Empirical evidence indicates that greater central bank independence, freedom “from direct political or governmental influence” (Walsh, 2005: 21), is associated with lower inflation (Fischer, 1995). Although difficult to quantify, Fischer estimates that an increase in the inflation rate from 0 to 10% could cost 2-3% of GNP (Fischer, 1981: 23). This essay firstly examines the time-inconsistency literature, specifically the Barro-Gordon Model (BGM) and Rogoff’s ‘Conservative’ Central Banker. Section 3 then analyses ‘Political Business Cycles’. CB should be able to operate free of government influence due to the association between lower levels of CBI and higher inflation rates.

## Dynamic-Inconsistency Literature

### Barro-Gordon Model

We examine a mathematically simplified version (Macmillan, 2020) of the Barro-Gordon Model (1983). The CB aims to minimise a loss function, shown by (1), that is identical to governmental preferences.

L=1/2 [a(π-π ̅ )^2+ (y-ky ̅ )^2]

The model assumes that the target rate of inflation is zero (π ̅=0). The target value of output in the economy is ky ̅. Since k>1, the target value is above the natural rate of output (ky ̅>y ̅). ‘a’ reflects the relative prioritisation of inflation targeting relative to employment and is assumed to be constant and >1. Derived from equation (1), social welfare is maximised when inflation and output values hit their targets.

The economy is modelled using the expectations-augmented Philips Curve (2), whereby actual output only differs from the natural rate if the Private Sector (PS) does not correctly anticipate inflation (π≠π^e). The long-run PC is assumed to be vertical.

y= y ̅+b(π-π^e)

The model employs a sequential game between the PS and the CB: the CB firstly announces an inflation target (π ̅=0), the PS then set their inflation expectations (π^e) and finally the CB sets monetary policy, aware of π^e. Note three assumptions. The PS are committed to π^e once expectations have been formed. This is rationalised by firms having to form employee contracts based on future nominal wages and π^e. This is a one-period game whereby monetary policy (MP) cannot be changed once set. Thirdly, it unrealistically assumes that the CB can use MP to precisely hit target values and there are no shocks to the economy.

Firstly, the CB announces it will set MP to achieve its inflation target (π ̅=0). Substituting equation (2) into equation (1) and setting π ̅=0, we reach equation (3).

L= 1/2[aπ^2+((1-k) y ̅+b(π-π^e ))^2]

PS then sets π^e=0. Differentiating equation (3) with respect to π and setting to 0, derives the loss-minimizing optimal inflation rate π, shown by equation (4). Substituting (4) into equation (1) gives the optimal output rate, given π^e=0, shown by equation (5). The associated loss function is given by equation (6).

π_B=b/(a+b^2 )(k-1)y ̅

y_B=((a+kb^2)/(a+b^2 ))y ̅

L_B=1/2(a/(a+b^2 ))((〖k-1)〗^2 y ̅^2)

L_A=1/2(y ̅-ky ̅^2)

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Place Order
In equation (4), since a, b and k >1, π > π ̅=0. Comparing equations (6) and (7), if the CB had set π=0, given π^e (7), the loss would have been greater. Once the PS forms π^e, the CB creates ‘surprise inflation’ (A to B) to move closer to the output target value of ky ̅. Expansionary MP shifts the economy to a lower indifference curve (IC), representing increased social welfare.

This inflation bias is aggravated if the PS has identical information to the CB. Understanding the CB’s incentive for expansionary MP, the PS will doubt the credibility of the CB and expect a higher rate of actual inflation that announced. Point D on Figure 1 represents the Rational Expectations Equilibrium; the CB has no incentive to create inflation as employing MP would move the economy to a higher IC. The losses at point D are substantially higher than at points A or B. This is derived by setting π^e= π then as previously, finding the optimal inflation rate and loss function (8).

L_D=1/2(((a+b^2)/a)(〖k-1)〗^2 y ̅^2)

The model provides a theoretical basis for the negative empirical relationship between inflation and CBI. Even with a “perfectly benevolent CB” (Rogoff, 1985: 1171), the delay between announcing their target and implementation of MP results in high inflation.

### ‘Conservative’ Central Bank Model

Rogoff’s ‘conservative’ central banker i.e. one that places a greater emphasis on inflation than society does, proposes a partial solution to the systematic inflation bias.

Adjusting (1), Rogoff assumes that CB places a greater weight on inflation stabilisation than bringing output closer to its target value. Therefore, ‘a’ is denoted by a ̂, such that a ̂>a>1. The CB loss function differs from governmental/societal preferences (9).

L=1/2 [a ̂(π-π ̅ )^2+ (y-ky ̅ )^2]

This adjustment results in a flatter IC curve due to the greater aversion to inflation; the CB would only consider a policy that increases inflation if it significantly decreased unemployment. The new rational expectations equilibrium reduces the inflation bias to π_E and welfare losses, compared to the previous scenario (point D). This provides a theoretical basis as to why CB should be free from government influence help mitigate against the inflation bias of non-independent CB.

The model assumes that preferences of central bankers can be identified, even though individual attitudes are often not explicitly defined (Persson and Tabellini, 1997: 39). Although Rogoff defends the model’s consistency, claiming that central bankers tend to be chosen from a set of relatively ‘conservative’ financiers (Rogoff, 1975: 1179), the model fails to explain why certain individuals are more ‘conservative’ (Bofinger, 2001:208). This criticism does not invalidate the model, the assumption can be realised through a CB having a constitutional price stability mandate (Persson and Tabellini, 1997: 39).

Theoretically, Rogoff’s model sub-optimally raises output variability (Fischer, 1995: 37). A ‘Conservative’ individual is willing to tolerate increased variability in output, thus failing to stabilise output as frequently. ‘Principle-agent’ style solutions, whereby the government designs contracts including escape clauses, suffer from implementation problems including optimally defining contract terms ex-ante (Mihov and Sibert, 2006: 25). However, empirical estimates find no correlation between CBI and increased output variability and Alesina and Summer (1993) conclude that CBI has no measurable impact on real economic performance. Therefore, CBI appears to be a ‘free lunch’ (Persson and Tabellini, 1997: 39).

CBI is commonly criticised for undemocratically delegating policy to ‘unelected officials’ (Chaudhuri, 2018: 10), even though greater independence does not necessarily imply reduced accountability (ibid., 12). However, government intervention to ensure price stability fails to solve the dynamic inconsistency issue. If the government incentivised CB to commit to price stability through fixing their incomes in nominal terms, politicians would have no incentive to enforce this due to their own myopic incentives for inflation (McCallum, 1995: 210).

## Political Business Cycles (PBC)

Nordhaus’ theory of PBC predicts expansionary MP before an election (Nordhaus, 1975). Nordhaus assumes that rational households are ignorant of the macroeconomic trade-off between inflation and output (ibid., 172). They form their expectations based on their perception of a ‘typical’ economic performance. In the long-run, voters prefer a lower unemployment and higher inflation outcome than is optimal (ibid., 178). Therefore, with the hope of maximising popularity and thus maximising ‘rents’ from re-election (Alesina et al., 1989: 59), politicians employ expansionary MP ahead of elections to create short-term boosts to growth and unemployment rates. This boom is inevitably followed by a slump in growth post-election. Allowing the CB to operate free of governmental influence removes this threat to price stability by entrusting policy to those who are not “tempted by the Sirens of partisan policies” (Nordhaus, 1975: 188).

Kramer finds that voters base their decision whether to re-elect the incumbent based on economic performance in the year of election (Fair, 1996: 89). A 10% decrease in per capita real income would lose the incumbent administration 4-5% of the votes, ceteris paribus (Kramer, 1971: 140). This finding raises the likelihood of PBC due to voter’s susceptibility to manipulation in the election year.

Finally, polarised, partisan political systems create a ‘second cycle’ (Alesina et al., 1989: 58) following changes in government. Governments strategically align their policies with the preferences of their ‘class defined’ core voting group. Resultingly, between 1960-1969, Republican and Conservative administrations employed policies generating comparatively higher unemployment and lower inflation, whereas Labour and Democratic administrations have reduced unemployment (Hibbs, 1997: 1467). The Conservative administration targeted lower inflation to align to the ‘typical’ conservative voter from upper income groups, who as lenders, would be economically hurt by high inflation (Fischer, 1985). CBI removes the destabilising price effects of this ‘second cycle’ as the CB should not alter its policy following a change in government.

## Conclusion

CBs should be able to operate free of governmental influence due to the decreased inflation rates associated with greater political independence, with no economic cost in terms of greater output variability. Despite criticism, Rogoff’s model does provide a partial solution to the systematic inflation bias in the BGM. Reducing political influence reduces the likelihood of PBC, thus enhancing price stability. Further study could examine the relationship between CBI and inflation for developing countries, specifically focusing on the heightened incentives to increase seignorage revenue due to the less developed tax income streams (Fischer, 1985).