the week before—they were simply trying to get a marriage license (he was a Spaniard), and had been in the office 5 days.
• Upon reaching the front of the queue, the lady told us that my visa had not been processed, because the application did not include the form which we were told was not required (after bringing it in!). This message could easily have been included online, or somebody could have called me. Instead, we spent 5 hours waiting in an office.

Surely the bureaucrats can’t be that stupid; why haven’t the problems been fixed?

First, a good proportion of the people who work in customer-facing roles for the INM are not very bright. Most seem relatively content stamping forms and giving irate visa applicants imaginative reasons for the stalling of their applications. In essence, they have no incentives (or power) to change anything, and so just do what is required of them. Fair enough, really.

This leaves the more senior people in the INM as culpable for their backward mess. For those at top, changing a process is a penstroke, changing a form a simple instruction.  So why don’t they do it?  Why is everything so bloody laborious?

I asked the same question to Sri Mulyani earlier this year when she came to the Treasury.  Her reply was that in Indonesia there is really no culture of corporate governance, whether in the public or private sector. It is easy there for managers to appoint their friends or family into jobs, and create redundant processes to occupy them. I have an inkling the same forces are at work here in Mexico. Bureaucracies in Mexico are at best semi-political. Politicians are able to repay those who assisted their election with public service jobs—not as staffers, but as employees of the bureaucracy.

Of course, nepotism be it through politics or poor corporate governance is really just a symptom of a broader, crippling lack of accountability in public decision-making. And nepotism itself isn’t the issue—inept decision-making is, which again stems from a lack of accountability.  As with Mountains and Muhammad, under the current political system in Mexico, I do not see much scope (or incentives) for public officials to improve their accountability. Without the political leadership, there are very few mechanisms for the popular improvement of bureaucracies.

What could possibly drive such political will? This is where we must be careful in identifying which solutions are feasible; Mexico’s long-run electoral dynamic has been exceptionally uncompetitive, even at the state and municipal level, where most of the action is.  Consequently, appeals to electoral competition are unlikely to be useful.  Potential solutions will recognise the patrimonial reality that a) Those running politicised bureaucracies have political ambition (ie. they care about future appointments), b) The future electoral prospects of candidates are greatly enhanced by appointing worthwhile bureaucrats now, and c) The candidate’s knowledge about the quality of appointments ex ante is imperfect. Clarifying this final point, potential appointments have publicly known and unknown qualities (which the appointee can choose to invest time in developing), with the publicly known qualities being substitutable for closeness to the candidate in gaining appointments.

I propose that customer-facing agencies generate poor-quality information about the qualities of appointees.  Customer’s complaints create a lot of ‘white noise’, and the agencies’ activities are not news-worthy anyhow. Because of this, there is very little publicly unknown information which could easily be incorporated into the publicly known information about the candidate. This is the opposite of what happens to finance ministers, whose policies and performance is very well known. The result? Heads of customer-facing agencies choose not to invest in improving their agencies, as the information will be later ignored. Instead, they spend time investing in their political relationships.

The feasible solution under this framework is to improve the quality of the information about appointees. This could be done by decreasing the noise of actual customer feedback, or by using independent auditing of processes to assess actual customer experiences.  I want to experiment with the first of these. Not sure how it will go, but I’m keen for the challenge!

Tomorrow I will be standing in front of the INM office in Guadalajara handing out links to this blog, soliciting responses from regular people about their experiences dealing with this inept agency. Will report back!

*Parente and Prescott, Barriers to Riches, MIT Press, 2000

In the last post, I mentioned that I’d not done much writing recently. This was a bit of a lie: below are some of my recent essays:

Rob Wiblin and I review Quiggin’s Zombie Economics in the CIS’s Policy. In all, we liked it.

Jan Libich and I argue that sensible monetary policy (in countries with monetary sovereignty) can help entrench sustainable fiscal policy. (Again, in Policy).

Jan Libich, Carl Walsh and I review a round-table event on fiscal-monetary interactions at the ACE2010.

Jan Libich, Petr Stehlik and I argue that monetary unions make it easier for small members to become fiscally incontinent.