Tsipras vs Merkel: A Sequential Bargaining Approach

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 The large victory of the Syriza party in Greece,  with Tsipras just
one seat below absolute majority (see Table 1 below) raises  the questions
:”What will happen now in the Eurozone? Is a Grexit scenario
possible?”My take here is that not much is likely to happen, except some
tough bargain between the new government and the Troika. Let’s consider the
following points:
 

Table 1: Election Results

  1. No one, neither the new government of 
    Greece nor the Troika, can credibly threat to “overturn the
    table”, abandon negotiations and let Greece exit the Euro. This
    outside option would be too costly for both parties. Greece has financing
    needs of about 25 billion in the next two years (IMF Fiscal Monitor, October
    20014)  and has no access to capital
    markets. A disorderly default on official debt would cut off Greek banks
    from collateralized  lending from the ECB, and would likely result in
    a dangerous banking and currency crisis. On the other  hand, a Grexit
    would send shock waves through the Eurozone: markets may once again 
    price exchange rate and default risks in peripheral countries’ (e.g.
    Italy) sovereign debt, jeopardizing the financial  stability of the
    area as a whole.
  2. If negotiations have to be, the question is: on
    what will they be? It is unlikely that a consistent debt restructuring can
    be agreed upon, for three reasons. First, after PSI in 2012, 
    official creditors who now hold about 83% of Greek debt have already
    granted large extensions of debt maturity (the average is 16.5 years (1),
    compared to about 7 in Italy) and have considerably reduced interest
    rates.  With a debt to GDP ratio above 175%, Greece pays about 4.5%
    of GDP in interests, less than Italy does, with 134%. Taking into account
    that interests on ECB’s debt  holdings
    flow back to Greece, the rate falls to less than 3% (2). Second, a
    restructuring would prompt similar requests from other peripheral EU
    debtor countries, opening up a Pandora’s box. Finally, the German
    electorate does not want to hear about debt forgiveness.
    It is more likely
    that negotiations will concern giving more time for fiscal adjustment.
    Although the new guidelines (3) for the Stability and Growth pact,
    similarly to Draghi’s QE, do not apply to Greece, some leeway could be
    made invoking the “cyclical clause”, that reduces fiscal
    adjustment when the (negative) output gap is very large. Consider 
    that Greece has made an unprecedented fiscal adjustment in recent years
    (see graph below), with a primary structural balance moving from -13.6% of
    GDP in 2011 to +5.4 % today,  thus concessions may be easier to
    justify.
Figure 1:
Cyclically Adjusted Primary Balance
(% Potential Output), IMF Data Mapper

Now assume that  Tsipras and Merkel bargain on the size of the
discount on the fiscal adjustment. How much is Tsipras going to get? A simple
back-of-the envelope calculation may help here.
If we use Rubinstein (4) sequential bargaining approach, with Tsipras and
Merkel making alternative offers and deciding to accept or reject, the answer
depends how patient are the two sides. It turns out that each side’s gets a
larger share of the pie the more “patient” she/he is, and the more
“impatient” is the opponent. The reason is that one can make a lower
offer/counter-offer to an impatient opponent. 
Table 2 below plots Tsipras’ equilibrium pay-off, the reduction in required
fiscal adjustment as a percentage of output, for different values of  the
discount  factors of the two sides. As the Troika becomes  more
impatient, its discount factor (d2) falls, by moving from left to right in the
table. Tsipras becomes  more impatient (d1 falls) by moving 
downwards.
                                                      
Table 2:  Tsipras’ Payoff
                                    Author
calculations based on Rubinstein (1982)
Since Tsipras faces a higher interest rate and political pressure than Merkel,
the solution is likely to lie below the principal diagonal of the pay-off
matrix. My best guess is that the equilibrium solution will be a number close
to 25%, which means that rather than  running a structural primary surplus
of the order of 5 % of potential output, as envisaged in the IMF projection
(see Figure 1 above), Tsipras could get away with a number close to 3.75 % .
Just some breathing space.
Footnotes
1.      
(1) F.Giuliano, Financial Times
Jan 25, 2015,  http://www.ft.com/intl/cms/s/0/6e5532c0-a310-11e4-ac1c-00144feab7de.html#axzz3Q1bm0Lx3

   (2) Zsolt Darvas, 2015, “Greek choices after the
elections”, Bruegel http://www.bruegel.org/nc/blog/detail/article/1551-greek-choices-after-the-elections 
(3) Paolo
Manasse, 2015, “The EU new fiscal flexibility guidelines: an assessment”,
forthcoming voxeu.org and http://paolomanasse.blogspot.it/2015/01/the-eu-new-fiscal-flexibility.html

4.    (4) Ariel Rubinstein, “Perfect Equilibrium in a Bargaining Model,”  Econometrica, 50(1982), 97-109.