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

Do We Need Unemployment Benefits?

What a bold question! Well, I assume it is. Because the following will sound pretty strange from a self-confessed left-wing radical, who belongs to a political side that is known to be keen on supporting the unemployed, and in the Moroccan case, very close to the unemployed graduate movement. Therefore, do allow me to put in a disclaimer: I absolutely feel sympathy towards the unemployed movement, but I disagree with their almost fetishist obsession with jobs in the civil service. Indeed, constitutional rights allow for any citizen to apply for a job in the public sector. However, this right is narrowed down by the law, then by administrative regulations. It seems that even the idea of an entrance exam is too much for the most extreme of them to bear.

Now that this matter is settled, let us turn to the idea itself; Why would Morocco need an unemployed benefits program? First, because the bulk of our unemployed population is not voluntary on the dole. They are genuinely looking for a job, and for many of them, the underground economy is providing for their living. Benefits, when properly designed and applied would allow them to live in dignity, and look for proper jobs. The way I see it, the benefits are there not to disturb some market mechanisms that are yet to be defined and enforced, but to set the standards for better labour-management relationship, and for the public authorities to encourage individuals to move from underground to legal, ‘official’ economy.

Let us first consider the figures on unemployment and inflation. The relationship is considered to be cardinal in mainstream academia. The well-known NAIRU (non accelerating inflation rate of unemployment) is a good start for us to estimate how deep involuntary unemployment is, and thus provide the public authorities with the financial means to deal with it.

Anti-inflationary policies have been more successful. Unemployment however, not so much. Or is it because of anti-inflationary policies? (World Bank & RDH Figures)

When one considers the relatively recent historical series on inflation and unemployment, one is surprised to notice that there was a surprisingly effective effort put into taming inflation (and Morocco can pride itself to be in a full deflation mode without much damage to growth) while policies, when carried out, look despairingly ineffective in view of the near stable level of unemployment. The question remains: why does unemployment remain that high? In a precedent post, I mentioned data that ruled out any serious effect minimum wage might have. There is also little, if no evidence pointing to relationship between labour legislation and unemployment. If anything, it is favourable to the management, especially in the important economic sectors like textile, Telecom services and other outsourced services. I should elaborate on that later on.

When simple econometric computations are run on unemployment and inflation, results look a bit inconclusive. Indeed, the Moroccan Philips Curve does not look like the theoretical one, and if anything, any correlation is too low and too insignificant to be of use. Though it might be too early to tell, there seems to be no direct link between anti-inflationary policies and unemployment. It does however deny policy makers from such argument.

They failed in addressing the problem because they did not devise the proper policies, not because of the so-called necessary trade-off between inflation and unemployment. To their credit, it must be pointed out that a particular sub-population was not fully cooperative; in fact, it was adamant in its claim for public service recruitment.

Moving on. The current level of unemployment can be reduced. Why so? Because even with sketchy econometric models, there is a way to compute the level of unemployed people that can be put to jobs. If I may direct the reader’s attention to a post I wrote on estimating the output gap for the Moroccan economy, the computations reached the conclusion that, as late as 2009, the Moroccan factory is producing below its productive capacity. The terms of the equation are simple: because output gap is negative, the economy can take on more labour so as to lift-up real GDP until the potential GDP is reached. We know the existing level of labour stock, we know exactly (well, with a confidence interval of 95%) how much labour adds to GDP, there remains only to compute how much is needed from the unemployed to bridge that gap in labour force. Estimates are such that an additional 5 basis points to the workforce  –ceteris paribus, mainly the capital stock- are needed to bridge the output gap, and certainly much more if capital stock was expanded too. 5% looks a lot (that is, after all, about 53% of the unemployment rate) but then again, because convergence process (the so-called catching-up) with potential output takes time, it remains quite a reasonable target. In absolute terms, that means some 482.000 people would find new jobs. Before I go any further, I must apologize for the sketchy figures, which is mainly due to the data (and my own limited knowledge on the particular field of labour economics)

No particular correlation can be observed from the graph

Now that we know the current level of unemployment can be cured up to 5%, why bother about introducing benefits for those on the dole? First because, just like other vulnerable populations, the public authorities rely on family and tribal solidarity to look after the special needs, the divorcées, the underdogs and the misfits. The large-scale shift in values, the rising individualism (whatever has been said on the matter, RDH surveys can testify) all these changes that are breaking -or already did so- the traditional mould so many people long for (and you know what they are called? reactionaries, that right) and so there’s a need to implement nation-wide programs, like the employment or support benefits. The targeted  population, following the HCP figures, would be as follows: about 700.000 unemployed with little or no qualification, not so much a burden on the nation, considering benefits are usually lower than the minimum wage;

Now, I don’t have much time, nor data to elaborate on how these benefits should be defined (and I think legislation here plays a critical role) but under the assumption of average benefits of MAD 1100 per month per individual is not only workable, but provides invaluable teachings in order to expand the program and protect the left-behind, while encouraging them to fight back and return to work. Incidentally, the whole annual cost for such a scheme is approximately MAD 7 Billion, that is 13% of a wealth tax levy on the millionaires in Morocco (at the low rate of 40%). So in essence, a benefit scheme is perfectly workable, so long as it works as it serves a two-fold objective: first, as a temporary stipend for those unemployed (that would include training costs, job lookout, etc…) and as the nation’s solidarity with those definitely unable to contribute to society.

I should like to devote a piece on how these benefits should be designed so as to encourage rather than subdue work, but there it is: it is high time we grabbed the bull by the horn and start a debate on how efficient benefits schemes should be. Their introduction is now beyond debate, it is a necessity.

Inflation, Output Gap and Monetary Policy in Morocco

What is to be discussed about money in Morocco? First, perhaps an attempt to correct some misconceptions about currency, monetary base and inflation. Read on twitter: “If money supply doubles, prices will double as well, holding physical output fixed”. The statement is mathematical, in these sense that it appeals to only one outcome out of two: true or false. The statement also asserts the old-style quantitative theory of money. By the way, the author of such sentence is not to blame, and I am grateful to them for providing me the opportunity, ney, the inspiration to write about something.

There’s indeed a popular misconception, which partially-educated journalists and politicians like to spread, about the kind of relationship between money supply, GDP and level of inflation. As far as Morocco is concerned, the new monetary theories hold particular in favour of my case. Milton Friedman once stated that “Inflation is always and everywhere a monetary phenomenon”. He was right at the time. The global trend this last year does not support the evidence. In the 1970’s (at times of high inflation, as we will see later on), that was true. But then again, that was the case because monetary supply was, for the better or the worse, restricted to greater proportions compared to nowadays. In fact, it is foolish to mistake the inflation/money supply relationship as a ‘post hoc ergo propter hoc‘ one. Inflation was quite high (due to other parameters that are too numerous to delineate here) and some economists -as well as policy-makers– thought, with some reasons, that high level of inflation was to be lived with, and that the Philips curve being considered to be very flat, any anti-inflationist policies were too expensive in terms of social and labour cost.

Inflation trend in Industrialized and Emerging countries

As it turned out, late 1970’s and through out the 1980’s, policies were quite aggressive against inflation, and, at the price of durable recession (but not deflation) reversed the trend, and with the 1990’s, the great moderation, i.e. a sustained low level of inflation was such that OECD countries enjoyed near-uninterrupted growth over two decades. On the other hand, monetary base expanded substantially over the same period. Graphs are quite enough to prove that, after the Volcker-style policies in disciplining inflation expectations, the world never had it so good with low inflation rates, and at the same time, credit allowances and monetary base grew at near-exponential rates. At the end of the day, our day, doubling money supply does not double prices. (even in Morocco)

Credit & Monetary base, on the other hand, exploded to exponential proportions

I mentioned in a previous article something about output gap and potential output. There were some interesting comments about how the results were obtained, and on second thoughts, I wondered if they were that well-founded. These results were a rough estimate; and a bad one too, not least because I did not proceed properly with the computations (I’d keep it very superficial) as it turned out.

So I will make it up to the reader by redoing the computations in a more rigorous way. The self-pride of a would-be economist is at stake. (it would also definitely deter me from following advices about writing short pieces…) The strict definition of potential output is : ‘the total gross domestic product (GDP) that could be produced by an economy if all its resources were fully employed’. Now the Cobb-Douglas function remains a reasonable starting point. There was a comment on how unlikely the parameters a and b are to remain constant, so that’s how we will proceed: a). We maintain the assumption GDP output is produced by means of Cobb-Douglas function, Capital and Labour are the main inputs, and Total productivity factor (also called Solow Residual) can be inferred from empirical data. Because of the discrepancies in available databases, we should focus on growth rates rather than actual figures. Used data is the World Bank Data.

b). Because we considered Cobb-Douglas, the logarithmic transformation is a good proxy for the growth rate of each component

ε term is there for statistical purposes, as it captures 'white noise'

its growth rate is the sum of labour and capital growth, and the growth rate in the Solow residual

When regression is run on output growth, labour and capital, results show that labour has a important part of output growth. Results also show that in facts, output production over the considered time period has increasing returns to scale, a result that is confirmed by academic papers on growth in emerging countries. There is therefore a residual of 2.2% accounting for growth that can be considered part of the Solow residual (the total productivity factor, or technical innovation). It must be pointed out however, that the estimation of the total productivity factors is less accurate than the coefficient α and β, but nonetheless, its quality is such that the coefficient can be trusted to render meaningful results. To sum up, the estimated parameters, while certainly not constant across time, do not change significantly too, and the obtained coefficients are significant, in the sense that future computations on that basis are going to deliver meaningful results as well.

The table shows the model to have a very high R², and estimated coefficients for both labour (l) and capital (k) show increasing return to scale (as 0.941+0.28>1)

Now, let us move to estimating the potential GDP. It is always difficult to estimate certain components of the potential output, so the method that suited us quite well in getting coefficients is going to be put to use, once more. Estimating Potential GDP, then.
so potential GDP is the level of output produced when the economy is at full employment, i.e. when the level of unemployment is at its feasible lowest (so-called natural unemployment rate) without triggering inflation (What is called NAIRU, or Non-accelerating inflation rate of unemployment). A much simpler way is to compute the growth rate of labour stock (which I did). Now that all the parameters have been computed to be of readable content (thanks to traditional econometric tools), we can therefore compute the output gap for the period, so as to move further in our quest for monetary policy.

As the graph shows, output gap in Morocco was quite hectic over the past two decades, and even though we did enjoy significant positive output (that are overall quite good for the economy) the volatility is such that benefits were immediately wiped out after a while. However, when recomputed into a normal frequence (i.e. fitted into a Gauss-Laplace distribution, regardless of time frame), the normalized  average over 20 years was -1.46 point of GDP (i.e., we lost, every year on average, 1.46 GDP growth because productivity was not full). Quite an indictment for the regime’s eulogist, considering that the loss of productivity could have taken the current GDP per capita from $ 2900 to $ 4400 (roughly the same wealth in Peru or Jamaica, and above Tunisia) and thus moves us from lower middle-income to middle income emerging markets.

Over the early 2000’s, output gap was positive on average, the trend next years is likely to be a period of negative output gap, which threatens with risk of recession

How could the monetary policy have accounted for such growth? First, it must be stated that the next batch of computations is even more sketchy, but that is due to the sparse information I have to scramble for. In monetary policy settings, it’s usually up to output and inflation targeting to define the announced rate. For the benefit of  the profane, the standard policy tool central bankers around the world is the Taylor Rule. J-B Taylor wrote in 1993 a paper assessing the Fed’s interest rate policy, and end up, by means of econometric computations, with an equation bringing together inflation targeting and output gap as follows:

Where the set interest rate is the real Hicksian interest rate and weighted gaps in expected inflation and output.

As I said before, it is difficult to verify the Taylor rule for Morocco, mainly because of patchy data on the targeted inflation rate (if there ever was, that is), but also because at the time there was little independence to be enjoyed from government (it is still the case, but the governor enjoys a wider margin). We can however get a good proxy of the equation as three-quarters of it is more or less within reach. Output gap has already been computed, there remains the equilibrium interest rate (for which a proxy can be found later on) Regular computations give the following results:

Starting from 2001, interest rates have been too low with the Taylor rate

The Taylor rule has limited effect here, mainly due to the abscence of inflation targeting for many years (to my knowledge, the Central Bank started only a couple of years ago)

I guess one of the exogenous reasons why there’s a wild discrepancy between computed and actual rates is due to the fact that we are not entirely free of our monetary policy, due to foreign trade. Morocco tries (or tried) to synchronize with significant European partners, and in order to get the best out of it, synchronized their interest rate with the ECB. That’s a good move, but then it makes us more dependent on France and Spain, at a time they are facing considerable challenge.

There’s also another danger to the current level of interest rates: it might sound very conservative, but there is a need for BAM to take interest rates to a higher level. I mentioned the conservatism cliché because left-wing economists in emerging countries tend to favour lower interest rates (for consumption stimulus purposes). But in this particular case, low rates profit to real estate speculators, and not the households struggling to buy their first home.

Morocco’s Growth Potential

First (real) post in 2011. I wish I could get more people read me, but apparently the posts are too long and too tedious to read. On a totally non-related subject,  I also discovered I am a bad writer, in the sense that I cannot convey my ideas in the way I want them to be. To my regular readers (and the bots that occasionally drop by) I say, thank you again -in your dozens- for taking the time to read some bits. As for Ibn Kafka’s challenge, I had the thought of writing more compact pieces (with other lengthy ones when I have free time). I’ll do my best in keeping up with a weekly posting.

Growth rate and Real GDp experience different rates: cumulative real GDP is exponential and convex, Real growth is logarithmic and concave

I wish economic debate in Morocco rose to higher standards. I mean, I’m reading columns on l’Economiste, or La Vie Eco, or even Economia, they don’t get to the bottom of things. I want to contribute.

Never wondered why the Moroccan economy never took off above a certain level of GDP growth?

Historically, the average real GDP growth per capita over the last 60 years was 5.51%, which is the nominal growth rate Morocco is experimenting for the last 5 years. A good figure, when compared to the average growth countries like the US was experiencing over a longer time series. Then again, it has been proven that poorer countries ten d to have a faster growth -at least in terms of capital productivity- due to their lower initial capital stock. This however, does not give much information about how the economy is doing compared to its potential. And the figures I display below show that our  economic potential has been systematically underused, and even the current trend shows that we are weakly catching up with the potential growth.

First, why focus on growth rate? Because, among others, growth is wealth creation, it means additional income for Moroccan agents , albeit in unequal fashion, it also means lower unemployment -although with unsubstantial results. Since we are not set on immediate institutional reforms getting better wealth redistribution, it is better to start on getting growth, and not only so: growth that gets the best out of potential GDP, so as to trigger these much needed structural reforms. Let me clear up this statement: the idea is that for the time being, our growth is erratic, because of the volatility of its origin, either due to seasonality issues, or because of their inherent weaknesses, like our exports. On the other hand, if growth was based on healthy economic dealing, i.e. on an economy that does not rely on rent, or speculation, or private monopolies to that matter, then not only structural and institutional reforms would have good basis to be implemented, but also, the urge for reform would be such that the incumbent policy makers would feel compelled to get them on tracks.

The idea of measuring our GDP potential growth gives a fair assessment of how good the economy is doing with respect to its level of inputs. Why so? Because, following the results, Morocco needs to be either on that level of output, or indeed any possibility that would not lead to a negative gap, deemed to destroy part of the capital stock. Potential GDP is the possible result that could have been obtained if workforce was at full employment, as well as capital stock used at maximum capacity with respect to the frontier of output production function (that is, in microeconomic setting, a production function). For purposes of simplifications -without loosing much sense of proportion- the Cobb-Douglas function does just fine (in facts, it is quite reasonable to use it, as indeed the HCP papers did consider the function as a realist proxy for output production.

It has also been assumed that for this Cobb Douglas, labour contribution is 2/3 and capital 1/3 (these are the parameters β and α). The levels of Capital and Labour are computed as the optimized GDP per labour, and the return of investment per GDP (meaning that FDIs were included as well). Numbers of such long time series are extracted from the U-Penn table, and have the benefit of being expressed in real terms.

Output gap (red line) and raw cumulated output gap (white line) over the last half a century. the Moroccan economy is barely touching the potential output these last years, a handicap due to that fact that output gap has been substantial for the last two decades.

Now that the potential GDP has been computed (and roughly estimated) it is quite puzzling to note that for all these many years, our GDP has been lagging behind its potential. En in the instances when the gap was positive, it was purely artificial, or short-lived. And on the other hand, it is worth pointing out that the cumulative gap had indeed deepened, especially right from the 1990’s, at a time when the under-used assets (among which, the dams the late King Hassan II was so proud of) needed to be replaced, or their high depreciation rate to be financed. This is nothing compared to the important investments that need to be undertaken for Morocco’s capital stock, as global trade and racing technological innovation compel us to do so. The fact that the Moroccan economy sustained a volatile, mostly negative output gap shows that the short term blunders the successive governments and policy-makers are guilty of, became gradually structural weaknesses. It is not only high time to address these handicaps, but it is going to be painful, long and unpopular with large scores of the Moroccan societies, not only vested interests.

What is quite strange is that institutions like Bank Al Maghrib do not take that into account in their reports. The output gap does not seem to be of prime interest (as far as the monetary policy is concerned) and it does not appear on the official reports. This casts great doubts on how relevant the policy is carried out. Next piece will deal with how relevant output gap is to the monetary policy.

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.