Tuesday, 30 December 2008

Generalisation and linkages in econometrics

Growth econometrics may benefit if it attempted to link new research with past research more thoroughly than it does at present, and establish new abstract generalisations for existing research. I have written before on GLE about how there are a handful of overarching theories which together encompass most of econometrics.

I am thinking particularly about testing and estimation of the model Y = X.B + error where Y is a vector of current growth rates by year, X is a transposed vector of lagged determinants, and B is a coefficient vector. X can include constants and lagged terms from Y. There have been recent developments on testing whether the B term is constant across countries, and estimation and comparison of country values when the terms are not constant.

Enough already. I shall return to this theme, when the time is right.

Growth effects of technology specific to a capital-labour ratio

The paper Appropriate Technology and Growth by Basu and Weil presents a model whose outcomes seem to describe two of the main behaviours of country growth in the world economy. The first is that growth can be highly non-linear and subject to sudden accelerations and slowdown. The second is that countries can form into different convergence clubs, meaning that incomes or growth rates tend to converge for separate groups of countries, and that the rates in separate groups may not coincide.

The paper assumes that technology is specific to a particular ratio of national capital to national income, and that a country produces improved technology for a band around its ratio. So a late-coming country could save a great deal, reach the band of innovation for the world's technological and wealth leaders, and then surf along in their wake receiving all their technological benefits, even enjoying a higher level of consumption than them.

The paper is clean in its equations and logic, visually appealing, and reflects observed behaviour. Since I like it, here are some unsolicited comments about its scope.

The capital to income ratio could measure many things. In theoretical works, the assumption of capital to income ratios being the key determinant is tolerable; in empirics it could become a real headache.

The paper is retrospective, and it is easier to produce perfect models of past events than future ones. The original work proposing the importance of capital to labour ratios for technology was prospective and earned major prizes, I believe.

I am sure a limiting distribution could be found when large numbers of countries are used in the model, and this distribution could be used as an approximation for smaller numbers. I haven't produced it.

The assumption of effortless technological catch-up for countries free-riding on an innovator seems too optimistic - which would be acknowledged, I think - but also could give misleading theoretical predictions. Followers have to do work to adopt technology, which probably means high level of research and development, and in some circumstances any follower will fall behind a leading innovator no matter what are their own efforts at copying. The adjustment for imperfect transfers could be readily included in the model.

Oil price pricing and previous expectations

Earlier this year I said that the expected world oil price would be around US$140 a barrel. The price is now around $38 per barrel. Did I go wrong and how?

The figure was an expectation, not a prediction for the actual price. It is an average of all possibilities for the price, so the fact that the price is $38 does not necessarily mean that the expectation was wrong. That said, the expectation would have looked more likely to be correct if the year end figure was somewhere between $120 and $160 a barrel, since my expectation implies that $38 would be an extreme value and quite unlikely.

The expectation was presented in the context of market predictions that the price would hit $200 or $300 dollars in the near future. The theory I used showed that price slowing was more likely than continuous acceleration. Acceleration would be the result of oligopolistic supply decisions, rather than changes in oil demand. My expectation appears more realistic than the market anticipation at the time.

The expectation was presented as being based on economic fundamentals, rather than oligopolistic pricing or market overreaction to price stimulii. Given the possibility that the market has presently overshot and is pricing too low relative to economic fundamentals, it is quite possible that a more objective pricing on fundamentals would have a higher oil price. However, we may say that even if the fundamentals-based price is, say $70, the price is still unlikely to have occurred in a price distribution with $140 as the expected value.

In retrospect, the very rapid growth in prices over the last decade looks like a bubble in which actual prices detached from economic fundamentals. I should have evaluated the economic-fundamentals price as lower, by projecting the mid 1990s figure at a growth rate lower than the observed rate. The projection rate should still have been higher than previous trends, by virtue of the emergence of the large developing countries. In retrospect, I should also have assessed that the price bubble presented significant downside risk both from market correction and from damage to aggregate demand. An expectation of $80 or $90 would have been better, and I hope I would have said this even if the price today was $200 or $140.

Odd bits and a clear-out

As it is approaching the end of the year, I thought I would clear out some ideas that have been hanging around for a while. So here goes...

Sunday, 28 December 2008

Two interesting ideas from astrophysics

I came across two interesting ideas from astrophysics in recent weeks. The first is that pressure affects gravity. Apparently it is a well known result from a century ago, but I didn't know it.

The second idea is that it could be possible to view what things looked like before the Big Bang created the current universe. The idea was implemented in an experiment, and is appealing in its directness: measure the distribution of the universe's distant energy and since the energy was generated shortly after the universe started, it may reflect the universe's condition at that time. The original paper is available here if you are interested.

Wednesday, 24 December 2008

Diffusion graphs for internet technology

And here are the corresponding graphs for the number of internet users. There appears to be some slow down in all countries, despite the still low income in many countries.

Diffusion curves of computer technology

Here are the corresponding graphs for computer technology. The diffusion curves are not obviously S-shaped, and lower income countries do not seem to be further down the curves this time.

Diffusion curves of telecommunications technology

It is sometimes proposed in technology diffusion research that a technology's spread follows an S-curve - slow at first, then quicker, then slow again. Here are the curves for the telephone mainline and mobile phone subscriptions for three African states, one developed nation, and one rapidly developing Asian country. They are pretty much in line with predictions, with less developed countries lower down the S-curves. The kink in the middle of several curves may arise because telephone mainline technology was becoming saturated by the 1980s, and mobile phone technology then started its own individual S-curve.

Monday, 22 December 2008

US limits military aid to countries with child soldiers

There is a report that the US government is to limit its military aid to governments whose armies have child soldiers in them. The bipartisan cosponsors of the bill have previously supported other measures aimed at reducing the worst excesses of conflict.

I am unsure how limited the limits are, but it could be a substantial measure as much US aid is linked to military assistance.

How can theory and empirics best serve policy?

Economics is a subject which aims for real world application. Clarifying the relation between theoretical analysis, empirical analysis, and policy may help to produce more useful research. Of interest here will be how understanding improves control of or response to economic events, and what the relative roles and potential are for theory and empirics.

We borrow the graphical representation from Classification and Regression Tree (CART) models to present a model for a real world relation between two economic quantities. Two nodes represent each of the quantities, and all their possible causal interactions are represented by paths connecting them. By interaction we mean a mechanism of covariation that is readily conceptually distinguished from other mechanisms. For example, if the first node represents domestic technology usage and the second node represents foreign technology usage, then one path may represent change in technology due to foreign direct investment and a second path may represent change in technology due to trade exposure. The paths may be split into sub-paths, with sub-nodes breaking up the path and representing quantities which causally vary as one of the end node quantities varies and whose variation leads to variation in the other end node quantity. Thus, the sub-paths represent chains of causality connecting the two variables. In the technology spread example, the sub-nodes along the foreign direct investment path may be {transfer to other companies in the economy beyond the immediate recipient of technology} then {skilled usage by all domestic companies} then {profitability of the operation} then {technology usage throughout the economy}. Further sub-nodes may be introduced if the mechanism of transfer is further deconstructed, such as introducing {the movement of people between foreign direct investing companies and the rest of the economy} as a sub-node between {the original transfer} and {the spread to other companies}.

The last three steps in the FDI path (skilled usage, profitability, and wide technology usage) are shared with the other path, capturing the effect of technology exposure through trade. Thus we have a graph showing the modelled interactions:

The upper path represents the FDI route for technology transfer. The lower path represents the trade path, and is less fully modelled.

In analysing such modelled graphs, a theory proposes the existence of a new path between two nodes, or the introduction of new nodes in an existing path. In the proposed technology graph, suggesting that licensing is also a means of technology transfer is a theory. Another theory is that trade exposure’s action on growth requires foreign importers to demand high production standards and a domestic knowledge base to adapt to the standards, introducing two new nodes in the lower path. The theories here would be more properly called hypotheses since they do not have to be correct, in which case the nodes would have no real world connection and the node quantity covariation is zero.

An empirical study tests the relation between quantities on two nodes, and may be informed by and test for the graph connections suggested by theory. It may test the relative strengths of two different paths between the nodes. If the empirical study tests the relation between quantities on two nodes separated by other sub-nodes, then an empirical test controlling for the sub-node quantities is removing the effect of the first node quantity acting along the sub-node paths, so that any robust remaining effect indicates the presence of other sub-paths between the two nodes.

Policy usually looks to control the variation in one node’s quantity in response to changes in other node quantities. It will often be indifferent to the precise paths taken from the control quantities to the response quantities. In the technology graph, a policymaker may wish to maximise the use of a technology in their economy by transferring it from abroad, and will use any means necessary to obtain the maximum throughput in the graph. Theory sometimes returns at this stage to specify decision rules by which the policymaker, having precisely stated outcome preferences, optimises the changes in control quantities. The decision rule is required for optimisation if all paths cannot simultaneously operate with their maximum response. In the technology graph, for example, increases in intellectual property rights protection may raise the level of investment but lower the ability of local companies to copy the technology.

Under these definitions, we can propose some best possible outcomes for policy from theoretical and empirical analysis. Theory could find new paths for a modelled situation and emphasise the most important ones. Empirics could show overall node covariation along multiple paths, show covariation along specified paths, compare covariation along different paths, and demonstrate how path covariation changes in response to path choices in the whole graph. Theory could also connect the entire analysis with policy by presenting means of exploiting the paths and proposing decision rules for changing node quantities that reflect policymaker objectives. A decision rule may be specific to the objective and not readily adaptable to alternative objectives, which in a competitive setting – for example in competition for the receipt of a particular technology – may give the policymaker an advantage in achieving their objectives over rivals with alternative objectives, at least until they can devise their own decision rule and compete on the basis of economic fundamentals.

Thursday, 18 December 2008

Macromodel displaying cyclical contraction - part 1

Here is a small macromodel showing sustained spirals in output in response to changes in expenditure preferences, capital accumulation, and different market stickinesses, with a competitive or monopolistically competitive labour market. It is in jpg form to allow display of detailed equations and graphs, and can be made larger by clicking on the image.

Macromodel displaying cyclical contraction - part 2

Macromodel displaying cyclical contraction - part 3

Macromodel displaying cyclical contraction - part 4

Monday, 15 December 2008

Linearising macroeconomic models

Linearisation of macroeconomic models is common in theoretical and empirical work, so it is worth considering when it is applicable.

A function f of some economic quantity x can be written as

f(x+e) = f(x) + e*f’(x) + O(e^2)

where the dash denotes differentiation and the O term is of order e^2. Linearisation assumes that e is small, so that the O term is negligible, or that there is no O term at all, so we can write

f(x+e) = f(x) + e*f’(x)

The truncation masks misspecified models for small variations of the data, since almost any model has a truncated form like this one. The linearization will not hold for larger variation and misspecified models. The linearization may not be much use unless we have a stable steady state, when small variations in x result in x returning to its initial value. If the model spec is correct, non-locally the linearization will not hold unless it happens to coincide with the full expansion and the O term is identically zero.

Either the quantities of interest are in a stable steady state which is often is probably not true in developing countries and frequently not true in developed countries either, so should be demonstrated but frequently isn’t. Or if the linearization coincides with the full expansion of f and so the O term can be neglected, then evidence of goodness of fit should be given across the full range of inputs, but again frequently isn’t.

How much economic activity happens? (Reprise)

The question came up once before on the blog. One way of answering it is to say that supply and demand will be equalised, so that the quantity of goods supplied is such that buyers and sellers agree on a common price. Equivalently, we could look at pricing in terms of marginal costs and marginal revenues. Or we could draw a supply and demand diagram, which would give more information because it shows the way in which adjustment to the equilibrium occurs.

None of the stated answers describes the full dynamics of the situation. A supply and demand diagram for example, together with knowledge about the presence of a market mechanism, does not tell us how long the adjustment will take. The set of supply and demand equations would have to be supplemented by an equation giving the market adjustment process over time when out of equilibrium, and the evolution of the equilibrium over time.

Compressing the set of equations into a compact form may yield analytical benefits. Representation in terms of maximisation or minimisation of an integral term seems promising, as it puts Lagrangian theory at our disposal.

Demonstrating the equivalence of the various forms of supply and demand interaction requires some algebraic microeconomic theory, but doesn’t appear intractable. To show the equivalence of integral minimisation to a supply and demand equalisation, it may also be possible to borrow a proof from physical science. The integral minimisation associated with energy conservation can be shown to be equivalent to the equalisation of motion forces and gravitational forces at each point in time, so the proof should translate.

Thursday, 11 December 2008

Exchange rates, tradables and non-tradables

I am reading a recent review of evidence on exchange rate fluctuations and the links to prices of internationally tradable goods and non-tradable goods. The evidence shows that exchange rate changes are closely linked to the variations in both tradable and non-tradable good prices domestically. Earlier theorists proposed that only tradable good prices would be closely linked with exchange rate fluctuations, since exchange rates are determined in part by purchases of currencies in order to buy tradable goods, and evidently not purchases of non-tradable goods.

Not having reached the end of the review yet, I haven't read the author's proposed theoretical resolution of the difficulty, but it does seem a priori that the proposition of no link between non-tradable prices and exchange rates is theoretically clearly flawed. One would expect the prices of tradable goods and non-tradable goods to operate within bands relative to each other that are reasonably similar even in entirely separate economies if the production functions and inputs for the goods are similar. So in economies where the exchange rates are determined by tradable prices, they will also be linked to non-tradable prices.

The review may propose this mechanism too. I'll find out today. In theoretical work, the effort is often in the exact mathematical modelling rather than the basic ideas.

Modelling transaction costs with geographic distance

I mentioned in a recent post that one can often improve models by increasing the detail in their microfoundations. The case of transaction costs in output models illustrates my point.

Suppose that annual output is modelled by annual output = A*capital^B where A and B are constants. Then we could include transaction costs as annual output = A*capital^B + K for K a constant depending on the expense of transaction, presumably depending on distance between buyers and sellers of the goods.

We could specify more detail: output per transaction = A2*capital^B2 + K2 for A2, B2, K2 constants, and then sum over the number n of transactions per year to get annual output = n*A2*capital*B2 + n*K2. So as the number of transactions increases, the advantage of local trading increases, other things being equal.

The observation isn't very smart, but illustrates a point.

Environmental damage as analogous to aggregate demand externalities

I am looking at whether environmental damage can be modelled macroeconomically in the same way as aggregate demand externalities. A quick search did not show anyone having modelled environmental damage in exactly the way I am thinking, but probably someone has done something similar.

Aggregate demand externalities arise when people's and companies' individual actions alter the total demand for all goods in the economy. These actions may be modelled assuming that the people and companies are not individually affected by their decisions as much as the whole economy. The collective effect of all actions on everyone in the economy can be large, however.

The way a macromodel including environmental damage could be set up seems clear enough. People assume their individual actions do not have much effect, but collectively they do. So there is scope for governmental action, depending on the model parameters.

Guinea worm eradication

Cases of the disease Guinea worm have approached a new low, and there are plans to eradicate it fully, according to reports.

Thanks to the government and private sector funders of the initiative.

Monday, 8 December 2008

Applications for MA Economic and Governmental Reform at the University of Westminster

Here's a reminder about applying and getting funded for the MA Economic and Governmental Reform at the University of Westminster.

I teach economics on a Master's course at the University of Westminster in London. The course title is MA Economic and Governmental Reform, and runs from September to September. We are presently recruiting for next year's course.

The course requirements are listed on its website (linked here), although there is some flexibility. Unavoidable ones are:

1. Reasonable English (or things won't make sense)
2. A first degree with some relevance to the topic, or a degree and relevant work experience
3. A job, or potential job, in government (people from NGOs have historically also performed well)
4. Willingness to work hard (or things will not be enjoyable)

African applicants are most welcome and have good performance records. Information on the course and obtaining funding is on the website. The course, like most in the UK, is expensive (£10,000), so students usually have applied for scholarships first. Early application is recommended.

Getting the most out of mining investment

Africa gets a small proportion of world investment, so it is important that the region derives the greatest possible advantage from its sizable mining investment. I will present here some suggestions to help with the task, as it concerns the spread of technology, a likely major factor in promoting economic growth.

Technology expansion theory distinguishes between technological spillovers, which are associated with increased local innovation following exposure to foreign technologies, and technological spread, which is increased local adoption of existing foreign technology. The latter is more relevant in Sub-Saharan Africa because of its lower levels of research and development expenditure. Included among the factors identified in studies as determining increased technological spread are: the local population’s exposure to foreign technology, its applicability to the rest of the economy, geographic or trading proximity of local firms to the technology operator, whether local firms can copy the technology without legal prosecution, whether local firms are competent enough to copy the technology, whether local firms have the managerial skills to implement the technology, and if there is sufficient domestic pressure to encourage copying or adaptation.

Many characteristics of mining investment do not tend to support technological spread through these mechanisms. The mining industry, above all of hydrocarbons, can have a small workforce with a high proportion of foreign managers, can have narrowly specific technology with a higher capital to labour ratio than the rest of the economy, may be geographically isolated or offshore, may be isolated by its security, may have few linkages with the rest of the economy, may have higher skill or experience requirements for operation than most local firms, and may operate in a local or international market with low competition.

These characteristics obstruct technology’s flow, but government decisions when negotiating contracts can help to remove the blockages. The following suggestions broadly correspond to each of the problems, although there is some overlap in their effects.

Local exposure to the mining industry’s technologies and procedures could be increased by requiring a reasonable proportion of local employees at every level of the company, from junior to senior managerial. Local participation does not require exact parity in remuneration, which will be determined by the operation of international and domestic markets separately, but in decision making and responsibility so that local employees have exposure to best international practice. The international company should have freedom of choice and training for their staff, within the parameters of selecting locals, since it is their knowledge and demands which are important for transferring skills. In addition, local exposure may be increased by requiring inspection of company equipment by government, university, and local company scientists, under the remit of national training programmes.

Further exposure may be encouraged by restrictions on the form foreign company participation takes. Foreign direct investment may be restricted, so that international companies may have to work through and with local partners, chosen by the international companies. A 50 percent partnership requirement may be a good way of exposing local participants to international expertise, standards, and demands.

Loose patent protection for mining technologies would reduce the risk and expense of copying technologies for local firms. Ordinarily, loose protection can be double-edged, since companies may be reluctant to invest in an economy at all if their intellectual property is threatened, or they may take measures to reduce its local exposure. Given the measures suggested above that deliberately expose local workers to their technology, copying becomes even more probable. However, in the case of mining investment, the typically low level of competition and high returns may make patent protection a secondary consideration.

In response to the risk of intellectual property loss, international companies may prefer to transfer older technologies which are not their most advanced or are not patent protected, but the choice may be advantageous for the receiving economy, since it may be more compatible with its overall development level. The adoption may be facilitated by local company investment, and by local research and development in the industry. Some studies indicate that much of the impact of local R&D is not through producing new goods – the finance for it is far below that in the rich economies – but in easing the transfer of existing knowledge.

Thursday, 4 December 2008

Covering all routes to growth

Economists who study economic growth have not agreed on the exact causes of growth in developing countries. Some stress that it is factor accumulation which is important, so that countries grow rapidly because they invest and educate at high levels; others stress that it is knowledge transfer from developed countries which is important, where knowledge includes both theoretical studies and applied, management skills; still other economists say that both contribute to growth. The last group seems to be the largest among leading professional economists, and examinations of the interactions between technology and accumulation lead to most interesting conclusions.

The rapidly growing East Asia countries tended to accumulate at high levels, but also adopted investment, trade, and educational regimes which led to accelerated transfers of technical knowledge. So it did not matter which route to growth was correct; they had both covered.

Moment conditions for unbiased double-endogenous IV estimation

I mentioned last Thursday that it may be possible to find an unbiased estimate of a parameter using IV methods if two endogenous variables have a known relation in the bias they produce in individual IV estimates. Here are the moment conditions corresponding to the expectation and variance assumptions given last time for an error u and endogenous instruments v and w:

E(v^2*u^2)-E(vu)^2 = a^2*(E(w^2*u^2)-E(wu)^2)

where a is an unknown constant.

What is happening is, these two equations allow a reduction by one in the number of parameters in u to be estimated, since we have two new equations but have added only one extra parameter, a. The reduction in the number of parameters to be estimated offsets the contribution of the unknown bias parameter to the number of parameters, and means that the system is as identified as it would be without the bias.

I think this representation makes the direction of further generalisations clear.

Estimating the CES production function

The CES production function assumes that economic output is given by

Output = alpha*(beta*K^gamma + (1-beta)*L^gamma)^(1/gamma)

where the Greek letters are constants, K is capital, and L is labour. It is defined for gamma<>0.

When we want to estimate the parameters, we can use non-linear least squares methods, or we can transform the equation a little to get

Output^gamma = alpha^gamma*beta*K^gamma + alpha^gamma*(1-beta)*L^gamma

and estimate the equation by constrained least squares. We may even introduce a country specific term, although it is added to output^gamma rather than to output which is more usual.

Here are the results of a non-linear least squares estimation, using panel data for world countries over the Penn World Tables range, with five year groupings of data:

y = 34.7 [0.24] + (0.52 [0.01] * K ^ 0.08 [0.30] + (1-0.52) * L ^ 0.08)^(1/0.08)

p-values are in square brackets.

gamma is close to zero, which is the value at which CES behaviour becomes identical to that of the Cobb-Douglas function. This very rough estimation indicates that the frequently used Cobb-Douglas estimation might not be too bad as an approximation.

To improve the estimation, more complicated estimation methods could be used, but the toolbox is smaller than with the Cobb-Douglas function because the CES form is harder to handle.

Tuesday, 2 December 2008

Maximising the speed and breadth of a technology’s spread

The discussion of multinational enterprises in the last post suggests their role in another often analysed phenomenon, the global spread of technology. Often the focus in the literature is on maximising knowledge spillovers from a company to local producers, so that the latter can produce as efficiently as the former. This mechanism is probably important in catch-up of incomes between countries. The underlying motivation is thus usually on increasing economic growth, but there are others. For example, international bodies may want to spread a technology as widely and quickly as possible if it is found to reduce the degree of global warming without lowering economic productivity.

If the spread of a technology is of interest in itself, then two major questions arise: whether the underlying technology is successful as a marketplace proposition, and how to maximise the spread of a technology given its viability. Evidently, if a technology is a commercial disaster, it is not going to get very far. Many papers on technology spread assume that a technology is already commercially viable, or use measures of local viability such as prices in the market. However, the available price data is not always reliable, so the default position is the first. It is reasonable to assume that a technology which has already been successful in one market, particularly an OECD technology leader where most formal R&D innovation occurs, is potentially commercially viable in other countries now or in their futures.

The second question has many aspects: would posting the design of the technology free of charge on the internet be most effective? Most companies could see it, but how would the innovation be encouraged in the first place? Perhaps innovators could be financially supported by their subsequent provision of the tacit knowledge required for the technology’s successful operation. But then, if the tacit knowledge is very large, the technology spread will be slow.

Alternatively the technology could be the property of a single multinational, and it could spread easily and efficiently through its subsidiaries. But then how would it get beyond the company? Other companies would have to innovate to copy the company, or the knowledge would have to leak from it. Both processes could be slow.

The most rapid spread may be from a large intergovernmental or philanthropic funded organisation creating a low-tacit knowledge technology, and presenting the technology free though publicly available or trade-based sources. Such efforts are probably infrequent in high-tech fields, although some parts of Internet and Web innovation may be partial examples. A possible commercial alternative might go something like this: a small high tech company establishes a niche in its domestic market, and licenses to foreign companies. Leakage of its ideas is very likely, as it will lack the financial resources to protect its intellectual property, but given its small size, licensing and export income may be sufficient to support domestic expansion or branding efforts. The business plan is risky, but in common with other start-ups, could lead to commensurate high returns.

The curious existence of multinational enterprises

I used to take the structure and presence of multinational enterprises for granted; recent readings have rid me of the prejudice. The literature on them points out that there is nothing inevitable about their existence. A company with a product to sell does not have to set up overseas, but could remain in its domestic market. Even given that profit maximisation might lead it to want to sell as widely as possible, it could export its products to the foreign market without physically being there, or it could sell licenses to a foreign company to manufacture its goods under its brands or using its technology.

The explanations for MNE existence turn on the high knowledge content of the goods they manufacture, where knowledge is understood either to be the explicit scientific, patentable content or the tacit content of a company’s productive organisation. The high knowledge content is a characterising feature of their production; some estimates have found that most of the world’s research and development is done by them.

Within the general recognition of the importance of MNE’s intellectual property, there are several competing explanations for their spread. One emphasises that companies wish to maintain tight control of their intellectual property, and local licensing would put it at risk. Another stresses that because of the high tacit content of goods, only the company itself can efficiently produce its own goods. A third underlines the role of trade barriers to exporting goods instead of local production, partially because countries wish to ensure knowledge spillovers.

Use of supply-demand graphs in economics research

Here are a few points on supply-demand graphs; it is not always obvious why they are favoured over algebraic solutions, so the points may help clarify.

1. Simultaneous equations expressing market supply-demand behaviour are often not solved explicitly, but by plotting in graphs (so showing how a market mechanism would adjust to obtain the equilibrium)
2. The effect of parameter variation is shown by shifts in graphs and then stated verbally
3. The effect of assumption variation is shown by shifts in graphs and then stated verbally
4. The verbal descriptions of effects on graphs are explicit (“rotates curves”, “shifts curves out”). The curves and the quantities and behaviour they describe are treated as synonymous (“the money supply grows shifting the demand curve to the right, which in turn increases profits”)

Algorithm generating theoretical economics papers

Here is an algorithm for generating the main sections of theoretical economics papers. It is an application of the earlier proposal for research paper structuring (also posted here), and has been tested against four recent famous economics papers.

1. Present a set of equations describing a situation (Whether a base situation or additional feature or adjusting feature)
2. Solve them
3. Deduce a property and discuss its implications (the property should arise by virtue of the base situation or its additional feature, and should concern an important topic)
4. Give a numerical calculation or table based on varied parameter values tried in the property equations
5. Highlight key variables used in the property
6. Describe the property’s relation to other properties in the paper or elsewhere.
7. Repeat from step 1 or step 3