All accountants should be trained in econometrics ...

The proposition about accounting and econometrics, a little more formally, is this:

It is necessary for professional accountants to be trained in econometrics.

Most accountants and, I believe, even most accounting professors would strongly disagree with the proposition. ( It is, I can assure you, nonetheless true. :) )  Before presenting the argument supporting the proposition, it's first necessary to have an understanding of what econometrics is.

    What is econometrics?  To paraphrase the econometrician Jeff Wooldridge, 

Econometrics is the discipline involved in estimation of, and inferences about, causal relationships between economic variables.

For example, suppose economic theory suggests a causal relationship between sunspots and the demand for electronic components; let's say theory suggests sunspots cause an increase in the demand for electronics components.  An inquisitive individual might want to answer at least two questions about the theory:  Is actual data consistent with the prediction that sunspots are, on average, associated with an increase in electronic component demand? And, what is the estimated average effect of (the average) sunspot on electronic component demand?  Both, no doubt, interesting questions ... .  
    Also, attributable to Jeff Wooldridge is the useful idea of a mutually-exclusive-and-exhaustive classification of things we need to know to make decisions: Things we need to know can either be (1) known, (2) estimated, or (3) assumed, where the (rational) decision-making preference ordering is known > estimated > assumed.  Econometric methods are necessary when relationships between economic variables are not known, and when it is a Bad Idea to assume them.  
    In the context of my proposition it is hopefully obvious that simply assuming values in financial statements is a Bad Idea.  It is also hopefully obvious that the values of many things reported in financial statements is not "known".  In any case, with this basic understanding of what econometrics is I'll turn to the main topic.

    Accounting requires econometrics. As background, accounting is basically comprised of the recognition, measurement, and disclosure of economic events and resources in financial statements:

• recognition refers to when events and resources are presented;
• measurement refers to how events and resources are valued; and
• disclosure refers to how such events and resources, recognition, and measurement are described in the statements.

Accounting measurement of many economic events and resources in a way approaching objective measurement requires use of econometric methods (and objectivity is an important characteristic of accounting measurement).  I will explain the idea using FAS 157, Fair Value Measurement and FAS 142, Goodwill and Other Intangible Assets, although I could just as easily use any of a dozen or so other accounting standards, which professional accountants must apply as part of their work.  Roughly speaking,  FAS 142 and 157 in combination require accountants to estimate the fair value of intangible assets, and reduce the financial statement value of the intangibles to the estimated value if less than previously reported.

    So why would estimating the fair value of intangible assets (among other things in financial statements) require use of econometric methods?  To answer, first consider the simplest expression of how fair value of intellectual property ("IP", one broad category of intangibles) is determined, where example numbers for factors influencing value are included for concreteness:

The equation says estimated fair value is a function of (i) expected future marginal profits attributable to the IP, (ii) expected future value of the IP, and (iii) estimated fair market expected risk-adjusted rate of return.  It is relatively easy to show expected future profits and values generally must be estimated using econometric methods, but I will simply focus (very carefully) on the estimated fair market expected risk-adjusted rate of return.  For example, given $1,000 in  expected future profits and value at the end of one year, if the estimated rate of return is .10, then the estimated fair value of the IP is about $909.

    But here's the problem for accountants: They don't know what a fair market's expected risk-adjusted rate of return is for the IP. Why? Because IP is almost by definition unique  and therefore unlike other IP that might have been sold.  Moreover, IP is rarely traded in open, fair markets.  This means that accountants (or someone else) must estimate what a fair market's expected risk-adjusted rate would be; that is, they must predict what the rate would be if the IP was traded in a fair market. 
    So, unless the accountants are willing to abrogate their responsibilities for accounting measurement (which they often do, by the way) or simply make an assumption about the rate (which they also do sometimes), then they must use econometric methods to estimate the rate.

    The argument is essentially complete at this point (QED, quod erat demonstrandum!), but to see this all a little more clearly consider the following graph:

Ignoring the questions posed in the graph momentarily, I will focus on what the graph represents:

• The graph represents a hypothetical relationship between a certain type of risk (e.g., the risk that a particular class of antibiotics will become obsolete due to development of a newer, better class of antibiotics) and the rate of return implicit in the way a fair market sets the price of the risk.
• The points shown on the graph represent actual observations ("data") of risk and rate of return set in a fair market (e.g., actual observations of expected market rates of return across different antibiotics each with different levels of risk).
• The line running through the data represents an estimate of the fair market relationship between the type of risk and the market rate of return on the risk.

Suppose we are accountants for "YX Pharma Corporation" with "Antibiotic X" for which we have a patent expiring in 10 years.  Antibiotic X represents about 1/2 of the revenues and profits for YX Pharma, and has never been offered for sale.  So, the IP represented by the Antibiotic X patent is not traded in any market, let alone traded in a fair market.  So we don't know its fair value. 

    This means we accountants must either estimate or assume the value of the Antibiotic X patent.  Our securities law attorneys have strongly advised us against simply making up an assumption  about the value of the patent without strong supporting data and analysis.  So, we must estimate the value:  Roughly speaking we must first predict expected future marginal profits and value of the patent. Then, because the patent for Antibiotic X doesn't trade in a fair market, we must use publicly-observable data on risk measures and fair market rates of return on other similar antibiotics to estimate the market's risk-return relationship.
    With our estimate of the (equation for) the market's risk-return relationship, we can then use our measure of risk for Antibiotic X and obtain an estimate of a fair market's expected risk-adjusted return on Antibiotic X (even though, as stated, it doesn't actually trade in any market).  The estimated rate would then be used in a valuation model similar to the one shown above (the FV equation) to obtain the FV estimate of the Antibiotic X patent.

    As suggested by the questions on the graph, the scenario poses a lot of important questions we accountants must answer:

• Where exactly do we get this market rate of return data; which competitors and which antibiotics; how do we separate overall observable market rates of return on competitors' equity from the rates on the antibiotic IP?
• What is the best way to estimate the risk-return relationship; what method(s); what exactly are we estimating (i.e., the most likely relationship, the most conservative, etc.)?
• What do we do about observations that don't seem to fit the average risk-return relationship; should they be included in our analysis and estimates?

It turns out that such questions (and their answers) are precisely the domain of econometrics.  Econometricians have largely worked out the general frameworks for thinking about such problems, as well as general solutions to them, over the last 50-60 years.

    So it follows that ...

Unless professional accountants want to abrogate their responsibility for accounting measurement to those trained in econometrics, they must be trained in econometrics themselves.

It would seem strange, almost pathetic really, if accountants were to abrogate the responsibility for accounting measurement--one of the three basic aspects of accounting--to others, don't you think?  :)  QED

MMc
São Paulo

A healthcare case for (and against) Wall Street ...

Enquiring minds want to know, or so we're led to believe. If they do, then perhaps they want to know some reasons why the US government seems fixated on making sure Wall Street, the stock market, is stable and successful. Of course, we all think we know the primary reason: People get panicky when their investment portfolio values--particularly those held in their retirement funds--head South. And these people vote in a way that's highly correlated with their investment portfolio growth. Alternatively, the conspiracy theorists among us believe there's some dark collusion between the US government and the investment banks. It seems, however, there might be other critically important reasons as well. Read on ...

The Medicare program is essentially heath care insurance covering most all US citizens over age 64; part of the US' long-term trend towards socialized medicine. Medicare spending is the third largest component of US federal government spending, representing approximately 16% of total expenditures. Suffice it to say, it's important to understand what drives this component of US government spending. I have come to believe that an important factor driving Medicare spending is closely related to the health of Wall Street, so to speak.

Microeconomic theory suggests Medicare spending is a function of:

• time, since prices tend to increase because of monetary inflation;
• population over age 64, since more people requires more expenditure; and
  
• societal wealth, since societies with more wealth tend to provide higher levels of government-funded social services).

If we are to estimate average effects of each of the factors on Medicare spending, it's necessary to develop an econometric model that can be estimated using observable data. While time and population are observable, societal wealth is not; at least it's not easily observable. There are good theoretical arguments, however, suggesting US equity market values are highly correlated with societal wealth. This in turn suggests using an observable index of equity market values, such as the S&P 500 Index, as a proxy for societal wealth in an econometric model. Putting this all together, stating the relationships in terms of annual percentage changes, and adding quadratic terms as (hopefully) an approximation of more general forms of non-linearities, results in a model like this:

I chose to model the growth rate in Medicare spending on physician and clinical services--an important subset of total Medicare spending--because I thought it was the component most directly associated with the over age 64 population.

Because such relationships tend to be non-stationary over time, I estimated the model using FGLS estimation with heteroscedasticity-robust standard errors and publicly-available data that I downloaded from www.freelunch.com with the following parameter estimate and statistical significance results:

Decimal numbers below the parameter estimates are p-values, showing the estimated probability the parameter is actually zero in the real world (i.e., the probability the factor has no effect on Medicare spending) given the sample data and that necessary assumptions underlying the model hold.

So what, you ask?  Consider the estimated marginal effects of a 20% change in S&P 500 returns on Medicare spending:

The econometric results suggest a 20% increase or decrease in the S&P 500 return results in an increase in Medicare spending for physician and clinical services, which at 2008 levels results in an estimated $14.5 billion increase in Medicare spending.  Hmmm ... that's a lot of money.


How often do 20% increases or decreases in S&P 500 returns occur?  Consider  the following histogram:

The histogram shows that 20% or greater absolute changes in the S&P 500 return from the prior year return occurred 14 times in the 41 year period ended 2008; so, about 34% of the time.  Ouch.  Moreover, consider what happens in the really volatile years:

Ouch, that hurts even more ... .  

Do the results make sense?  If humans (and politicians too) are into pain avoidance, one might suspect they would do their best to avoid volatile stock returns ... because apparently there are a lot more people seeing physicians, getting lab tests, etc. when the stock market goes crazy.  Considering (i) the high level of stress most people are under in developed, highly competitive  economies, and (ii) how many people obsess daily on their investment portfolio market values (e.g., even I go to Google finance daily to check on the markets and I don't even have any investments!), this seems entirely reasonable to me: Stock market volatility sends people over their health tipping points due to the  psychosomatic effects of the incremental stress.

So ... as promised by the title, here is the health care case for, and against, Wall Street:

Theory and evidence presented above, skeletal though it may be, suggest that (1) to the extent Wall Street firms promote stability in the financial markets, they are good for US health care, and (2) to the extent Wall Street firms promote instability in the financial markets, they are bad for US health care.

It's not completely clear, at least to me, whether Wall Street firms promote stability or instability in the financial markets.  My guess is that they benefit most, and most immediately, by promoting instability: Wall Street makes money from trading.  But perhaps if the conspiracy theorists are correct and the US government is trying to protect Wall Street firms from competition of various types, then lessening the pressure to produce trading profits might lead the firms to promote more stable financial markets.  But at this point, it seems the only thing to do is reserve judgment on whether Wall Street is good or bad for US health care.

MMc
São Paulo

The credit crunch/recession and why it's likely to continue ...

I often speak with entrepreneurs and managers and, even though unit sales volumes and revenues in their businesses have decreased by between 20% and 50% from 2007 levels (they're mostly in durable  products manufacturing), almost all of them say they're expecting a recovery to begin in the next 3 to 6 months.  The irony is they've now been saying just this for at least the last one and a half years!  So much for the economic theory of rational expectations.  Hope or ignorance springs eternal.  Enquiring minds would, no doubt, like to know which it is.  Let's see ...

The Problem. Most of us know at some level that the overall economic downturn experienced in the US is somehow related to "the credit crunch".  Many of those I've spoken with suggest all that's needed to obtain an economic recovery is to solve the credit crunch problem: "If credit was available, people would be more confident and start spending again.  Then everything would be ok."  There is obviously some truth to this and it seems apparent this is the major premise upon which the Federal Reserve is operating.  But if it were really just a matter of pumping money into the US economy, the US should be in the strongest, most robust recovery in the history of the World.  Sadly, this isn't the case.

So what is the problem?  The problem is that the credit crunch is comprised of two inter-related feedback cycles; the consumer demand feedback cycle and the capital cost and credit default cycle.  Some feedback cycles are good (negative feedback cycles, which tend to be self-correcting) and some are bad (positive feedback cycles, which tend to be self-reinforcing).  The two feedback cycles comprising the credit crunch feedback cycle are the latter kind.; the Bad Kind.  Let me explain.  Consider the consumer demand feedback cycle:

Consumer demand feedback cycle

I think the cycle diagram is fairly self-explanatory, but there are two important aspects to it: (1) trouble in any component of the cycle leads to trouble in the rest of the cycle, and (2) once trouble starts, only some exogenous factor --i.e., something outside the cycle--that influences a component in a beneficial way has the possibility of stopping the self-reinforcing cycle.  So, for example, the Federal Reserve might manipulate the money supply to (artificially) increase reserves in the banking system; hopefully, stimulating lending, reducing consumer credit delinquencies and defaults, increasing consumers' willingness and ability to spend, etc.

So far, so good; but is this likely to work?  It depends on whether all components of the feedback cycle are improved by the Fed's actions.  It turns out that increased producer demand for labor, and the resulting improvements throughout the cycle, might not occur.  Consider (what might be called) the capital cost and credit default feedback cycle:

The capital cost and credit default feedback cycle

The diagram shows the close, positive feedback relationship between banks and producers.  Importantly, it shows that as banks' financial conditions weaken, the availability of credit required by producers decreases, capital costs increase (for banks and producers, and in fact consumers too), producer profits decrease, all leading to an increase in producer credit delinquencies and defaults; thus further damaging banks' financial conditions.  Here too the Fed attempted to intervene in the feedback cycle by (in substance) buying "toxic assets" from the banks, thus improving bank capital ratios and increasing bank lending capacity.

Again, so far, so good.  But why is the US economy (seemingly?) still so weak; long after all the Fed's interventions in the money supply and banks' toxic asset problems?  Consider now a more complete representation of the problem, which I'll call the credit crunch feedback cycle, where the two feedback cycles discussed above interact:

The credit crunch feedback cycle

The diagram just fits the two previous diagrams together by linking (1) consumer credit delinquencies and defaults to decreased bank profits, and (2) decreased consumer demand to decreased capital availability to, and increased capital costs and decreased profits of, producers.  In short, once something in the feedback cycle goes bad, it makes a lot of things go bad. 

I think one begins to see the knotty, entangled nature of the problem here: Basically, to solve the problem in the near term of 2-3 years, it's necessary to positively influence all components of the cycle.  In principle, influencing just a few important components will set everything right in the long-run.  (This is the real problem: In the word of Keynes, "In the long-run we are all dead ...", which is why he advocated manipulating the economy.)  But given real world complexities and frictions, solving the problem(s) in the short-run is, as they say, difficult.

So, which is it?  Is it hope or ignorance that the US economy will begin to recover in the next 3-6 month?  I will let the reader be the judge.

Econometric analysis.  How might the credit crunch feed cycle theory, presented in very skeletal form above, be tested?  That is, how do we reasonably know whether it explains and predicts (part of) what's happening in the US economy?  A fairly simple seemingly unrelated regression model (Zellner 1963) based on the feedback cycle presented above might look something like this:

... where deltas are interpreted as percentage changes, D is demand, S is supply, CDD is credit delinquencies and defaults, M is money supply, and u represents effects of unobservable/unmodeled factors.  Of course, the model would need to be estimated, tested, and probably modified quite a bit to get  a model that might explain and predict well.  Sounds fun, don't you think?  Hmmm ... I thought so.

MMc

São Paulo

The case for pirates ...

... is an interesting, preliminary digression from the main purpose of the site.   Consider the relationship between average global temperatures and the number of pirates roaming the high seas.  I first became aware of the relationship while reading www.venganza.org (a, no doubt, respectable website!) and then did my own econometric analysis on the data published there; the results of which include the following graph:

Those interested in econometric methods might be interested in the following equation estimated using OLS:

So, what does it all mean?  Let's just say the results are consistent with the following hypotheses:

• There is generally a negative relationship between pirates and average global temperatures (GT); as active pirate counts increase, GT begins increasing again. decreases until there are approximately 36,000 active pirates, after which
• The optimal number of active pirates on our high seas is approximately 36,000 in the sense that GT reaches its minimum at that level.

I know:  It's also consistent with all kind of other hypotheses as well (e.g., like I've misapplied econometric methods and violated the Gauss-Markhov Theorem, which is true).  But it really is not completely unreasonable that pirates (and for that matter, terrorists and terrorism) reduce average global temperature:  Maybe pirates make oil super-tanker shipping more dangerous, costly, and slower, thus reducing oil consumption ... .  You get the idea.

But now we come to the main point:  We'll likely never know whether pirates are good or not for global warming.  We can only estimate these things, and our ability to estimate them depends on understanding econometric theory and methods adequately and--quite as importantly--our theory of the causal relationships between global temperatures, pirates, and all the other important causal factors influencing them.  The same is true about relationships between, say, equity prices and financial statement data.  So ... Rock on Econometrics!

MMc
São Paulo