It’s Wednesday and I just finished a ‘Conversation’ with the Economics Society of Australia, where I talked about Modern Monetary Theory (MMT) and its application to current policy issues. Some of the questions were excellent and challenging to answer, which is the best way. You can view an edited version of the discussion below and…

# Thinking in a macroeconomic way

As noted last week, I am now using Friday’s blog space to provide draft versions of the Modern Monetary Theory textbook that I am writing with my colleague and friend Randy Wray. We expect to complete the text by the end of this year. Comments are always welcome. Remember this is a textbook aimed at undergraduate students and so the writing will be different from my usual blog free-for-all. Note also that the text I post is just the work I am doing by way of the first draft so the material posted will not represent the complete text. Further it will change once the two of us have edited it. Anyway, this is what I wrote today.

**Chapter 1.2 – Thinking in a macroeconomic way**

Macroeconomics is a controversy-ridden area of study. In part, this is because the topic of study is seen as being of great significance to our nation and our daily lives even though the variables that are discussed are mostly difficult for us to understand.

The popular press and media is flooded with macroeconomics – the nightly news bulletin invariably has some commentator on speaking about macroeconomics issues – such as, as the real GDP growth rate, the inflation rate or the unemployment rate. The trend to the population being more exposed to macroeconomic terminology has increased over the last two or so decades and the advent of social media has made anyone who wants to be a macroeconomic commentator.

The so-called blogosphere is replete with self-styled macroeconomic experts who wax lyrical about all and sundry, often relying on intuitional logic to make their cases. The problem is that common sense is a dangerous guide to reality and not all opinion should be given equal privilege in public discourse. Our propensity to generalise from personal experience, as if the experience constitutes general knowledge, dominates the public debate – and the area of macroeconomics is a major arena for this sort of false reasoning.

A typical statement that is made in the public arena is that the government might run out of money if it doesn’t curb spending. Conservative politicians who seek to limit the spending ambit of government often attempt to give this statement authority by appealing to our intuition and experience.

They draw an analogy between the household and the sovereign government to assert that the microeconomic constraints that are imposed on individual or household choices apply equally without qualification to the government.

So we are told that governments, like households, have to live within their means. This analogy resonates strongly with voters because it attempts to relate the more amorphous finances of a government with our daily household finances. We know that we cannot run up our household debt forever and that we have to tighten our belts when our credit cards reach our borrowing limit.

We can borrow to enhance current spending, but eventually we have to sacrifice spending to pay the debts back. We intuitively understand that we cannot indefinitely live beyond our means.

Neoliberals draw an analogy between the two – household and government – because they know we will judge government deficits as being reckless, if their budget deficit rises. But the government is not a big household. It can consistently spend more than its revenue because it creates the currency.

Whereas households have to save (spend less than they earn) to spend more in the future, governments can purchase whatever they like whenever there are goods and services for sale in the currency they issue. Budget surpluses (taxation revenue greater than government spending) provide no greater capacity to governments to meet future needs, nor do budget deficits (taxation revenue less than government spending) erode that capacity.

Governments always have the capacity to spend in their own currencies. Why? Because they are the issuers of their own currencies, governments like Britain, the United States, Japan and Australia can never run out of money.

MMT teaches that our individual experience concerning our household budgets has no application to the government budget. We use the currency the government issues. Our individual experience about our own budgets does not generate knowledge about the government budget yet, on a daily basis, we act as if it does.

The “means” that the government has to consider are the real resources available to the economy and how best to deploy them. These are not financial considerations – there are no intrinsic “financial” constraints that are relevant to a currency-issuing government.

A household always has to consider its financial means. Common sense tells us that if we have “too much debt” then we can save and reduce that debt. But, whether public debt is problematic aside, if the government tries to “save” (another inapplicable conceptual transfer from the individual level) then public debt will probably rise.

Indeed, macroeconomics breathed life in the 1930s as a separate discipline of study from microeconomics because the dominant way of thinking at the time was riddled with errors of logic that led to spurious analytical reasoning and poor policy advice.

Microeconomics develops theories about the individual behavioural unit in the economy – the person, household, or firm. For example, it might seek to explain individual firm employment decisions and or the saving decisions of an individual income recipient.

We have learned that macroeconomics studies the aggregate outcomes of all firms and households. The question is how do we go from the individual unit (microeconomic) level to the economy-wide (macroeconomic) level? This is a question that the so-called aggregation problem seeks to address

Prior to the 1930s, there was no separate study called macroeconomics. The dominant school of thought in economics at the time considered macroeconomics to be a simple aggregation of the reasoning conducted at the individual unit or atomistic level.

To make statements about industry or markets or the economy as a whole, they sought to aggregate their atomistic analysis. For reasons that lie beyond this textbook, simple aggregation proved to be impossible using any reasonable basis.

The solution was to fudge the task and introduced the notion of a “representative household” to be the demand side of a goods and services (product) market and the “representative firm” to be the supply side of that market. Together they bought and sold a “composite good”. These aggregates were fictions and assumed away many of the interesting aspects of market interaction.

For example, if we simply sum all the individual demand relationships between price and spending intention we could form a representative household demand function.

But what if the spending intentions of each household or a segment of them were interdependent rather than independent. What if one household changed their demand once they found out what the spending intentions of the next-door neighbour was (for example, the notion of keeping up with the Jones!)? Then a simple summation is impossible to achieve.

But these issues were abstracted from and the representative firm and household were just bigger versions of the atomistic unit and the underlying principles that sought to explain the behaviour of the representative firm or household were simply those that were used to explain behaviour at the individual level.

The economy was seen as being just like a household or single firm. Accordingly, changes in behaviour or circumstances that might benefit the individual or the firm are automatically claimed to be of benefit to the economy as a whole.

In the Great Depression, this erroneous logic guided policy in the early 1930s and the crisis deepened. At that time, John Maynard Keynes and others sought to expose the logical error that the dominant orthodoxy had made in their approach to aggregation. In that debate, which we consider in Chapter 7, the logic was identified as a compositional fallacy – which led to the development of macroeconomics as a separate discipline from microeconomics. Karl Marx had appreciated this fallacy in the mid-1800s.

Compositional fallacies are errors in logic that arise when we infer that something, which is true at the individual level, is also true at the aggregate level. The fallacy of composition arises when actions that are logical, correct and/or rational at the individual or micro level have no logic (and may be wrongful and/or irrational) at the aggregate or macro level.

Keynes led the attack on the mainstream thinking at the time – mid-1930s – by exposing several fallacies of composition. Lets consider two famous fallacies of composition in mainstream macroeconomics: (a) the paradox of thrift; and (b) the wage cutting solution to unemployment.

You will be familiar with these examples but perhaps not the reason why they are fallacious. We will consider the first fallacy here as an example, and the wage cutting fallacy in a later chapter.

The paradox of thrift refers to a case where individual virtue can be public vice. If an individual attempts to increase the proportion that he/she saves out of their disposable income (income after tax) – the so-called saving ratio – then if they approached the task in a disciplined manner they would probably succeed.

There is an old saying – look after the pennies and the pounds will look after themselves.

So by reducing their individual consumption spending a person can increase the proportion they save and enjoy higher future consumption possibilities as a consequence. The loss of spending to the overall economy of this individual’s adjustment would be small and so there would be no detrimental impacts on overall economic activity, which is crucially driven by aggregate spending.

But imagine if all individuals (consumers) sought the same goal and started to withdraw their spending *en masse*? Then total spending would fall significantly and, as you will learn from Chapter 5, national income falls (as production levels react to the lower spending) and unemployment rises. The impact of lost consumption on aggregate demand (spending) would be such that the economy would plunge into a recession and everyone would suffer.

Moreover, as a result of the income losses it is highly likely that total saving would actually fall along with consumption spending so the economy as a whole would be saving less.

The paradox of thrift tells us that what applies at a micro level (ability to increase saving if one is disciplined enough) does not apply at the macro level (if everyone attempts to increase saving, overall incomes fall and individuals would be thwarted in their attempts to increase their savings in total).

Why does the paradox of thrift arise? In other words, what is the source of this compositional fallacy?

The explanation lies in the fact that a basic rule of macroeconomics, which you will learn once you start thinking in a macroeconomic way, is that spending creates income and output. This economic activity, in turn, explains how employment is generated. Adjustments in spending drive adjustments in total production (output) in the economy.

So if all individuals reduce their spending (by attempting to save) the level of income falls rather than stays constant, as would be the case if just one person reduced their spending.

As total saving (the sum of all household saving) is a residual after all households have made their consumption spending choices from the available disposable income then national income shifts, in turn, feedback on total saving. When national income falls, consumption falls and total saving will also usually decline in absolute terms.

Keynes and others considered fallacies of composition such as the paradox of thrift to provide a *prima facie* case for considering the study of macroeconomics as a separate discipline. This development explicitly acknowledged that it is dangerous to engage in specific-to-general reasoning.

By assuming that we could simply add up the microeconomic relations to get the representative firm or household and the mainstream at the time were assuming that the aggregate unit faced the same constraints as the individual sub-units. So the individual saver might reasonably assume that changing his/her consumption choices would not impact on his/her income.

But we know that if all consumers act *en masse* then not only does their spending change but the income constraint also shifts and the logic that applied at the individual level will be spurious or fallacious at the aggregate level.

There are other fallacies of composition that we will examine in the course of this textbook.

For example, a current example relates to the insistence by the conservative policy makers on fiscal austerity.

During the Global Financial Crisis, the conservative reaction to the increasing government deficits has been to propose fiscal austerity and to encourage nations to cut domestic costs in order to stimulate their export sectors via increased competitiveness.

In isolation, that is, where one nation does this while all other nations are maintaining strong economic growth, this strategy might have a chance of working. But if all nations engage in austerity and cut their growth rates because overall spending declines, then imports will fall across the board, as will exports.

It is the interdependence between all countries via trade that undermines the policy suggestion in this case.

MMT contains a coherent logic that will teach you to resist falling into intuitive traps and compositional fallacies. MMT teaches you to think in a macroeconomics way.

COMING IN THIS INTRODUCTORY CHAPTER – WHAT HAS TO BE EXPLAINED BY A MACROECONOMIC MODEL – STYLISED FACTS.

**Annexe 1 – Essential analytical terminology**

[Note: This section may appear as *Chapter 4 Methods, Tools and Techniques*, which will present an array of empirical, mathematical and graphical techniques that help us engage in macroeconomics]

In this Appendix we present some analytical terminology that is used in the specification of macroeconomic models and which you will find throughout this book.

The level of mathematics that will be used throughout this book is no more sophisticated than the typical material that a student would encounter in the second-half of their secondary school studies. The most advanced analysis we employ is simultaneous equation technique and some simple calculus. For the most part, the mathematics is confined to algebraic representations of the behavioural theories and/or accounting statements that we advance and some simply solution exercises to determine the unknown aggregates we are interested in.

The practical material accompanying the analytical text will also provide a step-by-step sequence to mastering the techniques required.

We recognise that mathematical techniques are commonly used within the social sciences and that students will gain confidence in dealing with the standard conceptual and empirical literature in economics and more broadly if they develop some formal modelling skills in addition to the deep understanding that we hope to engender.

In Chapter 1, the concept of a model was introduced. It was stated that a macroeconomic model comprises the tools and theoretical connections to advance study of the main aggregates – employment, output and inflation.

A model is a generalisation about the way the system functions or behaves. It could easily be a narrative statement such as – a household will consume a proportion of their income after tax (disposable income). That theoretical statement might then be examined for its empirical relevance but will also stimulate further theoretical work trying to provide an explanation for that conjectured behaviour.

In economics, like other disciplines that use models, the narrative statement might be simplified with some mathematical statement. In this context, the models will be represented by a number of equations (which could be one), which describe relationships between variables of interest. The relationship between the variables is described in terms of some coefficients (or parameters). Usually a variable that we seek to explain is written on the left-hand side of the equals sign (=) and is then expressed in terms of some other variables on the right-hand side of the equals sign, which we consider are influential in explaining the value and movement of the left-hand side variable of interest.

For example, y = 2x is an equation which says that variable y is equal to 2 times variable x. So if x = 1, then we can solve for the value of y = 2 as a result of this equation. The left-side of the equals sign is of the same magnitude as the right-side (that is, an equation has equal left and right sides). You solve an equation by substituting values for the unknowns.

In the above example the number 2 is called a coefficient which is an estimate of the way in which y is related to x. A coefficient can also be called a parameter – which is a given in a model and might be estimated using econometric analysis (regression) or assumed by intuition). In that context, the coefficient’s value is unknown.

For example, we might have written the above equation as y = bx, where b is the unknown coefficient. You will note that we would be unable to “solve” for the value of y in this instance even if we knew the value of x. In the case above where we said x = 1, then all we could say that y = b. We would thus need to know what b was before we could fully solve for y. Further on in the book we will come back to this problem of too many unknowns.

But for now, it is sometimes useful to have models where we cannot solve for numerical values of the unknown variables of interest but we can simplify the equations to show the structure of the model in terms of what is important to understand in relation to our aggregates.

In the context of economic modelling, a variable is some measured economic aggregate (like consumption, output etc), which is denoted by some symbol that makes sense. The correspondence between the shorthand symbol and the variable is not always intuitive but conventions have been established, which we retain in this textbook.

So Y is often used to denote real GDP or National Income (but it can also be used to denote total output). C is usually used to denote final household consumption and I total private investment. X is typically used to denote exports and M imports although in some cases M is used to denote the stock of Money. In this text, M is exclusively used to denote imports.

There are two types of equations that are used in macroeconomic models: (a) identities which are true by definition – that is, as a matter of accounting – they are indisputable; and (b) behavioural equations which depict relations between variables that model behaviour – for example, consumption behaviour.

An example of an identity is the national income equation depicting aggregate demand and output, which we consider in Chapter 5:

Y = C + I + G + X – M

Note that in strict terms we write an equation that is an identity using the identity sign (three parallel horizontal lines) instead of the equals sign (two parallel horizontal lines). That distinguishes it from a behavioural equation which is always expressed using an equals sign (=).

A behavioural equation captures the hypotheses we form about how a particular variable is determined. These equations thus represent our conjectures (or theory) about how the economy works and obviously different theories will have different behavioural equations in their system of equations (that is, the economic model).

An example of a behavioural equation is the Consumption function:

C = C_{0} + cY_{d}

which says that final household consumption (C) is equal to some constant (C_{0}) plus some proportion (c) of final disposable income (Yd). The constant component (C_{0}) is the consumption that occurs if there is no income and might be construed as dis-saving.

Note that subscripts are often used to add information to a variable. So we append a subscript d to our income symbol Y to qualify it and denote disposable income (total income after taxes).

In macroeconomics, some behavioural coefficients are considered important and are given special attention. So the coefficient c in the Consumption function is called the marginal propensity to consume (MPC) and denotes the extra consumption per dollar of extra disposable income. So if c = 0.8 we know that for every extra dollar of disposable income that the economy produces 80 cents will be consumed.

The MPC is intrinsically related to the marginal propensity to save (MPS) which is the amount of every extra dollar generated that is saved (after households decide on their consumption). So the MPS = 1 – MPC by definition.

The importance of MPC is that is one of the key determinants of the expenditure multiplier (more about which later). We will consider this in Chapter 5 when we discuss the expenditure multiplier.

The other piece of jargon that we encounter is the difference between exogenous (pre-determined or given) variables and endogenous variables (which are determined by the solution to the system of equations).

An exogenous variable is known in advance of “solving” the system of equation. We take its value as given or pre-determined. We might say, by way of simplification, that government spending (G) is equal to $100 billion which means that its value is known and not determined by the values that the other variables take or are solved to.

But in a system of equations, the values of some variables are unknown and are only revealed when we “solve” the model for unknowns.

So if we have these two equations, which comprises a “system”:

(1) y = 2x

(2) x = 4

Then x is a pre-determined variable (with the value 4) and is thus exogenous. You do not know the value of y in advance and you have to solve the equations to reveal its value – so it is endogenous. It is determined by the solution to the system.

To solve this system we substitute the value of x in Equation (2) into Equation (1) so we get:

y = 2 times 4

y = 8

So the solution of a system merely involves substituting all the known values of the coefficients (in this case the 2 on the x) and the exogenous variables (in this case x = 4) into the equations that depict the endogenous variables (which in this case is only Equation (1) but there will typically be multiple endogenous variable equations).

In real modelling it becomes very complicated as to which variables can be considered endogenous and which are truly exogenous. At the extreme, everything might be considered endogenous and then things get mathematically complex and there is a whole body of theory in econometrics relating to the identification problem, which is well beyond this textbook.

We will also express our theories in graphical terms, which are an alternative to mathematical representation. Here are three ways to express the same theoretical idea.

1. Household consumption rises proportionately with disposable income but the proportion is less than one.

2. C = C_{0} + cY_{d}, where 0 < c < 1 and C_{0} is a constant (fixed value). The less than sign (<) tells us that the MPC lies between the value of 0 and 1, that is, it is positive but less than 1.
3. Graphical form:

If C_{0} = 100, and c = 0.8, and Y_{d} = 1000 then total consumption would be 900. We could have solved the equation C = C0 + cYd by inserting the known values of the parameters and explanatory variable (in this case disposable income) into the equation and solving it.

Thus:

C = C_{0} + cY_{d} = 100 + 0.8 x 1000 = 900.

You can also see that by tracing a vertical line from where Disposable income equals 1000 up to the graph line and then tracing across the vertical axis we derive the value of Consumption by where that line crosses the vertical axis.

It was stated that the slope of the line is the Marginal Propensity to Consume (c). How do we derive a slope of a line and what does it mean? In Chapter 3 we will deal with applications of the slope of a line when we study the principle of the spending multiplier.

In general terms the following will be useful.

SIMPLE CALCULUS AND GRAPH TO BE INSERTED HERE.

We recognise that different students have different ways in which they learn and accumulate knowledge. Some prefer the mathematical approach while others prefer the graphical approach. Others still learn better through reading the written word, even though that form of communication is prone to interpretative issues. In that regard, all the essential material in the text will be presented in all three ways (sometimes the mathematics will appear in the Annexe of the relevant chapter sometimes within the main body of the text.

**Saturday Quiz**

The Saturday Quiz will be back tomorrow (from 04:00 Eastern Australian Time). I noted this week some person claimed they have worked out how I think. If they have I would appreciate them telling me so I would know too. But like all idle boasts … it has spurned action. I aim to disabuse that person of his conjecture in this week’s quiz. ðŸ™‚

That is enough for today!

Is it worth mentioning about the failures of ‘microeconomic grounding’ in the models of central banks.

The way models appear to be built at the moment is based on ‘microeconomic grounding’ and then patched with ugly hacks to fit the real world data.

It’s a bit like trying to get off a speeding ticket by suggesting you can’t possibly measure the speed of the car without changing it.

Hi Bill,

You underestimate the difference between an Old-British-Empire education and the pathetic, degraded American version of “secondary school”. I learned more from one fifth-form general maths course at an English school than I did in all the rest of my education here, and that was long before the really big decline set in. I find that there is no such thing as “a little” calculus. Having gone back years later to understand what I had missed, I can only say that there is no way to dumb it down enough to get the Yanks to understand it. Just do what’s necessary.

Cheers

Some minor suggestions — feel free to accept or reject.

(1) The title ‘”Thinking Macroeconomically” is catchier. And it seems to be a real word: http://en.wiktionary.org/wiki/macroeconomically

(2) “Conservative politicians who seek to limit the spending ambit of government often attempt to give this statement authority by appealing to our intuition and experience.”

I would say: politicians. It makes you sound less partisan (this being a textbook) and its actually true: almost ALL politicians live within this delusion.

(3) Perhaps find a more general term than “neoliberal”. “Mainstream”, “ill-informed” etc.

(4) “During the Global Financial Crisis, the conservative reaction to the increasing government deficits has been to propose fiscal austerity and to encourage nations to cut domestic costs in order to stimulate their export sectors via increased competitiveness.”

Again, I think if you just say “reaction” it works just as well and highlights that this is problem across the ideological spectrum.

(5) “Note that in strict terms we write an equation that is an identity using the identity sign (three parallel horizontal lines) instead of the equals sign (two parallel horizontal lines).”

Are you going to pursue this? I recently read Robinson and Eatwell’s introductory text and they were quite strict about this. I think they were right to do so. They pointed out that the old Keynesian series [Y = C + I; Y = C + S; S = I] was torn out of context by hostile critics and used to fuddle the theory because they took it as a ‘causal equation’ rather than an identity. (P. 216-217 if you want to look up the criticism they make).

=====================

All in all the book looks like its coming together. It’s very clearly written and I think that the use of maths, graphs and writing will be a very strong point. Many introductory texts fall down with too much of some and too little of another — mostly too much maths and graphs and too little writing, in my opinion. Keep at it though, good work.

Would Ohm’s Law be considered an identity? I have not seen it expressed with the identity symbol, but have not had cause to dispute its accuracy.

Use of o, O, to denote variables is confusing at first.

If the book is intended to be a textbook, I think it is a terrible idea to make reference to current events as such in the text. That’s ok in the preface though.

“MMT contains a coherent logic that…”

You’re the expert on economics, but have you thought of not using the words “MMT” or Modern Monetary Theory throughout the book? Or maybe just in the preface? Just present the economics as is…you can contrast with how things are usually presented, etc..but why not just write an economics book that uses MMT theory and logic instead of an MMT economics book?…it might come across less “cultish” to outsiders…again, maybe this is done is other economics textbooks but I don’t know, do Neo Keynesians refer to the term “Neo Keynesian thinking” throughout a textbook? (The current Austrians probably do it…which I think helps make my point). I think it is harder for ideas to be accepted by others if they are constantly reminded that their way of thinking is different…imagine a Keynesian reading part of your textbook – maybe they are starting to come around on an idea that MMT is pushing…(kind of like Krugman now is on board with the fact that bond yields are much lower in sovereign currency issuing countries regardless of “debt”), but then they are constantly hit with the words “MMT says” or “MMT way of thinking”. I think they will be less likely to refer to it or possibly use it in a class. Now, maybe you don’t care about that and you are only writing for the converted to reference and use – personally, I think your book could be much more than that.

I could be way off base, but that’s what struck me as I read this passage and the previous (more so in the previous one, however)

there’s something i can’t understand…

you say C = C0 + cYd

but what happens when C0>=Yd

I think it’s not rational to say one would spend more than C0 in that case, is it?

I haven’t read the above post, but I like the title “Thinking in a Macroeconomic way”. Reason is that I think the basic difference between MMTers and others is that MMTers fully understand macroeconomics and the implications of monetary sovereignty, whereas others (including some household name economists don’t).

I.e. there are plenty of articles by household name economists in reputable publications where they clearly treat the government / central bank machine as a microeconomic entity that, for example, can run out of money.

Let’s hope someone doesn’t do to Bills book what Hicks did to Keynes’.

“An example of a behavioural equation is the Consumption function:

C = C0 + cYd

which says that final household consumption (C) is equal to some constant (C0) . . . ”

I prefer final household consumption (C) is equal to some amount (Co).

Where Co is autonomous consumption {consumption that is not directly affected by income}.

This then ties in with the paradox of thrift?

“But imagine if all individuals (consumers) sought the same goal and started to withdraw their spending en masse? Then total spending would fall significantly . . . ”

Their average propensity to save increases {APC falls}.

This can be illustrated diagramatically by a reduction in autonomous consumption {Co falls}. This shifts the consumption function {and the aggregate demand/expenditure schedule} downwards.

Factors that MAY affect Co.

Co = Co(r,M/P,CC, EP):

Autonomous consumption expenditure is determined by the the rate of interest, r {negatively}; the real stock of money, M/P {positively}, the level of consumer confidence, CC, {positively} and the expected change in the price level, EP {positively}.

“Alan Dunn says:

Sunday, June 17, 2012 at 17:59

Let’s hope someone doesn’t do to Bills book what Hicks did to Keynes’.

It didn’t take long did it.

Bill,

‘For reasons that lie beyond this textbook, simple aggregation proved to be impossible using any reasonable basis.’

I would recommend a separate box dealing with the fallacy of composition, which is what I expect you may be referring to here. I needn’t be too technical.

Bill,

In logical terms, the triple line indicates equivalence, as in if and only if (iff), while the double lines indicate one of a number of kinds of identity, one being definitional identity. The former relates sentences, while the latter relates terms. I think this distinction should be adhered to throughout.

You define GDP in two distinct ways and then combine them. That these are definitions should be notated in some way in order to differentiate them from substantive identities, e.g., algebraic or accounting identities. The latter are substantive identities while the former only specify the meaning of terms. The former possess a truth value while the latter do not. As it stands, these are not distinguished.

It is easy to notate a definitional identity: =df, where the df is a subscript. This tells the “knowing” reader that the term on the left, the definiens, is defined in terms of the possibly complex term on the right, the definiendum.

Perhaps I should say for the sake of clarity that the identification of the two definienda re the definition of GDP is a trivial logical consequence of the two definitions. I know you know this, but it may be helpful to the student to point out that an additional inferential step is necessary to infer that the two definienda are identical involving a “law of logic”. This resultant identity is not itself a definition.

Phil is right to point out the importance of this issue but I disagree with him on how to deal with it.

Corrigendum: I meant to say that definitions do not possess truth value while substantive identities do.

Bill, it has not gone unnoticed by some of us that economists are rather cavalier with their treatment of their data. For instance, it was once common to consider error estimates in data tables (cf. Morgenstern, On the Accuracy of Economic Observations, 2nd Ed. (1963)). Now it hardly ever occurs. Nor do common statistical tests see the light of day in economic analyses. I don’t mean hypothesis testing of which ever stripe (Neyman-Pearson, Fisher, Bayesian) but even such things as statistical power, or effect sizes, or confidence limits.

It may be that you and Randy think that this material goes beyond your brief, but I would suggest that, in order to show the student how to deal competently with data similarly to the way it is done in other social sciences, a separate box or two or three, whenever necessary, dealing with the data statistically could be incorporated into the text, and this would include graphing of the data. Caveat: just as virtually all intro macroecon texts are unsatisfactory, so are many introductory statistical texts, especially when it comes to hypothesis testing – they are a mess. Hence, my implied avoidance of them above.

Bill, when I mentioned Morgenstern, I didn’t mean to suggest that we necessarily use the same procedures he did, just analogous ones, some of which will remain the same. He wrote his book around the time that Mandelbrot showed that finance data did not follow a Gaussian distribution but rather a Cauchy-Mandelbrot-Lorentzian distribution for which there is no calculable mean or variance. This of course puts paid to many risk analyses. But it provides independent support for Keynes’ notion of what I would call ontological uncertainty (as opposed to epistemic uncertainty, which I would ascribe to Knight), what Keynes called, simply, uncertainty.

Bill, I know I have mentioned this before, no doubt ad nauseum, but I think it would be adventitious to differentiate between a theory and a model, rather than follow the standard usage. For a logician, a model is a non-linguistic structure in which a theory is true. A theory is a set of propositions. A proposition can be interpreted as being the “meaning” of a sentence. The straightforward view you can take is to view theories as sets of sentences, or propositions, that are true or false, excepting the definitions occurring within them.

You may well encounter a problem in dealing with computer simulations where you might be expected to deal with the issue of whether a computer program is a theory. For some, programs appear to possess characteristics of both theories and models as I have “defined” them. For your purposes, I think this problem can be avoided. You can easily claim that this matter goes beyond the scope of the book.

Theories Vs Models: There just happens to be a superb discussion of the theory-model distinction I wish you and Randy to take on board if only encased in an box set off from the text and containing an explanation of why you are not going down this route. The source is: Patrick Suppes, “A Comparison of the Meaning and the Uses of Models in Mathematics and the Empirical Sciences”. In Hans Freudenthal, ed., The Concept of the Role of the Model in Mathematics and Natural and Social Sciences. Reidel: 1961. (The ungrammaticality of the title is in the original.) Suppes does use economics as one of his social science examples.

This is just to show that discussions of this distinction have a history however short and is not just a hobby horse of mine.