Thesis Working Paper n°3

In his March 1968 Presidential address, Milton Friedman[1] summarized the broad aims of every mainstream economic policy: ‘high employment, stable prices, and rapid growth’. He was also quick to point out that these goals are not always easy to bring together, and while these aims seem to be the consensus among economists, instrument policies designed to implement these objectives do not elicit the same agreement.

Monetary Policy is one of these instruments that were the subject of much debate; The global economy moved from a decade-long era of low inflation and robust growth –both of which were considered to be partly the result of sound monetary policy- to that of an economy hurled into financial turmoil, and ultimately, into persistent depression. Central bankers, just like government, put together policies and instruments to deal these economies out of recession in ways that were unimaginable a couple of years ago (ironically, Friedman finds the tight FED policy in the 1920’s as a factor in the Great Contraction. It seems Central bankers today did not make the same mistake). Although there is much debate about the efficiency of monetary policies –especially on the long run-, the fact remains, the historically low levels of interest rates are contributing to sustain world growth and OECD growth in particular. In contrast with other policy instruments, monetary policy moved to be a subtle tool, one that is not as interventionist as, say a fiscal stimulus or tax cuts, but proves to be, at least in the short run, a very powerful and effective instrument.

Just as Friedman underlined, monetary policy is there to avoid mistakes. And it seems that this negative proposition somewhat overshadows the other assigned objective to the Central Bank, namely ‘to provide a stable back-ground for the economy’ (Friedman does acknowledge the monetary policy’s ability to balance off non-monetary shocks, though). Later on, empirical research by Taylor[2] (1993) provides policy makers with both a theoretical and practical tool to engage in a more active (but not necessarily activist) policy scope in setting interest rates.

We deal with the following: In a game theory setting, the central bank has to assign levels of interest rates and output as targets for the economy (i.e. other players) to factor-in their own computations. These targets are not computed ex-nihilo; they are the outcome of preferences over two main variables, i.e. the levels of inflation and unemployment, both of which are considered to be the main, if not the only parameters the monetary policy-makers care about. We shall prove that, if a certain set of conditions is met, the monetary policy can deliver systematically optimal welfare for the economy. We shall also verify that this optimal welfare is a Nash and strategy-proof equilibrium as per a social choice function designed by the Central Bank. As a policy-maker, the first step is to delineate the Central Bank’s preferences over levels of inflation and unemployment, levels that can be proxy for setting interest rates and output gap targets, these targets are in turn set so as to reach a certain common welfare (whose existence and salient properties are to be proven and verified in the process)

Barro & Gordon[3] (1981) provided a simple but accurate model of Unemployment and Inflation, which will be adapted to fit in some game theory axioms used in this paper. The Barro-Gordon model can then be used to describe the Central Bank’s preferences and thus provide insight of the way of it computes both interest rates and output gap. This preliminary study of the Central Bank’s own preferences is crucial to the other players in the economy, as it conditions, up to a point, their own expectations and ultimately, their response to the Central Bank’s decisions. We shall also verify whether pre-commitment and other institutional arrangements (such as independence from the Government or ‘special interest’ groups) can help to reach a Pareto-optimal social welfare. Once conditions of rationality and Pareto-optimality are verified, The game theory setting will provide us with elements defining the equilibriums –if there are any-, first in a simple bargaining process between the Central Bank, and a Private Firm. We shall then move to a multi-players game, and verify again that earlier predictions about the Central bank’s preferences can yield an optimal welfare to the economy. Finally, we shall consider the conditions whereby the ‘Lucas Critique’[4] effect is either minimized, or precluded altogether.

We shall consider the improved version of Kydland & Prescott (1977) model, by Gordon (1980):

Where U_t and U_tⁿ are respectively the unemployment rate and the ‘natural’ rate of unemployment,  π_t and π_t^e respectively the inflation rate and the equilibrium, ‘anticipated’ inflation rate. As a policy-maker, the central bank values these parameters, but does also take into account a ‘social cost’ function defined by the deviation of both variables from respective anchor values:

We shall however use an altered version of the said model, namely by introducing different axioms/assumptions, mainly about the use of the information set and the inflationary expectations. The rational expectation equilibrium π_t is computed on the assumption that “Because there are many private agents, they [the agents] neglect any effect of their methods for formulating π_t^e on the policymaker’s choice of π_t”[5]. We will not however retain such assumption;

Indeed, in the first very simplified instance, Central Bank faces only one private agent – and so inflationary expectations are going to be part of a strategic game, the information set will have a different use to both players. Then, in a more generalized setting, the Central Bank faces n non atomistic players, which means that their own inflationary expectations cannot be treated as given by the Central bank. Quite the opposite, the social function it devises has to be strategy proof with respect to each player’s anticipations.

This non-atomicity assumption is essential in computing the Central Bank’s desired level of inflation (and thus, the target levels of interest rates and output gap). It goes without saying that the proposed equilibrium in the Barro & Gordon model does not fit in this particular instance. The equilibrium can no longer be computed directly as a rule, but becomes a strategic game whereby each player has a certain type preference over unemployment and inflation (and react accordingly when recording signals of interest rates and output gap), and it is up to the Central Bank to devise a social function that completes the objectives assigned above.

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[1] Milton Friedman, ‘The Role Of Monetary Policy’ Presidential Address to the 80^th Meeting of the American Economic Association. The American Economic Review, Vol. LVIII, Number 1 March 1968

[2] Taylor, John B. ‘Discretion versus Policy Rules in Practice’ Carnegie-Rochester Conference Series on Public Policy (1993)

[3] Robert Barro & David Gordon, ‘A Positive Theory of Monetary Policy in a Natural-rate Model’ Working Paper n°807, NBER November 1981

[4] Tesfatsion, Leigh ‘Notes on the Lucas Critique’ Iowa State University (2010)

[5] Robert Barro & David Gordon, p.34

Thesis Working Paper n°1

This year is definitely being bitchy all the way down to early spring. Can it get any worse? (I am masochist, so It’s a bit of wishful thinking)

I’m getting pieces together for the thesis; it’s definitely going into game theory as a theoretical background in describing how a central bank should set the optimal interest rate, and how the fact that rate can be credible when a certain set of conditions are satisfied. I am having an enormous amount of fun in trying to get things going around… In an economic universe, the Central Bank has few objectives to fulfill: “stabilizing inflation around an inflation target and stabilizing the real economy, represented by the output gap“. (Svensson, 1999) the output gap is a reference to the gap between the actual GDP and the optimal GDP, or potential output, and can be roughly computed with the labour and net capital productivity, plus the total productivity factors, which can be proxy for technical innovation (or how to combine factors differently to get a higher output, or the same amount of output for lower level of capital and labour)

Because I claim to be a monetarist, and because I am fully in favour of an independent -but responsible before an elected body of representatives- central bank, I believe this institution is the one adequately geared to influence other players into accepting it as the best level of interest rate they should act upon. The game theory technique is there to prove that it can set a rate and an output target such that all players -that is economic actors- would stand by the targets as credible signals and would yield larger common welfare if they did not.

There is of course a strong assumption going on about the Central Bank’s motives: following institutional backgrounds, banks like the Federal Reserve has a triple objective to fulfill: inflation, growth and employment (Federal Reserve act, Section 2.a) the European Central Bank on the other hand, is mainly focused on inflation, and growth is a purely secondary objective, contrary to the Fed whose 3 objectives are of equal importance; these are even more stressed upon when put in perspective with regard to the kind of relationship their entertain with the political power; There is a wide-range consensus among economists about the virtues of an independent Central Bank, for all of the benefits it brings in terms of credibility, and thus efficiency in monetary policy-making.  As for the Moroccan central bank (Bank Al Maghrib) things are certainly different, but that is another matter.

Another assumption is that other players are interest-rate sensitive: firms are likely to expand or restrain their investment; The assumption looks credible, even though there are occurrences of sub-optimal or indeed irrational decision-making regardless of what the levels of interest rates are. In a dynamic setting, some players, like the unions or households do not change their behaviour overnight, as indeed there is a certain delay (a lag variable that can empirically observed thanks to econometrics) and would therefore blur the bank’s decision;

– Starting/working assumptions:

The Central Bank handles interest rates setting and assigning to the economy a target output (or in most cases, a target output gap) both of which variables are set in a fashion such to maximize common welfare, namely by selecting a pair (r,Y) that yields to the Nash axioms (or at least, to start with, Pareto conditions). These decisions are taken subject to other players’ respective preferences sets. The Central Bank is considered benevolent, and pursues no agenda of its own (that is to say, the Nash pair is the Bank’s own preference).

The aim is to prove that in monetary policy, there exist a Nash pair (r,Y) for which common welfare is maximized, and that Game Theory techniques and findings would help describing mechanisms and strategies that would allow the Central Bank, under specified conditions, to reach this equilibrium set over time. The difference with the ‘regular’ Game Theory setting and the present attempt to model the monetary policy lies in lotteries and risk aversion. The first one is relegated to random events (as perhaps used in econometric study) the second one would be rather about time preferences, as we can assume that agents value time, and would rather reach an agreement sooner rather than later.

Therefore, the starting concepts for this paper are going to be related to bargaining issues: for each Player i there is a function [f(r,Y)] called a utility function, such that one lottery is preferred to another if and only if the expected utility of the first exceeds that of the second.

– Simple Model: We borrow elements from the bargaining model as specified by Osborne & Rubinstein with a simple monetary set: two players, Central Bank (CB) and a Business Firm (BF) in an economy, which have to reach agreement on a specific set (r,Y). Both have their own preferences (CB’s is exogenous to its own condition) We keep the definition 2.1. For the agreements pair (S,d) where S is the set of all feasible pairs (r,Y). Of all Nash axioms (SYM, PAR, IIA & INV) only the symmetry assumption has to be dropped, as CB and BF display different preferences. The feasible set of pairs (r,Y) is divided up between desirable pairs’ sets –to which both players want to yield- and worst outcome possible (WOP) which both players want to avoid at any price. (and is the primary component of bargaining cost)The border between both sub-sets is set by the economy’s own productive capacities (or indeed how far the output gap can be sustained without slipping down into recession) Let us start with the bargaining game of alternating offers, and define monetary policy setting as follow:

1/ CB announces a pair (r,Y) to BF. BF has three ways to go: accept the pair, refuse it or refuse it and submit to CB an alternative pair. If BF accepts or refuses point blank, the game is over, and both parties reach a pair (r,Y) that belongs to the disagreement pair, an outcome both of which are made worse off when reached.

2/ CB, in turns, accepts the pair, refuses it or re-computes another pair (r,Y) and submits to BF.

3/ The game is rolling as long as each players refuse the proposed pair and proposes another.

We have to assume beforehand that CB has access to complete information (a fair assumption as CB uses resources to obtain sufficient information to make an accurate decision- an assumption to be discussed later on) and therefore whatever decision made is necessarily optimal. We can also assume that BF has access to complete information as well, and knows why CB fields its strategy. We also assume both players to adopt an optimal strategy at each point of the bargain, that is, that they are able to order their preferred pairs and play them accordingly at each knot of the game.

This proves that an equilibrium set of pairs (r,Y) can be reached very quickly, as both players know each others’ respective preferences, and if there are resistances from one part or the other, the disagreement –that is, the delay in reaching agreement- does not go further than a couple of periods. In a sequential equilibrium however, ‘We can interpret the equilibrium as follows. The players regard a deviation as a sign of weakness, which they “punish” by playing according to a sequential equilibrium in which the player who did not deviate is better off. Note that there is delay in this equilibrium even though no information is revealed along the equilibrium path.’

This can be used to provide a first-hand punishment deterrent to hurry both CB and BF to reach an equilibrium pair. The time value can be used as well, as indeed the longer both parties reach agreement, the more painful –or indeed the less desirable- the equilibrium pair would be. In real life, that is the case when CB fails to convince other economic players that they will stick to their decision, or that their announcement was not credible. That compels the bank to come after with a much stringent, more constraining announcement, something that could have been avoided if they took their signal seriously in the first place. As mentioned before, the central bank has objectives to stabilize inflation by setting optimal interest rate, and computing optimal (resp. minimal) output (output gap). For the time being, we set up for the output gap, as described in the paper by Gaspar & Smets. Their starting assumption was that both the Central Bank and the private sector (in our case, BF) observe the potential output, an assumption that can be deemed to be realistic, in view of semi-perfect information universe they evolve in.

Wandering Thoughts Vol.3

It’s starting to clear up. I have found a tutor for my final year paper. It should be something about game theory and monetary policy. Very early days indeed, but I have great hopes that it will bring some goods news afterwards.

Plus this year is turning out to be quite important for the future. Well, in any case I’ll be putting some posts on the subject from time to time, it is good practise for the ultimate chore. Obviously, I would like to write something about Moroccan politics, but in our case, silly season took over a long time ago home politics. Of course, troubles down under and Tangier’s imbroglio are all very well, but the barycentre of power remains the monarchy acting as a core, and tribal interests gravitating around. Nothing perhaps that legislative elections are now less than 2 years ahead, and I am increasingly making my mind up about abstention. I would very much like to devote some pieces about it, but that would be too soon, and even I have to comply with media agenda from time to time.

Part of the assignment is to read papers and prepare one that says what others -very bright and quite famous- have written about subjects that are but widely discussed. And I, little voice of would-be PhD holder, comment -elegantly of course- on these illustrious scholars’ work. It looks and sounds a boring job, and up to a point, it is. But the delightful trouble with economics is that under seemingly unadorned papers, interesting facts and theories are read-worthy.

Reading: Barro and Gordon’s paper (1983). In monetary policy, whatever subject one wants to discuss. “we often observe high and variable rates of monetary growth, and a tendency for monetary authorities to pursue countercyclical policies. This behaviour is shown to be consistent with a rational expectations equilibrium in a discretionary environment where the policy-maker pursues a reasonable objective, but where pre-commitments on monetary growth are precluded.” is the part of their abstract I am interested in: how do other players, especially commercial and investment banks, react to monetary policies. These policies are countercyclical indeed, and I will elaborate on that, just as the paper does so on “equilibrium rates of monetary growth/inflation [and how they] depend on various parameters, including the slope of the Phillips Curve”. For the time being, unemployment is not the prime concern (well not that I aver it to be secondary, it’s just that it is of minor interest to my subject)

There’s a bit I am quite interested in, the pre-commitment policy to set an inflation target and stand by it. Indeed, findings are such that under these conditions, players tend to play by the rules. In Game Theory Gibberish, the core of all possible coalitions (or combinatory allocations) is non empty (players find a settlement they prefer to any other outcome).  On the other hand, since we are conjecturing in terms of game theory,  if the policy is sequential (meaning implemented in different time periods) then players make up their mind along – following their own backward inductions, and the achieved equilibrium would be so when actual policy and the anticipated one converge to one. What is anticipated is of course up to the players themselves. Then there’s some stuff about rational expectations and so on. Really engaging, I’m telling you !

jovial Peter Mandelson and Gordon Brown. rare picture where the former British PM is caught smiling. Mandelson's account was not very kind to Brown

Oh, I was meant to write about it too, but then I fear I will not be up to expectations for it. Still, one has to give it a go. I’ve just finished Lord Mandelson’s book “The Third Man”. I don’t know, but between Moroccan politics as full of palpitations as our Prime Minister is charismatic (and yes, I am referring to the real PM, not the Gov’oma one), and French politics polarized into a civil war -short of large-scale violence hopefully-, I got on very keenly to British politics. Not that they are saints, but there is a certain touch of “grown-ups” compared to the others.

So, back on the Third Man, Mandelson gives his own account of the rise and dismay of New Labour, his years in office, near power and in the wilderness, all of that through the Shakespearian relationship Blair, Gordon and him had since they met till Blair resigned his premiership in 2007. To a certain extent, his account is very touching: The guileless reader would be charmed by the talent and intellect he displays through his memories and past actions as one of New Labour’s architects. One could almost feel sorry he was dubbed “Prince of Darkness” or “Lord Vador”… I still laugh at the puns BBC broadcasts like The News Quizz or the Now Show; Behind the pleasant caricatures and witty apophthegms, he remained throughout a key player in the strategy -a word that comes very often in his book- Labour designed and followed in media and power management.

Spin doctors? his pals Jonathan Powell and Alistair Campbell, his pro-Brown bitter opponents like Charlie Whelan are but the tip of an iceberg of what British, US and soon to be European politics is about. Researchers, advisers and party officials that are increasingly taking over party machines in the UK- the current Labour leader was an economic adviser to Gordon Brown when he was Chancellor, and the current Chancellor spent most of his career as a researcher at the Conservative HQ. Anyway, back on the book, Mandelson’s story is a fascinating one. I do hope Andrew Rawnsley’s own account would prompt the reader to have a look at it.

The inflationist food for thought

According to the latest (to date) IMF working paper concerning Morocco, everything is going fine in Morocco; Indeed,

” Moroccan banks are stable, profitable, adequately capitalized, and resilient to shocks, but the financial system as a whole will need to adapt to the inherent risks of changing macroeconomic policies and conditions. Major reforms have been achieved since the 2002 FSAP within a policy of actively promoting economic and financial sector opening”.

So in essence, the banking and financial system is stable. It is however, quite fragile, or rather, should develop some more resilient mechanisms. The IMF namely states that:

“BAM and other supervisory bodies require the necessary operational independence and resources, supported by accountability structures, to conduct an autonomous monetary policy and effective supervision. The authorities have taken welcome steps in this context, and promulgated the new articles of incorporation of BAM confirming its autonomy, a new banking law, a new anti-money laundering law, and a large number of secondary regulations.”

The Moroccan economy is doing well, admittedly because of the sound macroeconomic policy successive governments followed since the late 1990’s. These policies included low inflation-oriented policies, conservative fiscal policy, and shy attempts in implementing a policy rate by conceding more autonomy to the Central Bank. This set of policies is considered to be the standard and sound macroeconomic policy every responsible government should follow.

Let us first tackle the inflation policy. Bank Al Maghrib made an announcement of the ‘target inflation’ for 2010, and set it to 1.2%, a rate of historical low of course. It is, however, a figure quite difficult to match, because of the other economic parameters party in ‘shaping’ the inflation rate.

According to the Bank’s own monthly monetary report (Dec.2009), inflation rate set at 1.4% in September 2009, a figure in line with the global inflation (due mainly to the effects of a global recession).

Going back to the inflation policies, the national/total consumption is considered to be of sizable influence on inflation rate (I will come back on that later on). Basically, the report points out:

‘La consommation finale nationale devrait croître de 7,3% en 2009, rythme moins rapide que celui des trois dernières années mais qui demeure supérieur à la moyenne de la décennie. Concernant plus particulièrement la consommation finale des ménages, elle devrait augmenter de 7,1% après une progression moyenne de 10,9% durant la période 2006-2008.

Globalement, les principaux indicateurs disponibles à fin octobre laissent présager la poursuite de la bonne orientation de la consommation des ménages durant les prochains trimestres.’

(a trend confirmed in the June issue : ‘Au total, la consommation finale nationale devrait croître en 2010 à un rythme situé entre 6 et 7% en termes réels.’)

Now, Olivier Blancard, with other economist colleagues, produced an interesting piece (rather a working paper, really) a couple of months ago for the IMF. “Rethinking Macroeconomic Policy”; and there was a bit about inflation policy:

‘Stable and low inflation was presented as the primary, if not exclusive, mandate of central banks. This was the result of a coincidence between the reputational need of central bankers to focus on inflation rather than activity (and their desire, at the start of the period, to decrease inflation from the high levels of the 1970s) and the intellectual support for inflation targeting provided by the New Keynesian model. In the benchmark version of that model, constant inflation is indeed the optimal policy, delivering a zero output gap (defined as the distance from the level of output that would prevail in the absence of nominal rigidities), which turns out to be the best possible outcome for activity given the imperfections present in the economy’

What about our own policies on that matter? First off, let us have a look to the Bank’s views on inflation; the latest issue of the Revue de la Conjoncture Monétaire et Financière (May, 2010); They produced a couple of interesting graphs that speak for themselves:

Monthly versus Year-to-Date Inflation (Source: BAM)

The good news is, core inflation is pretty stable. Economists tend to use the core inflation rather than CPI (Consumer Price Index) fluctuations because they need to capture the relevant data, and oust any volatile random error term (mainly in econometrical techniques)

However, the graph below somewhat confirms a thesis I held to be true: our inflation is heavily correlated to current consumption goods (say, food like edible oil, sugar, wheat, etc…) as shown on the following graph:

 

 

Inflation component breakdown

 

 

 

 

While it is true inflation is gradually beaten down (which, ceteris paribus, is a good thing for the consumer), the Central Bank, as well as the Finance ministry, seem to have failed to address its volatility. In essence, the finance ministry implemented stabilizing inflation policies, succeeded in doing so, but only with the core inflation, and not on the CPI, which is quite critical, for it has a definite impact on the Moroccan consumers’ purchase power.

Blanchard then goes on: “There was an increasing consensus that inflation should not only be stable, but very low (most central banks chose a target around 2 percent). […] In a world of small shocks, 2 percent inflation seemed to provide a sufficient cushion to make the zero lower bound unimportant. Thus, the focus was on the importance of commitment and the ability of central banks to affect inflation expectations’.

Leaving the neo-Keynesian theoretical background aside, the kind of inflation the Moroccan economy experiences is of the highest interest to me: I believe every sound government and every sensible Central Bank should make inflation control policy on of their top priorities (beside economic growth and addressing inequalities, for the ministry that is).

However, it is quite odd that, while it undeniably preserves purchase power and good public finances, a certain ‘acceptable’ level of inflation is needed to boost businesses and, to some extent, help retail investors as well. In layman’s terms, the ‘good level’ of inflation alleviates the real debt burden a bit on businesses (for they actually pay lower real interest) and allow for retail investors to build up their portfolio on financial markets and exchange. However, the kind of inflation we are discussing here does not benefit to businesses neither household in Morocco.

We have seen earlier on that while core inflation is remarkably stable, the CPI components are much more volatile. And it is recognized to be so : ‘Impactée principalement par des chocs ponctuels, l’inflation demeure modérée au cours des derniers mois. En effet, après s’être établie à 0,1% en février, l’inflation annuelle est passée à 0,9% en mars. L’analyse détaillée des différentes composantes de l’IPC laisse indiquer que cette évolution traduit exclusivement le renchérissement des prix des produits alimentaires volatils, l’inflation sous-jacente n’ayant que légèrement progressé, pour se situer à 0,2% au lieu de 0,1% un mois auparavant.’

We are through the looking glasses here: the CPI is definitely what makes the inflation rate goes up, and there are several ways to explain it so:

– CPI underlying commodity prices went up on the period from Q4 2009 to Q2 2010. It is quite possible, for a constant domestic demand, to take on inflation because of a rise in commodity prices. The first idea is to look at future commodities indices. According to the Bloomberg figures, futures prices were quite volatile from October 2009 to May 2010, but were they

Let us take an even more systematic approach. The following graphs depict Exchange Traded Commodities tracking benchmark indices, all of which give a fair idea of how likely the commodities’ prices behaved during the past 6 months. The selected commodities benchmark are Oil Brent for Oil (ETF Securities Brent Oil Index), then the UBS CMCI Wheat Index for Crop/Wheat and finally UBS CMCI Sugar Index for Sugar. (All of which are listed on the London Stock Exchange, and for anyone interested in discussing the technicalities of index rebalancing as well as the relevant choices, I would with vivid alacrity)

CPI inflation in Morocco looks quite decorrelated with respect to commodities fluctuations

The result is quite puzzling: there seems to be no noticeable relation (lagging or dynamic) between inflation fluctuations, and the selected commodities, though these are most important in the Moroccan consumption basket. The commodities’ prices are, therefore, not the main explaining factor for the CPI inflation.

– Domestic demand went up on the same period:

‘La consommation finale nationale devrait croître de 7,3% en 2009, rythme moins rapide que celui des trois dernières années mais qui demeure supérieur à la moyenne de la décennie. Concernant plus particulièrement la consommation finale des ménages, elle devrait augmenter de 7,1% après une progression moyenne de 10,9% durant la période 2006-2008’.
Basically, in a moody conjecture, the main variable that pulled our economic growth was the domestic consumption.
My two cents are up. I shall write very soon on the topic of inflation and conumption relation. However, It must be pointed out that the Central Bank and the FInance Ministry, while achieving a relative success in dealing with inflation, the two bodies failed in addressing volatility inflation, and thus, the main objective every policymaker should make theirs: stable long term growth.