Techniques For Finding SFC Model Solutions

The advantage of standard Stock-Flow Consistent (SFC) models is their analytical tractability. Although some researchers might want to include infinite horizon utility function optimisations, there is little value added if you cannot find the solution to the model. We start off with SFC models that we can find the solution, and then we can incrementally add complexity, so long as a solution method is available. I discuss various techniques to solve these models.

Models Are Not Frequency Invariant

If we create multiple discrete time models of the same mathematical system, and those models are at different frequencies, those models will result in different outputs if those outputs are converted back to a common frequency. For example, this means that the output of an economic model which runs at a monthly frequency will have different outputs than a quarterly model, if we convert the monthly time series into quarterly. This is unfortunate, but this is generally going to be a small problem relative to the other issues economic models face. We only need to worry about this effect if we have an extremely low frequency, such as seen in some overlapping generations (OLG) models.

Discrete Time Models And The Sampling Frequency

Economic data are available in discrete time; that is, they are time series that are available in the form of samples at a fixed frequency (for example, quarterly, monthly, daily). Similarly, most complex economic models are specified in terms of a discrete time specification. By contrast, models in physics, or things like analog circuits, are defined in continuous time: time series are defined at "all times" (the time axis is a subset of the real line). Building economic models using continuous time has been done, but doing so creates many problems. However, one of the issues with discrete time models is the choice of the sampling frequency: too low a frequency means that you might not be able to model some dynamics.

DSGE Macro As An "All You Can Eat" Buffet (Part 2)

I previously discussed what I think can be done with mathematical models within economics; fundamental uncertainty about economic outcomes means that we are typically stuck working with partial models of the economy. The Dynamic Stochastic General Equilibrium (DSGE) literature appears to provide a satisfactory set of partial models to work with. In fact, the "publish or perish" imperative means there is an almost unlimited "all you can eat" buffet of DSGE models you can gorge yourself on. Unfortunately, a huge set of models with contradictory implications are only useful in a sociological sense: they allow leaders to provide a "scientific"-sounding justification for whatever policy their prior biases push them to undertake. (This article is a second part of a two-part article; link to Part 1).

DSGE Macro As An "All You Can Eat" Buffet (Part 1)

The ongoing online debate regarding mainstream Dynamic Stochastic General Equilibrium (DSGE) models has again heated up. Professor Simon Wren-Lewis of Oxford discussed whether mainstream macro was eclectic; provoking a response from Professor Lars P. Syll of Malmö University, the latest of which is "'Deep Parameters' And Microfoundations". I am not interested in the entire spectrum of their debate, rather on the question of eclectic models. (This is the first part of a two-part series.)

Introduction To The Frequency Domain With R

The use of frequency domain concepts is extremely useful when it comes to the analysis of systems. A good portion of communication and control system theory is done almost exclusively within the frequency domain. The advantage of the frequency domain is that it can more easily incorporate uncertainty than time domain analysis. Since the conversion of a signal to a frequency domain representation is a mathematical operator, this is a very mathematical topic. But I believe that many principles can be understood by just working with data and the Fast Fourier Transform (FFT). This article explains some of the fundamentals of the FFT using the open source R programming language. Later articles will then cover more advanced concepts.

Why You Should Never Use The Hodrick-Prescott Filter

One very common task in finance and economics is to calculate the underlying trend of a time series. This is a well-known problem in communication systems, and it is accomplished by designing a low-pass filter: a filter that eliminates high-frequency components of an input. For hard-to-understand reasons, some economists use the Hodrick-Prescott Filter (the "HP Filter") as a low-pass filter. Unfortunately, the HP Filter violates several principles of filter design, and generates misleading output. As a result, it should never be used. Although this topic sounds fairly technical, problems can be easily illustrated graphically. Even if you are not interested in filtering series yourself, these problems must be kept in mind when looking at economists' research if it is based upon the use of this filter. The conclusions may be based on defects created by the filtering technique.

No, The Fed Is Keeping Rates Low

As is now well known, Ben Bernanke has just launched a blog (welcome!) at the Brookings Institution. His first analysis post was "Why are interest rates so low?". He offers an explanation using textbook economic theory. As one might guess, I disagree with him about the framework used. However, my argument here is that even if I grant that his framework is (roughly) correct, he is still not able to draw the conclusions that he does.

Further Comments On The Apparent Limitations Of OLG Models

This article is a short response to the article Sam and Janet go to College, by Professor Roger Farmer. The original impetus for that article was to respond to comments I made earlier. I have looked at the papers he suggested, and I am still circling back to roughly where I was earlier with regards to overlapping generations (OLG) models. I still have not found any OLG models which meet my fairly strong criteria for what constitutes a useful economic model for analysing fiscal policy. I explain those criteria here, as I did not want to spam his website with a 1000 word comment. Since the literature is huge, and I do not have access to an academic library, that does not mean such models do not exist. I am simply unaware of them. But they are certainly well hidden from the public domain. Moreover, I have my doubts about the analytical tractability of such models.

Monetary Impotence And The Triumph Of The Fiscal Theory Of The Price Level

There has been an ongoing debate about how monetary policy interacts with the zero bound on interest rates. Paul Krugman has recently posted an article, "The Simple Analytics of Monetary Impotence (Wonkish)", in which he gives a simplified Dynamic Stochastic General Equilibrium (DSGE) model which he says demonstrates something about monetary policy when at the zero bound. When I look at the model, it appears that there are internal contradictions to his suggested solution. Instead, it appears that the model solution is determined by the Fiscal Theory of the Price Level (FTPL). When it comes to DSGE models, it appears that all roads lead to the FTPL.

Should A Central Bank Care About Loanable Funds?

Loanable funds theory appears innocuous: the idea that you can apply standard supply and demand curves to the market for financing. However, there are problems with this approach, as the result of how the financial markets operate in a modern economy. In this article, I look at a recent method of recasting loanable funds into a New Keynesian model, and I show why it is still questionable when put into this more modern format. Central banks are free to ignore "loanable funds" when setting interest rates, even within these mainstream models.

If r < g, DSGE Model Assumptions Break Down

The relationship between interest rates and the growth rate of the economy is critical for government fiscal dynamics. In the literature for Dynamic Stochastic General Equilibrium (DSGE) models, the discussion of the governmental budget constraint appears to have an embedded assumption that the real interest rate on government debt is greater than the economic growth rate (“r>g”). However, there is no reason that this has to be true, and the mathematics of the budget constraint fails if the condition does not hold. This poses a problem for the constraint, as a true mathematical constraint is something that is always true. Once this constraint is dropped, a good portion of the recent academic literature discussing fiscal policy becomes irrelevant. (Despite my opportunistic use of “r” and “g” in the title of this article – in order to capitalise on the popularity of a recent book – it has nothing to do with inequality.)

Inequality In Savings Drives Wealth Inequality

Paul Krugman discusses the dynamics of wealth inequality in a recent blog: Notes on Piketty (Wonkish). (Note: The article is behind a New York Times paywall, but you can view a number of their articles free within a month.) In it, he uses the standard Solow model to explain rising inequality. Although I do not have a formal model, my reading of a stock-flow consistent models implies that his analysis is not quite correct. The driving force behind wealth inequality is the differential in savings amongst households, and with a second order effect being that larger portfolios may have greater returns on their assets.

SFC Modelling And Government Finance Catastrophes

I am now looking at using Stock-Flow Consistent (SFC) modelling to describe (central) government finance. This is a much simpler task than attempting to model everything within the economy, so I do not have to worry about a lot of thorny problems. In this article, I explain a rule of thumb to deal with long-term fiscal policy expectations. To illustrate, I give an example of an obviously unsustainable fiscal policy that gives rises to an expected future inflationary catastrophe. This article is mainly about model-building; I will discuss in a future article how this relates to the real world fiscal outlook.

Draft Article: Solution Properties of Stock-Flow Consistent DSGE Models

Solution Properties of Stock-Flow Consistent Models by Brian Romanchuk

This paper is the mathematical proof of the statements I made in this earlier article. I am putting this out now as a means of getting comments. The paper is written in the same mathematical style I used to write in before I bailed from academia, and it is not light reading with punchy quotes.

DSGE Models: Without Capitalists, You Cannot Model Capitalism

One of the key defects of macro Dynamic Stochastic General Equilibrium (DSGE) models is the use of the utility optimisation by a single Representative Household to drive the solution. If there is only a single household in the economy, it has own the equity of the business sector as well as being the source of labour. Therefore, there is no conflict between labour and capital, and the solution to the household optimisation problem is trivial - it is the "full employment" solution (always).

This article explains this rather academic point. However, there is an important implication for the analysis of bond markets. (It is no accident I have been writing about DSGE models.) Properly understood, rising income inequality will cause government debt levels to rise regardless of the wishes of the government sector. This effect cannot appear in a model with a representative household. It is literally impossible to correctly model government debt dynamics using models within this framework.

What Is Ricardian Equivalence, And Why It Does Not Hold

Ricardian Equivalence is a theoretical concept that has been used to argue that fiscal policy is not effective. The argument is that increased government spending implies higher future taxes, so households will increase savings to cancel out the increase in government spending. This concept has been heavily disputed; see this blog entry by Bill Mitchell for an example. He argues that various assumptions are too restrictive in the models that show the “Ricardian Equivalence” effect.

In this article, I will introduce the “inter-temporal governmental budget constraint”, which is the equation which provides the justification for Ricardian Equivalence. I also show why this equation does not hold if term premia are non-zero. The chart above gives an example that shows the error in its prediction about the Net Present Value of future primary surpluses can become arbitrarily large. This has obvious implications for models that incorporate this constraint, as well as the usage of the concept in the analysis of fiscal sustainability.

A Poor Specification Of Fiscal Policy Means That DSGE Models Will Not Be Properly Identified

In my previous post, I discussed how the use of the primary balance as the point of departure for the analysis of fiscal policy was problematic. Those observations need to be kept in mind when looking at many mainstream analyses of fiscal sustainability. However, in this post, I look at an implication that is less obvious. Dynamic Stochastic General Equilibrium (DSGE) models which use the primary balance (or a similarly poor specification) to model fiscal policy cannot be properly fitted to empirical data.

There is a great deal of controversy about DSGE models. Their underlying assumptions appear bizarre. However, the usual justification for their use is that they can be fitted to data, and answer empirical questions that are demanded by policy makers (“What happens if we hike rates by 100 basis points?”). However, DSGE model parameters may be incorrectly identified in a systematic fashion due the misspecification of fiscal dynamics. This undercuts their purported usefulness for generating scenario forecasts.

This poor identification of model parameters will generate models that imply that monetary policy is more effective than is warranted. As a result, the run of forecast errors by central banks since the end of financial crisis is more easily understood…

Why Engineers Stopped Using Optimal Control Rules (Wonkish)

I find it amusing that there is a resurgence of interest in optimal control rules within economics (the latest point of interest is this paper by English, Lopez-Solido and Tetlow; there were earlier speeches by Janet Yellen). When I was a doctoral student of Control Systems Engineering in the early 1990’s, optimal control had been abandoned as a failure almost a generation earlier by engineers (late 1960’s – mid 1970’s). As I discuss below, when applied to real world engineering systems, optimal control rules had a distressing tendency to cause systems to be physically destroyed.

It may be that their application to the path of the U.S. policy rate would lead to less disastrous results, but it seems likely that this experience should lead us to treat such policy rules with a certain amount of caution.

Currency Regimes Matter If Policymakers Understand Them

In this article, Antonia Fatas argues that exchange rate regimes (like the euro) have limited power to explain differences of economic outcomes. It is based on an article by Andrew K. Rose, which looks at the currency regimes of smaller (mainly developing) economies during the global financial crisis.  

Paul Krugman responded here, noting that bond yields only rose due debt concerns in the euro countries. From the point of view of the bond markets, that is a crucial point: a country that does not control the currency of its debt emissions is just another credit market borrower, and can end up facing prohibitive default risk premia. 

Since his article illustrates that point well, I will discuss here the non-interest rate aspects of this debate. The currency regime is a critical component of Modern Monetary Theory (MMT), and so this debate is very important for understanding MMT.

Antonia Fatas’ main point is this:

I have written before my views that run contrary to the conventional wisdom. Many believe that while the Euro might make sense as part of a political process of European integration, it has had clear negative consequences on economic performance, consequences that are obvious when one looks at the effects of the current crisis in the Euro periphery countries. In several blog posts (here or here) I have provided anecdotal evidence that this conclusion is not supported by the data by comparing the performance of countries in and out of the Euro area and also by looking at the consequences of previous crisis when some of the Euro countries still had their exchange rate.

But what happens if one goes beyond the anecdotes and tries to systematically analyze the difference in performance of different exchange rate regimes? Unfortunately this is a difficult task. My own reading of the literature was that the evidence is mixed and inconclusive, there are no strong empirical results that prove that the exchange rate system has a significant effect on economic performance. But most of these academic papers were quite old.

My view is that membership of the euro is a bad idea, and will ultimately prove damaging to the economies of the countries concerned. However, he is correct that these problems may not show up in standard statistical tests. For example, it is possible that you could run a panel regression on GDP growth rates versus currency regimes and find no statistically significant relationship (this may change if we get a few more centuries of data). Why? A statistical test has an embedded underlying mathematical model of the relationship between the variables analysed. However, you need to look at the underlying economic dynamics, and see whether they are compatible with those implicit models.

The analysis by Andrew K. Rose is mainly of a panel of developing economies, and I do not find it controversial that he saw no effect of currency regimes in those economies during the Global Financial Crisis (GFC). The GFC was centered in the developed economies, and the emerging markets were unusually not a source of financial instability. This was the consensus opinion in published financial market research during the crisis. Therefore, I believe this particular analysis has little applicability to the situation of the euro member countries.

Returning to the question of euro members versus the developed economies with free floating currency regimes, I believe that the statistical differences will show up only in the following two areas:

1. Bond yields (as discussed in Paul Krugman’s article). Only euro zone markets have seen central government bond yields decouple from cash rates.
2. Countries with unusually high youth unemployment and underemployment rates (>40%). Although unemployment is too high across almost all the developed economies, the unusual total breakdowns in the employment market have only occurred along the Eurozone periphery.

That said, I find it unsurprising that statistical tests on GDP growth rates (for example) could appear inconclusive when testing whether Eurozone membership is a negative. To see why, we need to look at the economic dynamics as to why this could be so.

Exchange Rates Don’t Matter, Currency Regimes Do

My first point is that exchange rates (i.e., the price of a currency) have a limited impact on developed economies, but the currency regime (e.g., a fixed currency peg versus a floating currency does) does matter in terms of policy options that are open. (I have a bias towards exchange rate movements having limited impact on domestic economic variables; not everyone will agree with that.)

The euro is only a fixed exchange rate system within the member countries. The euro has weakened versus Asian trade competitors, so the euro does not pose a problem for euro zone countries in aggregate when analysing the impact of trade. The periphery faces a too high exchange rate, but they are outweighed in the aggregates by the larger German and French economies that are benefitting from a weaker currency. Therefore, any statistical panel of a trade effect should show a mixed effect, and the sign will depend upon how the countries are weighted within the panel.

However, the currency regime matters in how it restricts government policy (this is emphasised by the MMT theorists). Under normal circumstances, a fixed currency regime presents no binding constraints upon a government. The only time the peg matters is if the markets believe the government is unwilling to tolerate a too-strong exchange rate which is leading to current account deficits. Speculation against the currency will show up in financing problems for the government – it has to have higher interest rates to attract capital to finance a current account deficit. (Conversely, a too strong exchange rate poses little problems; the government can “sterilise” capital inflows without negatively impacting the domestic economy.) Therefore, economic differences only show up when a fixed peg is under attack. This is only a small subset of most observed data sets, and so if we do a statistical test on the entire observed data set, this will probably not show up as being statistically significant.

Observed Economic Behaviour Is Driven By Automatic Stabilisers

When we look at observed economic data, we are not observing how a capitalist economy operates without intervention. The data is the result of the interactions between the private sector and the public sector, including policymakers (fiscal and monetary) who are attempting to steer the economy in some direction. Within economics, this idea is known as Friedman’s Thermostat (as discussed by Nick Rowe in this article). (In my old field of control theory, this is the difference between an “open loop” system, and a “closed loop” system that has control feedback applied to its operation.) Nick Rowe presumably attaches a great deal of significance to the operation of monetary policy, but I emphasise the role of non-discretionary aspect of fiscal policy. In other words, the “automatic stabilisers” of the Welfare State.

My simulation of an arbitrary debt limit shows what would probably happen if the automatic stabilisers were suddenly turned off: the economy goes into freefall. This is effectively what happened during the pre-Welfare State era, when the government sector was too small to stabilise the economy. However, the Eurozone periphery did not turn off the welfare state; they allowed it to operate. Their austerity plans were largely based on cutting program spending. This meant that their deficits exploded above planned levels, and so the economy was eventually stabilised despite the planned austerity. This was made possible by ECB interventions. Since the euro is not pegged to a commodity, it is possible to finance their trade deficits with a fiat currency, and so the periphery did not face truly hard financing constraint.

Policymakers Need To Understand Their Options Within The Currency Regime

In order for there to be a difference in economic outcomes between nations with currency pegs and those with free-floating currencies, policymakers in the free-floating nations have to understand the constraints they face. However, after the worst of the crisis was over, many policymakers in the developed countries acted as if they faced the constraints of a fixed currency regime. The most well-known example is the decision by U.K. policymakers to voluntarily impose the same sort of austerity policies that Eurozone policymakers were forced* to impose. U.K. economic performance suffered as a result.

As a result, the economic performance of the “free floating” currency nations was punished by policies that replicated pegged currency regime performance. Therefore, it should be no surprise that a country like Germany, which did not get hit directly by the credit excesses before the GFC, and for whom the currency peg does not bind policy, could have a “better” performance than a badly-managed “free floating” currency nation. That said, no free-floating nation is likely to replicate the disastrous performance of the Eurozone periphery with their 40+% youth unemployment rates. Therefore, the statistical difference will have to be of the form of looking for extremely bad economic outcomes, and see which currency regime produced them.

* One could argue that the ECB could have allowed policymakers to avoid austerity policies; however, the ECB argued that it was following European law. I have no idea whether there was a legal way to avoid austerity policies, but it was clear there was no political will to do so.

(c) Brian Romanchuk 2013