Banking on Reform: Political Parties and Central Bank Independence in the Industrial Democracies

Appendix: A Model of Monetary Policy-Making

ApPENDIX A Model of Monetary Policy-Making The monetary policy-making game involves three players: the government (G), the central bank bureaucrat (B), and the median legislator ofthe governing coalition (L). L represents the government's backbench legislators and coalition partners . The government may propose to retain the status quo or initiate a policy change, P. The policy change, if enacted, produces a new policy outcome. The central bank bureaucrat also makes a policy recommendation, either endorsing or criticizing the potential policy change. After observing the government's policy choice and the bureaucrat's policy recommendation, the legislator decides whether to approve or veto the policy change. I evaluate two possible scenarios. In the first, the government lacks any ex-post authority over the bureaucrat. In the second, the government can impose a penalty on the central banker. Information Structure Before the players, G, B, and L, choose their strategies, Nature selects the value of a random variable, D, which determines the outcome produced by enacting P. Variable D takes on two values, 1 (with probability d) and 0 (with probability I-d), where 0 sq > P2. If D == 1 (i.e., if P leads to Pi)' then L prefers to enact P. If D == 0 (i.e., if P leads to P2)' then L prefers the status quo. Therefore, the three possible payoffs are ordered as follows: UL(PI) > uL(sq) > U L(P2). The payoffs of G, E( uG ), are a function of two elements: the realized outcome , denoted uG(.), and L's vote on policy. The relative magnitudes of UG(PI)' uG(sq), and U G (P2) vary according to G's policy preferences: Order 1: PI> sq > P2 Appendix 183 Order 2: sq > PI > P2 Order 3: sq > P2> PI Order 4: PI> P2 > sq Order 5: P2 > PI > sq Order 6: P2 > sq > PI. G also incurs a cost k if L votes against his policy choice. This part of G's payoffreflects the negative consequences ofa legislative veto. The magnitude of k is larger than any possible gain in utility from achieving his preferred policy outcome. That is, G prefers to sacrifice his preferred policy outcome to avoid a legislative veto. B's payoffs, E(uB), differ between two scenarios, depending on the government 's ex-post authority. In the first scenario, E( uB) is a function of the realized outcome, uB(.), and L's vote on policy. The relative magnitudes of UB(PI ), uB(sq), and UB(P2) vary according to B's policy preferences. As with G, B has six possible preference orderings. B also incurs a cost, C, if L votes against B's policy recommendation. The magnitude of Cis larger than any possible gain in utility from attaining her preferred policy outcome. That is, B prefers to avoid a legislative veto even if she could ensure her most preferred policy outcome. In the second scenario, the government has ex-post authority over the bureaucrat . In this case, B's policy payoffs are a function of three elements: the realized outcome, uB(.), L's policy vote and G's policy recommendation.The first two components ofB's policy payoffs, uB(.) and c, are the same as in the first scenario. In this scenario, however, B incurs a cost, t, if the substance of B's action differs from G's policy recommendation. That is, if G chooses to pursue a policy change P (and sends a message, M), but B criticizes the policy choice (sends message C), Bincurs cost t. If G chooses to retain the status quo (sends message Q), but Bendorses a policy change (sends message E), B also incurs cost t. This cost t reflects the cost of ex-post action by the government against the bureaucrat, including dismissal, budget cuts, and so on. As with c, the magnitude of t is larger than any possible gain in utility from attaining her preferred policy outcome. Sequence of Moves The sequence of moves is as follows: 1. Nature chooses D (i.e., whether a change in policy, P, leads to PI or P2) and informs G and B. 184 Appendix PAYOFFS Government Bank Bureaucrat Legislator G B L U Pl UG(Pl) UB(Pl) UL(Pl) d sq uG(sq)-k UB(sq)-C UL(sq) M U Pl UG(Pl) UB(Pl)-C UL(Pl) d sq uG(sq)-k UB(sq) UL(sq) U Pl...