## 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.

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)

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

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.

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.

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:

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.

## Thesis Working Paper n°2

Description of the Monetary Policy as a bargaining process between two players:

* a. Players features*: The Central Bank (CB) and a representative private firm (PF) bargain for a pair are respectively were i(e) and Y(e) the equilibrium interest rate and output.

Each player has specific preference utility function, where the bank seeks to stabilize output via interest rate (in optimal settings, it would systematically set up interest rates so as to maximize potential output). We assume for the time being that the central bank does not take into account inflation directly into its computations (inflation is captured by the potential output). Central Bank’s preferences are captured by an altered version of the Taylor Equation such:

The Private firm, on the other hand, has a preference for high output and low interest rates, which means that its utility function is such:

This is due to the fact that the firm prefers low interest rates for valuation purposes and investment cost. High output generates higher profits and higher levels of cash flows (leading to higher valuation again).

It can be inferred from these preferences that both players have contradicting interests (and in facts the Firm does not take into account the potential output) and so the bargaining model is an attempt to seek an equilibrium.

* b. Game:* The game is a mapping

** **

Where :

The bargaining is a standard Rubinstein-Osborne model, where the set of agreement pairs is described as follows:

The game starts with the Central Bank announcing a pair . The firm has the choice of accepting the pair or rejecting it. If it accepts it, the game is over, and the economy produces Y(e) at an interest rate i(e).

If it rejects the Bank’s proposal, then the game moves to stage 2, whereby it’s the firm’s turn to propose a pair

The bank has in turn the choice of settling for it, or moves to stage 3, and proposes another pair,

and so on and so forth. We assume that the actions take in a finite time set T, but at each period t, the proposed set from one player or the other is such:

This can be explained as the ‘price of disagreement’. For the central bank, it is damaging its policy-making credibility, or because danger of inflation, when not dealt with at the time, compels the bank to be more stringent in pushing for scheduled higher interest rates and lower output target (and by computation, a negative output gap). As for the firm, the punitive discount rate can be explained either by the uncertainty risk or because of the future negative effects non controlled inflation has on its valuation or profits.

The assumptions described in Osborne & Rubinstein on the extensive form hold: each player has a continuum of choices over the pair (i,Y). For this game to lead to a subgame perfect equilibrium, the following properties are to be verified:

1/Disagreement is the worst outcome: that can be easily verified with the punitive time factor: at every node of bargaining, the worst outcome is to reject the offer, as the utility derived from the next stage is lower than the previous one.

2/ Desirability for a particular outcome is embedded in both players’ preferences as described earlier on

3/ Time is valuable, and is also verified with the punitive discount factor δ.

4/ Continuity: the assumption of continuity needs to be discussed. As specified before, both players have defined intervals respectvely for interest rates and output. The series are therefore bounded but also converge to equilibrium state because it is the

most desirable at every node of the bargaining process:

5/ Stability is also defined by the effect of discount time factor.

6/ Increasing loss to delay: the discount factor also fulfils the condition.

This game has therefore a perfect subgame equilibrium. That means, at every node of the game, the reached equilibrium is part of the larger game, and because utility out of a Nash agreement is higher at stage t-1 compared to stage t, both parties have every incentive to agree right from the start. Next piece is dealing with the requirements the Central Bank has to meet in order to be credible in its decision/announcement.

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